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9-i Chapter 9âNoise and Vibration Control Table of Contents 9.1Â INTRODUCTION 9-1Â 9.1.1Â Scope 9-1Â 9.1.2Â Relevant Literature 9-2Â 9.1.3Â Some Fundamentals 9-2Â 188.8.131.52Â Sound Levels 9-2Â 184.108.40.206Â Vibration Levels 9-3Â 9.1.4Â Design Criteria 9-3Â 9.2Â NOISE CONTROL DESIGN 9-4Â 9.2.1Â Wheel/Rail Rolling Noise 9-4Â 220.127.116.11Â Types of Rolling Noise 9-5Â 18.104.22.168.1Â Normal Rolling Noise 9-5Â 22.214.171.124.2Â Impact Noise 9-8Â 126.96.36.199.3Â Rail Corrugation Noise 9-8Â 188.8.131.52.4Â Grinding Artifact Noise 9-14Â 184.108.40.206.5Â Singing Rail 9-15Â 220.127.116.11Â Factors Affecting Rolling Noise 9-15Â 18.104.22.168.1Â Wheel Dynamics 9-15Â 22.214.171.124.2Â Rail Dynamics 9-17Â 126.96.36.199.3Â Resilient Direct Fixation Fasteners 9-22Â 188.8.131.52.4Â Ballasted Track 9-23Â 184.108.40.206.5Â Contact Stiffness 9-23Â 220.127.116.11Â Treatments for Rolling Noise Control 9-24Â 18.104.22.168.1Â Continuous Welded Rail 9-24Â 22.214.171.124.2Â Hardened Rail 9-24Â 126.96.36.199.3Â Rail Grinding 9-24Â 188.8.131.52.4Â Rail Support Spacing 9-28Â 184.108.40.206.5Â Direct Fixation Fastener Design 9-29Â 220.127.116.11.6Â Trackbed Acoustical Absorption 9-31Â 18.104.22.168.7Â Tuned Rail Vibration Absorbers 9-31Â 22.214.171.124.8Â Rail Vibration Dampers 9-32Â 126.96.36.199.9Â Wear-Resistant Hardfacing 9-32Â 188.8.131.52.10Â Low-Height Sound Barriers 9-32Â 9.2.2Â Special Trackwork Noise 9-33Â 184.108.40.206Â Solid Manganese Frogs 9-33Â 220.127.116.11Â Flange-Bearing Frog 9-33Â 18.104.22.168Â Lift Over Frog 9-33Â 22.214.171.124Â Rail-Bound Manganese Frogs 9-34Â 126.96.36.199Â Movable Point Frogs 9-34Â 188.8.131.52Â Spring Frogs 9-34
Track Design Handbook for Light Rail Transit, Second Edition 9-ii 9.2.3Â Curving Noise 9-34Â 184.108.40.206Â Types of Curving Noise 9-35Â 220.127.116.11.1Â Longitudinal Slip 9-35Â 18.104.22.168.2Â Lateral Slip 9-35Â 22.214.171.124.3Â Flanging and Flanging Noise 9-38Â 126.96.36.199Â Treatments for Curving Noise 9-39Â 188.8.131.52.1Â Flange Lubrication 9-39Â 184.108.40.206.2Â Top-of-Rail Lubrication 9-40Â 220.127.116.11.3Â Friction Modifiers 9-40Â 18.104.22.168.4Â Water Sprays 9-40Â 22.214.171.124.5Â Rail Head Inlays 9-40Â 126.96.36.199.6Â Track Gauge 9-40Â 188.8.131.52.7Â Asymmetrical Rail Profile 9-41Â 184.108.40.206.8Â Rail Vibration Dampers 9-41Â 220.127.116.11.9Â Tuned Rail Vibration Absorbers 9-41Â 18.104.22.168.10Â Double Restrained Curves 9-41Â 22.214.171.124.11Â Low Rail Cant 9-42Â 9.3Â VIBRATION CONTROL 9-42Â 9.3.1Â Vibration Generation 9-43Â 9.3.2Â Ground-Borne Noise and Vibration Prediction 9-44Â 9.3.3Â Vibration Control Provisions 9-44Â 126.96.36.199Â Floating Slab Track 9-44Â 188.8.131.52Â Resiliently Supported Bi-Block Ties 9-46Â 184.108.40.206Â Ballast Mats 9-47Â 220.127.116.11Â Tire-Derived Aggregate (TDA) 9-47Â 18.104.22.168Â Resilient Direct Fixation Fastener Design for Vibration Isolation 9-49Â 22.214.171.124Â Rail Grinding 9-57Â 126.96.36.199Â Rail Undulation 9-57Â 188.8.131.52Â Vehicle Primary Suspension Design 9-58Â 184.108.40.206Â Resilient Wheels 9-59Â 220.127.116.11Â Subgrade Treatment 9-59Â 18.104.22.168Â Special Trackwork 9-59Â 22.214.171.124Â Distance 9-59Â 126.96.36.199Â Trenching 9-59Â 188.8.131.52Â Pile Supported Track 9-61Â 9.4Â WHEEL/RAIL PROFILES AND CONTACT STIFFNESS AND STRESS 9-61Â 9.4.1Â Contact Dimensions 9-62Â 9.4.2Â Stresses 9-63Â 184.108.40.206Â Normal Stress 9-63Â 220.127.116.11Â Shear Stress 9-67Â 9.4.3Â Contact Stiffness 9-70Â 9.4.4Â Residual Stress AccumulationâShakedown 9-72Â 9.4.5Â Work Hardening 9-72Â 9.5Â REFERENCES 9-72
Noise and Vibration Control iii-9 List of Figures Figure 9.2.1 Change in elastic modulus and rail head curvature required to generate wheel/rail excitation equivalent to roughness excitation (Remington, 1988) 9-6 Figure 9.2.2 Examples of wheel/rail noise 9-9 Figure 9.2.3 Very short pitch corrugation 01-9 Figure 9.2.4 Short-pitch corrugation 11-9 Figure 9.2.5 Corrugation on San Francisco cable car track 21-9 Figure 9.2.6 Radial mechanical acceleration response of TriMet Type 2 vehicle resilient wheel 61-9 Figure 9.2.7 Input mechanical impedance of TriMet resilient wheel 9-17 Figure 9.2.8 Vertical pinned-pinned resonance frequency vs. rail support separation for various rails 81-9 Figure 9.2.9 Mechanical input impedance of 115 RE rail on discrete supports 9-19 Figure 9.2.10 Input impedance of 115 RE rail (0 to 2000 Hz) 02-9 Figure 9.2.11 Theoretical vertical rail velocity responses at about 50 ft [15 m] from vertical forces directed against the rail head 22-9 Figure 9.2.12 Geometry of curve negotiation and lateral slip 63-9 Figure 9.2.13 Truck crabbing under actual conditions 63-9 Figure 9.2.14 Transverse acceleration response of TriMet Type II resilient wheel 9-38 Figure 9.3.1 Vibration isolation performance of tire-derived aggregate installed in 2005 9-48 Figure 9.3.2 Vibration isolation of DF fasteners for various rail support moduli 9-51 Figure 9.3.3 Dynamic transfer stiffness of bonded direct fixation fastener of nominal static stiffness of 400,000 lb/in [70 KN/mm] 55-9 Figure 9.3.4 Mode shape of an idealized fastener consisting of a 0.5-inch [12.5-mm] thick by 18-inch [304-mm] long by 8-inch [203-mm] wide top plate supporting a 30-inch [750-mm] long section of 115 RE rail 65-9 Figure 9.3.5 Mode shape of an idealized fastener consisting of a 0.75-inch [19-mm] thick by 12-inch [304-mm] long by 8-inch [203-mm] wide top plate supporting a 30-inch [750-mm] long section of 115 RE rail 65-9 Figure 9.3.6 Rotated view of Figure 9.3.5 75-9 Figure 9.3.7 Measured ground vibration insertion gain of styrofoam-filled trench at Toronto Transit Commission 06-9 Figure 9.4.1 Contact geometry vs. rail head radius for 28-inch [711-mm] diameter wheel with linear tread profile 26-9 Figure 9.4.2 Contact area vs. tread profile 46-9 Figure 9.4.3 Maximum contact pressure vs. head radius for 28-inch [711-mm] diameter linear tread radii 56-9 Figure 9.4.4 Maximum contact pressure vs. rail head radius for various concave tread radii 9-66
Track Design Handbook for Light Rail Transit, Second Edition vi-9 Figure 9.4.5 Depth of maximum shear and maximum shear vs. contact ellipse aspect ratio (Johnson, 1992) 86-9 Figure 9.4.6 Maximum shear stress vs. head radius for three tread profiles 9-69 Figure 9.4.7 Variation of dynamic contact stiffness with rail head radius 9-71 List of Tables Table 9.2.1 Corrugation categories (After Grassie, 2010) 31-9 Table 9.2.2 Corrugation growth rates at MTRC Hong Kong for various track curvatures in 1992 (After Dring, 1994) 41-9 Table 9.3.1 Maximum stress and deflection for 30,000 lb [133 kN] point load 9-53 Table 9.3.2 Rail undulation limits 9-58
CHAPTER 9âNOISE AND VIBRATION CONTROL 9.1 INTRODUCTION Wayside noise and vibration and car interior noise are important factors in the design of new transit track or retrofit of existing track. All too often, noise and vibration are ignored until well into the design phase, at which point incorporation of the most cost-effective solutions may not be possible. Successful noise and vibration control require consideration of both the track and the vehicle as a system, because the interaction of the wheel and the rail is responsible for the bulk of wayside noise and vibration impacts. This chapter attempts to summarize the main issues and theories related to noise and vibration production and control and the related issues concerning rail wear, identify areas where insufficient knowledge exists, and provide guidance with respect to track design for acceptable levels of noise and vibration. While many of the treatments considered here can be selected and designed by the transit track engineer, the design of some provisions, such as floating slabs or vibration absorbers, should be conducted by those who have considerable experience with designing and specifying vibration isolation systems, have an engineering or physics background, and understand the principles of noise and vibration control. Noise and vibration control provisions should be included in track design to avoid impacting wayside communities, transit users, and transit employees. Noise and vibration can usually be held to acceptable levels at reasonable cost with appropriate design and maintenance provisions, especially if the vehicle and track are considered as a system rather than as separate, independent components. For example, expensive track vibration isolation systems might be avoided where vehicles with low primary suspension vertical stiffness are used, whereas vehicles with high primary suspension stiffness might produce vibration that might require a floating slab to isolate the trackâan expensive proposition. The choice of vibration isolation provisions depends on vehicle dynamic characteristics, and the track and vehicle design teams must coordinate their designs during and after the early stages of any project. Mitigation could involve considerable expense, weight, space, or special procurements. Late consideration of noise and vibration isolation may preclude some treatments simply because insufficient time exists to obtain them or to implement design changes. 9.1.1 Scope This chapter is divided into three principal topics, the first being wheel/rail noise, the second structure-borne and ground-borne noise and vibration, and the third wheel/rail contact stresses. All of these topics are interrelated. For example, fastener selection for ground- or structure-borne noise control may affect wheel/rail noise, and rail corrugation is influenced by track design parameters and contact stresses. Vehicle "on-board" treatments are not discussed here, as these are beyond the limits of track design. However, considerable discussion is included regarding vehicle design parameters that may influence the selection of track design provisions. Low-profile sound barriers located close to the rail or acoustical absorption placed between the rails may be considered as part of the 1-9
Track Design Handbook for Light Rail Transit, Second Edition 9-2 track design, as they may influence the track support design and maintenance. However, wayside sound barriers would not be considered under track design. 9.1.2 Relevant Literature Many studies of rail transportation noise and vibration have been conducted, producing detailed technical reports containing comprehensive information concerning rail transit noise and vibration prediction and control. Particularly useful sources of information include the following: â¢ The FTA Guidance Manual, Transit Noise and Vibration Impact Assessment and Control â¢ The Handbook of Urban Rail Noise and Vibration Control, a handbook on all aspects of rail transit noise and vibration control published by US DOT/TSC (now the John A. Volpe National Transportation Systems Center), a document that should serve as a companion to this chapter. â¢ A review of the state-of-the-art in wheel/rail noise control has been prepared in TCRP Report 23, which includes numerous references to technical reports and other literature, and which provides guidelines for selection of rail transit noise control provisions. â¢ A review of ground-borne noise and vibration prediction and control was performed in 1984, including preparation of an annotated bibliography. The document provides information concerning vibration isolation performance for various track design configurations. â¢ The proceedings of the International Workshop on Railway and Tracked Transit System Noise (IWRN), which are usually published in the Journal of Sound and Vibration. The proceedings have recently been published by Springer. Many papers concerning noise and vibration prediction and control are published each year in TCRP Research Results Digests, and journals such as the Journal of Sound and Vibration, Wear, Journal of the Acoustical Society of America, Transportation Research Record, and so on. General handbooks concerning noise and vibration control and design include the Handbook of Noise Control and the Shock and Vibration Handbook. 9.1.3 Some Fundamentals Excellent references to acoustical and vibration terminology are provided by Beranek, Harris, and by Harris and Crede. Also, the usage employed here is consistent with the FTA guidance manual. 18.104.22.168 Sound Levels Sound is a dynamically varying pressure fluctuation in air that occurs over the frequency range of human hearing, here taken to extend from about 16 Hz to 20 KHz. Sound is conveniently described with a logarithmic decibel scale (dB). Mathematically, the level in decibels of a sound is equal to 20 times the logarithm to base 10 of the ratio of the root-mean-square sound pressure and a reference pressure of 20 micro-Pascal: L(dB) = 20 Log10 (p/p0), p0 = 20 Ã 10-6 Pa = 10 Log10(p2/p02) The A-Weighted sound level is obtained by filtering the analog sound pressure signal obtained with a pressure-sensitive microphone with an A-Weighting network that deemphasizes the low-
Noise and Vibration Control 9-3 frequency components of noise below about 500 Hz and above about 10 KHz. The A- Weighting network approximates the frequency response of a personâs ear at low listening levels and is used almost universally to characterize industrial, occupational, and community noise. The unit of the A-Weighted noise level in decibels is abbreviated as âdBA.â Unless otherwise indicated, all sound levels discussed here are in dBA. The energy associated with a sound pressure is proportional to the square of the sound pressure amplitude. The above formula indicates that reducing the sound energy by a factor of 2 reduces the sound level by only 3 decibels, a difference that may be barely perceptible to the casual listener if frequency and event characteristics remain unchanged. An increase or decrease of sound level by 10 dB is often interpreted as a doubling or halving, respectively, of perceived, sound, even though the sound energy increases or decreases by a factor of 10. 22.214.171.124 Vibration Levels Vibration is commonly described in terms of displacement, velocity, or acceleration. Velocity correlates well with human response, and criteria for human exposure to vibration produced by rail transit operations are stated in terms of vibration velocity level in decibels. The decibel scale represents vibration in the same manner as the does the decibel scale for noise. The unit of vibration velocity level is designated as VdB, dBV, or simply dB. Unless otherwise stated, vibration velocity levels will be in decibels relative to 1 micro-inch per second: L(VdB) = 20 Log10 (v/v0), v0 = 1 Ã 10-6 in/sec The metric system is used around the world, notwithstanding the engineering community in the United States. Reference vibration velocity magnitudes used for defining the decibel scale include 10-6 m/sec (1 micron per second), 10-6 cm/sec, 5 Ã 10-6 cm/sec, and 10-9 m/sec. Vibration acceleration is also described with a decibel scale. Reference acceleration magnitudes include the micro-g (9.8 Ã 10-6 m/sec) and 10-6 m/sec2. The reference velocity and acceleration employed here are 1 micro-in/sec (25 micron/sec) and 1 micro-g (9.8 Ã 10-6 m/sec). The ground-borne or structure-borne sound produced by a vibrating surface such as a building wall, wheel, or rail is directly proportional the vibration amplitude of the surface at specific frequency. Thus, a 10-decibel change in the level of a vibrating surface produces the same 10- decibel change in radiated sound, greatly simplifying the calculation of sound levels from vibration levels. Further, the attenuation of vibration or noise due to various vibration and noise control provisions is most conveniently described with decibels. Thus, if the sound level is attenuated by 10 dB from point A to point B, the level at point B is simply determined by subtracting 10 dB from the sound level at point A. 9.1.4 Design Criteria Guidelines have been developed by the Federal Transit Administration (FTA) and the American Public Transportation Association (APTA). The FTA guidance manual provides criteria for both airborne noise and vibration in terms of the energy equivalent levels (Leq) and day-night levels (Ldn) and ground-borne noise in terms of maximum levels and integrates the noise impact analysis for combined rail and bus transit operations. The FTA guidance manual
Track Design Handbook for Light Rail Transit, Second Edition 9-4 recommends criteria for floor vibration in residences and institutions. The residential vibration criteria follow the recommendations provided in ANSI Standard S2.71-1983 (R 2006). These criteria are for maximum â octave band root-mean-square vibration velocity levels measured over any 1-second period during vehicle passage. The FTA guidance manual is generally used to assess impacts for federally funded projects and is recommended by the FTA for all rail transit projects, including bus transit. Refer to the FTA guidance manual for detailed description of the recommendations. The APTA guidelines recommend limits on maximum pass-by noise levels (i.e., the maximum noise levels that occur during an individual vehicle or train pass-by), as well as limits on the noise caused by ancillary facilities (i.e., fixed services associated with the transit system). The APTA guidelines have been supplanted by the FTA guidelines and are rarely, if ever, used for new construction. For most practical situations, the wayside noise levels and impact mitigation measures resulting from applying the FTA and APTA guidelines are very similar, although not identical. Design criteria for many existing transit systems were based on the APTA guide. No criteria for ground vibration are provided in the APTA guide. TCRP Project D-12 developed criteria for acceptable levels of rail-transit-generated, ground-borne noise and vibration in buildings. See TCRP Web-Only Document 48 for more details. 9.2 NOISE CONTROL DESIGN This article addresses wheel/rail noise and track-based noise control treatments. This very complicated subject has received the attention of numerous researchers and practitioners, and a chapter such as this cannot address all of the aspects of wheel/rail noise in complete detail. Even so, sufficient detail is provided to expose the user to various aspects of wheel/rail noise and provide direction for further investigation as may be desired. Article 9.2.1 addresses the rolling noise that occurs on tangent track or moderately curved track. This is further broken down into ânormal rolling noiseâ, âimpact noiseâ, rail corrugation noise, grinding artifact noise, and singing rail. Article 9.2.2 deals with special trackwork noise, which is a form of impact noise related to special trackwork. Article 9.2.3 is concerned with curving noise, including wheel squeal and flanging noise, one of the most significant types of rail transit noise. Transit vehicle auxiliary equipment also produces noise. Examples include roof-mounted HVAC equipment, brakes, and horns. These vehicle auxiliary equipment noise sources are not specifically treated here, although they may influence wayside-based noise control provisions. The user is referred to TCRP Report 23, Wheel/Rail Noise Control Manual. The material presented below is focused primarily on track-based noise control design 9.2.1 Wheel/Rail Rolling Noise Rolling noise is produced primarily by rail and wheel surface roughness with characteristic wavelength of several inches down to a fraction of an inch. Rolling noise is distinct from curving noise, both in nature and in generating mechanism. Rolling noise is radiated by the wheels and rails and may also be radiated by the structure supporting the track, such as elevated steel or concrete structures. This latter form of structure-radiated noise is termed âstructure-borneâ and is dealt with in the section regarding structure-borne and ground-borne noise and vibration control.
Noise and Vibration Control 9-5 126.96.36.199 Types of Rolling Noise The categories of wheel/rail noise include the following: â¢ Normal rolling noise â¢ Impact noise due to loss of contact between the wheel and rail, caused by rail head defects, gaps, and joints â¢ Rail corrugation noise, sometimes referred to as roaring rail noise â¢ Grinding artifact noise â¢ Singing rail 188.8.131.52.1 Normal Rolling Noise Normal rolling noise is broadband noise produced by reasonably smooth rail and wheel treads. The following generating mechanisms have been identified as sources of normal rolling noise: â¢ Wheel and rail roughness â¢ Parameter variation of rail head geometry or moduli â¢ Dynamic creep â¢ Aerodynamic noise Wheel and Rail Roughness Wheel and rail surface roughness is the major cause of rolling noise; the greater the roughness amplitude, the greater the rail vibration and wayside noise. Assuming that the wheel/rail contact stiffness is infinite, the rail and wheel tire would displace relative to each other by an amount equal to the sum of their roughness amplitudes. The ratio of rail motion relative to wheel motion at a specific frequency will depend on the dynamic characteristics of the rail and wheel and the contact stiffness, all of which are represented by their respective mechanical impedances as a function of frequency. At short wavelengths relative to the contact patch dimension, surface roughness is believed to be attenuated by averaging the roughness across the contact patch in a direction parallel with the rail, an effect known as contact patch filtering. Thus, fine regular grinding or milling marks less than 0.040 to 0.80 inch [1 or 2 mm] in wavelength would produce less noise than roughness of equivalent amplitude at wavelengths on the order of an inch. Excessive wheel/rail conformity has been identified as a cause of spin creep corrugation, leading to increased noise. Secondly, the contact mechanical impedance (stiffness) between the wheel and rail becomes large with a high degree of conformal contact, and may exceed the mechanical impedances of the rail and of the wheel tread, causing high-frequency contact forces. Good low-noise performance has been obtained at the BART ballast-and-tie test track with 119RE rail (modified through rail grinding to about a 10-inch [300 mm] crown radius) and cylindrical wheels that provide a rounded contact geometry, indicating that minimal conformal contact is desirable for low-noise operation on tangent track. High conformal contact may produce lower contact stresses in the rail head than a rounded contact zone for the same force, but this benefit may be canceled by high-frequency contact forces and spin slip. More discussion of this is provided below.
Track Design Handbook for Light Rail Transit, Second Edition 9-6 Parameter Variation Parameter variation refers to the variation of contact stiffness due to variation of the rail head crown radius and variation of rail and wheel steel elastic moduli. The effects of fractional changes in Youngâs elastic modulus and of the radius of curvature of the rail head as a function of wavelength necessary to generate wheel/rail noise equivalent to that generated by surface roughness are illustrated in Figure 9.2.1. The wavelength of greatest interest is 1 to 2 inches, corresponding to a frequency of about 500 to 1,000 Hz for a vehicle speed of about 55 mph, the maximum speed of typical light rail vehicles. Over this range, a variation in modulus of 3 to 10% is required to produce the same noise as that produced by normal rail roughness. Figure 9.2.1 Change in elastic modulus and rail head curvature required to generate wheel/rail excitation equivalent to roughness excitation (Remington, 1988) Variation of rail head ball or crown radius of curvature also induces a dynamic response in the wheel and rail. A variation of rail head curvature on the order of 10 to 50% produces noise levels similar to those produced by rail height variation alone. Rail head crown radius variation will normally accompany rail height variation, especially where corrugation is present or a high degree of conformal contact exists. Maintaining a uniform rail head radius is necessary to fully realize the benefits of grinding rail to maintain uniform head height. Irregular definition of the contact wear strip indicates excessive rail head radius variation. Reducing the width of the contact zone, thus reducing conformal contact, also reduces the sensitivity to head curvature variation. A high degree of conformal contact exacerbates the effects of rail head radius variation. PARAMETER VARIATION 0.001 0.01 0.1 1 10 1 10 100 1000 WAVELENGTH - MM FR A C TI O N A L C H A N G E CURVATURE MODULUS
Noise and Vibration Control 9-7 Dynamic Creep Dynamic creep includes both longitudinal and lateral dynamic creep, roll slip parallel with the rail, and spin creep of the wheel about a vertical axis normal to the wheel/rail contact area. Longitudinal creep is wheel creep in a direction parallel with the rail and is usually not considered in design and noise analysis. However, qualitative changes in wheel/rail noise on newly ground rail with an irregular transverse grinding pattern in the rail surface are audible as a train accelerates or decelerates, suggesting that longitudinal creep may play a role. Secondly, one may observe longitudinal striations in rail corrugation with martensite formation, presumably caused by frictional heating of the contact area. Lateral creep is wheel slip across the rail running surface in a direction transverse to the rail, and is the cause of wheel squeal. Lateral creep at tangent track may occur during unloading cycles at high frequencies on abnormally rough or corrugated rail and may be responsible for short-pitch corrugation at some tangent track. Lateral creep may occur at tangent track due to poor truck steering (crabbing) caused by poorly matched wheel diameters and wheel tapers. Extreme crabbing may be caused by false flanging, where the field side of the tire tread has a larger radius than the middle running surface of the tire tread. The cure for this latter condition involves regular wheel truing, as opposed to track maintenance. Cylindrical wheels do not promote crabbing unless their diameters are mismatched within a wheel set, but also do not promote steering or prevent crabbing. Moreover, a cylindrical wheel profile may rapidly develop a negative taper (false flange). Some degree of wheel taper is desirable to increase the time before a false flange can develop prior to truing. In general, a false flange condition should never be allowed to develop. Spin creep is caused by a wheel taper that produces a rolling radius differential between the field and gauge sides of the contact patch. Spin rotation of the wheel tire is rotation about a vertical axis through the tire center. Spin creep has been associated with high corrugation rates. Roll slip refers to rolling contact with slip at the edges of the contact zone. Some slip, continuous or otherwise, is required at the edges of the contact zone, as with Heathcote slip of a bearing in its groove, required by the conformal contact of curved contact surfaces. Reduction of the contact zone width would reduce conformal contact and thus potentially reduce roll slip. However, roll slip is a necessary consequence of the finite size of the contact zone and cannot be eliminated. Wheel and rail vibration modes may influence the formation of corrugation due to roll slip. Aerodynamic Noise Aerodynamic noise, due to high-velocity air jets emanating from grinding grooves in the rail, has been claimed to produce a high-frequency whistling noise. No test data have been obtained to confirm this claim. This noise, if present, may be indistinguishable from wheel/rail noise radiation. Fine rail grinding (acoustic grinding) that avoids course grinding marks should, presumably, reduce this type of noise, if it exists. Other sources of aerodynamic noise include air turbulence about the wheels and trucks and traction motor blower noise. Neither of these is controllable by the track designer, but traction
Track Design Handbook for Light Rail Transit, Second Edition 9-8 motor blower noise can, under certain circumstances, dominate the wayside noise spectrum if not properly treated. Aerodynamic noise due to air turbulence about the wheels and trucks at light rail transit speeds should not be significant. Ballasted track will tend to reduce aerodynamic and auxiliary equipment noise by absorbing sound beneath the vehicle. 184.108.40.206.2 Impact Noise Impact noise is a special type of wheel/rail noise occurring on tangent track with high amplitude roughness due to special trackwork, corrugation or spalling, rail joints, rail defects, or other discontinuities in the rail running surface and wheel flats. Impact noise is probably the most apparent noise on older transit systems that do not practice regular rail grinding and wheel truing. Even with continuous welded rail, rail welds and insulating joints must be carefully formed to reduce impact noise generation. Rail joint maintenance is important on older systems employing jointed rail. Remington provides a summary of impact noise generation that involves non-linear wheel/rail interaction due to contact separation and is closely related to impact noise generation theory at special trackwork. I. L. Ver categorizes impact noise by type of rail irregularity, train direction, and speed. Interestingly, impact noise becomes less dominant relative to general rolling noise as speed increases. This occurs for spalls in the rail head or rail gaps, for example, where the wheel actually traverses the gap before the rail can rise up to the wheel. 220.127.116.11.3 Rail Corrugation Noise Rail corrugation is periodic rail roughness with longitudinal wavelengths extending from a fraction of an inch up to 6 inches [1 cm up to 15 cm] or more. Short-pitch corrugation is most relevant to wayside noise from rail transit systems. Rail corrugation may be of low amplitude, as during its initial stages, or may involve deep corrugation leading to wheel/rail contact separation (impact noise). Rail corrugation with contact separation causes excessive rolling noise of a particularly harsh character and very high sound level. The terms "roaring rail," âroar,â and "howl" describe noise produced by corrugated rail. If rail corrugation exists, the wayside noise level will be higher than that of normal rolling noise by as much as 10 decibels, and the frequency spectrum will contain peaks and associated harmonics, producing an unpleasant tonal character. Examples of wayside noise from corrugated and uncorrugated rail are presented in Figure 9.2.2. These data are â octave band plots of noise measured at about 50 ft [15 m] from ballast and tie track. All of the vehicles represented had resilient Bochum 54 wheels. The data collected at Sacramento RTD and the Los Angeles Blue Line contain a pronounced peak at 800 Hz, which is due to moderate rail corrugation at about 1.5 to 2 years after the last grinding and possibly grinding marks. The data shown for the Portland TriMet system were obtained about 5 years after the last grinding, but do not contain a peak at 800 Hz. An inspection of the wheels at the Sacramento RTD and Los Angeles Blue Line indicated moderate wheel tread hollowing with moderate false flange. The Portland TriMet wheels are ground regularly, and inspections of these wheels suggested little false flange. Whether or not wheel truing practices contribute to rail corrugation at the Sacramento RTD or the LAMTA Long Beach Blue line is a matter for additional investigation, and conditions may have changed considerably since these data were collected. The tie spacing at these tracks is nominally 30 inches [750 mm], which supports a pinned-pinned mode in the rail at about 800 Hz for RE115 rail, which may contribute to rail corrugation growth.
Rail c lower preve more with h where maint system system the m orrugation is contact stat nt randomiza readily than igh amplitud high current aining rail sm s. Rail co s, and contr ost effective Figur more difficu ic loads, the tion of whee do high cont e corrugatio s are require oothness is rrugation is olling rail cor means of con e 9.2.2 Exa lt to control o uniformity of l/rail forces. act loads, al n. Wheel/ra d for acceler probably mo the principal rugation is ke trolling rail co 9-9 mples of wh n rail transit transit vehi Low contac lowing whee il contact se ation and reg re important cause of e y to minimiz rrugation is Noise eel/rail noise systems tha cles, and the t loads allow l/rail contact paration ma enerative br for transit s xcessive noi ing rail transi rail grinding. and Vibrat n railroads b uniformity o the wheel a separation to y involve el aking of the v ystems than se levels on t system nois Detailed disc ion Contro ecause of th f speeds tha nd rail to sl occur on ra ectrical arcin ehicle. Thu heavy freig many trans e. At presen ussions of ra l e t ip il g s, ht it t, il
Track Design Handbook for Light Rail Transit, Second Edition 9-10 corrugation noise are included in TCRP Report 23. Rail grinding, including acoustic grinding, is discussed in detail by Zarembski. Figure 9.2.3 is a photograph of very short-pitch corrugation for a light rail system with embedded track and resilient wheels. The wavelength is less than 1 inch [2.5 cm], and the width is relatively small compared to the width of the rail head. The lighter portions of the periodic patterns are referred to as âwhite etching layerâ in the literature. Wild et al. indicates that the white etching layer is due to nanocrystalline martensite and cementite particles. The white etching layer occurs at the peaks of the corrugation, where the steel is generally much harder than at the troughs. According to Hutchings, martensite is formed by heating and rapid quenching by conduction of heat into the bulk of the metal and may also be facilitated by shear stress. Both of these processes may occur during wheel/rail contact dynamic slip, the heating due to friction. The longitudinal striations suggest a longitudinal slip, perhaps related to torsional oscillation of the wheel set. There is no evidence of rail grinding marks that might have contributed to this pattern. Figure 9.2.3 Very short pitch corrugation Very short-pitch corrugation has been claimed to occur at Sound Transit embedded and direct fixation track. The nature of the corrugation appears to be related to rail grinding marks, but a dynamic mechanism may also be responsible. (This is discussed in more detail regarding rail grinding artifact noise in Article 18.104.22.168.4 of this chapter.) Figure 9.2.4 is a photograph of conventional short-pitch corrugation of wavelength on the order of 3 to 4 inches. This was observed a few feet away from the very short pitch corrugation shown in
Noise and Vibration Control 9-11 Figure 9.2.3. Again, martensite formation and longitudinal striations suggest longitudinal slip. These corrugations were observed at a relatively short section of track, where three-car trains accelerated from a station stop through the corrugated section. Thus, train speed was varying, in spite of the apparent uniform wavelength. The maximum train speed was probably about 15 to 20 mph. The vehicles were low-floor vehicles with resilient wheels. The rail was evidently 115 RE, embedded in an elastomer. The corrugation appeared to be an anomalous condition at this system, but is representative of corrugations at many other systems. In particular, the uniformity of wavelength in the presence of varying train speed suggests a geometric cause of the corrugation, as opposed to a mechanical resonance. The geometric parameters involved include rail head ball radius, and wheel tread profile and radius. The nature of the rail support was not determined. These corrugations produced a low-frequency rumble (ground-borne noise) that was perceptible to the feet. However, the corrugation depth was not perceptible to touch. Figure 9.2.4 Short-pitch corrugation Figure 9.2.5 is a photograph of rail corrugation on the California Street cable car line in San Francisco. The cable car wheels are of small diameter and are non-powered since the vehicles are towed by the cable hidden beneath the street surface. The corrugation patterns extend across most of the rail head and are very regular, with a wavelength of less than 1 inch. These corrugations do not occur on the downhill slopes, possibly because of wood block brakes that rub the rail to help control descent (on the cable.) One possibility is that the resins left by the blocks may affect wheel/rail contact adhesion; another is that the blocks simply smooth out the corrugation before it can occur. While the cable car system is not representative of typical light rail systems, the corrugation processes may be very similar, and attention is called to the high degree of wheel rail conformal contact.
Track Design Handbook for Light Rail Transit, Second Edition 9-12 Figure 9.2.5 Corrugation on San Francisco cable car track Very short pitch corrugation has been claimed at the Seattle Sound Transit system at both direct fixation track and embedded track. Similar observations have been observed at TriMet. Rail corrugation is particularly problematic at the Detroit People Mover system, the TTC Scarborough Line, and the Vancouver Skytrain system, all of which employ linear induction motors (LIM) for propulsion, without tractive effort at the wheels. Most interestingly, anecdotal information suggests that rail corrugation may occur at areas where the LIM vehicle with non- powered wheels is accelerating! No satisfactory information has been obtained to explain this phenomenon. The return currents pass through a return rail, rather than through the track rails, so electrical heating does not appear to be a cause. The wheels of these vehicles are of small diameter, so that the contact stresses may be greater than would be the case with larger diameter wheels. Still, the vehicles are relatively lightweight. The self-steering truck is designed to promote curving and reduce squeal. Friction between the bolster and frame, however, may prevent full steering of the vehicle, even on tangents, thus promoting lateral slip. Spin slip was identified as the cause of corrugation at the Vancouver Skytrain system. Corrugation mechanisms include spin slip of the tire about a vertical axis through the contact area, lateral oscillation of the tire, pinned-pinned resonances of the rail, primary suspension resonance, track resonance (or P2 resonance), torsional resonance of the wheel set, and periodic creep within the contact zone. Corrugation may occur on ballast-and-tie track, direct fixation track, and embedded track.
Noise and Vibration Control 9-13 The literature is rich with various theories regarding rail corrugation. A summary of corrugation observations at heavy rail transit systems and one light rail system is provided in TCRP Research Results Digest 26. Table 9.2.1 provides a summary of corrugation types and formative mechanisms as described by Grassie. Grassie indicates that all types of corrugation are essentially constant frequency phenomena, a hypothesis that is contrary to some earlier theories. The pinned-pinned mode of rail vibration is essentially a constant frequency phenomenon, related to discrete rail supports, a geometric characteristic. However, rail corrugation occurs at embedded track without discrete rail supports, indicating that other mechanisms besides pinned- pinned modes and discrete track supports may cause corrugation. Ciavarella and Barber have developed a theory of rail corrugation that is independent of pinned-pinned modes or other resonances, suggesting that rail corrugation wavelength may be induced by an existing periodic roughness in the running surface. One prediction regarding rail corrugation can be made: corrugation is likely to occur if the rails are not ground regularly. Table 9.2.1 Corrugation categories (After Grassie, 2010) Type Wavelength fixing mechanism Track type Typical frequency â Hz Damage mechanism Pinned-pinned Pinned-pinned resonance Tangent and high rails 400-1200 Wear Rutting 2nd torsional resonance of driven axles Low rail 250-400 Other P2 resonance P2 resonance Tangent or high rails 50-100 Wear Heavy haul P2 resonance Tangent and curves 50-100 Plastic flow in troughs Light rail P2 resonance Tangent and curves 50-100 Plastic bending Trackform specific Trackform specific Tangent or curves â Wear Rutting corrugation is related to torsional resonance of the wheel set. Rutting corrugation may not be relevant to light rail systems with resilient wheels. Not all light rail or heavy rail systems use resilient wheels, so rutting corrugation may yet be a significant factor at some systems. The P2 resonance is the resonance of the wheel set and rail on the track support stiffness. This is also greatly modified by the resilient wheel, so one may speak of a resonance of the tire and rail on the track support, and the resonance of the axle set and wheel centers on the resilient wheel springs. The vibration is probably coupled such that the P2 resonance is not clearly defined for resilient wheels. Track curvature influences corrugation rates. Dring reports that corrugation rates at wavelengths of 4 to 10 inches [100 to 240 mm] were measured at the MTRC Island Line in Hong Kong. The results are listed in Table 9.2.2. These data suggest that at relatively modest curve radii of 1,300 feet [400 m] or less, corrugation depth might reach as much as 0.052 inch [1 mm] within as little
Track Design Handbook for Light Rail Transit, Second Edition 9-14 as 1 year. Corrugation rates were evidently reduced by 60 to 70% relative to 1992 values after full scale implementation of modified wheel profiles. These profiles were developed in combination with rail profiles to control both rail corrugation and shelling. The MTRC vehicle is a conventional rapid transit vehicle with solid wheels, and results for light rail vehicles with resilient wheels may differ. The MTRC rail corrugations are believed to be due to plastic deformation, related to high contact forces at track resonance frequencies governed by the wheel set unsprung mass and the track stiffness. Dring also reports short pitch corrugation at the MTRC, at wavelengths of 2 to 3.5 inches [50 to 90 mm]. The depth of these short pitch corrugations did not exceed 0.002 inch [0.05 mm]. These were prevalent on the low rail and characterized by âwhiteâ patches (inferred here to mean martensite, indicative of heating due to slip). Table 9.2.2 Corrugation growth rates at MTRC Hong Kong for various track curvatures in 1992 (After Dring, 1994) Curve Radius Corrugation Growth Rate M feet mm / week 0.001 inch/week < 400 <1,300 0.025 1 400 to 1000 1,300 to 3,300 0.01 0.4 > 1000 > 3,300 0.001 0.04 New rails are evidently more prone to corrugation than older rails at the MTRC due to lack of work hardening, which may require considerable periods of time. Even so, the MTRC axle loads are evidently high for rail transit. Rail grinding soon after rail installation would likely require additional grinding after work hardening has taken place. As discussed below, residual stress accumulation due to contact loading (shakedown) reduces the propensity for additional plastic deformation and thus might reduce the propensity for rail corrugation of the type described by Dring. Residual stress accumulation might be relatively rapid after installation. Noise levels at the MTRC were observed to increase by 7 to 10 dB as the corrugation approached 0.016 to 0.020 inch [0.4 to 0.5 mm], providing an indication of the significance of corrugation amplitude. Thereafter, interior noise levels remained relatively constant with increasing corrugation depth (possibly due to loss of contact between the wheel and rail). At these corrugation amplitudes, the wheel and rail tend to separate from each other, if only for a millisecond at a time. (This may have some implication regarding signaling.) 22.214.171.124.4 Grinding Artifact Noise Grinding artifact noise is caused by periodic grinding patterns left in the rail by rail grinding machines, and these patterns can be confused with corrugation. The noise produced by periodic grinding marks is similar to gear noise, such as the sound of worn differential ring-and-pinion gears in automobiles. While preferable to corrugation noise, such noise may be objectionable. The grinding artifacts are caused by irregular or excessively rough grinding wheels and high rates of metal removal due to coarse grinding at high grinding train traveling speed. Grinding procedures involving high grinding train traveling speed and single passes are most prone to leaving grinding artifacts. Grinding marks on head-hardened or alloy rail may not be easily worn
Noise and Vibration Control 9-15 down by lightweight rail transit vehicles as opposed to freight trains. Rail grinding methods used on freight railroads may not be valid for rail transit. Rail corrugation has been associated with grinding marks left by rail grinding machines at TriMet and Sound Transit. Anecdotal evidence obtained at these systems suggests that residual grinding marks may trigger subsequent rail corrugation. As noted above, natural corrugation at very short wavelengths comparable with grinding mark wavelengths can occur. Some interaction may occur between periodic grinding artifacts and the tire, such that the grinding artifact amplitude may increase in severity, causing corrugation at the same wavelength. Ciavarella and Barber have developed just such a theory where existing periodic roughness may lead to rail corrugation at the same wavelength. 126.96.36.199.5 Singing Rail Singing rail is noise radiated by the rail at large distances ahead of and behind the train, and is due to rail bending waves propagating at velocities in excess of the velocity of sound in air. Singing rail is most apparent with soft direct fixation fasteners with low damping. Uniform spacing of rail supports also produces stop bands and pass bands in the bending wave vibration spectrum. Resilient rail pads or direct fixation (DF) fasteners that support the rail through elastomeric elements tend to decouple the rail from the rail support, broadening the spectrum of vibration transmission throughout the audio range. Singing rail is apparent at Bixby Knolls on the Los Angeles Blue Line in California, and at the Collingswood station near Philadelphia. The rail at Bixby Knolls is ballasted track with concrete ties, spring clips, and pads, at a 30-inch [750-mm] pitch. The rail at Collingswood station is supported by unconventional direct fixation with the rail head and web directly supported by elastomeric shoulders, leaving the base of the rail hanging free. 188.8.131.52 Factors Affecting Rolling Noise Various factors and features of track design that influence rolling noise are described below. These factors may also influence ground vibration and ground-borne or structure-borne noise, although the frequency regime is much lower with structure-borne noise and vibration. The term âstructureâ refers to the trackbed or aerial structure, as opposed to the rail. 184.108.40.206.1 Wheel Dynamics The dynamic response of the wheel set substantially affects high-frequency rail and wheel vibration and thus wayside noise. The response is affected by axle bending modes beginning at about 80 to 120 Hz, wheel and/or tire resonances above 400 Hz, and spring-mass resonances of resilient wheels. Figure 9.2.6 illustrates the radial acceleration response of a typical resilient wheel. The first radial distortional mode of the tire is at about 500 Hz, followed by numerous radial modes at higher frequencies. One may expect peaks in wayside noise spectrum at these frequencies, related to noise radiation by the wheel.
Track Design Handbook for Light Rail Transit, Second Edition 9-16 Figure 9.2.6 Radial mechanical acceleration response of TriMet Type 2 vehicle resilient wheel Figure 9.2.7 shows the corresponding radial mechanical impedance of the tire of the same wheel. The mechanical impedance represents the reaction force of the tire to an input velocity and is directly related to the acceleration response shown in Figure 9.2.6. The minima of the radial mechanical impedance correspond to radial resonances of the wheel and tire. The maxima of the radial impedance correspond to anti-resonances at which frequencies maximum wheel reaction forces would occur. (The picture is actually more complicated, as the dynamics of the rail must be taken into account.) In this case, the highest peak in the mechanical impedance curve occurs at about 775 Hz, where the impedance is 5,000 lb-sec/in [0.875 KN-sec/mm]. Assuming a rail surface roughness of 0.001 inch [0.0254 mm], the corresponding reaction force of the wheel would be 24,350 lb [113 KN], exceeding the static load. The actual force would differ, due to the compliance of the rail, but one can see how a modest rail roughness or wheel flat can produce high contact forces, wear, and noise. Contact separation is a distinct possibility for track with rough running surfaces. Contact separation would tend to occur less at AW3 loading than AW0 loading, due to the higher static contact load. 70 80 90 100 110 120 130 140 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Radial_untreated D R IV E PO IN T FR F M A G N IT U D E (d B re 1 .0 m ic ro -g /lb ) FREQUENCY (Hz)
Noise and Vibration Control 71-9 Figure 9.2.7 Input mechanical impedance of TriMet resilient wheel 220.127.116.11.2 Rail Dynamics The dynamic response of the rail strongly influences wayside noise radiation. Up to about 400 Hz, the rail behaves as a simple beam on an elastic foundation. At higher frequencies, standing waves occur between the rail supports. The first of these is the pinned-pinned mode, where the wavelength of the standing wave is equal to twice the fastener pitch. The maximum amplitude of vibration occurs midway between the fasteners, and the minimum amplitude occurs at each fastener position. Estimates of the pinned-pinned mode resonance frequencies based on Timoshenko beam theory are presented in Figure 9.2.8. The pinned-pinned mode resonance frequencies of 115 RE rail supported at pitches of 36 inches and 30 inches [900 mm and 750 mm] are about 500 Hz and 750 Hz, respectively. The pinned-pinned mode resonance frequency increases with increasing rail size, but not rapidly. TRIMET RESILIENT WHEEL - RADIAL IMPEDANCE 10 100 1000 10000 100000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 FREQUENCY - HZ M E C H A N IC A L I M P E D A N C E - L B -S E C /I N
Track Design Handbook for Light Rail Transit, Second Edition 9-18 Figure 9.2.8 Vertical pinned-pinned resonance frequency vs. rail support separation for various rails Grassie and Edwards have identified the pinned-pinned mode as being responsible for one form of short pitch corrugation. However, short pitch corrugation has been observed at embedded track with continuous elastomer support, for which no pinned-pinned mode exists, indicating that other factors may contribute to rail corrugation besides pinned-pinned modes. (These factors may include the vertical and lateral rigid body modes of the resilient wheel tire, tire running surface profile, torsional vibration of the axle and wheel centers, and perhaps other causes.) Figure 9.2.9 illustrates the mechanical input impedance of the rail head for forces acting vertically against the head, based on exact solutions for a Timoshenko beam discretely supported at 30- inch [750-mm] spacing by fasteners with vertical dynamic stiffness of 250,000 lb/in [44 MN/m]. The first curve is the input impedance directly over the fastener, and the second is the input impedance at a point midway between fasteners. The measured mechanical impedance of the TriMet resilient wheel is shown for comparison. Both of the rail impedance functions contain a dip at about 100 Hz, which is the resonance of the rail on the fasteners, and would be predicted by a continuously supported rail with equivalent rail support modulus. The curves depart considerably above 200 Hz due to the discrete nature of the rail support. The railâs high-frequency input 0 500 1000 1500 2000 2500 3000 3500 12 18 24 30 36 42 RAIL SUPPORT PITCH - INCHES FR EQ U EN C Y - H Z 132 LB/YD 115 LB/YD 100 LB/YD 90 LB/YD
Noise and Vibration Control 91-9 mechanical impedance depends strongly on whether the input point is between the fasteners, over a fastener, or at some other point between these. Thus, as the wheel rolls over the rail, it sees a rapidly varying mechanical impedance at high frequencies depending on its position relative to the fasteners. Figure 9.2.9 Mechanical input impedance of 115 RE rail on discrete supports Except at a few isolated frequencies, the mechanical impedance of the rail substantially exceeds that of the wheel tire above roughly 2,000 Hz. The greatest opportunity for complex interaction of the wheel tire and rail occurs at frequencies below 2,000 Hz, especially near the pinned-pinned RE115 RAIL ON 250KIP/IN FASTENERS AT 30IN PITCH - VERTICAL IMPEDANCE 10 100 1000 10000 100000 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 FREQUENCY - HZ M E C H A N IC A L IM P E D A N C E - L B -S E C /IN OVER BETWEEN TRIMET RESILIENT WHEEL
Track Design Handbook for Light Rail Transit, Second Edition 02-9 mode. Figure 9.2.10 is an expanded view of Figure 9.2.9, which shows how close the pinned- pinned mode is to a major anti-resonance of the resilient wheel. Figure 9.2.10 Input impedance of 115 RE rail (0 to 2000 Hz) Timoshenko beam theory is excellent for analysis of high-frequency rail vibration up to about 1,000 or 1,500 Hz. Above 1,000 Hz, the vibration modes of the rail flange and web enter into the response. That is, the rail no longer bends as a simple beam, but âbreaks upâ into local modes, greatly complicating the response relative to those shown in Figures 9.2.9 and 9.2.10. The lateral vibration response of the rail is also very important, as distortional vibration of the rail web may occur at frequencies in the neighborhood of 1,000 Hz and above. The tireâs vibration response is RE115 RAIL ON 250KIP/IN FASTENERS AT 30IN PITCH - VERTICAL IMPEDANCE 10 100 1000 10000 100000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 FREQUENCY - HZ M E C H A N IC A L IM P E D A N C E - L B -S E C /IN OVER BETWEEN TRIMET RESILIENT WHEEL
Noise and Vibration Control 9-21 similarly complicated. Thus, beam theory for detailed modeling of wheel/rail interaction at frequencies above 1,000 or 2,000 Hz may be of little quantitative value. Finite element analysis offers a much more complete picture of rail and wheel vibration at the cost of considerable computer time. Figure 9.2.11 illustrates the theoretical vertical vibration response of the rail at a distance of about 50 ft [15 m] from vertical forces applied to the top of the railâone force located at a point above the fastener and the other force located between the fasteners. This model corresponds to that represented in Figure 9.2.9 and Figure 9.2.10. The rail is 115 RE with 250,000 lb/in [44 KN/mm] fasteners at 30-inch (750-mm] spacing. Bending waves propagate in the rail at frequencies between the rail-on-fastener resonance frequency and about 700 Hz. Between this frequency and the pinned-pinned mode frequency of about 770 Hz, vibration transmitted along the rail is greatly attenuated, depending on the rail support dynamic characteristics and uniformity of the spacing, producing what is termed a "stop band." As shown in Figure 9.2.11, the stop band can be very dramatic; at 50 ft [15 m] from the source, the rail response is nil. Between the pinned-pinned mode frequency and the next higher cutoff frequency, bending waves may propagate freely in a "pass band." The theoretical transmission of vibration in the rail contains a series of stop bands and pass bands. The railâs ability to radiate noise will be affected by the widths of the stop and pass bands, and a slight randomness in the support separation may significantly alter the stop and pass band characteristics. Grassie indicates that introduction of randomness in the rail support is intuitively attractive, but suggests that pinned-pinned mode would move to those frequencies representative of the mean spacing. However, the pinned- pinned mode is the result of periodic supports with uniform spacing, and introduction of randomness would tend to destroy the pinned-pinned mode and associated stop bands and pass bands of rail bending waves. Reducing the rail support pitch will increase the pinned-pinned mode frequency and those of the pass bands and stop bands, as noted above. (The ripples of the responses shown in Figure 9.2.11 are numerical artifacts related to the use of a finite number of rail supports, in this case, 256, and finite rail length.) The main point here is that the response of the wheel and rail above 500 Hz is very complicated and that the propensity for adverse interaction between these components, leading to tonal components of wayside noise and possibly corrugation, is high. Track design should, ideally, be directed toward minimizing the chances of these interactions. Reducing the rail support spacing and introducing damping into the track support system should be useful for this purpose. Also, some types of direct fixation fasteners support the rail directly through an elastomer element, decoupling the rail from the top plate or base plate so that the rail is free to act as an infinite unsupported beam without pinned-pinned modes. A free infinite rail exhibits considerable damping due to rail vibration energy being radiated away from the source, and, as a result, might be less susceptible to rail corrugation. Axle spacing also affects the response of the rail. That is, bending waves reflect between the tires as the truck moves down the track. Selection of fastener spacing to avoid undesirable amplification of rail vibration between the wheel sets may be possible. To the extent that anti-resonances occur in the wheel tire, choosing the fastener pitch such that the first anti-resonance of the tire falls within the railâs stop band might be an attractive approach to controlling singing rail. Research in this area is needed to explore these design options.
Track Design Handbook for Light Rail Transit, Second Edition 9-22 Figure 9.2.11 Theoretical vertical rail velocity responses at about 50 ft [15 m] from vertical forces directed against the rail head 18.104.22.168.3 Resilient Direct Fixation Fasteners The input mechanical impedance of the fastener influences the response of the rail, as indicated in Figure 9.2.8, Figure 9.2.9, and Figure 9.2.10. In general, very stiff fasteners reduce the response of the rail at the expense of increasing structure-borne noise and vibration. Soft fasteners allow the rail to vibrate more than stiff fasteners do. Fasteners that support the rail with elastomer shoulders may have little effect on rail vibration at high frequencies (above perhaps 200 Hz), because the mechanical impedance of the elastomer decreases with increasing frequency. Soft fasteners with very massive top plates in direct contact with the rail tend to block the response of the rail at high frequencies, thus promoting the pinned-pinned mode. Resonances of the top plate may further affect rail response. To complicate matters more, the base of the rail, the clip, and the shoulder of the fastener combine to further influence the dynamic stiffness âseenâ by the rail. Details concerning rail fastener performance characteristics are presented in Article 22.214.171.124.5.
Noise and Vibration Control 9-23 126.96.36.199.4 Ballasted Track Noise from ballasted track is usually less than from resilient direct fixation track, due to the acoustical absorption provided by the ballast. The character of wayside noise from ballasted track also differs significantly from that produced at direct fixation track, probably due to differing dynamic characteristics of the rail support and rail support separation, as well as the amount of trackbed sound absorption. For example, the cross ties at ballasted track may be placed with a slightly random separation that tends to destroy the pinned-pinned mode of rail vibration, where direct fixation track fasteners are usually installed at precise separations. Ballasted track with wood ties, tie plates, and cut spikes probably provides greater damping than track with concrete ties with rail clips or direct fixation fasteners. These factors tend to reduce reverberation (standing waves) of vibration in the rail, making the rail sound âdeadâ compared to direct fixation track. 188.8.131.52.5 Contact Stiffness Contact stiffness is the ratio of the contact vertical force to the relative vertical deflection of the wheel tire and rail, assumed here to be the relative deflection of their respective neutral axes. The mechanical impedance of the contact stiffness is inversely proportional to the frequency. If the contact stiffness is small relative to the stiffness of the wheel or rail, wheel/rail forces will be controlled by the contact stiffness, such that a halving of contact stiffness would halve the dynamic forces driving the wheel and rail, thus reducing wheel/rail forces and noise by six decibels. The contact stiffness is typically about 6,000,000 lb/in [1,050 KN/mm] for a rail head radius of 10 inches [254 mm] and linear tread profile. The contact mechanical impedance at 1 KHz is Zc (1,000 Hz) = 6,000,000 lb/in / (2 Ã 3.14159 Ã 1,000 Hz) = 955 lb-sec/in In S.I. units, this is Zc (1,000 Hz) = 1.05E9 N/m / (2 Ã 3.14159 Ã 1,000 Hz) = 167,000 N/m or 0.167 KN/mm This can be compared with the measured input mechanical impedances of the resilient wheel, shown in Figure 9.2.7, and that of the rail, shown in Figure 9.2.9. At 1,000 Hz, the impedance is comparable with those of the wheel and rail. Most importantly, the contact mechanical impedance is significantly less than that of the wheel at the anti-resonance frequencies of the tire. These anti-resonances produce peaks in the wheel/rail contact forces, and these forces are reduced if the contact mechanical impedance is less than the tire and rail mechanical impedance. The contact mechanical impedance decreases to 500 lb-sec/in [0.0875 KN/mm] at 2,000 Hz and 250 lb-sec/in [0.0438 KN/mm] at 4,000 Hz. Thus, the contact impedance becomes small relative to that of the rail at frequencies above 2,000 Hz, but remains comparable to the mechanical impedance of the wheel. The contact stiffness tends to dominate the rail response and reduce the vibration of the rail at these higher frequencies.
Track Design Handbook for Light Rail Transit, Second Edition 9-24 With high conformal contact, the contact stiffness may increase to 20,000 lb/in [3.5 KN/mm], with a contact mechanical impedance on the order of 3,000 lb-sec/in [0.525 KN-sec/mm], comparable with that of the rail. Thus, rail vibration at high frequencies should be high with high conformal contact! As it turns out, though, high-frequency wayside rolling noise above 4,000 Hz is usually less important than at 500 to 1,000 Hz, at least for a low degree of conformal contact. More research is needed, including field testing, to determine the effect of contact stiffness, or more specifically, conformal contact, on wayside noise. The contact stiffness does not vary greatly over the range of rail head crown radii for a typical wheel with straight taper. The contact stiffness varies about 16% for head radii between 6 inches [150 mm] and 15 inches [375 mm]. Under the most optimistic scenario, reducing the rail head radius would decrease contact forces, and thus noise, by at most 1.5 dB, unless the starting point is a high degree of conformal contact. Thus, from the point of view of track design, the head radius should be sufficiently small to avoid development of fully conformal contact across the rail head for any reasonable wheel truing interval. The current AREMA standard for 115RE rail specifies a rail head crown radius of 8 inches [200 mm], which would be consistent with avoiding conformal contact at the running surface on tangent track. Conformal contact at low radius curves will occur at the gauge corner, as this is controlled by the wheel profile at the throat and the gauge corner radius, both subject to wear, and should not necessarily be avoided. 184.108.40.206 Treatments for Rolling Noise Control Track-oriented treatments for controlling rolling noise are described below, with emphasis on those treatments that are common in the industry. 220.127.116.11.1 Continuous Welded Rail Rolling noise levels with properly ground continuous welded rail and trued wheels in good condition are the lowest that can be achieved without resorting to extraordinary noise control measures. Impact noise from rail joints can be clearly audible with moderately maintained track. Noise from continuous welded rail may be as much as 5 dB lower than noise from jointed rail. Continuous welded rail requires less maintenance than jointed rail, so the benefits of low noise are more easily retained. 18.104.22.168.2 Hardened Rail Hardened rail is less prone to rail corrugation and wear than rails of softer steel. Head-hardened and fully heat-treated rails are employed at curves and at station areas where acceleration/deceleration occurs. Hardened rail may prove beneficial for tangent track and at moderately curved track as well. Hardened rails should be carefully ground so as to avoid grinding artifacts that will not be worn down by subsequent vehicle operations. Further, excessive heating of the rail during grinding must be prevented to avoid loss of hardness. This is particularly important for work-hardened rail and/or rails with accumulated internal stresses due to wheel contact loading (shakedown). (See Article 9.4.4.) 22.214.171.124.3 Rail Grinding Rail grinding combined with wheel truing is the most effective method for controlling wheel/rail rolling noise. With ground rail and trued wheels, wheel/rail noise levels at tangent ballasted track are comparable with the combined noise levels from traction motors, gears, and fans. Rail grinding and rail grinders are discussed in detail in TCRP Report 23.
Noise and Vibration Control 9-25 Initial Grind Even though rail grinding is usually the task of the transit system operator, an initial grind may be performed after track construction to remove mill scale from the rail for better traction and electrical conductivity. The grinding must establish a smooth finish and must maintain the head profile. After run-in and shakedown stress accumulation, the rail may be ground a second time to reestablish a smooth running surface. The second grind need not be aggressive or require significant metal removal, as it would essentially be a dressing operation. If the rail is not ground initially, high contact forces due to roughness may occur, producing irregular hardness that may be difficult to smooth out over time. Initial grinding to remove scale and smooth the rail will provide a quiet system from start, also minimizing adverse community reaction to noise. Overheating Aggressive grinding may reduce running surface hardness by overheating. Thus, metal removal should not be conducted at such a high rate that it heats the rail excessively. Multi-stone grinders may avoid overheating. Any grinding program should be reviewed carefully with grinding contractors and engineers to ensure that head hardness is preserved. Grinding Marks Rail grinding should be done in a manner that does not introduce deep grinding marks into the rail. This is particularly important for hardened rail, as subsequent vehicle operations may not wear away the grinding marks. Some claim that grinding marks are acceptable, as they will be worn away over time. This is not likely to occur with head-hardened rail and light transit loadings. Grinding artifacts can be minimized with multiple grinding facets that closely mimic the desired crown and gauge corner radii, fine grit stone, and low translation grinding train speed. Grinding should ideally provide a smooth finish. Grinding with an eight-stone grinder evidently reduced the amplitude of grinding marks at TriMet. Sixteen-stone grinders should provide a smoother finish than would four- or eight-stone grinders, given the same number of passes. An eight-stone or sixteen-stone grinder can accomplish the same profile and finish with fewer passes than a four-stone grinder can. Grinding involving only a single pass with a four-stone grinder should be avoided. Grinding procedures that result in a wavelength that produces a characteristic frequency during train passage that is comparable with the pinned-pinned mode frequency of the rail should be avoided. For typical light rail systems with a maximum speed of 55 mph, the translational speed is 968 in/sec [24.6 m/sec]. The pinnedâpinned modal frequency of the rail at 30-inches [750-mm] pitch would be about 800 Hz, corresponding to a wavelength in the rail of about 1.2 inches [30 mm]. Grinding artifact pitches should be substantially less than this, and a conservative criterion would be 0.6 inch [15 mm]. However, short pitch corrugations with this wavelength have been noted at systems such as Sound Transit, suggesting that further investigation of the relationship between grinding procedures and corrugation rates should be conducted.
Track Design Handbook for Light Rail Transit, Second Edition 9-26 Rail grinding should be conducted in a manner that avoids coincidence between the rail grinding pattern pitch and rail corrugation wavelengths. Grinding train speeds, grinding wheel rotation speeds, and chronic corrugation frequencies should be reviewed before grinding. Rail grinding with a finish grind, or âacousticâ grind, with narrow facets and very short grinding pitch avoids coincidence with corrugation wavelengths. A persistent howling noise developed at TriMetâs ballasted track after grinding with the four-stone grinder. The cause may have been related to speed and grinding depth. An eight-stone grinder was brought in and the rail was reground to profile with 2 to 3 passes at 2.5 mph [4.0 km/h] pass rate with fine grit stones. The howling noise was eliminated. TriMetâs position now is to specify an eight-stone grinder for all future grinding. Grinding at Curves Rail grinding at curves is desirable to control surface fatigue and defects, especially where lubrication is used. Lubricants can be forced into surface fatigue cracks under high stress and further open these fatigue cracks. This problem is probably greatest for heavy haul freights, but may occur at transit systems with soft rail. System Layout Rail grinding strategies should be considered when laying out track. Staging locations, such as pocket tracks and turnouts, for storing grinding equipment (as well as other track maintenance equipment) should be provided to minimize travel time. Grinding can be performed only if there is adequate access to the track during non-revenue hours or by single tracking, and grinding time can be maximized by minimizing travel time to and from the grinder storage location and the treatment section. Some grinders may have difficulty negotiating curves in tunnels or may be unable to grind rail on very short-radius curves. Adequate clearance must be included in track and structure designs to accommodate rail grinding machines. The ability to grind rail is a major factor in track layout and design. Rail Profile The optimal grinding procedure includes grinding the rail to achieve a head profile crown radius of about 8 to 11 inches [200 to 450 mm]. (The AREMA specification for 115RE is 8 inches [200 mm].) This should ideally be achieved with grinding facets of about 1/16 inch [2 mm]. The rail head curvature has to be small enough that conformal contact of the wheel and rail would not occur for the maximally worn wheel. A rail head crown radius of as little as 8 inches [200 mm] may be appropriate for systems with infrequent wheel truing to avoid conformal contact. TriMetâs grinding approach for ballasted track does not include grinding to a precise ball radius, but grinding facets on the top of the rail at the gauge side and field sides, and then grinding the crown. This leaves grinding marks, but wear over a reasonable length of time eliminates the grinding marks and produces an approximate ball radius. TriMet has conducted very precise profile grinding with good surface finish, but has found this to be time consuming and impractical. Grinding time is limited to between 1 and 4 a.m., which does not leave much âsparkâ time. (Grinding marks may not wear away with time on tangent track with head-hardened rail.)
Noise and Vibration Control 9-27 TriMet grinds the rail flat at embedded track sections, due to the difficulty of grinding a profile without the stone contacting the pavement or tram shoulder. This does not cause a problem with noise or steering, as train speeds are low on embedded track (on the order of 15 mph in downtown areas). Grinding Machines Sixteen-stone grinders reduce the grinding time necessary to produce the desired contour relative to the time required with four-stone or eight-stone grinders. Computer-controlled grinders with various grinding profiles stored in memory simplify setup and further reduce grinding time. Grinding car speeds should be low enough to reduce the wavelength of grinding patterns to perhaps 0.25 inch [6 mm]. However, the speed should not be so slow as to excessively heat the rail and reduce its hardness. Grinding pressure and grinding train speed must be considered in developing a grinding program. Vertical axis grinders with offset axes may be needed to grind embedded grooved (girder) rail. Horizontal axis grinders are capable of grinding grooved rail, but are not necessarily suitable for establishing good rail profile. Using standard tee-rail sections at embedded track might provide the greatest flexibility with respect to grinding embedded curves, although even here the presence of pavement may interfere with grinding. Grinding Intervals Periodic track inspections for corrugation growth and noise increase should be conducted to identify appropriate grinding intervals. A grinding interval equal to the exponential corrugation growth time (time for corrugation to grow by 167%) gives a rough estimate of the optimum grinding interval that minimizes metal removal. Portlandâs TriMet, for example, tries to grind rail every 3 years. TriMet attempts to grind all rails every 2 to 3 years or as needed to remove corrugations. Normally, two to four passes are made with a four-stone grinder to recover a rough rail profile and establish a 0.75-inch [19-mm] wide contact strip; the last pass is made at a low speed to reduce grinding marks. Rutting Rail head profiles and tread profiles must be designed to work together. Kalousek and Johnson suggest that varying the location of the contact zone on the rail head may reduce rutting of the wheel tread and thus reduce wear that might greatly increase conformal contact and spin slip on tangent tracks. Conformal Contact At curved track, the preference is for single-point contact of the wheel tread and rail, which necessarily requires that the rail gauge corner radius must be less than the radius of the tire throat. The wheel and rail will tend to wear together over time, producing conformal contact at the gauge corner and tread throat. That is, if the wheels are trued regularly, so that the rail sees the same wheel profile for all vehicles, the gauge corner should wear to the wheelâs throat profile. This may reduce contact stresses and reduce gauge face wear and fatigue. Single-point contact
Track Design Handbook for Light Rail Transit, Second Edition 9-28 will promote a rolling radius differential with tapered wheel profiles, thus improving curving performance and reducing wear. High wheel/rail conformity on tangents, caused by a large rail head radius and/or hollowed wheel treads, may promote spin slip corrugation. Also, as discussed in Article 9.4.3, high conformal contact greatly increases contact stiffness, increasing contact forces between the tread and rail, and thus wear and noise. High conformal contact should be avoided on tangent track regardless of wheel wear and tread hollowing, requiring an effective wheel truing program. If wheel tread profiles were always linear, the rail head profile could be 11 to 14 inches [280 mm to 356 mm], giving a well-rounded contact area and low contact stiffness. However, tread wear, not necessarily producing false flanging, will increase conformal contact, as discussed in Article 0, so that a smaller rail head crown radius is needed in the absence of an aggressive wheel truing program. The crown radius should not be less than 8 inches [200 mm], otherwise rutting of the wheel will be exacerbated. See Article 9.4.1 for a discussion of contact dimensions versus rail head radii and wheel tread negative profile radii. Rail Roughness Monitoring Measurement systems are available for quantifying rail corrugation amplitude and wavelength, rail roughness, and grinding finish. These instruments should be capable of measuring corrugation amplitudes with a resolution of 4 microinches [0.1 micro-m]. The shortest corrugation pitches are on the order of 0.5 inch [12.5 mm]. Thus, the instrument should be capable of documenting wavelengths as short as 0.2 inch [5 mm]. Corrugations may have relatively long wavelengths. However, those that contribute to wayside noise and ground-borne noise would likely have wavelengths on the order of 4 inches [100 mm] or less. An instrument should be capable of measuring wavelengths of at least this length, and preferably to 40 inches [1,000 mm]. Measuring wave undulation at longer wavelengths is generally difficult and may require a laser profilometer. 126.96.36.199.4 Rail Support Spacing Grassie suggests that reduction of fastener pitch may help control rail corrugation related to the pinned-pinned mode of the rail. The pinned-pinned mode frequency is controlled by fastener spacing, or pitch, and is typically 800 and 500 Hz for fastener pitches of 30 and 36 inches [750 to 900 mm], respectively. Reducing the fastener spacing to 24 inches [600 mm] would drive the pinned-pinned mode resonance frequency well above 1,000 Hz, where the associated wavelength would be short enough to allow the contact patch to smooth out incipient short-pitch corrugation and thus reduce corrugation rates. (This has yet to be demonstrated.) The contact impedance decreases inversely with increasing frequency, so that increasing the pinned-pinned mode frequency may help the contact âspringâ to isolate the tire and rail at this frequency. (Again, this has yet to be demonstrated.) In view of the above, direct fixation fastener pitch of 24 inches [60 cm] would be ideal, but has to be balanced against cost. However, the cost of the fastener could be lessened because the load requirements would be less than those of fasteners designed to support the rail at larger pitches. Installation costs, however, would go up. Irregular spacing of fasteners, perhaps at 30 +/- 3 inches [750 +/- 75 mm], will reduce the pinned- pinned resonance effect. (This may explain why rail corrugation is less apparent at ballast and tie track relative to direct fixation track.) The degree of randomization need not be great, perhaps as
Noise and Vibration Control 9-29 little as 5 or 10%. Langley discusses the similarity between material damping and a slight randomization of spacing between periodic supports of a beam on its forced response. Allowing a slight variation of fastener spacing may allow the designer to be more flexible in laying out reinforcing bar, thus simplifying track design. Not replacing fasteners at precisely the same location as original fasteners would also simplify retrofit while accomplishing some randomization. Track designers tend to locate fasteners on either rail directly opposite of each other. The result of this is that the wheels of the wheel set pass over the fasteners or between fasteners simultaneously. The effects of this on wheel/rail noise are not known, although parametric forces at both rails due to variation in rail head stiffness would be in phase and thus efficient producers of ground vibration at the fastener passage frequency. Locating fasteners in an alternating pattern would avoid in-phase parametric-related force transmission to the invert. No noise control benefit is apparent for maintaining fasteners exactly opposite each other. Thus, in curves, fasteners can be installed at nominal spacing without worrying about keeping fasteners in line. 188.8.131.52.5 Direct Fixation Fastener Design Resilient direct fixation fasteners support the rail and provide modest vibration isolation, depending on stiffness and dynamic characteristics. The most common form of resilient direct fixation fastener consists of top and bottom steel plates bonded to an elastomer pad. Early designs feature rolled steel top and bottom plates, possibly with the anchor bolt extending through the top plate for lateral restraint. Modern designs incorporate forged top plates with anchor bolts that anchor the bottom plate, so that the top plate is retained by the vulcanized bond between the elastomer and metal components, and by the interlocking geometry of these components. The top plate provides shoulders that both confine the rail laterally and retain the rail clips. Looseness Airborne rattling noises due to looseness between the rail and its support are also eliminated with the typical bonded direct fixation fastener employing spring clips. For example, resilient elastomeric direct fixation fasteners reduced wayside noise from NYCTA steel elevated structures relative to levels for conventional timber tie and cut-spike track, much of which was due to eliminating looseness in the rail support. Stiffness Soft fasteners allow greater rail vibration and transmission of vibration along the rail than stiff fasteners, promoting âsinging rail.â Soft natural rubber fasteners with low loss factor (damping) promote efficient propagation of bending waves that radiate noise. Wayside airborne noise levels may be increased by about 6 dB per halving of fastener stiffness, notwithstanding other factors. However, soft fasteners are useful for controlling structure-borne noise and vibration. An elastomer with a high loss factor will absorb rail vibration energy, thus reducing noise radiated by the rail. Neoprene is an attractive elastomer for this purpose, and neoprene has the added advantage of resistance to ozone and oils. Neoprene may be the preferred elastomer for direct fixation fasteners destined for concrete aerial structures or slab track at grade. However, neoprene should not be used where vibration isolation is required to control structure-radiated or ground-borne noise. Where vibration isolation is needed more than airborne noise control, such as on steel elevated structures or in subway tunnels, natural rubber is the preferred elastomer,
Track Design Handbook for Light Rail Transit, Second Edition 9-30 providing a dynamic-to-static stiffness ratio of less than 1.4. Thus, the selection of rail fastener stiffness and damping should be based on whether the track will be on an aerial structure, at grade, or in a tunnel. Top Plate Stiffness The effects of fastener top plate bending on rail-radiated wayside noise has not been experimentally determined. However, significant absorption of rail vibration might be expected at the top plate resonance frequency. Introduction of damping into the system and exploiting the top plate resonance may be beneficial in reducing pinned-pinned resonances. However, quite the opposite is suggested by Grassie, who provides an example of short-pitch rail corrugation related to top plate resonance. Also, see the discussion regarding top plate design in Article 184.108.40.206.5, for an illustration of top plate bending vibration at high frequencies. Also, see the discussion below regarding Â¼-wave resonance absorption. Rail Pads RailCorp in Sydney, Australia, uses rail pads with direct fixation track (which includes high- compliance fasteners). No corrugation was observed on direct fixation or ballasted track on the RailCorp system in Sydney, although RailCorp has indicated that they are concerned with corrugation. Rail pads are used extensively in Europe and East Asia for both tie and ballast track and resilient direct fixation track. The rail pad may damp the pinned-pinned mode vibration in the rail, as well as decouple the rail from the fastenerâs top plate mass at high frequencies. Jones and Thompson, referring to a paper by Hempelmann, suggest that reducing the rail pad stiffness can reduce the probability of short pitch corrugation, especially directly over the tie.  Grassie suggests that rail corrugation is affected very little by resilient rail pads unless the rail pad provides the bulk of the resilience of the rail support. Rail corrugation related to the selection of rail pad stiffness occurred on resiliently supported bi-block tie track in Baltimore. These examples are not directly related to direct fixation, but they suggest that the rail pad might influence the pinned-pinned mode, especially for very stiff direct fixation fasteners or for fasteners with a massive top plate. This can be investigated easily by laboratory testing as well as numerical modeling. The standard pitch for direct fixation track in Sydney is 24 inches [600 mm], considerably shorter than the 30-inch [750-mm] pitch used in the United States. The pinned-pinned mode frequency is significantly higher with 24-inch [600-mm] spacing than with 30-inch [750-mm] spacing. One can see how a combination of short rail support pitch and damping may have favorable performance characteristics. Quarter-Wave Resonance An elastomer will exhibit a resonance due to standing waves propagating in the elastomer at some velocity determined by Youngâs modulus of elasticity and shape factor. In the case of elastomer in shear, such as with the so-called Cologne Egg fastener, the propagation velocity would be controlled by the shear modulus of the elastomer. A downward motion of the elastomer will induce a wave in the elastomer, and this wave will be reflected back from the base of the elastomer. The reflected wave arriving at the top of the elastomer will be in phase with the downward motion that produced the wave at the âquarter-waveâ resonance frequency, producing a resonance dip in the mechanical impedance as seen by the top plate and/or rail. At this frequency, absorption of rail vibration energy reaches a maximum. This feature has been
Noise and Vibration Control 9-31 suggested by Remington as a rail noise control if the thickness of the elastomer is large enough to reduce the quarter-wave resonance frequency down to perhaps 500 to 1,000 Hz. The thickness of the elastomer would have to be on the order of 1 to 2 inches [25 mm to 50 mm], however, for a compression mode fastener. Elastomer in shear would allow a smaller elastomer thickness. 220.127.116.11.6 Trackbed Acoustical Absorption Ballasted track is well known to produce about 5 dB less wayside noise than direct fixation track due to the sound absorption provided by the ballast and differences in the track support characteristics. Acoustically absorptive concrete or glass-fiber panels placed very close to the rail may reduce noise by perhaps 3 decibels when installed on direct fixation track. Such panels would have no effect on ballasted track because the ballast already provides substantial acoustical absorption. Track inspection and maintenance must be considered before applying this treatment. 18.104.22.168.7 Tuned Rail Vibration Absorbers Rail vibration absorbers are tuned resonant mechanical elements that are attached to the rail base and web to absorb vibration energy and thus reduce noise radiation by the rail. Substantial clearance beneath the rail may be required for installation. The absorbers can have multiple elements, providing a multi-degree-of-freedom system with highly damped modes tuned to a number of frequencies. Vibration absorbers may be impractical on ballasted track unless they can be positioned clear of the ballast to maintain electrical isolation. If electrical isolation is not a factor, piling the ballast above the rail base should provide substantial absorption without vibration absorbers. The absorber is effective where the track exhibits little damping, such as at ballasted track with concrete cross ties, resilient rail pads, and clips or at direct fixation track. Data provided by some manufacturers indicate a reduction of about 3 to 5 dB in rail vibration at â -octave band frequencies between 300 and 2,000 Hz for 70-mph [111-km/h] trains on tangent track with absorbers mounted on each rail, one between each rail fastener. The mass of each absorber was 50 lb [23 Kg]. Tests conducted at Portlandâs TriMet under TCRP Project C-03A indicate that wayside and undercar noise was actually about 1 to 2 dB higher with rail vibration absorbers than without. These tests are definitive, as they were conducted before and after installation of the absorbers. In spite of the adverse result, qualitative observations by TriMet engineers and others were that the noise during passage of light rail vehicles was less with the absorbers than without. That is, the absorbers produced an apparent noise reduction by eliminating the propagation of waves in the rails within the pass band frequency range defined by the discrete rail supports. That is, the sound was less reverberant. This particular track consisted of 115 RE rail with concrete ties, rail pads, and clips. The quantitative noise reduction attributable to rail vibration absorbers may be nil where the wheel and vehicle auxiliary equipment dominate the wayside noise. This would most likely arise on ballasted track, which provides substantial acoustical absorption. One may expect a qualitative reduction of rail reverberation and âsinging rail,â both related to pinned-pinned modes. As such, they may be particularly attractive in reducing the perception of
Track Design Handbook for Light Rail Transit, Second Edition 9-32 noise and improving the acceptance of transit by the public and may also have benefits in controlling rail corrugation, which has obvious long-term maintenance cost benefits. Thus, rail vibration absorbers might be considered for treatment of chronic rail corrugation at curves or other problematic sections of track. The main disadvantage of rail vibration absorbers is increased maintenance costs related to the clips, nuts, and bolts required to clamp the absorbers to the rail. Water retention and possible corrosion should be of concern. Inspection of the rail may be impeded. The cost of rail vibration absorbers may be comparable with that of resilient direct fixation fasteners. 22.214.171.124.8 Rail Vibration Dampers Rail damping treatments are elastomer pads or sheets that bear against the rail flange, web, or both. They differ from rail vibration absorbers in that they do not have a vibrating mass; hence, they are not âtunedâ to specific frequencies. They are most effective, however, at controlling high- frequency distortional mode resonances of the rail, including specifically the base and web. They may also be effective at controlling bending resonances of the rail, specifically the pinned-pinned mode. As with tuned vibration absorbers, the quantitative noise reduction attributable to rail vibration dampers may be nil, especially if the wheel-radiated noise and vehicle auxiliary equipment noise dominate the wayside noise. However, one may expect a qualitative noise reduction of rail reverberation and âsinging rail.â As such, rail vibration dampers may be particularly attractive in reducing the perception of noise and improving the acceptance of transit by the public. They may also have benefits in controlling rail corrugation, which has obvious long- term cost benefits. The main disadvantage of rail vibration dampers includes obscuring the rail for the purpose of inspection. In areas where the track is not exposed to continuous moisture or drains freely enough that corrosion may not be significant, the rail vibration damper may be attractive. The damper should drain freely and not collect water against the rail and promote corrosion. 126.96.36.199.9 Wear-Resistant Hardfacing âHardfacingâ is the application of a metal alloy inlay to the rail head by welding. The procedure involves cutting or grinding a longitudinal groove in the rail surface and welding a bead of the alloy into the groove. The Riflex welding technique has been used on a limited basis in the United States, primarily for wear reduction, but has been promoted in Europe since the early 1980s for rail corrugation control and wheel squeal. For additional information on Riflex welding, refer to Chapter 5, Article 5.2.5 in this Handbook. 188.8.131.52.10 Low-Height Sound Barriers Low-height barriers placed very close to the rail have been explored in Europe for controlling wheel/rail noise, perhaps just outside the wheelâs clearance envelope. In one extreme case, an aerial structure has been designed to provide a trough in which the vehicle runs, blocking sound transmission to the wayside. Acoustical absorption is used to absorb sound energy before it escapes to the wayside. The height of the barriers must be determined by careful analysis. A 1- to 2-inch [2.5 to 5 cm] thick glass-fiber or mineral wool blanket or board with perforated protective cover should be incorporated on the rail side of the barrier. Adding sound absorption to the concrete slab surface of direct fixation track can be effective, but maintenance and access for
Noise and Vibration Control 9-33 inspection should be considered. Low-height barriers placed immediately adjacent to the rails may interfere with rail grinding. Thus, they should be demountable to allow rail maintenance. 9.2.2 Special Trackwork Noise Special trackwork includes switches, turnouts, and crossovers. The noise generated at special trackwork by wheels traversing frog gaps and related connections is a special case of impact noise. Impact noise is generated at turnouts as the wheel passes the switch point, the joint between the closer rail and the frog casting, the frog gap, and the joint between the frog casting and following rail. Impact noise can be minimized by eliminating joints and by maintaining the frog. Various frog designs are used in transit track: solid manganese, flange bearing, lift over, rail- bound manganese, spring, and movable point frogs. Special frogs, including movable point, swing nose, and spring frogs, have been developed to minimize impact forces by eliminating the fixed gap associated with the frog, and special frogs can be a practical noise control provision for many transit systems. For additional information on frog design, refer to Article 6.6. The following guidelines are provided for frog design selection for noise control. 184.108.40.206 Solid Manganese Frogs Solid manganese frogs with welded toe and heel joints provide an almost continuous running surface except for the open flangeway. Coordinated wheel and frog design along with effective track maintenance and wheel truing should provide adequate low-noise operation. Hollow, worn wheels with false flanges will contribute to noise and vibration when traversing through the frog. 220.127.116.11 Flange-Bearing Frog Flange-bearing frogs with welded toe and heel joints are similar to the solid manganese frog design except that the frog supports the wheel flange while traversing the flangeway opening in the frog point area. The depth of the flangeway is reduced to a limit to support the wheel in the point area. If the wheel and frog are properly maintained, this design reduces the impact of the wheel in the open flangeway frog point area. Gradual ramping of the flangeway is critical to avoiding impact noise. A vertical spiral might alleviate impact noise as the wheel flange contacts the ramp. However, the flange height and flangeway depth must be carefully controlled to allow a spiral to work properly. Flange-bearing frogs are usually used in low-speed applications, such as crossovers. Some longitudinal slip and torsion of the wheel set must occur as the wheel rolls over the flange- bearing portion due to the increased diameter of the flange relative to the tire. This is less of a problem at 90-degree diamonds, although some instantaneous acceleration and deceleration occur as the flanges pass over the flange-bearing portion. These effects contribute to wear of the flange and flange-bearing portion of the flangeway. 18.104.22.168 Lift Over Frog Lift over frogs with welded toe and heel joints are similar to the flange-bearing design except the frog provides a continuous main line running rail surface and open flangeway. The lateral move flangeway is omitted in this design.
Track Design Handbook for Light Rail Transit, Second Edition 9-34 When a movement occurs for the diverging route, the frog flangeway and wing rail portion is ramped up to a level that allows the wheel to pass over the main line open flangeway and running rail head. If the wheel and frog are properly maintained, this design eliminates impact on the main line moves and reduces the impact of the wheel in the diverging direction. The three frog designs described above are recommended for light rail transit installations to reduce noise and vibration. The frogs can be considered for three track types: ballasted, direct fixation, and embedded special trackwork. 22.214.171.124 Rail-Bound Manganese Frogs Rail-bound manganese frogs with the running rail surrounding the central manganese portion of the frog introduce interface openings in the running rail surface in addition to the flangeway openings. Light rail main line track installations should always consider welded joints at the toe and heel of the frog. The manganese-to-rail-steel interface in the frog design introduces a joint in the running surface that severely impacts the wheel and is the source of wheel batter noise and vibrations from the outset of installation. They are not as quiet as the frogs described above. 126.96.36.199 Movable Point Frogs Movable point frogs are perhaps the most effective of the various frogs for elimination of impact noise associated with fixed flangeway gap frogs. The frog flangeway is eliminated by laterally moving the nose of the frog in the direction in which the train is traveling. The movable point frog generally requires additional signaling, switch control circuits, and an additional switch machine to move the point of the frog. Movable point frogs have been incorporated on people mover systems in Canada and in Australia, but have received little application on light rail transit systems in the United States. 188.8.131.52 Spring Frogs Spring frogs also eliminate the impact noise associated with fixed flangeway gap frogs for trains traversing the frog in a normal tangent direction. The spring frog includes a spring-loaded point, which maintains the continuity of the railâs running surface for normal tangent operations. For diverging movements, the normally closed frog is pushed open by the wheel flange. Additional noise associated with trains making diverging movements may occur because the train wheels must still pass through the fixed portion of the frog. Thus, use of these frogs in noise-sensitive areas where a significant number of diverging movements will occur will not significantly mitigate the noise impacts associated with standard frogs. 9.2.3 Curving Noise Curving noise includes wheel squeal and flanging noise. Curving noise is one of the most serious types of noise produced by light rail transit systems and can occur at both short- and long-radius curves. In a central business district, pedestrians and patrons are in close proximity to embedded track curves, and, consequently, they are exposed to potentially high levels of squeal noise. The high level noise at discrete squeal frequencies is easily perceptible and annoying. Curving noise may be intermittent due to varying contact surface properties, surface contaminants, or curving dynamics of the vehicle and rail. On wet days, wheel squeal may be eliminated when negotiating all or most of a curve.
Noise and Vibration Control 9-35 184.108.40.206 Types of Curving Noise The three assumed types of vibratory motion producing curving noise are the following: â¢ Longitudinal slip with non-linear rotational oscillation of the tire about its axle. â¢ Lateral slip with non-linear lateral oscillation of the tire across the rail head. â¢ Wheel flanging involving contact with the gauge face of the rail and tire slip across the rail head. 220.127.116.11.1 Longitudinal Slip Longitudinal slip occurs on curves where the distance traversed at the high rail is greater than at the low rail. Wheel taper is sufficient to compensate for differential slip on curves with radii in excess of about 2,000 ft [610 m], although shorter radii may be accommodated by profile grinding of the rail head and gauge widening (which has undesirable effects). Further, Rudd reports that elastic compression of the inner wheel and extension of the outer wheel tread under torque can compensate for the wheel differential velocities, thus reducing the propensity for longitudinal slip. Rudd further notes that trucks with independently driven wheels also squeal. The consensus of opinion is that longitudinal slip is not a cause of wheel squeal. However, it may cause a low-frequency rubbing sound if the slip is oscillatory. 18.104.22.168.2 Lateral Slip Wheel squeal is sustained, saturated, non-linear transverse oscillation of the tire tread due to lateral creep or stick-slip of the tire across the rail head caused by the finite angle of attack (AOT) of the tire and rail. Curving Geometry Figure 9.2.12 illustrates the geometry of curve negotiation by a transit vehicle truck. Lateral slip across the rail head is necessitated by the finite wheel base (B) of the truck and the radius of curvature of the rail, where no longitudinal flexibility exists in the axle suspension. However, Figure 9.2.13 illustrates the actual crabbing of a truck. In this case, the leading axle of the truck rides towards the high rail, limited only by flange contact of the high rail wheel against the gauge face of the rail. The trailing axle travels between the high and low rail, and the low rail wheel flange might, in fact, be in contact with the low rail gauge face. Gauge widening, common on many transit systems, increases the actual creep angle (angle of attack) and exacerbates the generation of wheel squeal. For additional information on truck rotation and behavior in curves, refer to Chapter 4, Articles 4.2 and 4.3. Wheel squeal occurs most often at the low rail leading wheel, where flange contact with the rail gauge face does not normally occur. If a low rail restraining rail pulls the high rail wheel away from the high rail gauge face, lateral creep and wheel squeal can occur at the high rail wheel as well. For this reason, the rubbing of the tire against the restraining rail may be mistakenly blamed for causing wheel squeal. The friction between the wheel and rail running surfaces during lateral slip varies non-linearly with the lateral creep, defined as the lateral slip velocity divided by the forward rolling velocity. The coefficient of friction initially increases with increasing creep rate, reaching its maximum at a creep rate of about 0.09, and declining thereafter. The negative slope describes a negative
Track Design Handbook for Light Rail Transit, Second Edition 9-36 damping effect that will produce regenerative oscillation or squeal if the damping is sufficient to overcome the internal damping of the system. Figure 9.2.12 Geometry of curve negotiation and lateral slip Figure 9.2.13 Truck crabbing under actual conditions Squeal would not be expected for curve radii greater than 410 to 830 ft [125 to 253 m] and a wheelbase of 7.5 ft [2,280 mm], the lower limit being approached when there is no gauge widening. As illustrated above, gauge widening allows the creep angle to increase. A typical
Noise and Vibration Control 9-37 assumption is that squeal does not occur for curves with radii greater than about 700 ft [200 m], corresponding to a dimensionless creep rate equal to 0.7 B/R, where B is the wheelbase and R is the curve radius. Low-Floor Vehicles Recently, the performance of âlow-floorâ transit vehicles with independently rotating wheels on center trucks and integral non-rotating center body sections has been studied by Griffen. These vehicles have a reputation for higher noise levels during curving than those with conventional motored trucks and wheel sets, due to non-steering center trucks. The wheels of the center trucks rotate independently of one another, as they are not connected by solid axles. Thus, the self-steering feature of tapered wheels will not cause the high rail wheel to travel faster through the curve than the low rail wheel. Flanging noise during curving at curves with radii as large as 400 ft [122 m] can be substantial, requiring lubrication to control both noise and wear. Meteorological Conditions Meteorological conditions may affect the generation of squeal. In wet weather, for example, wheel squeal is greatly reduced due to the change in friction characteristics caused by moisture. Wheel squeal may be naturally inhibited in areas of high humidity. Tire Resonances Wheel squeal involves distortional vibration of the tire, usually at frequencies above 1,000 Hz. Wheel squeal can be inhibited by damping treatment of the tire, such as by vibration absorbers or ring dampers, which damp the tireâs distortional mode of vibration. The damping must be sufficient to overcome the negative damping associated with the friction-creep curve. Figure 9.2.14 illustrates the lateral acceleration response of the TriMet Type II Vehicle resilient wheel, with and without vibration absorbers. (This response corresponds to the radial response shown in Figure 9.2.6.) The tireâs lateral rigid body mode is at a frequency of less than 100 Hz, and the first distortional mode is again at about 500 Hz, followed by modes at about 1,400 and 2,600 Hz. All these resonances cause a very complex response that greatly complicates the analysis of wheel/rail interaction at audible frequencies. In particular, curving noise will exhibit frequency components that are related to the lateral tire resonances shown in Figure 9.2.14. To the extent that vibration absorbers reduce the resonant response of the tire as shown in the figure, a reduction of wheel squeal might be expected. However, this is a non-linear oscillation, and if the positive damping provided by the absorber does not compensate sufficiently for the negative damping related to friction-creep, little reduction may be achieved. The resulting squeal may become saturated, limited only by the non-linearity of the tireâs elastic response. From the track designerâs perspective, controlling lateral slip by rail profile design, gauge, and superelevation is important. Usually, resilient wheels such as those used at TriMet and other systems do not produce wheel squeal at curves, possibly due to the damping provided by the elastomer elements. The tire plane may also rotate relative to the axle, such that the conditions for wheel squeal are not sustained long enough to produce squeal. This does not prevent flanging noise, as discussed below. Further, resilient wheels do produce sustained wheel squeal, although usually for short
Track Design Handbook for Light Rail Transit, Second Edition 9-38 periods of time on the order of a second or two. This may be contrasted with solid wheels, where the sustained squeal may occur throughout curve negotiation. Figure 9.2.14 Transverse acceleration response of TriMet Type II resilient wheel 22.214.171.124.3 Flanging and Flanging Noise Flanging involves a combination of the flange rubbing against the high rail gauge face and lateral slip of the tire across the rail head. Wheel flange rubbing against the high rail occurs on short- radius curves with significant crabbing of the wheel set, which may be exacerbated at gauge- widened curves, as illustrated in Figure 9.2.13. Stick-slip noise is generated during this process. However, the mechanism differs from that of sustained wheel squeal. In the case of flanging, the flange runs up against the gauge face, and the transverse reaction force against the flange and friction force between the tire and rail top surface induces a couple about a vertical axis through the center of the wheel. Eventually, as the wheel continues to roll, the tire rotates about the vertical until the friction is overcome, inducing a short chirp, again due to non-linearity of the 70 80 90 100 110 120 130 140 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 UNTREATED WHEEL WITH VIBRATION ABSORBERS D R IV E PO IN T FR F M A G N IT U D E (d B re 1 .0 m ic ro -g /lb ) FREQUENCY (Hz)
Noise and Vibration Control 9-39 friction-creep curve and negative damping. The returning rotation and resulting slip ceases as soon as the tire reaches an equilibrium position, at which point the flange again approaches and contacts the gauge face. This process is repeated in an irregular fashion, producing intermittent squeal or chirping that can be objectionable, although it is usually not of the same magnitude as sustained wheel squeal. One may think of the wheel as âwaddling down the rail.â Flanging noise is very apparent with vehicles using resilient wheels, perhaps because the sustained wheel squeal does not usually occur to mask the flanging noise or perhaps because the resilient wheel tire is allowed to rotate about the vertical. Flange rubbing against the gauge face does not clearly produce wheel squeal or chirping. However, considerable wear of the gauge face and flange occurs, and a high angle of attack promotes the wear process. As the gauge face and wheel flanges wear, the angle of attack can increase, thus exacerbating gauge face and wheel flange wear. As a result, flanging noise can increase. 126.96.36.199 Treatments for Curving Noise A number of mitigation measures are available for controlling wheel squeal. The most effective of these from a track design point of view is lubrication. Resilient and damped wheels are not a component of track design, but their use greatly reduces the need for track or wayside noise control provisions. As with rolling noise control, curving noise control is a system problem rather than simply a vehicle or track design problem, and the track design engineer should be aware of various vehicle-based noise control provisions. Treatments that may be incorporated in track design are discussed below. 188.8.131.52.1 Flange Lubrication Wayside flange lubricators lubricate the rail gauge face, restraining rail, and wheel flange. The effectiveness of this type of lubrication in reducing noise can be substantial. Without lubrication, maximum wheel squeal noise levels may exceed 100 dBA. With lubrication, wheel squeal noise levels have been reduced by approximately 15 to 25 dB. The wheel squeal reduction is achieved by migration of a small amount of lubricant onto the top of the rail head. Back of flange lubrication necessarily transfers lubrication to the restraining rail. However, while the lubricant tends to migrate to the running rail head, thus reducing wheel squeal due to lateral slip, traction loss occurs. The wheel tread and rail running surfaces cannot be lubricated without loss of adhesion and braking effectiveness. Loss of braking effectiveness will result in wheel flatting, which produces excessive rolling noise, a counterproductive result of improper lubrication. Erratic wheel-to-rail electrical contact from the use of uncontrolled wayside lubricants is also a concern. Environmental degradation by lubricants is a serious consideration; thus lubricants should be biodegradable to the maximum extent possible. Current lubricants include (1) conventional petroleum products, (2) vegetable-oil-based grease, (3) Teflon-based lubricants, and (4) friction modifiers. Portlandâs TriMet has experimented with all forms of lubricants and has, evidently, as of this writing, settled on the Teflon-based lubricant as the most practical. Anecdotal evidence also indicates that the San Diego light rail system employs Teflon lubricants with flange lubricators with good success, achieving considerable carry distance on the order of miles.
Track Design Handbook for Light Rail Transit, Second Edition 9-40 184.108.40.206.2 Top-of-Rail Lubrication Top-of-rail lubricators control wheel squeal by applying a controlled amount of lubricant to the top of the rail. Early versions of this included a conventional wiping bar with a canvas flap that directs the lubricant to the top of the rail. Recent designs include holes drilled through the rail head to allow lubricant to be pumped directly to the running contact surface of the rail. 220.127.116.11.3 Friction Modifiers Friction modifiers applied to the rail head improve adhesion and flatten the friction/creep curve, thereby reducing or eliminating negative damping and wheel squeal while enhancing traction and braking. A problem associated with friction modifiers is clogging of distribution piping, as the modifier is not entirely a viscous fluid. Current technologies may have resolved this problem. (Friction modifiers are also applied directly to the wheel tread with âdry sticksâ loaded directly from spring-loaded magazines.) 18.104.22.168.4 Water Sprays Water sprays on curved track are used to control wheel squeal and flanging noise at some systems. Both the high and low rails can be treated. Water sprays may induce corrosion that is not conducive to electrical contact and may not be advisable for lightly used track or track where signaling may be affected. Water sprays would likely pose less of an environmental problem than grease or oil, but cannot be used during freezing weather. 22.214.171.124.5 Rail Head Inlays The friction versus creep curve can be modified by treatment of the rail heads with a babbit-like (soft malleable metal) material. This treatment has eliminated wheel squeal, reducing noise levels by approximately 20 dB. However, after several months of service, âchronic squeal reappeared.â The loss of performance was likely due to wear of the material, allowing wheel tread contact with the native rail steel. Refer to Chapter 5, Article 5.2.5, for additional information concerning rail head treatments. Stainless steel inlays are used for improving electrical conductivity, a treatment which may affect wheel squeal generation. However, to the extent that wheel squeal involves lateral slip, any inlay would be expected to wear away. 126.96.36.199.6 Track Gauge Gauge narrowing promotes curving and reduces angle of attack, lateral creep, and flanging noise. However, the wheel and rail gauges used on trolley systems typically vary by â inch [3 mm], and this slight variation in gauge may dictate against gauge narrowing in curves to prevent the flanges from binding when axle spacing is taken into consideration. Refer to Chapter 4, Article 4.2.4 for additional information concerning track and wheel gauge, specifically the use of Nytram plots to evaluate wheel flange clearances. Gauge narrowing by approximately â inch [3 mm] was employed at TriMetâs short-radius curves of radii 90 ft to 100 ft [27.5 m to 30.5 m] to control flanging noise and squeal. Gauge widening (perhaps combined with restraining rail) has been incorporated in track design in an attempt to control squeal and promote curving, but this has produced the opposite effect. Gauge widening appears to be a holdover from steam locomotive days when three-axle trucks were in use. Gauge widening is not specifically necessary to prevent excessive flange wear for two-axle trucks. Quite the opposite, gauge widening promotes crabbing because the natural tendency of a truck is to crab its way through a curve, with the high rail wheel flange of the
Noise and Vibration Control 9-41 leading axle riding against the high rail gauge face, as illustrated in Figure 9.2.13. Gauge widening should not be used to control curving noise. 188.8.131.52.7 Asymmetrical Rail Profile Asymmetrical rail head profiles are designed to increase the wheel rolling radius differential and promote self-steering of the truck through the curve, which requires a longitudinally flexible truck suspension. In this case, the contact zone of the high rail is moved toward the gauge corner and the larger diameter of the tapered wheel, while the contact zone at the low rail is moved to the field side and the smaller diameter of the tapered wheel. The wheel taper thus allows the high rail wheel to travel a greater distance than the low rail wheel per revolution without slip. In so doing, the axles tend to line up with the curve radius, thus reducing the angle of attack and lateral slip. While this approach is attractive, it is only effective for curve radii on the order of 700 ft [200 m] or more and is less effective with primary suspensions with very high longitudinal stiffness. This provision has been used in Los Angeles and Vancouver. 184.108.40.206.8 Rail Vibration Dampers Rail vibration dampers are described in Article 220.127.116.11.8. A rail vibration damper is a viscoelastic constrained layer damping system applied to the rail web. The constrained layer is held against the rail web with a steel plate and spring clip under and about the base of the rail. The absorbers can be applied with minimal disturbance of track, provided that they are short enough to fit between the rail supports. Rail vibration absorbers are not specifically expected to eliminate wheel squeal, as most of the vibration strain energy is in the wheel tire. They might reduce some of the rail vibration energy to the extent that it involves resonances in the rail. Tests were conducted at the MBTA Green Lineâs short-radius curve at Government Center with limited success. A second design includes a damping compound that is bonded to the rail web and constraining steel plate, without the use of a steel spring clip. The performance of this type of absorber may be of limited effectiveness in controlling wheel squeal, although some rail-radiated noise reduction might be obtained. 18.104.22.168.9 Tuned Rail Vibration Absorbers Tuned rail vibration absorbers are discussed in Article 22.214.171.124.7 with respect to rolling noise control. Rail vibration absorbers are reputed to control wheel squeal and also reduce rolling noise. The most attractive design at present incorporates a series of tuned dampers that bear against both the rail foot and the rail web. Thus, vibration energy is absorbed from both of these elements of the rail. The absorbers are clamped to the rail with bolts, and a plate extends beneath the base of the rail. These systems have been used in Europe, but not in North America. This technology has been tested at TriMet at both tangent and curved track. While tuned vibration absorbers may give favorable qualitative performance with respect to rolling noise, their ability to control wheel flanging noise where resilient wheels are used is limited at best. 126.96.36.199.10 Double Restrained Curves Double restraining rails are designed to reduce the angle of attack and promote steering of the truck without flange contact on gauge-widened curves. In this case, the leading high rail wheel flange can be brought away from the high rail by the low rail, or inner, restraining rail, and the trailing low rail wheel flange can be moved away from the low rail gauge face by the high rail restraining rail, thus reducing angle of attack and lateral creep. Longitudinal slip would also be
Track Design Handbook for Light Rail Transit, Second Edition 9-42 reduced with conical tread profiles, provided that wheels are trued with adequate frequency. A detailed analysis of curving and flangeway clearances must be done if success is to be obtained. The restraining rails would have to be carefully adjusted to optimize performance, but wear over time may reduce or eliminate any effectiveness that they might have to offer. The restraining rail flangeway width would have to be controlled to prevent binding of the wheel set or climbing of the flange onto the restraining rail. Wear of the restraining rail may require frequent adjustment, thus leading to increased maintenance cost. The restraining rails should be liberally lubricated to reduce squeal noise and wear due to friction between the wheel and restraining rail. Lateral slip of the wheels will still occur, as illustrated in Figure 9.2.12, so top-of-rail lubrication may be required to prevent squeal, although this might be achieved by migration of gauge face lubricant to the top of rail. Although this approach is theoretically attractive in reducing crab angle, mixed results may be achieved. Examples can be cited where double restrained curves did not prevent sustained wheel squeal, such as the Boston Blue Line downtown turn-around curve. The double restrained curve at the Portland TriMet Sylvan Hills East Portal did not prevent wheel squeal and flanging noise. Thus, double restraining rails for controlling wheel squeal are not specifically recommended for noise control. Refer to Chapter 4, Article 4.3 for additional information concerning guarded track and restraining rail. 188.8.131.52.11 Low Rail Cant Researchers at TNO in the Netherlands have produced experiments suggesting that canting the low rail towards the field side may allow a negative feedback effect that inhibits stick-slip of the leading low rail tire across the rail head, thus eliminating squeal. Rail freight vehicles have been observed to traverse curves with jointed ballast and wood tie track with tie plates and cut spikes without squealing, while similar vehicles on newly installed continuous welded rail with concrete ties, spring clips, and tie pads, produced substantial squeal. The wood tie track might have allowed the low rail to roll toward the field side, thereby inhibiting stick-slip oscillation of the low rail leading tire. The efficacy of using rail cant to reduce squeal at transit is unknown, but is mentioned here as a possible design concept that may be explored. Additional research is required. 9.3 VIBRATION CONTROL Ground-borne noise and vibration are phenomena of all rail transit systems that, if not controlled, can significantly impact residences, hospitals, concert halls, museums, recording studios, and other sensitive land uses. New light rail transit alignments include abandoned railroad rights-of- way passing through adjacent residential developments. Residences located within 3 ft [1 m] of the right-of-way limits are not uncommon, and there are instances where apartment buildings are built directly over light rail systems with little provision for vibration isolation. Vibration impacts on hospitals, sensitive âhigh-techâ manufacturing facilities, or research facilities may occur. Transit- oriented developments (TOD) are attractive, in that they combine commercial and residential structures with transit station structures. In this case, control of structure-borne noise is critical. The most cost-effective mitigation measure for transit-oriented development is to provide a vibration-isolated track, right at the source.
Noise and Vibration Control 9-43 Ground-borne noise is heard as a low level rumble and may adversely impact residences, hospitals, concert halls, and other areas or land uses where quiet is either desirable or required. Ground-borne vibration in buildings may be felt as a low-frequency floor motion or detected as secondary noise such as rattling windows or dishes. Building owners often claim that ground- borne vibration is responsible for building settlement and damage, although no demonstrated cases of this occurring have been verified. Literature concerning rail transit ground-borne noise and vibration control is rich with empirical and theoretical studies conducted in North America, Europe, Australia, the Far East, and South America. A substantial review of the state-of-the-art in ground-borne noise and vibration prediction and control was conducted in 1984 for the U.S. Department of Transportation. Recent research includes studies on the nature of subway/soil interaction, surface track vibration generation, and extensive down-hole testing to assess vibration propagation in soils. The prediction of ground- borne noise and vibration has advanced to a highly developed state, relying on shear wave velocity and seismic refraction data, borehole impulse testing, seismic modeling, and detailed finite element modeling of structures and surrounding soils. As a result, vibration predictions can be reasonably accurate. Special track isolation designs are now regularly considered as a means to control perceptible ground vibration in addition to audible ground-borne noise. 9.3.1 Vibration Generation Ground vibration from rail transit vehicles is produced by wheel/rail interaction, driven by roughness in the wheels and rail running surfaces, rail undulation, discrete track structures, track irregularities, and imbalance of rotating components such as wheels and axles. The spectrum of low-frequency ground vibration is affected strongly by axle spacing, truck spacing, and wheel diameter. Vibration forces are imparted to the track invert or soil surface through embedded track, direct fixation fasteners, or ballast. These forces cause the transit structure and soil to vibrate, radiating vibration energy away from the track in the form of body and surface waves. Body waves are shear and compression waves, with respective shear and compression wave propagation velocities. Body waves attenuate (or lose amplitude) at a rate of roughly 6 dB (50% in amplitude) as the distance from a point source doubles without material damping (energy absorption) in the soil. The rate of attenuation is 3 dB per doubling of distance from a line source such as a train. Of these two types of waves, the shear wave is the most important. For surface track, the ground vibration includes Rayleigh surface waves that attenuate at a rate of 3 dB (30% in amplitude) as distance from the point source doubles without material damping or reflection from lower soil layers. The rate of attenuation of a Rayleigh surface wave from a line source is nil without material damping. Fortunately, surface soils have considerable material damping. Rayleigh surface waves are the major carrier of vibration energy from the surface track, but non-homogeneities in the soil may convert significant portions of the Rayleigh surface wave energy into body waves. Within one wavelength of the track, near-field responses dominate the response. Structure/soil interaction significantly affects the radiation of vibration energy into the surrounding soil. Heavy tunnel structures produce lower levels of ground vibration than lightweight tunnels, depending on soil stiffness and frequency of excitation. However, the opposite has been observed
Track Design Handbook for Light Rail Transit, Second Edition 9-44 for large cut-and-cover box structures very close to the ground surface relative to circular tunnels. Near-surface subway structures produce vibration more easily than deep structures. Ground vibration excites building foundations and structures. Vibrating surfaces of the rooms then radiate noise into the room as ground-borne noise. The interior sound level is then controlled by the degree of acoustical absorption contained in the room. Secondary noise, such as rattling windows, might be observed in extreme cases. 9.3.2 Ground-Borne Noise and Vibration Prediction A number of procedures are available to determine needed ground-borne noise and vibration control provisions. The main procedure is an empirical approach involving transfer function testing of soils and buildings. The procedure has been adopted by the FTA and FRA for assessing ground-borne noise and vibration impacts by rail transit and high-speed rail projects, respectively. The predictions of ground vibration and ground-borne noise are described in detail in the FTA guidelines for rail transit noise and vibration impact assessment. Screening procedures and detailed prediction techniques are also described. The state-of-the-art in predicting ground vibration has recently advanced significantly to include detailed finite element modeling of soil/structure interaction, numerical analysis of vibration propagation in layered soils using both analytical and finite element modeling methods, and multiple-degree-of-freedom modeling of transit vehicles and track. These methods are very powerful for analyzing changes in structure design, structure depth, and vehicle designs. Ground vibration has been predicted to long ranges on the order of 3,000 ft [1,000 m] by seismic modeling for the Sound Transit system tunnels proposed for the University of Washington Campus. Vibratory compactors have been employed for measuring long-range responses on the campus. Thus, a variety of prediction tools have been developed. 9.3.3 Vibration Control Provisions Numerous methods for controlling ground-borne noise and vibration include continuous floating slab track, resiliently supported two-block ties, ballast mats, tire-derived aggregate (TDA), resilient direct fixation fasteners, precision rail, alignment modification, low-stiffness vehicle primary suspension systems, and transmission path modification. Achieving the most practical solution at reasonable cost is of great importance in vibration mitigation design. Factors to consider include maintainability, ease of inspection, and cleanliness. 184.108.40.206 Floating Slab Track Floating slab track is a special type of track structure that is beyond the normal designs discussed in Chapter 4. The floating slab concept would be an additional requirement to normal track structure. Track structure design must allow for floating slabs where they are needed, as the floating slab usually requires additional invert depth. Floating slab systems consist of two basic types: â¢ Continuous cast-in-place floating slabs are constructed by placing a permanent sheet metal form on elastomer isolators and filling the form with concrete. The floating slabs measure
Noise and Vibration Control 9-45 approximately 20 ft [6 m] or more along the track and 10 ft [3 m] transverse to the track. The depth of the slab is generally 12 to 18 inches [300 to 450 mm]. Some construction techniques involve using the tunnel invert as a form for the slab, then jacking the slab to design elevation. â¢ Discontinuous âdouble tieâ precast floating slabs measure about 4 to 5 feet [1.2 to 1.5 m] along the track and 10 ft [3 m] transverse to the track. The depth, and thus the mass, of the slab may vary from about 8 to 24 inches [200 to 600 mm]. The weight of the slab may range from 4,400 to 15,000 lb [2,000 to 7,000 Kg]. The most common configuration is with a 4,400 lb [1,800 Kg] slab that is 8 inches [200 mm] thick. The slabs are referred to as double ties because they support each rail with two direct fixation fasteners, giving a total of four direct fixation fasteners per slab. The design resonance frequency of a floating slab system is the resonance frequency for the combined floating slab and vehicle truck mass distributed over the length of the vehicle. The design resonance frequency of the continuous floating slab and vehicle combination is typically on the order of 16 Hz, while that of the discontinuous precast double tie floating slab and vehicle combination ranges from 8 to 16 Hz, depending on isolation needs. With a continuous floating slab, the entrained air stiffness must be included with the isolator spring stiffness when computing the resonance frequency. The normal configuration for the discrete double tie design includes four natural rubber isolators. Additional isolators are incorporated to increase the isolation stiffness at transition regions between non-isolated and isolated track. The main support pad design should provide low shear strain and control lateral slip between the bearing surface of the pad and concrete surfaces. Lateral slip is further reduced by gluing the pads to the concrete surfaces. The typical main support pad is about 3 to 4 inches [75 to 100 mm] thick, with an overall diameter of 12 to 16 inches [300 to 400 mm]. The isolators used at almost all floating slabs in the United States are manufactured from natural rubber. Synthetic rubber formulations exhibit higher creep rates than natural rubber formulations. Natural rubber formulations exhibit low creep over time, high reliability, and dimensional stability. Natural rubber pads are not subject to corrosion and provide natural material damping that controls the amplification of vibration at resonance. Natural rubber pads give a virtually maintenance-free isolation system. Steel coil springs are used for many continuous poured-in-place floating slabs in Europe and the Far East. Steel coil springs provide a low ratio of dynamic-to-static stiffness, essentially equal to unity. This can be an advantage where a low resonance frequency system with high attenuation is needed, but static deflection must be kept to a minimum. The disadvantages of steel coil spring isolators include low damping with potentially high amplification at resonance, surge at audible frequencies, and corrosion. Neoprene noise pads and dampers are usually employed to control spring surge. Corrosion-inhibiting coatings are applied to the springâs metal components. Provisions are made in the slab design to allow easy removal and replacement of springs that might be corroded. In North America, a steel coil spring floating slab track was installed in Charlotte, North Carolina. Numerous steel spring systems have been installed in Europe and the Far East, some providing exceptionally low isolation frequency and high attenuation.
Track Design Handbook for Light Rail Transit, Second Edition 9-46 Concerns exist regarding debris accumulating beneath floating slabs and how to remove such debris. Another concern is the possibility of the gaps between discontinuous floating slabs trapping the feet of persons escaping down a tunnel during an emergency. Both of these concerns may be avoided by providing flexible seals. Access holes or cut-outs in the slab can provide access for debris removal. Low-frequency floating slabs have been developed for controlling structure-borne noise at combined residential and transit station structures and controlling low-frequency ground vibration impacts on sensitive research and manufacturing facilities. In the former case, the slab isolation frequency is about 8 Hz. In the latter case, the isolation frequency may be on the order of 5 Hz. Low-frequency continuous poured-in-place floating slabs with steel coil spring isolators, developed by GERB, have been installed in a number of systems around the world, including the installation at Charlotte, North Carolina, on the Charlotte Area Transit System (CATS) LYNX Blue Line. Low-frequency discontinuous double tie floating slabs with natural rubber isolators have been designed for the North Link tunnels at Sound Transit to control low-frequency ground vibration at long-range receivers on the University of Washington Campus, the MARTA Northside Extension to control medical building vibration, and the Chatswood Interchange in Chatswood, New South Wales (Sydney). This latter project involved vibration isolation of commuter trains from a station structure that would also support a high-rise condominium tower. 220.127.116.11 Resiliently Supported Bi-Block Ties Resiliently supported bi-block tie designs are referred to as encased direct fixation track in Article 18.104.22.168. With resiliently supported bi-block tie designs, each rail is supported on individual concrete blocks set in an elastomer boot encased by the concrete slab or invert. A stiff elastomer or plastic rail seat pad protects the concrete block at the rail base, which is retained by a spring clip or other fastening system. The main advantage of the bi-block tie system is that anchor bolts are not required, thus reducing part count and improving reliability. The design used for light rail transit vibration isolation must provide a low rail support modulus, achieved by including a closed-cell elastomer foam (or micro-cellular pad) between the bottom of the concrete block and invert inside the elastomer boot. A static stiffness on the order of 100,000 lb/in [18 KN/mm] can be obtained, although the dynamic stiffness is likely to be much higher. The high-frequency (above 200 Hz) vibration isolation provided by resiliently supported two-block ties is believed to be higher than that of very stiff direct fixation fasteners. The low-frequency vibration isolation provided by the two-block tie should be comparable to that provided by soft fasteners. Damping has been postulated as a cause for the low-frequency vibration isolation provided by some of the two-block systems. Rail corrugation associated with the resiliently supported tie system has been reported, although this appears to be related to the interaction of the rail with the concrete block through the rail seat pad. The design constitutes a two-degree-of-freedom vibration isolation system. As a result, the rail and block can vibrate against each other, at high frequencies, thus possibly contributing to rail corrugation. Reducing the rail seat pad stiffness appears to defer the onset of rail corrugation. Rail pads that are too soft may induce clip fatigue, so clip design must be carefully reviewed. Other concerns include abrasion of the concrete block and production of fines that are trapped in the boot. Water can be trapped in the boot as well.
Noise and Vibration Control 9-47 22.214.171.124 Ballast Mats Ballast mats control ground-borne noise and vibration from ballasted track and have been incorporated as the principal isolation system. Two configurations of ballast mats have been employed for surface track. The first includes a concrete base or tub with a ballast mat consisting of inverted natural rubber cone springs placed on a concrete base beneath the ballast. The second, and potentially less effective, design incorporates a uniform ballast mat placed directly on tamped soil or compacted subballast. (Ballast mats have also been placed on a concrete âbath tubâ slab with the track slab consisting of a second pour concrete slab supporting the rails.) Conventional installations of ballast mats in European subways have concrete bases for which vibration insertion losses have been predicted to be higher than observed in practice. Surface track application presents challenges that limit the effectiveness of ballast mat installations. The shear modulus of the soil at or near the surface may be low and can offer a track support modulus comparable to that of the ballast mat, thus rendering the ballast mat less effective than if it were employed in a tunnel or concrete U-wall section. The vibration reductions are limited to the frequency range in excess of about 30 Hz. For ballast mats on compacted subgrade, the insertion loss would likely be about 5 to 8 dB at 40 Hz. For ballast mats on a concrete base or concrete invert, the insertion loss at 40 Hz would be between 7 and 10 dB. The most effective ballast mat is a profiled mat with a natural rubber elastomer on a concrete base or trough. This type of installation provides the greatest vibration isolation, about 10 dB at 40 to 50 Hz. The ballast mat is too stiff to provide sufficient vibration reduction at lower frequencies and is, therefore, not a substitute for floating slab track. There may be some minimal amplification of vibration at the ballast mat resonance frequency in the range of 16 to 30 Hz. The selection of a ballast mat should favor low static and dynamic stiffness, low creep, good drainage, and ease of installation. Considerable disparities exist between the dynamic stiffness of various ballast mats, even though their static stiffness may be similar. The most desirable material is natural rubber, which exhibits a low dynamic-to-static stiffness ratio of about 1.4 or less. These high-performance natural rubber mats may cost more than synthetic elastomer mats, but may be the only choice in critically sensitive locations. Specifications for ballast mats should include dynamic stiffness requirements for the intended frequency range over which vibration isolation is desired. If this is not done, much less isolation than expected may actually be achieved, rendering the vibration isolation provision ineffective and possibly detrimental. There is a very distinct possibility that providing a ballast mat may increase low-frequency vibration in the 16- to 25-Hz region by a few decibels. If this is the range of the most significant vibration, the ballast mat may actually exacerbate a vibration impact. Thus, great care must be exercised in design, specification, and installation of the ballast mat. A further consideration is ballast pulverization and penetration into the mat. Ballast mats have been incorporated in the track structure to reduce pulverization. 126.96.36.199 Tire-Derived Aggregate (TDA) Tire-derived aggregate (TDA) is used for isolating ballasted track and consists essentially of shredded tires of particular sieve size. The tire-derived aggregate is attractive because it (1) is economical, (2) provides a use for waste tires, and (3) is easy to install. The typical installation consists of 12 inches [300 mm] of TDA wrapped in geo-textile, placed on compacted subgrade,
Track Design Handbook for Light Rail Transit, Second Edition 9-48 and covered with 12 inches [300 mm] of subballast and 12 inches [300 mm] of ballast, directly beneath the cross ties. The TDA is compacted in place. Variations in design may exist. The vibration isolation effectiveness of TDA track is comparable or perhaps slightly better than that of the most effective ballast mats. Figure 9.3.1 shows the measured vibration response of the ground near a ballasted track section of the VTA Line in San Jose, California, with TDA relative to without TDA underlayment. The treatment installation was as described above. The treatment was effective above 25 Hz, providing as much as 10 dB reduction at 63 to 125 Hz. The aggregate was installed in 2005, and the measurement data with aggregate are for the years 2005, 2006, and 2009. Some loss of vibration isolation performance is appears to have occurred by year 2009 relative to years 2005 and 2006, perhaps due to further compaction or fines. However, this result is also within experimental error. No additional data have been collected. Figure 9.3.1 Vibration isolation performance of tire-derived aggregate installed in 2005 As of this writing, the FTA has not approved TDA as a vibration control measure for general use, but its use has been provisionally approved on the BART extension to San Jose. It has been TDA TRACK ISOLATION PERFORMANCE SAN JOSE VTA VASONA LINE -20 -10 0 10 4 8 16 31.5 63 125 250 FREQUENCY - HZ R EL A TI VE V IB R A TI O N L EV EL - D B YEAR 2009 YEAR 2006 YEAR 2005
Noise and Vibration Control 9-49 installed on the San Jose VTA system on the Vasona Line and also in Denver as part of the T- Rex project. A record of performance is being developed. 188.8.131.52 Resilient Direct Fixation Fastener Design for Vibration Isolation Resilient direct fixation fasteners used for supporting the rail on concrete slabs or inverts are very common at heavy rail transit systems where subway and aerial structures are involved. Resilient direct fixation fasteners control structure-borne and ground-borne noise and vibration and can be provided with a wide range of stiffness values, allowing the designer to adjust rail support modulus as needed. In general, soft fasteners transmit less structure-borne or ground-borne noise and vibration than stiff fasteners do, whereas stiff fasteners reduce rail vibration and rail-radiated noise more than soft fasteners do. The selection of a fastenerâs stiffness will, to some extent, depend on the type of structure and the nature of the vibration or noise that is to be controlled. The static stiffness ranges of fasteners are described as follows: Soft: 50,000 to 80,000 lb/in [9 to 14.2 KN/mm] Medium: 80,000 to 140,000 lb/in [14.2 to 25 KN/mm] Stiff: 140,000 lb/in [25 KN/mm] or greater Two basic types of fasteners are available. One type is a fastener with elastomer bonded to a base plate and top plate and is referred to as a bonded fastener. The second type of fastener consists of an elastomer sandwiched between a base plate and top plate without bonding. In some cases, the base plate may be absent, as with the original TTC resilient fastener employed on the YSNE tunnels. In other cases, the rail is supported directly by the elastomer. The stiffness of the fastener is controlled by the durometer and geometry of the elastomer. Solid elastomer is essentially incompressible, so the compliance of an elastomer spring in compression is achieved by providing free surfaces that allow the elastomer to expand as the elastomer is deflected under load. The ratio of the area of one loaded surface to the area of the free surface is the âshape factorâ of the elastomer spring. Elastomer springs with low shape factors are softer than elastomer springs with high shape factors. An elastomer spring with infinite shape factor is for most purposes considered infinitely stiff. High-compliance fasteners with static stiffness less than 80,000 lb/in [14 KN/mm] use elastomer in shear to provide good rail head control with low vertical stiffness and can be effective in reducing ground vibration and ground-borne noise at frequencies above about 30 Hz. The elastomer-in-shear design can provide a vertical static stiffness as low as 50,000 lb/in [9 KN/mm] and can employ a captive top plate within the bottom plate, providing stability in the event of elastomer failure (which rarely, if ever, occurs). For additional information on direct fixation fasteners, refer to Chapter 5 in this Handbook. Some non-bonded fasteners employ a closed-cell urethane cellular pad with a highly non-linear load deflection curve that is actually concave downward. One form of urethane is subject to water absorption and degradation. The type used for track isolation is supposedly resistant to water absorption. These elastomers do not require unloaded free surfaces (shape factor) to provide resilience. These unbounded fasteners required anchor bolts to pass through the top plate to retain the top plate and also laterally restrain the fastener. Springs provide
Track Design Handbook for Light Rail Transit, Second Edition 9-50 precompression. This type of fastener has not gained significant application in the United States, although the New York Transit Authority has evidently installed some of these. A low-stiffness fastener will allow the rail to deflect over a larger distance under static load than a high-stiffness fastener. The axle load is distributed over more fasteners with low stiffness than over fasteners with high stiffness, reducing anchor bolt and plinth stresses. Low rail support stiffness is advantageous in reducing the vertical resonance frequency of the rail on the fastener stiffness and the so-called P2 resonance frequency. High-compliance fasteners isolate the rail from concrete invert non-uniformity and, thus, reduce very-low-frequency vibration that might otherwise occur. This is beneficial in areas where low- frequency vibration might impact vibration-sensitive manufacturing facilities or where a subway or slab track is located in soft soil close to residences or other sensitive uses. Dynamic-to-Static Stiffness Ratio The ratio of vertical dynamic-to-static stiffness describes the stiffness of the fastener at frequencies associated with ground vibration and noise. A low ratio is generally associated with high-quality natural rubber elastomer and desirable for vibration isolation. The ratio is obtained by dividing the dynamic stiffness (measured with a servo-actuated hydraulic ram) by the static stiffness determined over the majority of the load range. The ratio is not entirely a material property of the elastomer, but is also a function of shape factor. A desirable upper limit is 1.4, easily obtained with fasteners manufactured with natural rubber or a derivative thereof. Dynamic- to-static stiffness ratios of 1.3 are not uncommon with natural rubber elastomer in shear. As a rule, elastomers capable of meeting the limit of 1.4 are high quality and generally exhibit low creep. Fasteners with neoprene elastomer usually have a dynamic-to-static stiffness ratio greater than 1.7 and as high as 4. As noted in Article 184.108.40.206.5, a neoprene elastomer may be desirable for controlling rail noise radiated from at-grade or aerial structure track due to the material damping of the elastomer. Thus, the choice of a specific type of elastomer may depend on whether ground-borne vibration isolation or airborne noise reduction is desired. Stiffness Selection The vibration isolation effectiveness of a rail fastening system is generally controlled by the dynamic rail support modulus, computed by dividing the fastenerâs dynamic stiffness by the rail support pitch, or center-to-center spacing. The vibration isolation performance of resilient direct fixation fasteners as a function of rail support modulus relative to a rail support modulus of 4,300 lb/in2 [30 MN/m2] assumed for the TTC standard unbounded fastener with single 45 Durometer natural rubber pad (circa 1970) was investigated by Bender. The results are summarized in Figure 9.3.2. (The TTC pad may actually be considerably stiffer than represented here.) The model assumes an unsprung solid wheel set mass rolling on the rail, without consideration for the vehicle truck dynamics. These predictions are reasonably well supported by field tests conducted by the author over the years and are used for DF fastener stiffness selection. The maximum rail stresses and deflections due to bending as a function of rail support modulus are listed in Table 9.3.1 for a 30,000 lb load [133 kN] point.  The theoretical analysis employed for the predictions given in Figure 9.3.2 indicates that the net force transmitted by discrete resilient direct fixation fasteners over the frequencies indicated is
Noise and Vibration Control 9-51 equivalent to that predicted by a single-degree-of-freedom isolator with rail mass per unit length supported by the rail support modulus. This simple result simplifies the problem of computing the transmitted force for continuous rail support. The assumption of continuous rail support is adequate for frequencies up to about half of the pinned-pinned mode frequency of the discretely supported rail, or about 300Hz. A good dynamic rail support modulus for vibration isolation that is similar to that often assumed for ballast-and-tie track is 3,000 lb/in2 [21 MN/m2] or less. This implies a rail fastener dynamic stiffness of 90,000 lb/in [16 KN/mm] for a pitch of 30 inches [750 mm] or static stiffness of 65,000 lb/in [11.4 KN/mm]. Fasteners capable of providing this low stiffness incorporate natural rubber- in-shear. Bonded fasteners with elastomer in compression can also provide low stiffness if the elastomer is sufficiently thick, with sufficiently low shape factor. Figure 9.3.2 Vibration isolation of DF fasteners for various rail support moduli
Track Design Handbook for Light Rail Transit, Second Edition 9-52 Aerial Structures The selection of the fasteners for aerial structure application should be based, among other things, on whether the aerial structure would be constructed with concrete or steel or a combination thereof. All-concrete aerial structures tend to radiate less structure-borne noise than that radiated by the rail and wheel. Steel structures radiate considerable low-frequency noise, and concrete deck and steel box girder aerial structures may produce low-frequency rumble. Thus, a stiff neoprene elastomer with greater loss factor than that of natural rubber may be preferable for a fully concrete aerial structure application, while a high-compliance fastener may be preferable for steel elevated structures or composite steel box elevated structures where maximal isolation is preferred. An analysis of the relative contributions of the rail and structure to radiated noise was conducted for the NYCTA. Testing at the NYCTA showed that softer fasteners performed better than stiffer fasteners in controlling noise radiation by steel elevated structures. The best performance was obtained with bonded resilient direct fixation fasteners with static stiffness of about 100,000 lb/in [17.5 KN/mm], a ratio of dynamic-to-static stiffness of less than 1.4, linear load/versus deflection characteristic, and top plate bending resonance in excess of 800 Hz. The tendency today in direct fixation track design is to provide fasteners with static stiffness on the order of 50,000 lb/in to 150,000 lb/in [9 to 27 MN/m], utilizing natural rubber elastomer or a blend of natural rubber and synthetic rubber. As noted above, while natural rubber has desirable properties for vibration isolation, the low damping capacity of these materials may allow efficient bending wave propagation and consequent noise radiation by the rail. Elastomeric fasteners with medium stiffness and damping, such as neoprene, are suitable for concrete aerial structures where rail-radiated noise is dominant. Natural rubber fasteners with low stiffness and low damping are suitable for tunnels to control ground-borne noise and vibration and for steel elevated structures or aerial structures with steel box or I-Beam girders to control structure- radiated noise. Non-linear Load vs. Deflection The load vs. deflection curve of the fastener should be linear within +/-15% of the mean static stiffness over the load range to avoid excessive stiffness while providing good rail support. Most of the vibration energy transmitted by a fastener to the invert is transmitted when the rail is directly over the fastener or within several feet. Fasteners with highly non-linear load versus deflection characteristic are much stiffer when the wheel is passing over the fastener than when supporting just the rail. The vibration forces transmitted by the stiffness are proportional to the dynamic stiffness of the fastener, which is typically 1.4 times the tangent to the load vs. deflection curve under the maximum operating load. Specifying linearity in an unambiguous way is critical in the procurement process. The fastener should provide full three-degree-of-freedom isolation. Horizontal snubbing is sometimes achieved by incorporating a positive restraint between the top and bottom plate that can cause high non-linearity of the load deflection curve and compromise vibration isolation. Hard snubbers should be avoided in fasteners, because they limit vibration isolation to the vertical direction only. The fastener should have a finite lateral stiffness measured at the rail base to ensure both an adequate degree of horizontal position control and sufficient lateral compliance to provide three-
Noise and Vibration Control 9-53 degree-of-freedom vibration isolation. Fasteners with elastomer in shear provide a linear load deflection curve and excellent vibration isolation performance over a wide range of loads. Top Plate Design Weakness in the top plate tends to reduce the stiffness of the fastener, but allows the top plate to resonate in bending between 500 and 1,000 Hz, amplifying transmitted forces at resonance. Many, many, other resonances occur, some of which may be important, and many which may not. The top plate bending is singled out because its frequency is typically within the range of audible wheel/rail noise and also within the range of short pitch corrugation frequencies. Table 9.3.1 Maximum stress and deflection for 30,000 lb [133 kN] point load RAIL SUPPORT MODULUS MAXIMUM STRESS DEFLECTION LB/IN2 MN/M2 LB/IN2 MN/M2 INCHES MM 400 2.8 22,000 152 0.565 14.3 800 5.5 19,300 133 0.344 8.7 1,600 11 16,000 110 0.196 5.0 3,200 22 13,500 93 0.117 3.0 4,300 30 12,500 86 0.093 2.4 Although transmitted forces are amplified, the resonance produces a minimum in the mechanical input impedance of the top plate, as seen by the rail. At this frequency, the fastener looks like a dynamic absorber, absorbing vibration energy from the rail and eliminating singing rail at this frequency. See the discussion above regarding tuning of the top plate and also the Â¼-wave resonance absorption of the fastener in Article 0. As a result, a top plate designed to maximize vibration isolation may be less effective at controlling rail vibration and noise than a relatively weak top plate that resonates at frequencies between 500 and 1000Hz, the important frequency range of tangent track rolling noise. The measured vertical transfer dynamic stiffness of an early design bonded fastener is plotted in Figure 9.3.3 for various static loads. The transfer stiffness is defined as the transmitted force relative to the deflection of the rail web (or centroid of the rail). The measured static stiffness of the fastener was about 300,000 lb/in [53 KN/mm] at static loads between 2,000 and 5,000 lb [9 KN and 22 KN]. The nominal dynamic stiffness was about 500,000 to 600,000 lb/in [87.5 KN/mm to 105 KN/mm] between 200 and 500 Hz. The maxima of these transfer stiffness curves at 700 to 750 Hz are due to resonance of the top plate that increases the transfer stiffness of the fastener by as much as a factor of 3 or 4 to about 1,400,000 lb/in [245 KN/mm] at the resonance frequency. This resonance amplifies transmitted forces and structure-borne noise and vibration. The corresponding input stiffness to the top plate was not measured and should not be confused with the transfer stiffness. This mode of vibration was investigated with a finite element model. The nominal elastomer stiffness of 267,000 lb/in [47 KN/mm] was assumed to be distributed uniformly under the top plate, which measures 8 inches [203 mm] longitudinal with the rail by 18 inches [457 mm]
Track Design Handbook for Light Rail Transit, Second Edition 9-54 transverse to the rail by 0.5 inch [12.5 mm] thick. The rail section is 115RE, modeled as a 30- inch [762-mm] long section, free at either end. For this model, the computed resonance frequency of the rail and top plate in vertical translation is 147 Hz, but bending of the top plate reduces the stiffness and brings the computed resonance frequency down to 140 Hz. (The length of 30 inches [750 mm] was chosen to represent the tributary portion of the rail for a given fastener. This approach is not an accurate representation because the rest of the rail and fasteners that would affect the resonance of the rail in bending are not included.) Figure 9.3.4 illustrates the bending mode associated with top plate bending resonance. In this example, the top plate is bending symmetrically about the vertical rail center plane, with little motion by the rail. The fundamental mode frequency is 561 Hz, at which frequency amplification of transmitted forces would occur. The calculated resonance frequency may be compared with the peak in the transfer stiffness test data shown in Figure 9.3.3. The top plate bending stiffness may be increased by both reducing the transverse dimension of the top plate and increasing its thickness. Figure 9.3.5 illustrates the top plate bending resonance with a top plate of 0.75 inch [19 mm] thickness and 12 inches [304 mm] transverse dimension and 8 inches [200 mm] longitudinal dimension. The rail is again 30 inches [750 mm] of 115 RE rail, and the nominal stiffness of the fastener is again 267,000 lb/in [47 KN/mm]. This mode may be compared with the mode shape for the 0.5-inch [12.5-mm] thick top plate shown in Figure 9.3.4. This mode of vibration involves symmetric bending of the fastener top plate about the rail vertical center plane. The modal resonance frequency is now 1,433 Hz, which may be compared with the frequency of 561 Hz obtained for the symmetric mode shown in Figure 9.3.4. In this case, a substantial portion of the bending energy is in the rail as well as the top plate, as the rail is bending over the fastener. A better view of this mode is provided in Figure 9.3.6. The top plate resonance frequency is controlled by the bending stiffness of the plate, the transverse bending stiffness of the rail base, and the stiffness of the elastomer. The resonance frequencies of the above examples would be less with softer elastomer. The difference with the thick, stubby top plate would less, as the stiffness of the top plate is much higher than that of the elastomer to begin with. A high-resonance-frequency top plate requires that the overall thickness of the fastener be large enough to allow for a thick top plate. A minimum of 2 inches [50 mm] should be made available between the rail base and invert for high-compliance fasteners. The elastomer strain can be kept to a practical minimum under static load with a 2-inch [50-mm] thick fastener. Increasing the thickness of the top plate should increase its strength and reliability, with less working of the rail clip due to top plate flexure under static load and strain vibration. Thickening the top plate will increase the cost of top plate castings, although the increase should be relatively small in comparison to the overall cost of the fastener. Fasteners designed for vibration isolation should have stiff top plates that avoid increasing the transfer stiffness of the fastener and amplifying vibration forces in the frequency of structure- borne noise and ground-borne noise. Dissipation in the soil will reduce high-frequency ground- borne noise, so groundâborne noise is less of an issue than structure-radiated noise. Resilient fasteners with stiff top plates will minimize structure-radiated noise from aerial structures with
Noise and Vibration Control 55-9 steel box or I-Beam girders or steel elevated structures. However, this has to be balanced against the loss of rail vibration absorption at frequencies in the range of 500 to 1,000 Hz. Some fasteners support the rail with elastomer shoulders, such that no fastener metal is in contact with the rail. This type of fastener can provide very low stiffness and support the rail with minimal clearance between the rail and invert. The elastomer isolates the rail from the mass of the fastener base plate and invert. At high frequencies, the effect is as though the rail is freely suspended in space. The input mechanical impedance of such a rail consists in equal parts of reactive and resistive impedance, making the rail behave as though it were well damped. Figure 9.3.3 Dynamic transfer stiffness of bonded direct fixation fastener of nominal static stiffness of 400,000 lb/in [70 KN/mm] 0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0 1800.0 2000.0 100 200 300 400 500 600 700 800 900 1000 FREQUENCY - Hz D Y N A M IC S T IF F N E S S -1 00 0 L B /IN 2 KIP 3 KIP 4 KIP 5 KIP 6 KIP
Track Design Handbook for Light Rail Transit, Second Edition 9-56 Figure 9.3.4 Mode shape of an idealized fastener consisting of a 0.5-inch [12.5-mm] thick by 18-inch [304-mm] long by 8-inch [203-mm] wide top plate supporting a 30-inch [750-mm] long section of 115 RE rail Figure 9.3.5 Mode shape of an idealized fastener consisting of a 0.75-inch [19-mm] thick by 12-inch [304-mm] long by 8-inch [203-mm] wide top plate supporting a 30-inch [750-mm] long section of 115 RE rail
Noise and Vibration Control 75-9 Figure 9.3.6 Rotated view of Figure 9.3.5 220.127.116.11 Rail Grinding Rail grinding to eliminate checks, spalls, and undulation of the rail head reduces ground-borne noise and vibration, provided that the vehicle wheels are well maintained. This applies especially to corrugated rail. Rail grinding to reduce ground vibration at low frequencies must remove long wavelength roughness and corrugation, which may require special grinders with long grinding bars or special controls. Rail grinding will have the greatest benefit at frequencies above 15 to 30Hz for normally worn rail, including rail with short pitch corrugation. The benefit at low frequencies is relatively modest, due to the wavelengths involved. However, removing checks and spalls would be expected to reduce vibration across a broad frequency range, including low frequencies. 18.104.22.168 Rail Undulation Although often overlooked or not considered during track design, rail straightness is fundamentally important in controlling ground vibration below 10 Hz in critically sensitive areas such as university campuses, semiconductor manufacturing plants, and research institutes. Roller-straightened rails have produced ground vibration spectral components that can be related to the straightener roller diameter. Substantial vibration below 10 Hz was generated by unit trains after replacing "gag-press" straightened rail with roller-straightened rail with excessive vertical undulation at Kamloops. The result was substantial community reaction and litigation. Narrowband analyses of the wayside ground vibration data identified a linear relation between frequency peaks and train speed that related directly to the roller diameters of the straightening machine and rolls. Subsequent field measurements of rail profile with a laser collimator confirmed the vibration data. The roller-straightened rail was replaced with new rail that was also roller straightened, but to CORUS (formerly British Steel) specifications. Repeat measurements
Track Design Handbook for Light Rail Transit, Second Edition 9-58 indicated a substantial reduction of ground vibration, even though the effects of the roller straightener pitch diameter were still identifiable in the wayside ground vibration spectra. This experience suggests using "super-straight" rail for sensitive areas where a low-frequency vibration impact is predicted. Examples include alignments in very close proximity to sensitive receivers of all types in areas with very soft soil, alignments adjacent to or through university campuses where engineering and scientific research occurs, and alignments in proximity to sensitive manufacturing facilities, such as semiconductor manufacturing. As manufacturing technology and fundamental research advances, this problem will become more important. Controlling low-frequency vibration due to rail undulation by controlling rail straightness should be far less costly than the installation of a floating slab track structure. Soft fasteners would provide no positive benefit and may even exacerbate low-frequency vibration of this type. Corrective rail grinding is incapable of removing rail height undulation over long wavelengths of 6 feet or more. Rail straightness specifications may likely be included in procurement specifications for rail destined for high-speed rail systems, as excessively undulating rail would require additional maintenance of track and perhaps the subgrade. Thus, straight rail will likely become more available with time. Suggested limits on peak-to-valley undulation are listed in Table 9.3.2. These may apply to both horizontal and vertical deviations. The rail manufacturer should be consulted with respect to manufacturing capability and quality assurance. Table 9.3.2 Rail undulation limits Length 80 inches [2 m] 120 inches [3 m] Limit 0.008 inch [0.2 mm] 0.12 inch [0.3 mm] 22.214.171.124 Vehicle Primary Suspension Design Vehicle primary suspension design is not part of track design, but has a direct bearing on wayside ground vibration amplitudes. Selection of trackwork vibration isolation provisions should ideally be based on the type of vehicle involved. In general, vehicles with soft primary suspensions produce lower levels of ground-borne noise and vibration than vehicles with stiff suspensions. Differences in suspension characteristics may be sufficient to eliminate the need for floating slab isolation at otherwise critically sensitive locations. Introduction of vehicles with stiff primary suspensions relative to existing vehicles with soft suspensions may introduce vibrations in the 10- to 25-Hz frequency region. The selection of chevron-type suspension systems in lieu of stiff rubber journal bushing suspension systems may provide sufficient vibration reduction to reduce the need for other vibration isolation provisions in the frequency range of about 16 to 31.5 Hz. Most modern light rail transit vehicles in the United States incorporate chevron primary suspension systems with low vertical stiffness, thus reducing the demand on vibration isolation elements in the track. If the vehicles have stiff primary suspension systems, such as rubber journal bearing springs, particular attention should be paid to low-frequency vibration control in track at the primary suspension resonance frequency.
Noise and Vibration Control 9-59 126.96.36.199 Resilient Wheels Resilient wheels might provide some degree of vibration isolation above 80 Hz relative to solid steel wheels, depending on elastomer stiffness, by reduction of the unsprung mass. Resilient wheels actually modify the P2 resonance, or track resonance, by introduction of another mass- spring element between the rail and axle or wheel center. The resilient wheel will introduce an additional resonance of the axle mass and wheel center on the resilient wheel springs, and this resonance may amplify ground vibration at the resonance frequency. Details on this have not been investigated, but the resonance frequency was calculated to be about 50 Hz for the axle and wheel centers with Bochum 54 wheels. Strong spectral peaks at the 50 and 63 Hz â -octave bands have been observed in the wayside ground vibration spectrum for light rail vehicles at some systems with resilient wheels and no spectral peaks at others using the same wheel. Rail corrugation would be the likely cause, and other factors are likely important as well. More research is required to further define the cause of this type of corrugation and determine which, if any, track design parameters may influence its generation. Resilient wheels are widely used on light rail systems because they control wheel squeal at curves and reduce truck vibration. 188.8.131.52 Subgrade Treatment The vibration amplitude response of soil is roughly inversely proportional to the stiffness of the soil. Therefore, stiff soils tend to vibrate less than soft soils. Grouting of soils or soil stabilization with lime for organic soils or cement for sandy materials is attractive where very soft soils are encountered. However, grouting may increase the efficiency of high-frequency vibration propagation between track and building structures, so care must be exercised in treatment design. Grouting of soils has been conducted at high-speed lines in Europe for vibration control, and rail-car-mounted grouting systems may be available. 184.108.40.206 Special Trackwork Turnouts and crossovers are sources of vibration. As the wheels traverse the frogs and joints, impact forces are produced that cause vibration. Grinding the frog to maintain contact with a properly profiled wheel can minimize impact forces at frogs. Spring frogs and movable point frogs are designed to maintain a continuous running surface. Spring frogs are practical for low-speed turnouts, while movable point frogs are more suited to high-speed turnouts. Refer to Chapter 6 for additional discussion on frog types. Also, refer to Article 9.2.2 for discussion of impact noise generation and details affecting frog designs. 220.127.116.11 Distance The track should be located as far from sensitive structures as practicable within the limits of the right-of-way. Where wide rights-of-way exist, some latitude in locating the track may exist. A shift of as little as 10 ft [3 m] away from a sensitive structure may produce a beneficial reduction of vibration for receivers bordering the right-of-way. Sensitive receivers located within 50 ft [15 m] of the track centerline are particularly in danger of being impacted by ground vibration from transit operations. However, ground vibration and ground-borne noise impacts have occurred at sensitive receivers at significantly greater distances. 18.104.22.168 Trenching Open trenches have been considered for vibration reduction, but are of limited effectiveness below 30 Hz for a depth of 20 ft [7 m] and even less for shallower trenches. At higher
Track Design Handbook for Light Rail Transit, Second Edition 9-60 frequencies, the vibration reduction of a trench filled with Styrofoam may be as little as 3 to 6 dB. Concrete barriers embedded in the soil have also been considered. While they may interrupt surface wave propagation, their mass must be substantial to provide sufficient vibration reduction. Detailed finite element modeling is necessary in this case to predict performance. A number of theoretical studies of vibration barrier insertion losses have been conducted and continue to be studied.   Practical design guidelines are provided by Richart et al. In particular, the trench depth must be similar to the Rayleigh surface wave length to obtain an appreciable vibration reduction on the order of 12 dB (75% reduction). For a Rayleigh wave propagation velocity of 400 ft/sec [122 m/s] and excitation frequency of about 8 Hz, the primary suspension resonance frequency of a typical chevron suspension system, the wavelength would be 50 ft [15 m]. Thus, the trench would have to be on the order of 50 ft [15 m] to be effective. On the other hand, the Rayleigh wavelength at the track resonance frequency of 50 Hz, responsible for ground-borne noise, would be about 8 ft [2.4 m], and the depth of the trench would also have to be on the order of 8 ft [2.4 m]. Thus, trenches might be most practical for controlling ground- borne noise as opposed to low-frequency perceptible vibration. An example of vibration isolation provided by trenching is presented in Figure 9.3.7. Figure 9.3.7 Measured ground vibration insertion gain of styrofoam-filled trench at Toronto Transit Commission These data were obtained by the TTC for evaluation of a 14-ft [4.3-m] deep trench containing a 4- inch [100-mm] thick layer of Styrofoam and back-filled with soil. The test train was a light rail vehicle on surface ballast and tie track. Test distances were 22 to 32 ft [6.7 to 9.8 m] from the TRENCH FILLED WITH PLASTIC FOAM -20 -10 0 10 20 8 16 31.6 63 125 250 FREQUENCY - HZ R E L A T IV E V IB R A T IO N L E V E L - D B WEST BOUND TRAINS AT 46 FT (14 M) EASTBOUND TRAINS AT 32 FT (10 M) AVERAGE VIBRATION RESPONSE SUGGESTED DESIGN CURVE
Noise and Vibration Control 9-61 near track. The results are averages for eastbound and westbound operation. A suggested design curve is shown. However, finite element modeling should be conducted as part of any trench design since results depend on soil stiffness and distances of both track and receiver from the trench. For example, the trench would be ineffective for receivers at large distances from the track. 22.214.171.124 Pile-Supported Track Piling used to reinforce a track support system can be effective in reducing ground vibration over a broad range of frequencies. An example would be a concrete slab track supported by piles or ballasted track on a concrete trough supported by piles. Performance improvement is likely to be substantial if the piles can be extended to rock layers within about 65 ft [20 m] of the ground surface or foundation. Standing wave resonances may occur in long piles, so there is a limit on the effectiveness of piles in controlling audible ground-borne noise. Unfortunately, piles may interfere with utilities. Piling may be attractive for civil reasons, and the added benefits of vibration control can be realized with appropriate attention to design. 9.4 WHEEL/RAIL PROFILES AND CONTACT STIFFNESS AND STRESS Wheel and rail contact geometry affects the traction, or pressure, distribution in the contact area, stress distributions in the rail head, and the contact stiffness. The contact stiffness affects the dynamic interaction and vibration of the wheel and rail in response to surface roughness. Maintaining a low contact stiffness helps to maintain low dynamic contact forces and thus low wheel and rail vibration. Wayside noise and ground vibration are directly proportional to wheel and rail vibration. Thus, low contact stiffness is important for controlling noise and vibration. Surface defects and plastic deformation are related to stress distributions in the rail head and contribute to roughness of the rail running surface. Controlling stresses in the rail is thus of interest from a maintenance as well as noise control point of view. However, as discussed below, minimizing the magnitude of the stress is not necessarily consistent with minimizing the contact stiffness. Rail corrugation is a complex regenerative process that may affect both soft and hard rails. Rail corrugation may be due to abrasion or excessive stresses, depending on the corrugation process. The corrugation process is not clearly understood in many cases, but wheel and rail vibration necessarily influence corrugation and wear. The specifics of rail corrugation are discussed in Article 9.2, specifically Article 126.96.36.199.3. This discussion uses Hertzian contact theory to explore the relationship between contact geometry, contact stiffness, and stress at tangent track where short-pitch corrugation generally occurs. The tire radius and rail head curvature can be well controlled on tangent track by grinding and wheel truing, so Hertzian contact theory can be applied in a straightforward way. Tangential tractions due to lateral creep, curving, braking, and acceleration are not discussed here due to their complexity; nevertheless they are important as well.
Track Design Handbook for Light Rail Transit, Second Edition 9-62 9.4.1 Contact Dimensions The wheel/rail Hertzian contact tractions are functions of the wheelâs rolling radius (or diameter), transverse tread profile, the rail head crown radius, the modulus of elasticity of steel, and the wheel load. The wheel/rail contact geometry is elliptical in shape with major and minor axes aligned with the rail or transverse to the rail, depending on the radii of curvature of the contacting surfaces. The contact dimensions are calculated with Hertzian contact theory, excellent discussions of which are provided by Timoshenko and Goodier and by Johnson. Assuming a constant radius of curvature of the wheel tread profile and rail head running surface, the contact geometry and equal-stress contours in the contact zone will assume concentric ellipses. Representative major and minor axes of the contact area for a 28-inch [711-mm] diameter wheel with linear tread profile for various rail head radii are plotted in Figure 9.4.1. The principal axes of the contact ellipse are equal when the rail head radius equals the tire radius with a straight tread profile. In this case, the contact area is a circle, and the equal-stress and equal surface traction contours would also be circles. As the head radius is reduced, the dimension of the contact parallel with the rail increases, and the dimension transverse to the rail decreases. For a 9-inch [229 mm] head radius, the longitudinal and transverse major axes of the edge of the contact ellipse are 0.4 and 0.3 inch [10.2 and 7.6 mm], respectively. Figure 9.4.1 Contact geometry vs. rail head radius for a 28-inch [711-mm] diameter wheel with linear tread profile Figure 9.4.2 illustrates the contact area as a function of head radius for three wheel tread profiles: linear, concave with a 28-inch [711-mm] radius, and concave with a 14-inch [356-mm] CONTACT DIMENSIONS vs RAIL BALL RADIUS FLAT TREAD PROFILE 28-IN WHEEL DIAMETER WHEEL LOAD = 10,000LBS 0 0.1 0.2 0.3 0.4 0.5 5 6 7 8 9 10 11 12 13 14 15 BALL RADIUS - IN C O N TA C T D IM EN SI O N S - I N C H ES LONGITUDINAL AXIS - IN TRANSVERSE AXIS - IN
Noise and Vibration Control 9-63 radius. The contact area is relatively insensitive to head radius for wheel treads with linear profiles and concave profiles of 28 inches [711 mm]. However, with a concave profile of 14 inches [356 mm], the contact area increases rapidly with head radius above 10 inches [250 mm]. The contact area approaches 0.3 inch2 [194 mm2] as the head radius approaches 13.9 inches [153 mm], a condition of almost fully conformal contact. The contact ellipse dimensions in this case are 2.71 inches [68.8 mm] transverse and 0.15 inch [3.8 mm] longitudinal. At 14-inches [356-mm] tread radius, the contact area is undefined, as the contact geometry is a line contact across the rail head. Interestingly, the longitudinal and transverse axes are approximately equal at 0.37 inch [9.4 mm] with a 7-inch [178-mm] rail head radius. The contact area in this case is about 0.1 inches2 [64.5 mm2]. 9.4.2 Stresses Two stresses are produced by a vertical load on the rail surface. One is the principal stress balancing the normal traction at the contact and the other is the maximum shear stress, which is at some distance beneath the surface of the rail. 188.8.131.52 Normal Stress A positive contact pressure, or normal traction, is balanced by a negative stress in the rail at the surface. This is the result of a sign convention, where a positive principal stress is due to stretching of the material, and a negative principal stress is due to compression. The stresses are discussed here in terms of pressure. The maximum contact pressure occurs at the center of the contact and is theoretically 50% higher than the average pressure over the contact zone. The maximum contact pressure and average pressure versus rail head crown radius is plotted in Figure 9.4.3 for a 28-inch [711-mm] diameter wheel with linear (flat) tread profile. The variation of maximum pressure with head radius for linear and concave tread profiles is plotted in Figure 9.4.4. The maximum contact pressure decreases monotonously with increasing head radius. The stresses are highest with the linear (flat) wheel tread profile, ranging from 200,000 psi [1,424 MPa] with a 5-inch [127-mm] crown radius, down to about 140,000 psi [997 Mpa] with a 14-inch [356-mm] crown radius. The lowest contact pressure maximum occurs with a 14-inch [356-mm] radius concave tread profile. In this case, the contact pressure declines rapidly to 50,000 psi as the head radius approaches 14 inches [356 mm], the fully conformal contact condition. The above pressures are comparable with endurance limits for rail steel in good condition and above the limit for rail steel in moderately corroded condition, which limit may be as low as 60,000 psi [127 Mpa]. Timoshenko calculates a contact pressure of 63,000 psi [449 Mpa] for a 1,000-lb [4,448-N] wheel load, where the wheel radius is 15.8 inches [400 mm] and the rail head radius is 12 inches [305 mm]. (Timoshenko, as it turns out, published much on rail stresses.) So, even at a 1,000-lb [4,448-N] load, the contact pressures of a typical railroad rail/wheel combination are at the endurance limit. The maximum contact pressure increases as the cube root of the load, so the maximum contact pressure at a 10,000-lb [44,480-N] load would be 136,000 psi [968 Mpa]. Reducing the wheel diameter and head radius simply increases the maximum contact pressure.
Track Design Handbook for Light Rail Transit, Second Edition 9-64 Figure 9.4.2 Contact area vs. tread profile CONTACT DIMENSIONS vs RAIL BALL RADIUS FLAT TREAD PROFILE 28-IN WHEEL DIAMETER WHEEL LOAD = 10,000LBS 0 0.1 0.2 0.3 0.4 5 6 7 8 9 10 11 12 13 14 15 BALL RADIUS - IN C O N TA C T A R EA - SQ U A R E IN C H ES FLAT WHEEL PROFILE -28IN HOLLOW TREAD -14IN HOLLOW TREAD
Noise and Vibration Control 9-65 Figure 9.4.3 Maximum contact pressure vs. head radius for 28-inch [711-mm] diameter linear tread radii CONTACT PRESSURE vs RAIL BALL RADIUS FLAT TREAD PROFILE 28IN DIAMETER WHEEL WHEEL LOAD = 10,000LBS 0 50,000 100,000 150,000 200,000 250,000 5 6 7 8 9 10 11 12 13 14 15 BALL RADIUS - IN C O N TA C T PR ES SU R E - P SI MAXIMUM PRESSURE - PSI AVERAGE STRESS - PSI
Track Design Handbook for Light Rail Transit, Second Edition 9-66 Figure 9.4.4 Maximum contact pressure vs. rail head radius for various concave tread radii CONTACT PRESSURE vs RAIL BALL RADIUS 28IN DIAMETER WHEEL 14IN RADIUS HOLLOW TREAD PROFILE WHEEL LOAD = 10,000LBS 0 50,000 100,000 150,000 200,000 250,000 5 6 7 8 9 10 11 12 13 14 15 BALL RADIUS - IN PR ES SU R E - P SI LINEAR TREAD - MAXIMUM PRESSURE - PSI -28IN HOLLOW TREAD - MAXIMUM PRESSURE - PSI -14IN HOLLOW TREAD - MAXIMUM PRESSURE - PSI
Noise and Vibration Control 9-67 The depth of the negative stress (compressive stress) distribution increases as the contact geometry approaches a line contact condition, which may occur with concave tread profiles that match the rail head profile or in curves where the throat and gauge corner radii match. 184.108.40.206 Shear Stress The shear stress is very important with respect to metal fatigue. The point of maximum shear occurs below the center of the contact area for nominally circular contact areas. For this reason, running surface fatigue and rail failures often begin at some point beneath the surface. The depth of maximum shear stress is estimated by Kerr to be 0.6 times the radius of the contact area, assuming a uniform distribution of contact pressure (which is not an entirely realistic assumption, but facilitates the discussion). Timoshenko gives a depth of 0.47 times the contact radius for circular contacts. Assuming a contact mean dimension on the order of 0.37-inch [9.4-mm]âas indicated in Figure 9.4.1 for a 14-inch [356-mm] rail head radius and a 28-inch [711-mm] diameter wheel with linear tread profile (this corresponds to a circular contact area)âthe depth of maximum shear stress, according to Timoshenko, would occur at about 0.174 inch [4.4 mm] below the rail surface. The shear stress distribution is more complicated for high aspect ratio elliptical contact areas. Figure 9.4.5 illustrates the variation of the depth below the contact surface at which the maximum shear stress occurs and the maximum shear stress variation as a function of the ratio of the minor and major axes of the contact ellipse. For a line contact, the depth to the point of maximum shear would be about 0.8 times one half of the minor axis length, although the minor axis is ill-defined in this case. This is an extreme case, but represents the condition of fully conformal contact. The ratio decreases to about 0.485 for circular contacts, where the major and minor axes are equal. Assuming a contact area radius of 0.37 inch, the depth below the surface would be 0.18 inch [4.6 mm], in good agreement with the result given by Timoshenko. The ratio of maximum shear stress to maximum contact pressure is also plotted in Figure 9.4.5 as a function of the contact area aspect ratio. The ratio of the maximum shear stress to the maximum contact pressure at the surface remains relatively constant at about 0.31 to 0.32 as a function of the ratio of minor to major axes. Thus, for a contact pressure of nominally 150,000 psi [1067 MPa], the shear stress below the surface would be about 50,000 psi [356 MPa]. To the extent that increasing the aspect ratio contact would tend to reduce contact pressure, the shear stress would also be reduced, regardless of the aspect ratio. The maximum shear stress versus rail head crown radius is plotted in Figure 9.4.6 for three wheel tread profiles: linear, concave with 28-inch [711-mm] radius, and concave with 14-inch [356-mm] radius. These were obtained from the maximum contact pressures plotted in Figure 9.4.4 and the ratios plotted in Figure 9.4.5. The wheel diameter is again assumed to be 28 inches [711 mm]. The linear tread profile produces the highest shear stress, ranging from 65,000 psi [463 MPa] for a head radius of 5 inches [127 mm], down to about 43,000 psi [306 MPa] for a head radius of 14 inches [356 mm]. These stresses are reduced to about 60,000 psi [427 MPa] and 37,000 psi [263 MPa], respectively, for a concave tread profile with 28-inch [711-mm] radius. The shear stresses with a concave tread of 14 inches [356 mm] in radius are
Track Design Handbook for Light Rail Transit, Second Edition 9-68 lower still, ranging from 55,000 psi [391 MPa] with a 5-inch [127-mm] head radius down to less than 30,000 psi [214 MPa] with a 12-inch [305-mm] head radius. Figure 9.4.5 Depth of maximum shear and maximum shear vs. contact ellipse aspect ratio (Johnson, 1992) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.2 0.4 0.6 0.8 1 MINOR/MAJOR AXIS - b/a R A TI O z/b = DEPTH / MINOR AXIS t1/p0=SHEAR STRESS / MAXIMUM PRESSURE
Noise and Vibration Control 9-69 Figure 9.4.6 Maximum shear stress vs. head radius for three tread profiles CONTACT PRESSURE vs RAIL BALL RADIUS 28IN DIAMETER WHEEL WHEEL LOAD = 10,000LBS 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 5 6 7 8 9 10 11 12 13 14 15 BALL RADIUS - IN PR ES SU R E - P SI LINEAR TREAD PROFILE -28IN CONCAVE TREAD -14IN CONCAVE TREAD
Track Design Handbook for Light Rail Transit, Second Edition 9-70 As the head radius increases further, the shear stress drops rapidly, becoming poorly defined at the fully conformal contact conditions with a 14-inch [356-mm] head radius. The fatigue limit for shear stress is roughly about 50% of the fatigue limit in tension. If a rail steel has a fatigue limit of about 100,000 psi [825 MPa], the fatigue limit would be about 50,000 psi [345 MPa]. The shear stress would be at a minimum of 43,000 psi [296 MPa] for a fully rounded contact area achieved with a 14-inch [356-mm] rail crown radius and 28-inch [711-mm] wheel with linear tread, less than the shear fatigue limit. Introduction of a radius in the tread profile, producing some degree of conformal contact, reduces this further. While conformal contact might appear to be desirable to reduce contact pressures and shear stresses, increasing conformal contact increases contact stiffness, which increases dynamic forces that are superimposed on the static load, thus increasing contact dynamic pressures and dynamic shear stress. This is discussed further below. 9.4.3 Contact Stiffness The dynamic contact stiffness at a given load is the increment in contact force produced by an increment in relative deflection of the wheel tread and rail centers of gravity, or neutral axes. The dynamic contact stiffness is equal to 1.5 times the static load divided by the static relative deflection of the wheel and rail. The static stiffness divided by the static deflection is a function of load as well. Thus, the dynamic Hertzian contact stiffness is non-linear. The deflection is proportional to the two-thirds root of the load. Thus, the dynamic contact stiffness is proportional to the cube root of the load. The contact stiffness as a function of rail head radius is plotted in Figure 9.4.7 for the three tread profiles considered above. The contact stiffness remains between about 5,000,000 lb/in [875 KN/mm] and 7,000,000 lb/in [1,226 KN/m] for rail head radii between 5 inches [127 mm] and 14 inches [356 mm] for the linear and 28 inches [711 mm] radius concave tread profile and wheel radius of 28 inches [711 mm]. For the 14-inch radius tread profile, the contact stiffness increases rapidly with rail crown radii greater than about 13 inches [330 mm], becoming very large as the radius approaches 14 inches [711 mm]. That is, as the rail head and wheel tread contact approach the condition of fully conformal contact, the contact stiffness increases very rapidly. As the contact stiffness increases, high-frequency vibration of the wheel and rail and associated dynamic stresses increase. Avoiding fully conformal contact would appear to be desirable from a track and wheel design point of view. The contact mechanical impedance is obtained by dividing the contact stiffness by the product of two, pi, and the frequency in Hz (2Ïf). At corrugation frequencies on the order of 1,000 Hz, the contact mechanical impedance of a contact stiffness of 6,000,000 lb/in [1050 KN/mm] would be about 954 lb-sec/in [0.167 KN-sec/mm], roughly comparable with the mechanical impedances of the wheel and rail as shown in Figure 9.2.7, Figure 9.2.9, and Figure 9.2.10. Rail corrugation commonly occurs at a frequency of about 800 Hz. The mechanical impedance of a rigid wheel weighing 500 lb [227 Kg] at 800Hz would be 6,511 lb-sec/in [1.1 KN-sec/mm]. The contact mechanical impedance at 800 Hz would be about 1,200 lb-sec/in [0.21 KN-sec/mm], much smaller than that of the wheel. Resonances of the wheel would complicate this analysis considerably.
Noise and Vibration Control 9-71 Figure 9.4.7 Variation of dynamic contact stiffness with rail head radius Fully conformal contact is a condition that is frequently associated with rail corrugation, and the above results suggest that fully conformal contact would greatly exacerbate wheel/rail forces and CONTACT PRESSURE vs RAIL BALL RADIUS 28IN DIAMETER WHEEL WHEEL LOAD = 10,000LBS 0 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000 5 6 7 8 9 10 11 12 13 14 15 BALL RADIUS - IN C O N TA C T ST IF FN ES S - L B /IN LINEAR TREAD PROFILE -28IN CONCAVE TREAD -14IN CONCAVE TREAD
Track Design Handbook for Light Rail Transit, Second Edition 9-72 corrugation. The contact acts like a cushion at frequencies above perhaps several hundred Hertz, reducing dynamic contact stresses and noise. Increasing the contact stiffness by increasing wheel/rail conformal contact increases the high-frequency contact forces between the wheel and rail and thus increases wheel/rail noise. Fully conformal contact should be prevented, at least on tangent track, to reduce wheel/rail dynamic forces, reduce corrugation rates, and reduce noise. 9.4.4 Residual Stress AccumulationâShakedown As noted above, the contact stresses induced during rolling contact under even modest loads are substantial. Residual stresses may be induced in the rail running surface during train operations, and these residual stresses protect the rail running surface from cyclic fatigue. This process is called âshakedown.â Shakedown does not harden the rail, in the sense of resistance to wear, but simply moves the internal stress state by plastic deformation to a position where subsequent contact stresses do not produce plastic yield. This process is well described by K. L. Johnson. 9.4.5 Work Hardening Additional operation over long periods may work harden the rail. However, at rail transit loadings, work hardening also may not occur. While contact stresses may initially exceed the yield stress, shakedown stress accumulation may impede long-term work hardening. To the extent that a hardened running surface is desirable to reduce wear and corrugation rates, head-hardened or alloy rail should be procured. 9.5 REFERENCES  Transit Noise and Vibration Impact Assessment, Office of Planning and Environment, Federal Transit Administration, FTA-VA-90-1003-06, May 2006.  Saurenman, H. J., G. P. Wilson, J. T. Nelson, Handbook of Urban Rail Noise and Vibration Control, Wilson, Ihrig & Associates, Inc., for USDOT/TSC, 1982, UMTA-MA-06- 0099-82-1.  Nelson, J. T., TCRP Report 23, Wheel/Rail Noise Control Manual, Transportation Research Board, National Research Council, Washington DC, 1997.  Nelson, J. T., H. J. Saurenman, G. P. Wilson, State-of-the-Art Review: Prediction and Control of Ground-Borne Noise and Vibration from Rail Transit Trains, Final Report, Wilson, Ihrig & Associates, Inc., for US Department of Transportation, Urban Mass Transit Administration, UMTA-MA-06-0049-83-4.  Journal of Sound and Vibration, Academic Press, Ltd., Published by Harcourt Brace Jovanovich, London.  Noise and Vibration Mitigation for Rail Transportation Systems, Springer-Verlag, Berlin Heidelberg, 2008.  Handbook of Noise Control, Ed. Cyril M. Harris, McGraw-Hill Book Company.
Noise and Vibration Control 9-73  Shock and Vibration Handbook, Ed. C. M. Harris, C. E. Crede, McGraw-Hill Book Company.  L. L. Beranek, ed., Noise and Vibration Control, McGraw-Hill Book Company, New York, 1971, 650 pg.  Cyril M. Harris, Handbook of Noise Control, 2nd ed., McGraw-Hill Book Company, New York, 1979.  Harris, C. M., Crede, C. E., Shock and Vibration Handbook, 2nd ed., McGraw-Hill, New York, 1976.  ANSI Standard S1.4 (Standard for Sound Level Meters).  Transit Noise and Vibration Impact Assessment, for the U.S. Department of Transportation, Federal Transit Administration, FTA-VA-90-1003-06, May 2006.  1981 Guidelines for Design of Rapid Transit Facilities, American Public Transit Association (APTA), Washington DC, June 1981.  ANSI S2.71-1983 (R 2006) (formerly ANSI S3.29-1983), Guide to the Evaluation of Human Exposure to Vibration in Buildings, Publ. Acoustical Society of America, approved by American National Standard Institute.  Mechanical Impedance, Shock and Vibration Handbook, 2nd ed., Ed. C.M. Harris, and C. E. Crede, Chapter 10, McGraw-Hill, 1976.  Remington, P., J., âWheel/Rail Rolling Noise: What We Know, What We Donât Know, Where Do We Go from Here,â Journal of Sound and Vibration, Vol. 120, No.2, (1988) pp. 203â226.  Kalousek, J., and K. L. Johnson, An Investigation of Short Pitch Wheel and Rail Corrugation on the Vancouver Skytrain Mass Transit System, Proc. Institute Mechanical Engineers, Part F, Vol. 206 (F2), 1992, pp. 127â135.  Observation by the author.  This claim was made during a comment by environmental engineers working on TriMetâs Hillsboro line. Some theoretical justification can be made for this, and the effect would be similar to that involved with certain aspects of highway tire/pavement noise generation.  Remington, P. J., âWheel/Rail Rolling Noise, What Do We Know, What Donât We Know, Where Do We Go from Here,â Journal of Sound and Vibration, Vol. 120, No. 2, pp. 203â 226.  Ver, I. L., C. S. Ventres, and M. M. Miles, âWheel/Rail NoiseâPart III: Impact Noise Generation by Wheel and Rail Discontinuities,â Journal of Sound and Vibration, Vol. 46, No. 3, 1976, pp. 395â417.  Nelson, James T., TCRP Report 23: Wheel/Rail Noise Control Manual, Transportation Research Board, National Research Council, Washington, DC, 1997, pg. 132.  Zarembski, A. M., The Art and Science of Rail Grinding, Simmons-Boardman Books, Inc., Omaha, Nebraska, 2005.
Track Design Handbook for Light Rail Transit, Second Edition 9-74  Wild, E., Wang, L., Hasse, B., Wroblewski, T., Goerigk, G., and Pyzalla, A., âMicrostructure Alterations at the Surface of Heavily Corrugated Rail with Strong Ripple Formation,â Wear, Vol. 254, Issue 9, May 2003, pp. 876-883.  Hutchings, I. M., Tribology: Friction and Wear of Engineering Materials, CRC Press, Boca Raton (1992) pg. 96.  Personal observation of the author at the TTC Scarborough Line.  Brickle, B., TCRP Research Results Digest 26: Rail Corrugation Mitigation in Transit, Transportation Research Board, National Research Council, June 1998.  Grassie, S. L., âRail Corrugation: Characteristics, Causes, and Treatments,â Proc. ImechE Vol. 223 Part F: J. Rail and Rapid Transit, pg. 264.  Ciavarella, M., and Barber, J., âInfluence of Longitudinal Creepage and Wheel Inertia on Short Pitch Corrugation: A Resonance-Free Mechanism to Explain the Roaring Rail Phenomenon,â Proc. IMechE Vol. 222 Part J: J. Engineering Tribology, pp. 171â181.  J. Dring, âRail Corrugations and Noise on the Mass Transit Railway Corporation of Hong Kong,â Contact Mechanics and Wear of Rail/Wheel Systems, Preliminary Proceedings, Ed. J. Kalousek, Vancouver, Canada, July 24-28, 1994, (Publisher Unknown, but contact J. Kalousek at National Research Council, Canada).  Comments by TriMet engineers.  Grassie, S. L., Edwards, J. W., âDevelopment of Corrugation as a Result of Varying Normal Load,â Wear 265, 2008, pp. 1150â1155.  Authorâs observation of corrugation at urethane-embedded track in Portland, Oregon.  Observation by the author at the BART test track.  Nelson, James T., TCRP Report 23: Wheel/Rail Noise Control Manual, Transportation Research Board, National Research Council, 1997, pp. 143â156.  Presentation given by G. Batchinsky at the APTA track design committee meeting in Philadelphia, 2010.  Corrugation does occur on embedded girder rail at TriMet. The corrugation produces a low-frequency rumble where train speeds are on the order of 15 to 25 mph (24 kph to 40 kph). Grinding with a horizontal axis grinder is effective in controlling corrugation at embedded track. (Personal observation, J. Nelson.)  Conversation with TriMet engineers by the author (2010).  Telephone conversation with Ken Kirse of TriMet, 22 January 2010.  Kalousek, J. and Johnson, K. L., âAn Investigation of Short Pitch Wheel and Rail Corrugation on the Vancouver Skytrain Mass Transit System,â Proc. Instn. Mech. Engrs., Part F, Vol. 206 (F2) (1992), pp. 127â135.  Grassie, S., L., âRail Corrugation: Characteristics, Causes, and Treatments,â Review Paper 581, Proc. IMechE, Vol. 223, Part F: J. Rail and Rapid Transit (2009).
Noise and Vibration Control 9-75  R. S. Langley, âOn the Forced Response of One-Dimensional Periodic Structures: Vibration Localization by Damping,â Journal of Sound and Vibration, (1994) Vol. 178, No.3, pp. 411â428.  Personal observation by James T. Nelson while working on the Chatswood Interchange project (2004).  Jones, C. J. C., and Thompson, D. J., âMeans of Controlling Rolling Noise at Source,â Noise and Vibration from High Speed Trains, Ed. Viktor Krylov, Thomas Telford Publishing, London, 2001, p. 180.  Hempelmann, K. âShort Pitch Corrugation on Railway Railsâa Linear Model for Prediction,â Fortschriftberichte, Series 12, No. 231 VDI, Dusseldorf (1994) (This paper was cited by Jones and Thompson, see Reference 45.)  Remington, P. J., Wittig, L. E., , and Bronsdon, R. L., Prediction of Noise Reduction in Urban Rail Elevated Structures, Bolt Beranek & Newman, Inc., for US DOT/UMTA (July 1982).  Crockett, A. R., and Pyke, J., âViaduct Design for Minimization of Direct and Structure Radiated Train Noise,â Proceedings International Workshop on Railway Noise, Ile des Embiez, France, 5 November 1998. (See also JSV).  Rudd, M. J., âWheel/Rail Noise, Part II: Wheel Squeal,â Journal of Sound and Vibration, 46(3), 1976, p. 385.  Griffin, T., TCRP Report 114: Center Truck Performance on Low-Floor Light Rail Vehicles, Transportation Research Board of the National Academies, Washington, DC, 2006.  J. Nelson observed a lack of curving noise at the Long Beach Blue Line 90- and 100-ft radius curves, next to the ocean. However, elastomer embedment, RE115 rail, salt spray, and use of HPF may be bigger factors.  Wilson, Ihrig & Associates, TCRP Report 67: Wheel and Rail Vibration Absorber Testing and Demonstration, Transportation Research Board, National Research Council, Washington, DC, 2001, pp. 12â13.  Nelson, J. T., Saurenman, H. J., State-of-the-Art Review: Prediction and Control of Groundborne Noise and Vibration from Rail Transit Trains, Report by Wilson, Ihrig & Associates for U. S. DOT/TSC, Urban Mass Transit Administration, UMTA-MA-06-0049- 83-4 (December 1983).  Transit Noise and Vibration Impact Assessment, Harris, Miller, Miller & Hanson, Inc., for the Federal Transit Administration, U.S. Department of Transportation, Washington, DC, April 1995, DOT-T-95-16.  Crockett, A. R., and R. A. Carman, Finite Element Analysis of Vibration Levels in Layered Soils Adjacent to Proposed Transit Tunnel Alignments, Proceedings of Internoise 97, Budapest, Hungary, 25-27 August 1997, Institute of Noise Control Engineering.
Track Design Handbook for Light Rail Transit, Second Edition 9-76  Nelson, J. T., Prediction of Ground Vibration Using Seismic Reflectivity Methods for a Porous Soil, Proceedings of the IWRN 1998 Conference, Isle de Embiez, November 1998.  Nelson, J. T., âRecent Developments in Ground-Borne Noise and Vibration Control,â Journal of Sound and Vibration, 193(1), pp.367-376, (1996).  Wolfe, S., L., Evaluation of Tire Derived Aggregate as Installed Beneath Ballast and Tie Light Rail TrackâResults of 2009 Field Tests, Final Report, Wilson, Ihrig & Associates for Dana N. Humphrey, Consulting Engineer, Project funded by California Integrated Waste Management Board, June 2009.  Bender, E. K., Kurze, U. J., Nayak, P. R., Ungar, E. E., Effects of Rail Fastener Stiffness on Vibration Transmitted to Buildings Adjacent to Structures, Report by Bolt Beranek & Newman, for Washington Area Metropolitan Transportation Authority (1969).  Remington, P. J., and Witig, L. E., âPrediction of the Effectiveness of Noise Control Treatments in Urban Rail Elevated Structures,â Journal of the Acoustical Society of America, v.78(6), December 1985, pp. 2017â2033.  Nelson, J. T., Noise Reduction Performance of Resilient Rail Fasteners on Steel Solid Web Stringer Elevated Structures, NYCTA Elevated Structure Noise TestsâFinal Report, Wilson, Ihrig & Associates for USDOT/TSC, March 1989, UMTA-NY-06-0087-89-1.  Cremer, L., Heckle, M. Structure-Borne Sound, Tr. E. E. Ungar, Springer-Verlag, New York, 1973, p. 254.  Nelson, J. T., and S. L. Wolfe, Kamloops Railroad Ground Vibration Data Analysis and Recommendations for Control, Technical Report, Wilson, Ihrig & Associates, Inc., for CN Rail.  Beskos, D. E., Daskupta, B., and Vardoulakis, I. G., âVibration Isolation Using Open or In- Filled Trenches,â Journal of Computational Mechanics, v.1(1), 1986, pp. 43â63.  Ahmad, S., and Al-Hussaini, T.M., âSimplified Design for Vibration Screening by Open and In-Filled Trenches,â Geotechnical Engineering, v.117(1), 1991, pp. 67â88.  Yang, Y. and Hung, H., âA Parametric Study of Wave Barriers for Reduction of Train- Induced Vibrations,â International Journal for Numerical Methods in Engineering, v40(20), 1997, pp. 3729â3747  Richart, F. E., Hall, J. R., Woods, R. D., Vibration of Soils and Foundations, Prentice Hall, 1970, pp. 247â262.  S. T. Lawrence, Toronto Transit Commission, âTTC-LRT TRACKBED STUDIES, Ground- borne Vibration Testing, Measurement, and Evaluation Program,â APTA, Rapid Transit Conference, San Francisco, California, 17-19 June, 1980.  Timoshenko, S., and Goodier, J. N., Theory of Elasticity, McGraw-Hill Book Company, New York, 1951, pp. 372â382.  Johnson, K. L., Contact Mechanics, Cambridge University Press, Cambridge, UK, 1992, pp. 90â106.
Noise and Vibration Control 77-9  Kerr, A. D., Fundamentals of Railway Engineering, Simmons-Boardman Books, Inc., Omaha, 2003, p. 126.  Johnson, K., L., Contact Mechanics, Cambridge University Press, Cambridge, UK, 1992, pp. 286â295.