Track Design Handbook for Light Rail Transit, Second Edition (2012) / Chapter Skim
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From page 466... ...
9-i Chapter 9 -- Noise and Vibration Control Table of Contents 9.1 INTRODUCTION 9-1 9.1.1 Scope 9-1 9.1.2 Relevant Literature 9-2 9.1.3 Some Fundamentals 9-2 9.1.3.1 Sound Levels 9-2 9.1.3.2 Vibration Levels 9-3 9.1.4 Design Criteria 9-3 9.2 NOISE CONTROL DESIGN 9-4 9.2.1 Wheel/Rail Rolling Noise 9-4 9.2.1.1 Types of Rolling Noise 9-5 9.2.1.1.1 Normal Rolling Noise 9-5 9.2.1.1.2 Impact Noise 9-8 9.2.1.1.3 Rail Corrugation Noise 9-8 9.2.1.1.4 Grinding Artifact Noise 9-14 9.2.1.1.5 Singing Rail 9-15 9.2.1.2 Factors Affecting Rolling Noise 9-15 9.2.1.2.1 Wheel Dynamics 9-15 9.2.1.2.2 Rail Dynamics 9-17 9.2.1.2.3 Resilient Direct Fixation Fasteners 9-22 9.2.1.2.4 Ballasted Track 9-23 9.2.1.2.5 Contact Stiffness 9-23 9.2.1.3 Treatments for Rolling Noise Control 9-24 9.2.1.3.1 Continuous Welded Rail 9-24 9.2.1.3.2 Hardened Rail 9-24 9.2.1.3.3 Rail Grinding 9-24 9.2.1.3.4 Rail Support Spacing 9-28 9.2.1.3.5 Direct Fixation Fastener Design 9-29 9.2.1.3.6 Trackbed Acoustical Absorption 9-31 9.2.1.3.7 Tuned Rail Vibration Absorbers 9-31 9.2.1.3.8 Rail Vibration Dampers 9-32 9.2.1.3.9 Wear-Resistant Hardfacing 9-32 9.2.1.3.10 Low-Height Sound Barriers 9-32 9.2.2 Special Trackwork Noise 9-33 9.2.2.1 Solid Manganese Frogs 9-33 9.2.2.2 Flange-Bearing Frog 9-33 9.2.2.3 Lift Over Frog 9-33 9.2.2.4 Rail-Bound Manganese Frogs 9-34 9.2.2.5 Movable Point Frogs 9-34 9.2.2.6 Spring Frogs 9-34
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From page 467... ...
Track Design Handbook for Light Rail Transit, Second Edition 9-ii 9.2.3 Curving Noise 9-34 9.2.3.1 Types of Curving Noise 9-35 9.2.3.1.1 Longitudinal Slip 9-35 9.2.3.1.2 Lateral Slip 9-35 9.2.3.1.3 Flanging and Flanging Noise 9-38 9.2.3.2 Treatments for Curving Noise 9-39 9.2.3.2.1 Flange Lubrication 9-39 9.2.3.2.2 Top-of-Rail Lubrication 9-40 9.2.3.2.3 Friction Modifiers 9-40 9.2.3.2.4 Water Sprays 9-40 9.2.3.2.5 Rail Head Inlays 9-40 9.2.3.2.6 Track Gauge 9-40 9.2.3.2.7 Asymmetrical Rail Profile 9-41 9.2.3.2.8 Rail Vibration Dampers 9-41 9.2.3.2.9 Tuned Rail Vibration Absorbers 9-41 9.2.3.2.10 Double Restrained Curves 9-41 9.2.3.2.11 Low Rail Cant 9-42 9.3 VIBRATION CONTROL 9-42 9.3.1 Vibration Generation 9-43 9.3.2 Ground-Borne Noise and Vibration Prediction 9-44 9.3.3 Vibration Control Provisions 9-44 9.3.3.1 Floating Slab Track 9-44 9.3.3.2 Resiliently Supported Bi-Block Ties 9-46 9.3.3.3 Ballast Mats 9-47 9.3.3.4 Tire-Derived Aggregate (TDA) 9-47 9.3.3.5 Resilient Direct Fixation Fastener Design for Vibration Isolation 9-49 9.3.3.6 Rail Grinding 9-57 9.3.3.7 Rail Undulation 9-57 9.3.3.8 Vehicle Primary Suspension Design 9-58 9.3.3.9 Resilient Wheels 9-59 9.3.3.10 Subgrade Treatment 9-59 9.3.3.11 Special Trackwork 9-59 9.3.3.12 Distance 9-59 9.3.3.13 Trenching 9-59 9.3.3.14 Pile Supported Track 9-61 9.4 WHEEL/RAIL PROFILES AND CONTACT STIFFNESS AND STRESS 9-61 9.4.1 Contact Dimensions 9-62 9.4.2 Stresses 9-63 9.4.2.1 Normal Stress 9-63 9.4.2.2 Shear Stress 9-67 9.4.3 Contact Stiffness 9-70 9.4.4 Residual Stress Accumulation -- Shakedown 9-72 9.4.5 Work Hardening 9-72 9.5 REFERENCES 9-72
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From page 468... ...
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)
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From page 469... ...
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)
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From page 470... ...
CHAPTER 9 -- NOISE 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.
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From page 471... ...
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.
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From page 472... ...
Noise and Vibration Control 9-3 frequency components of noise below about 500 Hz and above about 10 KHz.[12] The AWeighting network approximates the frequency response of a person's ear at low listening levels and is used almost universally to characterize industrial, occupational, and community noise.
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From page 473... ...
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)
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From page 474... ...
Noise and Vibration Control 9-5 9.2.1.1 Types of Rolling Noise The categories of wheel/rail noise include the following: • Normal rolling noise • Impact noise due to loss of contact between the wheel and rail, caused by rail head defects, gaps, and joints • Rail corrugation noise, sometimes referred to as roaring rail noise • Grinding artifact noise • Singing rail 9.2.1.1.1 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: • Wheel and rail roughness • Parameter variation of rail head geometry or moduli • Dynamic creep • 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.
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From page 475... ...
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.[17] The effects of fractional changes in Young's 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.
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From page 476... ...
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.
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From page 477... ...
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.
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From page 478... ...
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.
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From page 479... ...
Track Design Handbook for Light Rail Transit, Second Edition 9-10 corrugation noise are included in TCRP Report 23.[3] Rail grinding, including acoustic grinding, is discussed in detail by Zarembski.[24]
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From page 480... ...
Noise and Vibration Control 9-11 Figure 9.2.3. Again, martensite formation and longitudinal striations suggest longitudinal slip.
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From page 481... ...
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.
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From page 482... ...
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.[28]
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From page 483... ...
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.
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From page 484... ...
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.
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From page 485... ...
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.
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From page 486... ...
Noise and Vibration Control 71-9 Figure 9.2.7 Input mechanical impedance of TriMet resilient wheel 9.2.1.2.2 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.
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From page 487... ...
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.[33]
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From page 488... ...
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.
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From page 489... ...
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 pinnedpinned mode is to a major anti-resonance of the resilient wheel.
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From page 490... ...
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.
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From page 491... ...
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 9.2.1.2.3 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.
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From page 492... ...
Noise and Vibration Control 9-23 9.2.1.2.4 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.
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From page 493... ...
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]
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From page 494... ...
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.
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From page 495... ...
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.
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From page 496... ...
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)
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From page 497... ...
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.[41]
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From page 498... ...
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.[43]
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From page 499... ...
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.
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From page 500... ...
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.[47] The thickness of the elastomer would have to be on the order of 1 to 2 inches [25 mm to 50 mm]
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From page 501... ...
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.
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From page 502... ...
Noise and Vibration Control 9-33 inspection should be considered. Low-height barriers placed immediately adjacent to the rails may interfere with rail grinding.
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From page 503... ...
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.
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From page 504... ...
Noise and Vibration Control 9-35 9.2.3.1 Types of Curving Noise The three assumed types of vibratory motion producing curving noise are the following: • Longitudinal slip with non-linear rotational oscillation of the tire about its axle. • Lateral slip with non-linear lateral oscillation of the tire across the rail head.
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From page 505... ...
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]
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From page 506... ...
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.
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From page 507... ...
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.
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From page 508... ...
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.
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From page 509... ...
Track Design Handbook for Light Rail Transit, Second Edition 9-40 9.2.3.2.2 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.
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From page 510... ...
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.
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From page 511... ...
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.
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From page 512... ...
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.
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From page 513... ...
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.
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From page 514... ...
Noise and Vibration Control 9-45 approximately 20 ft [6 m] or more along the track and 10 ft [3 m]
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From page 515... ...
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.
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From page 516... ...
Noise and Vibration Control 9-47 9.3.3.3 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.
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From page 517... ...
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]
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From page 518... ...
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 TRex project. A record of performance is being developed.
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From page 519... ...
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.
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From page 520... ...
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.
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From page 521... ...
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.
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From page 522... ...
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.
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From page 523... ...
Track Design Handbook for Light Rail Transit, Second Edition 9-54 transverse to the rail by 0.5 inch [12.5 mm] thick.
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From page 524... ...
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.
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From page 525... ...
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]
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From page 526... ...
Noise and Vibration Control 75-9 Figure 9.3.6 Rotated view of Figure 9.3.5 9.3.3.6 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.
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From page 527... ...
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.
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From page 528... ...
Noise and Vibration Control 9-59 9.3.3.9 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 massspring element between the rail and axle or wheel center.
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From page 529... ...
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.
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From page 530... ...
Noise and Vibration Control 9-61 near track. The results are averages for eastbound and westbound operation.
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From page 531... ...
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 wheel's rolling radius (or diameter) , transverse tread profile, the rail head crown radius, the modulus of elasticity of steel, and the wheel load.
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From page 532... ...
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]
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From page 533... ...
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
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From page 534... ...
Noise and Vibration Control 9-65 Figure 9.4.3 Maximum contact pressure vs. head radius for 28-inch [711-mm]
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From page 535... ...
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
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From page 536... ...
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.
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From page 537... ...
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]
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From page 538... ...
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
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From page 539... ...
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.
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From page 540... ...
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
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From page 541... ...
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.
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From page 542... ...
Noise and Vibration Control 9-73 [8] Shock and Vibration Handbook, Ed.
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From page 543... ...
Track Design Handbook for Light Rail Transit, Second Edition 9-74 [25] Wild, E., Wang, L., Hasse, B., Wroblewski, T., Goerigk, G., and Pyzalla, A., "Microstructure Alterations at the Surface of Heavily Corrugated Rail with Strong Ripple Formation," Wear, Vol.
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From page 544... ...
Noise and Vibration Control 9-75 [43]
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From page 545... ...
Track Design Handbook for Light Rail Transit, Second Edition 9-76 [56] Nelson, J
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From page 546... ...
Noise and Vibration Control 77-9 [71]
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