Performance Based Track Geometry Phase 2 (2015)

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C H A P T E R 2 Research Approach 2.1 Vehicle Characterization and Ride Quality Testing TTCI partnered with PATH to participate in this research. PATH supported the project by providing a test vehicle for TTCI to perform characterization and ride quality tests. A typical transit car operating on the PATH system was selected and fully characterized. The data obtained from the characterization studies was used to develop a NUCARS model representing the vehicle. The characterized vehicle was equipped with instrumentation to collect revenue service passenger ride quality data using accelerometers and various displacement transducers. Track geometry measurements were collected and used as comparisons with predictions from the NUCARS model and for future PBTG NN training. 2.2 Vehicle Characterization Tests at PATH Vehicle characterization testing was performed on PATH property located in Harrison, New Jersey. PATH’s operating conditions provided a variety of track structures and a wide range of operating speeds for the ride quality testing. The following is a summary of the conditions that were tested on the PATH system: • Tunnel • Ballasted track with concrete ties • Direct fixation track • Curvature range from 1 (5279 feet) to 39 (150 feet) degrees • Third rail system • Rail profile 115 RE rail and 11 ARA-B rail Figure 1 shows a map of the PATH rail system. 5

Figure 1. PATH Rail System Map PATH’s PA5 passenger car (with all axles powered) was used for testing. The vehicle is manufactured by Kawasaki. Figure 2 shows a photograph and a schematic of the PA5 car. Table 1 summarizes some of the design specifications of the vehicle. Figure 2. PATH’s PA5 Car 6

Table 1. PATH Design Specifications PATH Railcar Design Specifications Weight Load Condition : AWO 72,450 pounds Load Condition : AW3 95,330 pounds Primary Suspension System Chevron Secondary Suspension System Airbag Wheel Profile PATH Design Cylindrical Wheel TTCI has often found that actual vehicle characteristics as assembled may vary considerably from the published design and measured individual components. In order to ensure an accurate NUCARS model of the PATH PA5 car, tests were conducted to measure suspension characteristics and carbody inertial and resonance characteristics. Testing included the following: • Characterization of the elastic elements of the primary and secondary suspension • Determination of the center of gravity of the railcar • Determination of the resonant frequencies of rigid body degrees of freedom of the railcar Results of the characterization tests were used to update and verify the preliminary NUCARS model. 2.2.1 Carbody Resonance Tests Carbody resonance testing was conducted to determine the rigid body modes of vibration of the PATH PA5 Car. Figure 3 shows an example of the rigid body modes that were excited during the test. The car was instrumented with accelerometers. Figure 4 shows the locations of the instrumentation and describes the accelerometers used in the test. The rigid body modes of vibration were each excited by hand by two TTCI engineers with assistance from PATH employees. Figure 3. Carbody Rigid Body Modes excited during Test 7

Location Number Description 1 Vertical and Lateral Accelerometer 2 Vertical and Lateral Accelerometer 3 Vertical and Lateral Accelerometer 4 Lateral Accelerometer (top) 5 Vertical Accelerometer The following equations are used to determine carbody resonance for measured accelerations: Bounce 𝑎𝑎1𝑣𝑣+𝑎𝑎2𝑣𝑣 2 +𝑎𝑎5𝑣𝑣 2 Pitch 𝑎𝑎1𝑣𝑣+𝑎𝑎2𝑣𝑣 2 − 𝑎𝑎5𝑣𝑣 Yaw 𝑎𝑎1𝑙𝑙+𝑎𝑎2𝑙𝑙 2 − 𝑎𝑎3𝑙𝑙 Roll 𝑎𝑎4𝑙𝑙 − 𝑎𝑎1𝑙𝑙+𝑎𝑎2𝑙𝑙+𝑎𝑎3𝑙𝑙 3 Figure 4. Acceleration Placement and Description Figure 5 shows an example of raw acceleration data recorded during the test. These accelerations were analyzed by calculating a Fast Fourier Transform (FFT). The FFT results were used to determine what rigid body modes were excited. The model was tuned using the measured data. Moments of inertias, center of gravity locations, and suspension properties were updated accordingly. Table 2 shows the measured modes and the modes “tuned in” the model. 8

Figure 5. Example of Carbody Resonance Data Table 2. Measured Rigid Body Mode Frequencies Compared to Model Rigid Body Mode Measured Frequency Model Frequency Difference Bounce 1.34 1.38 3.0% Pitch 1.39 1.40 0.7% Lower Center Roll 0.48 0.49 2.1% Yaw 1.46 1.48 1.4% UC Roll 1.65 1.64 -0.6% 2.2.2 Suspension Stiffness Tests Suspension stiffness tests were performed to measure the longitudinal, lateral, and vertical stiffness of the primary and secondary suspensions. A force was applied across the suspension system in the direction to be measured. The force was measured with a load cell. The displacement of the system was measured with a displacement transducer. A force/displacement graph can be generated to calculate the suspension stiffness. Longitudinal Stiffness Test The longitudinal stiffness test was performed to determine the primary and secondary effective stiffness in the longitudinal direction. A second PA5 car was placed on the same track directly in front of the test car with brakes applied. A hydraulic cylinder was connected between the two railcars to apply the load across the suspension. A load cell was used to determine the force needed to displace the suspension in the longitudinal direction. Displacement transducers were 9

placed across both the primary and secondary suspension systems to measure the displacement resulting from the applied load. Figures 6 and 7 show the test setup. Figure 6. Longitudinal Suspension Setup between Two Railcars Figure 7. Displacement Transducer for Longitudinal Suspension Test Force-displacement slopes were calculated for each run. The calculated stiffness values for all runs were averaged to determine the effective stiffness of the primary and secondary suspension systems. Figure 8 shows an example of the displacement and load measured during the test. Table 3 shows the values determined from the test in comparison to the manufacturer specified values. 10

Figure 8. Example of Longitudinal Stiffness Test Data Table 3. Longitudinal Suspension Characteristics Suspension Component Manufacturer Value Average Measured Value Difference Primary Suspension Stiffness per axle box (pair of chevrons) 67,380 lb/in 77,330 lb/in +14.8% Shear Stiffness of Airbag No manufacturer data available 1,625 lb/in N/A Traction Rod Stiffness in Longitudinal Direction No manufacturer data available 42,400 lb/in N/A Lateral Stiffness Test The lateral stiffness test was performed to determine the effective lateral stiffness values for the primary and secondary lateral suspension systems. A forklift was placed next to the lead truck of the PA5 car. A hydraulic cylinder was connected between them to apply the load across the suspension. A load cell was used to determine the force needed to displace the suspension in the lateral direction. Displacement transducers were placed across both the primary and secondary suspension systems to measure the displacement resulting from the applied load. Figure 9 shows the test setup. 11

Figure 9. Lateral Stiffness Test Setup Force-displacement slopes were calculated for each run. The calculated stiffness values for all runs were averaged to determine the effective stiffness of the primary and secondary suspension systems. Table 4 shows the values determined from the test in comparison to the manufacturer specified values. Table 4. Lateral Suspension Characteristics Suspension Component Manufacturer Value Average Measured Value Difference Primary Suspension Stiffness per axle box (pair of chevrons) 13,990 lb/in 19,414 lb/in +38.8 % Vertical Stiffness Test The vertical stiffness test was performed to determine the effective vertical stiffness for the secondary and primary lateral suspension systems. Secondary Suspension System The secondary suspension system of the PA5 car is an air suspension consisting of airbags and air reservoirs. The air suspension models used in NUCARS are based on the methods described by Oda and Nishimura3 and Berg.4. Figure 10 shows how the airbag systems are represented in the NUCARS model. Note that because of the arrangement of the damping in the system, the 3 Oda, N. and S. Nishimura. 1970. “Vibration of Air Suspension Bogies and their Design.” Bulletin of the JSME Vol. 13, No. 55. 4 Berg, Mats. 1999. “A Three-Dimensional Airspring Model with Friction and Orifice Damping.” Vehicle System Dynamics Supplement 33, pp. 528–539. 12

effective vertical and shear stiffness are nonlinear. The donut spring is a safety spring that will support the load of the car if the airbag system deflates. This spring was included in the model to accurately represent the vertical response of the car. Figure 10. Air Suspension Equivalent Mechanical System Secondary suspension stiffness was measured by placing hydraulic cylinders under the jacking points of the carbody at lead truck locations. Transducers were placed across the airbag suspension system to measure the displacement resulting from the load. Figure 11 shows the setup to measure the secondary suspension stiffness. Table 5 shows the secondary suspension system vertical stiffness values measured during the test. Figure 11. Secondary Suspension Vertical Test Setup = =Air Spring System StiffnessAirbag Stiffness (Pedestal Stiffness)= Donut Spring Stiffness= Reservoir Stiffness= Change of area Stiffness= Orifice Damping Equivalent Mechanical System Setup Kab Kr Kds Cor Airbag Donut Spring Airbag Kab Donut Spring Kds Reservoir Kr Damping Orifice Cor Secondary Suspension System Setup KA Donut Spring i i i i i i 13

Table 5. Secondary Suspension Vertical Stiffness Suspension Component Average Measured Value Total Air spring System Stiffness 3,066 lb/in Donut Spring Stiffness 18,351 lb/in Airbag Stiffness 8,525 lb/in Reservoir Stiffness 6,539 lb/in Primary Suspension System The primary suspension system consists of a pair of chevrons. Figure 12 shows a photograph of the system. The stiffness of the primary system was measured by placing the hydraulic actuators at the center of the truck. The actuators pushed up on the truck frame displacing the suspension. Displacement transducers were used to measure the displacement and a force/displacement curve was calculated. Figure 13 shows the test setup. Table 6 summarizes the results. Figure 12. Primary Suspension System – Chevron Figure 13. Primary Suspension Vertical Test Setup 14

Table 6. Primary Suspension Stiffness Suspension Component Manufacturer Value Average Measured Value Difference Primary Suspension Stiffness per axle box (pair of chevrons) 67,380 lb/in 77,330 lb/in +14.8% 2.3 On-Track Tests The goal of the on-track tests was to collect data to ascertain the ability of NUCARS and PBTG to properly predict vehicle performance and ride quality and to identify track geometry locations that need maintenance. The data collected was used to validate the NUCARS model output and build PBTG NNs. PA5 Car 5746 was instrumented and put in service on June 3, 2013. Data was taken in both directions between Journal Square Station and 33rd St Station in the morning and in both directions between Newark/Penn Station and World Trade Center Station in the afternoon. Load conditions from AW0 to AW4 (crush load) were measured throughout the test. The PATH and TTCI test team was onboard the train to monitor test and equipment. Accelerometers were mounted on the carbody and axle boxes. All accelerometers had to be placed outside of the carbody due to passengers being onboard during the time of testing. Table 7 summarizes the locations and types of accelerometers used during the test. Figures 14 to 18 show photographs of the instrumentation on the car. 15

Table 7. Ride Quality Test Accelerometer Locations Description Type of Measurements Notes 1 Axle Acceleration Longitudinal, Lateral, Vertical 2 Axle Acceleration Longitudinal, Lateral, Vertical 3 Axle Acceleration Longitudinal, Lateral, Vertical 4 Axle Acceleration Longitudinal, Lateral, Vertical 5 Driver’s Cab Acceleration Longitudinal, Lateral, Vertical Accelerometer placed on floor under driver’s seat. 6 Center of Carbody Accelerations Longitudinal, Lateral, Vertical Accelerometer could not be placed in the center due to equipment mounted underneath the car. Accelerometer was mounted on a beam centered longitudinally and about 30 inches from the centerline of carbody. A beam was used instead of carbody skin to minimize noise. 7 Carbody at truck centerline Accelerations Longitudinal, Lateral, Vertical Accelerometer was mounted on a beam. A beam was used instead of carbody skin to minimize noise. 8 Carbody at truck centerline Accelerations Longitudinal, Lateral, Vertical Accelerometer was mounted on a beam. A beam was used instead of carbody skin to minimize noise. 5 8 6 7 4 3 2 1 A-end B-end 16

Figure 14. Axle Box Accelerometer Figure 15. Carbody Accelerometer at Truck Centerline Figure 16. Carbody Accelerometer at Center of Car 17

Figure 17. Carbody Accelerometer in Driver’s Cab Figure 18. Instrumentation Setup 18

2.3.1 ISO 2631 Ride Quality Analysis Requirements The well recognized and widely used ISO 2631 standard was used for analysis of the passenger ride quality.5 The standard defines methods for quantifying whole body vibration and effects on human health and comfort, probability of vibration perception, and incidence of motion sickness. The following types of vibrations are covered in this standard: • Periodic vibration is oscillatory motion whose amplitude pattern repeats after fixed increments of time. • Random vibration is instantaneous and not specified at any instant of time. • Transient vibration is short duration and caused by mechanical shock. Table 8 shows the ride quality index specified in ISO 2631. The following are ways to analyze passenger ride quality • Basic method is used for general evaluation of ride quality. This method should only be used when the crest factor is less than nine. – Crest factor is ratio of the maximum instantaneous peak value of the frequency-weighted acceleration signal to its root-mean-square (RMS) value. • Running RMS method is used to evaluate vibration with occasional shocks and transient vibration. This is the method that is typically used for a more in-depth look at passenger ride quality. • Fourth power vibration dose (VDV) method is more sensitive to peaks in vibration. This method is used to look at the effect of discrete events on passenger ride quality. In this study the fourth power VDV method is used to evaluate passenger ride quality. It allows for better correlation between track geometry deviations and ride quality. Table 8. Passenger Ride Quality Index Weighted Vibration Magnitude (m/s2) Ride Quality Index Less than 0.315 Not uncomfortable 0.315 to 0.63 A little uncomfortable 0.5 to 1 Fairly uncomfortable 0.8 to 1.6 Uncomfortable 1.25 to 2.5 Very uncomfortable Greater than 2 Extremely uncomfortable 2.3.2 Journal Square to 33rd Street Figure 19 describes the location of test car 5746 in the train consist. The A-end of the car was leading from Journal Square to 33rd Street, and the B-end was leading from 33rd Street to Journal Square. Data was collected from 6 a.m. to approximately 11 a.m. on June 3, 2013. Load conditionsAW0 to AW4 (crush load) were measured during the test. 5 International Organization for Standardization (ISO).1997. Mechanical vibration and shock — Evaluation of human exposure to whole-body vibration Part 1: General requirements. ISO 2631-1:1997 (E), Second edition corrected and reprinted 1997-07-15, Switzerland 19

Figure 19. Consist Setup The acceleration data in the driver’s cab was analyzed in accordance with ISO 2631. Figures 20 and 21 show the fourth power VDV method. The VDV method is used to look at discrete events. This measure may be helpful when looking at a correlation between track geometry deviations and passenger ride quality. Between Pavonia-Newport and Christopher Street stations the VDV value was in the uncomfortable to very uncomfortable range. The measured values are summarized in Table 9. Table 9. VDV Values that exceeded Fairly Uncomfortable Ride Quality Index Station Measured VDV m/s1.75 Ride Quality Index Pavonia-Newport to Christopher Street Vertical 1.25 Uncomfortable to Very Uncomfortable Lateral 1.31 Uncomfortable to Very Uncomfortable Christopher Street to Pavonia-Newport Vertical 1.35 Uncomfortable to Very Uncomfortable Lateral 1.06 Uncomfortable to Very Uncomfortable Figure 20. VDV Ride Quality calculated for Journal Square to 33rd Street 1 2 Test Car 5746 653 7A B 0 0.5 1 1.5 2 2.5 3 Journal Square to Grove St Grove St. to Pavonia- Newport Pavonia-Newport to Christopher St. Christopher St. to 9th St. 9th St. to 14th St. 14th St to 23rd St 23rd St. to 33rd St. VD V (m /s ^1 .7 5) Vertical Lateral Longitunal Not Uncomfortable A Little Uncomfortable Fairly Uncomfortable Uncomfortable Very Uncomfortable Extremely Uncomfortable 20

Figure 21. VDV Ride Quality calculated for 33rd Street to Journal Square Figures 22 and 23 show the measured accelerations, speed, and track geometry between the stations. The vertical accelerations were excited between 4,000 and 8,000 feet. The maximum 2- second peak-to-peak is 0.37 g’s. In this area, the track is mainly tangent with a shallow curve of 4,100-foot radius with a superelevation of 1 inch. The average speed is 38 mph. There are some cross-level deviations in the tangent track and profile deviations corresponding to the start of the increase in vertical accelerations (illustrated in Figure 22). The frequencies excited in the vehicle are approximately 0.9 Hz and 1.34 Hz (corresponds to bounce), 1.43 Hz (corresponds to upper center roll). In the vertical profile, there is a deviation that occurs approximately every 62 feet. The speed the vehicle was traveling through this segment of track corresponds to a frequency of 0.9 Hz. The lateral accelerations are also excited in this section of track. Figure 23 illustrates the acceleration and corresponding alignment deviations. The maximum lateral 2-second peak-to- peak was 0.29 g’s. The frequencies excited in the vehicle in this section of track are approximately 0.48 (corresponds to lower center roll) and 0.76 Hz. The horizontal alignment of the track in this segment has a deviation approximately every 74 feet, which corresponds to a frequency of approximately 0.76 at an average speed of 38 mph. Figure 24 and 25 show the frequency content of both the vehicle and track geometry in the lateral and vertical directions. There appears to be a relationship between track geometry deviations and vehicle performance. PBTG NNs were developed to explore this relationship further. The results are discussed in Section 5. 0 0.5 1 1.5 2 2.5 3 33rd St. to 23rd St. 23rd St to 14th St. 14th St. to 9th St. 9th St. to Christopher St. Christopher st. to Pavonia-Newport Pavonia-Newport to Grove St. Grove St. to Journal Square VD V (m /s ^1 .7 5) Vertical Lateral Longitunal Not Uncomfortable A Little Uncomfortable Fairly Uncomfortable Uncomfortable Very Uncomfortable Extremely Uncomfortable 21

Figure 22. Vertical Accelerations compared to Track Geometry -40 -30 -20 -10 0 10 20 30 40 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Cu rv at ur e ( de g) Cr os s L ev el (in ) Distance (ft) Cross Level Curvature 0 5 10 15 20 25 30 35 40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Sp ee d ( mp h) Ve rti ca l A cc ele rat ion s ( g's ) Distante (ft) VerticalAccel-Cab Speed -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Pr of ile D ev iat ion (in ) Distance (ft) Left Profile Right Profile Profile deviations that excite vertical accelerations Cross-level deviations 22

Figure 23. Lateral Accelerations compared to Track Geometry 0 5 10 15 20 25 30 35 40 -0.30 -0.20 -0.10 0.00 0.10 0.20 0.30 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Sp ee d ( mp h) La te ra l A cc ele rat ion (g 's) Distance (ft) LateralAccel-Cab Speed -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Al ign me nt D ev iat ion (in ) Distance (ft) Left Alignment Right Alignment -40 -30 -20 -10 0 10 20 30 40 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Cu rv at ur e ( de g) Cr os s L ev el (in ) Distance (ft) Cross Level Curvature Alignment deviations that excite lateral accelerations 23

Figure 24. Lateral Frequency Content Figure 25. Vertical Frequency Content 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 0.0045 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 Tr ac k G eo m et ry M ag ni tu de Ve hi cl e Re sp on se M ag ni tu de Frequency (Hz) Vehicle Track Geometry 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 0.0000 0.0010 0.0020 0.0030 0.0040 0.0050 0.0060 0.0070 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 Tr ac k G eo m et ry M ag ni tu de Ve hi cl e Re sp on se M ag ni tu de Frequency (Hz) Vehicle Track Geometry Frequency = 0.9 Hz Frequency = 0.76 Hz 24

2.3.3 Newark to World Trade Center Figure 26 describes the location of test car 5746 in the train consist. The A-end of the car was leading from Newark to World Trade Center, and the B-end was leading in the other direction. Data was collected from 4:30 p.m. to approximately 7:15 p.m. on June 3, 2013. Load conditionsAW0 to AW4 (crush load) were measured during the test. Figure 26. Consist Setup Figures 27 and 28 show the ride quality measured and analyzed by the fourth power VDV method. Between Harrison and Journal Square stations the VDV value was in the fairly uncomfortable range. The measured values are summarized in Table 10. Table 10. VDV Values that exceeded Fairly Uncomfortable Ride Quality Index Station Measured VDV m/s1.75 Ride Quality Index Harrison to Journal Square Vertical 1.86 Very Uncomfortable Lateral 1.24 Uncomfortable Journal Square to Harrison Vertical 1.76 Very Uncomfortable Lateral 1.00 Uncomfortable Grove Street to Journal Square Vertical 1.23 Uncomfortable Lateral 0.85 Uncomfortable Figure 27. VDV Ride Quality calculated for Newark to World Trade Center 57461 2 3 4 6 7 8 0 0.5 1 1.5 2 2.5 3 Newark to Harrison Harrison to Journal Square Journal Square to Grove St. Grove St. to Exchange Place Exchance Place to WTC VD V (m /s ^1 .7 5) Vertical Lateral Longitunal Not Uncomfortable Little Uncomfortable Fairly Uncomfortable Uncomfortable Very Uncomfortable Extremely Uncomfortable 25

Figure 28. VDV Ride Quality calculated World Trade Center to Newark Figures 29 and 30 show the measured accelerations, speed, and track geometry between the stations. The vertical accelerations are excited between 0 and 12,000 feet. The maximum 2 second peak-to-peak acceleration is 0.54 g’s. In this area, the track has three curves ranging from 3.5 to 1 degree, and two reverse curves ranging from 1 to 2.5 degrees. The average speed is 40 mph. There are profile deviations in this area. The frequencies excited in the vehicle are approximately 1.25 Hz and 1.59 Hz. In the vertical profile, there is a deviation that occurs approximately every 33 feet. The speed the vehicle was traveling through this segment of track corresponds to a frequency of 1.2 Hz. The lateral accelerations are also excited in this section of track. Figure 30 illustrates the acceleration and corresponding alignment deviations. The maximum lateral 2 second peak-to- peak acceleration was 0.31 g’s. The frequency excited in the vehicle in this section of track is approximately 0.45 Hz (corresponds to lower center roll). In the horizontal alignment of the track in this segment, there is a deviation approximately every 130 feet. This corresponds to a frequency of approximately 0.45 at an average speed of 40 mph. Figures 31 and 32 show the frequency content of both the vehicle and track geometry in the vertical and lateral directions. There appears to be a relationship between track geometry deviations and vehicle performance. PBTG NNs were developed to explore this relationship further. The results are discussed in Section 5. 0 0.5 1 1.5 2 2.5 3 WTC to Exchange Place Exchange Place to Grove St. Grove St. to Journal Square Journal Square to Harrison Harrison to Newark VD V (m /s ^1 .7 5) Vertical Lateral Longitunal Not Uncomfortable Little Uncomfortable Fairly Uncomfortable Uncomfortable Very Uncomfortable Extremely Uncomfortable 26

Figure 29. Vertical Accelerations compared to Track Geometry 27

Figure 30. Lateral Accelerations compared to Track Geometry 28

Figure 31. Lateral Frequency Response Figure 32. Vertical Frequency Response 0.000 0.020 0.040 0.060 0.080 0.100 0.120 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.0 1.0 2.0 3.0 4.0 5.0 Tr ac k G eo m et ry M ag ni tu de Ve hi cl e Re sp on se M ag ni tu de Frequency (Hz) Vehicle-Lateral Track Profile-Lateral 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.0 1.0 2.0 3.0 4.0 5.0 Tr ac k G eo m et ry M ag ni tu de Ve hi cl e Re sp on se M ag ni tu de Frequency (Hz) Vehicle-Vertical Track Profile-Vertical 29