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49 This chapter presents the results from an experiment that was conducted to correlate objective measurements of dis- comfort caused by vehicle vibration to measures of road roughness on urban and low-speed roadways. The experi- ment included simultaneous measurements of longitudi- nal road profile and accelerations at interfaces between the vehicle and the driver on 29 urban and low-speed pavement sections using 3 test vehicles. Vibration levels were measured at three driver-to-vehicle interfaces: (1) seat/buttock, (2) seat/ back, and (3) floor/foot. Seat/buttock and seat/back vibration was measured in the vertical, lateral, and longitudinal direc- tions, and floor/foot vibration was measured in the vertical direction. This section briefly describes the test sections, test vehicles, instrumentation, and test conditions for the field experiment. Details are provided in Appendix C. The chapter describes standard methods used to quantify user discomfort from measured accelerations at driver-to-vehicle interfaces. These methods include the calculation of measures of overall dis- comfort, application of criteria for identifying the presence of transient vibration, and calculation of measures of transient vibration. This chapter examines the correlation between the IRI, variations of the IRI calculation algorithm, and Ride Num- ber (RN) and measures of discomfort and transient vibration severity. 4.1 Field Experiment 4.1.1 Test Sections The test program included 29 pavement sections on low- speed roads in urban and rural areas along six routes in south- eastern Michigan. Table 11 lists the name and the number of test sections for each route. The table also lists the county, functional class, and the range of posted speed limit for the test sections within each route. The test sections included the functional classes 3 (principal arterialâother) and 4 (minor arterial). The specific test sections within each route were selected to include a cross section of typical properties for local urban and low-speed roadways, including a variety of built-in features, such as intersection crossings, railway cross- ings, and utility covers. 4.1.2 Test Vehicles The measurements were conducted using three test vehi- cles: (1) a 2003 Nissan Altima, (2) a 2013 Hyundai Tucson, and (3) a 2008 GMC Savana. These vehicles represent three distinct market segments [a mid-sized sedan, a sport utility vehicle (SUV), and a full-sized van], and they differ from each other in geometry, mass distribution, and suspension characteristics. Figures 65 through 67 show side views of each vehicle. 4.1.3 Instrumentation The instrumentation included sensors for vehicle vibra- tion measurement, an inertial profiler, and redundant mea- surement of longitudinal distance. Vehicle vibration was measured using a suite of sensors at the driver-to-vehicle interfaces. Each vehicle was equipped with a servo-type accel- erometer mounted to the floor at the driverâs feet, and two instrumented seat pads with six degree-of-freedom inertial measurement units (IMUs). Figure 68 shows the seat pads mounted to the mid-sized sedan. Vertical accelerometers were also mounted to the left and right steering knuckle of each vehicle. The inertial profiler included servo-type accelerometers and line lasers on each side at the rear of the vehicle and rotational encoders mounted to both rear wheels. In addi- tion to the rotational encoders at the rear wheels, the system included an optical fifth wheel and a GPS system with RTK corrections. Figure 69 shows the instrumented SUV from a C H A P T E R 4 Ride Experiment
50 Route Test Sections County Functional Class Speed Limit Range (mi/hr) Jackson Road/Huron Street 3 Washtenaw 3 35 Grand River (M-5) 5 Wayne 3 35 Michigan Ave. (US-12) 9 Wayne 3 30â45 Fort Street (M-85) 4 Wayne 3 30â50 West Grand River 6 Livingston 4 30â55 M-52 2 Washtenaw 4 30 Table 11. Test routes. Figure 65. Mid-sized sedan (2003 Nissan Altima). Figure 66. SUV (2013 Hyundai Tucson). Figure 67. Full-sized van (2008 GMC Savana). Figure 68. Seat pads. Figure 69. Profiler and wheel encoder.
51 view that includes the profiler and the left wheel encoder. Comparison of the outputs of each alternative under differ- ent measurement conditions helped verify the calibration of the rotational encoders and the starting point of each test section. 4.1.4 Test Conditions The test plan called for three passes over each section at the posted speed limit and three additional passes at an additional test speed below the posted limit. For test sec- tions with a speed limit of 35 mi/hr (56 km/hr) or less, the additional test speed was 5 mi/hr (8 km/hr) below the speed limit. For test sections with a posted speed limit of 40 mi/hr (64 km/hr) or above, the additional test speed was 10 mi/hr (16 km/hr) below the posted speed limit. Each pass over a given test section included 16 seconds of travel from the same starting point, regardless of test speed. All of the intended runs are included in the study, with the following exceptions: (1) 1 of the test sections on Michigan Ave. was not tested with the mid-sized sedan, (2) 7 of the remaining 168 runs with the mid-sized sedan did not pass the data quality checks, and (3) 1 of the runs with the full-sized van did not pass the data quality checks. 4.2 Data Processing 4.2.1 Ride Sensor Processing Acceleration at driver-to-vehicle interfaces was evaluated as recommended by ISO 2631-1 and SAE J2834. ISO 2631-1 and SAE J2834 specify methods of quantifying âperiodic, ran- dom and transientâ vibration levels and estimating the effect of vibration exposure on comfort. In this context, ârandomâ refers to stationary vibration, which implies that the inten- sity of vibration is consistent throughout the test interval. âTransientâ vibration events include âdiscrete motion and vibration disturbancesâ (SAE J2834) or high peak values (Griffin 1986) that stand out compared to the prevailing vibra- tion level over a short time interval. This section describes the methods used to quantify the overall vibration magnitude (for random vibration) and to identify and quantify transient vibration events. 126.96.36.199 Random Vibration Root mean square (RMS) acceleration was calculated for each vibration data channel after application of frequency weighting functions recommended for evaluation of com- fort. These weighting functions correspond to those recom- mended specifically for the automotive driving environment by SAE J2834. Table 12 lists the weighting function applied to each data channel. Figures 70 and 71 show the weighting functions graphically. For many applications, the weighting functions are applied in the frequency domain to spectral density functions of raw acceleration signals. In this case, weighting functions were applied in the time domain using a series of digital fil- ters, because the filtered signals were needed for analysis of Interface Direction Weighting Function Multiplying Factor Seat/buttock Longitudinal Wd 1.0 Lateral Wd 1.0 Vertical Wb 1.0 Seat/back Longitudinal Wc 0.8 Lateral Wd 0.5 Vertical Wd 0.4 Floor/foot Vertical Wb 0.4 Table 12. Weighting functions and multiplying factors. Figure 70. Ride vibration weighting functions Wb and Wd.
52 transient events (See Section 188.8.131.52.). Each weighting func- tion required a combination of either three or four second- order digital filters, including a Butterworth high-pass filter, a Butterworth low-pass filter, an âacceleration-velocity tran- sitionâ (low-pass) filter, and an âupward step filter.â Once the weighting function was applied to a given chan- nel, the weighted RMS value (rmsaw) was calculated directly from the weighted signals in the time domain: â ( )= ï£® ï£°ï£¯ ï£¹ ï£»ï£º= 1 (3)2 1 1 2 rmsa N a iw w i N Where aw(i) is the âithâ sample in the weighted accelera- tion signal and N is the number of samples collected using a constant time step. A âpoint vibration totalâ (PVT) was calculated for each driver-to-vehicle interface as follows: ( )= + + (4)2 2 2 2 2 2 12PVT k rmsa k rmsa k rmsax wx y wy z wz Where the subscripts x, y, and z represent the longitudinal, lateral, and vertical directions, respectively. The point vibra- tion total value is the root sum of squares of the weighted RMS value in each direction with a standard multiplying factor (k) applied for each direction. Table 12 lists the stan- dard multiplying factor values for each direction at each inter- face. Note that only the vertical vibration was measured at the floor/foot interface, and the point vibration total is the RMS weighted vertical acceleration times the multiplying factor of 0.4. An âoverall vibration totalâ (OVT) value was also calcu- lated from the root sum of squares of the point vibration total values from the three driver-to-vehicle interfaces: ( )= + + (5)2 2 2 12OVT PVT PVT PVTff sbk sbt Where PVTff, PVTsbk, and PVTsbt are the point vibration total values for the floor/foot, seat/back, and seat/buttock interfaces, respectively. This study examined the correlation between roughness indices and OVT, PVTsbt, and rmsawz at the seat/buttock inter- face (rmsawzsbt), and rmsawz at the floor/foot interface (rmsawzff). 184.108.40.206 Transient Vibration Transient vibration was identified and quantified using three methods: (1) crest factor, (2) root-mean-quad (RMQ) acceleration, and (3) the maximum transient vibration (MTV) value. Crest factor is the ratio of the maximum abso- lute peak value of weighted acceleration to its RMS value. RMQ weighted acceleration (rmqaw) is calculated as follows: â ( )= ï£® ï£°ï£¯ ï£¹ ï£»ï£º= 1 (6)4 1 1 4 rmqa N a iw w i N MTV is calculated using a running RMS value with a short time interval, T, which corresponds to M samples collected at a constant sampling rate of M/T: 1 (7), 2 1 1 1 2 rmsa j M a iw T w i j M â( ) ( )= ï£® ï£°ï£¯ ï£¹ ï£»ï£º= + â Where rmsaw,T(j) is the RMS weighted acceleration for the interval of duration T beginning at sample point j. (For a test that produces N recorded samples, the index j will range from 1 to N â M + 1.) MTV is the maximum running RMS value observed during a test: ( )( )= = â +max , 1, 1 (8),MTV rmsa j j N Mw T SAE J2834 categorizes a âride specimenâ as transient if the ratio of RMQ weighted acceleration to RMS weighted Frequency (Hz) Gain Figure 71. Ride vibration weighting function Wc.
53 acceleration is greater than 1.5. In such cases, SAE J2834 rec- ommends the use of RMQ in place of RMS for quantifying discomfort. The supporting rationale notes that for transient ride specimens, âDiscomfort can be significantly influenced by peak values and underestimated by methods involving RMS averaging.â ISO 2631-1 classifies evaluation of ride comfort using RMS weighted acceleration as âsuitableâ if the crest factor is less than or equal to 9. When crest factor is above 9, RMS weighted acceleration âmay underestimate vibration severity with respect to comfortâ and additional evaluation methods are recommended. This includes MTV over a 1-second inter- val to account for âoccasional shocks and transient vibra- tion.â ISO 2631-1 further recommends reporting both RMS weighted acceleration and MTV when the ratio of MTV to RMS weighted acceleration is greater than or equal to 1.5. In this analysis, transient vibration is characterized using MTV or a 1-second interval, and a test is deemed to include transient vibration if MTV/ rmsaw > 1.5, rmqaw / rmsaw > 1.5, or crest factor > 9. 4.2.2 Roughness Indices This study examined the correlation between summary values of measured vibration discomfort and IRI, RN, and several adaptations of the IRI algorithm. 220.127.116.11 The IRI Algorithm The IRI is calculated from profile using a quarter-car simulation with standardized settings for vehicle properties and a standard simulation speed of 49.7 mi/hr (80 km/hr). When the standard settings for IRI are applied, the model is often called the âGolden Carâ (Sayers 1995). Figure 72 shows a schematic of the quarter-car model and provides a listing of the parameter values that define the Golden Car. Gillespie (1992) describes the components of the quarter-car model as follows: âAt each wheel position the vehicle behaves as a sprung mass (ms) sitting on a suspension with stiffness (ks) and damping (cs), which in turn is attached to the unsprung mass (mu) of the wheel, brake, and suspension components. The wheel contacts the road by a tire which acts like a spring (kt). Road inputs to the car flex the tire, stroke the suspen- sion, and cause the sprung and unsprung masses to vibrate in the vertical direction.â To simplify the underlying equations, cs, kt, ks, and mu are normalized by ms to produce C, K1, K2, and Î¼, respectively (Sayers 1995). Figure 72 also shows the base length (B) of a moving average applied to represent envelopment of roughness within the tire contact patch. The quarter-car model includes two degrees of freedom: one for vertical motion of the sprung mass and another for vertical motion of the unsprung mass. The IRI is calculated using the velocity across the suspension, which is the differ- ence between vertical velocity of the sprung and unsprung masses. In particular, the IRI is the average rectified spatial velocity across the suspension predicted by the Golden Car for a travel speed of 49.7 mi/hr (80 km/hr). âSpatial velocityâ signifies that motion is monitored as a function of the dis- tance traveled, rather than the passage of time. As such, the IRI algorithm calculates response in units of slope versus dis- tance, rather than velocity versus distance. The term âaverage rectifiedâ indicates that the index is calculated by averaging the absolute value of response. Although it is not strictly cor- rect, a more intuitive equivalent definition is the accumulated gross suspension stroke divided by travel distance, which is often expressed in inches per mile. Figure 73 shows gain for profile slope in terms of temporal frequency and wavelength. In terms of temporal frequency, the gain response is determined by the properties shown in Figure 72 and the selection of suspension stroke rate as the output. For example, the gain function has values above 0.5 in the frequency range from 0.77 to 17.08 Hz, with a peak at 1.41 Hz associated with resonant motion of the sprung mass Figure 72. Golden Car model (Sayers 1995). Figure 73. Golden Car model gain.
54 and a peak at 9.69 Hz associated with resonant motion of the unsprung mass. At a simulated travel speed of 49.7 mi/hr (80 km/hr), this corresponds to a gain function above 0.5 in the wavelength range from 4.27 to 94.8 ft (1.30 to 28.9 m) and peak response at 7.52 ft (2.29 m) and 51.8 ft (15.8 m). At other speeds the temporal frequency response remains the same, but the response in terms of wavelength shifts in proportion to speed. At simulated speeds below 49.7 mi/hr (80 km/hr), the sensitivity of the Golden Car shifts toward shorter wavelengths. Likewise, as the speed of an actual vehi- cle changes, the road features that affect its dynamic response change. When speed decreases, the importance of a portion of the long wavelength content in the road profile diminishes, and the importance of a portion of the short-wavelength content increases. Note that other aspects of the IRI algorithm and the Golden Car model affect the index they produce. First, an index may be cast in terms of response per time elapsed (e.g., inches per second) rather than distance traveled (e.g., inches per mile). This changes the interpretation of the index to a representation of roughness intensity experienced at a given speed. This is a contrast to the IRI, which is a geometric prop- erty of the road profile with a fixed definition (Sayers et al. 1986) Second, calculating the RMS of a Golden Car model output is another option for accumulating a summary index, rather than calculating the average rectified value. Third, the Golden Car model predicts responses other than the rate of suspension stroke, such as vertical acceleration of the sprung and unsprung masses, and tire deflection. 18.104.22.168 Golden Car Index Options Adaptations of the IRI algorithm using alternate simula- tion speeds, normalization type, summary index accumu- lation, and output quantities are examined to determine whether they improve correlation to discomfort measured on low-speed and urban roadways. This includes the following variations on simulation speed: â¢ Golden Car Average Rectified Slope (GCARS): This index is calculated by simulating Golden Car average recti- fied slope at a simulation speed other than 49.7 mi/hr (80 km/hr). Like the IRI, the output is based on accumu- lated suspension stroke, and is normalized by distance traveled. As such, it may be expressed in inches per mile. The simulation speed is shown as a subscript [e.g., at 35 mi/hr (56 km/hr), the index is given the abbrevia- tion GCARS35]. For a simulation speed of 49.7 mi/hr (80 km/hr), it is equal to the IRI. â¢ Golden Car Average Rectified Slope at Speed (GCARSV): This index is calculated by simulating Golden Car aver- age rectified slope at a simulation speed equal to the travel speed for each test run. For this index, the range of wave- lengths that affect the response shifts in proportion to the speed at which discomfort was measured. When the simu- lation speed is adapted for each test run, the subscript âVâ is used. Additionally, normalization is varied: â¢ Golden Car Average Rectified Velocity at Speed (GCARVV): This index is calculated by simulating Golden Car average rectified velocity at a simulation speed equal to the travel speed for each run. This index is based on accumulated suspension stroke, but it is normalized by time, rather than distance traveled. As such, it is expressed in units of veloc- ity, such as inches per second. For a given profile, GCARVV is equal to GCARSV times V. The accumulation method is varied for some versions of the index: â¢ Golden Car Root Mean Square Slope at Speed (GCRMSSV): This is GCARSV with the exception that RMS replaces the calculation of the average rectified value as the method of accumulating a summary value. â¢ Golden Car Root Mean Square Velocity at Speed (GCRMSVV): This is GCARVV with the exception that RMS replaces the calculation of the average rectified value as the method of accumulating a summary value. Adaptations are also examined that predict RMS sprung mass acceleration, rather than index values based on suspen- sion stroke: â¢ Golden-Car RMS Spring Mass Vertical Acceleration (GCRMSA): This index provides the RMS value of vertical acceleration of the sprung mass predicted by the Golden Car model at the standard simulation speed of 49.7 mi/hr (80 km/hr). The âsprung massâ in a quarter-car model is a portion of the vehicle above the suspension, and its closest counterpart among the vibration measurements for this experiment is vertical acceleration at the floor/ foot interface. â¢ Golden Car RMS Spring Mass Vertical Acceleration at Speed (GCRMSAV): This index provides the RMS value of vertical acceleration of the sprung mass predicted by the Golden Car model at a simulation speed equal to the travel speed for each run. The index options based on sprung mass acceleration may be expressed in units of acceleration (e.g., ft/sec2). For this research, it is normalized by acceleration due to gravity, and it is expressed in âgâ units.
55 22.214.171.124 Ride Number RN was developed to characterize user opinion of pave- ment rideability from measured road profiles (Janoff et al. 1985; Janoff 1988). The standard version of RN applies a band-pass filter to the profile, which was tuned to predict panel ratings of rideability (Sayers and Karamihas 1996b). The band-pass filter has output in units of profile slope and is primarily sensitive to roughness content in the range of wave- lengths from 1.25 ft (0.38 m) to 37.4 ft (11.4 m) (Karamihas et al. 1999). Pre-transform Ride Number (PTRN) is the RMS value of the filtered profile. In the standard definition, a PTRN value from the left and right wheel path is calculated individually and then combined into a single value using the RMS. RN is expressed on a 0â5 scale using the following transform: = â5 (9)160RN e PTRN Where PTRN is expressed in terms of âunitlessâ slope (e.g., inches per inch). 4.3 Results, Overall Roughness 4.3.1 IRI Figures 74â76 compare values of RMS weighted vertical acceleration at the floor/foot interface (rmsawzff) to the left IRI for the runs performed by each vehicle. The coefficient of determination for a linear fit (i.e., R2) was 0.78â0.80 for the three vehicles. The RMS residual for a linear fit was 0.0065 g, 0.0077 g, and 0.0071 g for the mid-sized sedan, SUV, and full- sized van, respectively. This is approximately 10 percent of the overall range in each case. Table 13 lists the values of R2 and RMS residual for cor- relation of left IRI to OVT, PVTsbt, rmsawzsbt, and rmsawzff for each vehicle. The left IRI relates best to RMS weighted vertical acceleration at the seat/buttock interface. The improvement over RMS weighted vertical acceleration at the floor/foot interface is due to the reduction in high frequency content in the acceleration by the seat, which corresponds to short- wavelength content outside of the waveband that affects the IRI. A similarly good relationship exists between the left IRI and the point vibration total at the seat/buttock interface (PVTsbt). However, the residual increases for prediction of overall vibration total (OVT) by the left IRI. This is due in part to the influence of vibration in the longitudinal and lat- eral directions, which are not explicitly captured by the IRI, and in part to the dynamic response at the seat back. 4.3.2 Mean Roughness Index (MRI) Table 14 lists the values of R2 and RMS residual for cor- relation of discomfort quantities to MRI. MRI is the average of the IRI values from the left and right wheel paths. RMS residuals are higher for the MRI than the left IRI in every case. Since vibration was measured at driver-to-vehicle interfaces on the left side of the vehicle, vibration and discomfort values correlated to roughness indices from the left wheel path much better than roughness indices from the right wheel path, and better than averaged values from both wheel paths in nearly every case. As such, the remaining index options derived from the Golden Car model are presented using calculations from the left wheel path only. 4.3.3 Ride Number Tables 15 and 16 list the values of R2 and RMS residual for correlation of discomfort quantities to RN calculated using the left wheel path only and using both wheel paths, respectively. Correlation was better using both wheel paths Figure 74. RMS weighted vertical acceleration, floor/foot interface, mid-sized sedan.
56 Figure 75. RMS weighted vertical acceleration, floor/foot interface, SUV. Figure 76. RMS weighted vertical acceleration, floor/foot interface, full-sized van. Discomfort mid-sized sedan SUV full-sized van Quantity RMS Resid. (g) R2 RMS Resid. (g) R2 RMS Resid. (g) R2 rmsawzff 0.0065 0.796 0.0077 0.778 0.0071 0.798 rmsawzsbt 0.0036 0.866 0.0057 0.820 0.0048 0.699 PVTsbt 0.0033 0.891 0.0057 0.827 0.0068 0.618 OVT 0.0046 0.897 0.0075 0.821 0.0096 0.643 Table 13. Correlation of vibration discomfort to left IRI. Discomfort mid-sized sedan SUV full-sized van Quantity RMS Resid. (g) R2 RMS Resid. (g) R2 RMS Resid. (g) R2 rmsawzff 0.0081 0.683 0.0087 0.712 0.0076 0.766 rmsawzsbt 0.0052 0.722 0.0068 0.741 0.0055 0.600 PVTsbt 0.0047 0.782 0.0065 0.778 0.0074 0.548 OVT 0.0065 0.791 0.0085 0.770 0.0104 0.583 Table 14. Correlation of vibration discomfort to MRI.
57 compared to using the left wheel path only for the SUV and the full-sized van, but not as good for the mid-sized sedan. Overall, correlation for RN was comparable to correlation for the IRI from the left wheel path. Correlation was improved for all discomfort quantities for the SUV, but improved for some and not for others for the mid-sized sedan and the full- sized van. Note that RN is meant to quantify user opinion of the rideability of roads. As such, it is not expected to directly correlate to objectively measured vibration discomfort. Rather, it is sensitive only to those aspects of road roughness that test subjects associated with the quality of the roadway. 4.3.4 Golden Car Indices Tables 17 and 18 list the values of R2 and RMS residual, respectively, for correlation of discomfort quantities to indi- ces derived from the Golden Car model (see Section 126.96.36.199.). To assist in the assessment of correlation level, Table 19 lists the difference in RMS residual for each index option rela- tive to the IRI, where a positive value indicates improvement (i.e., a reduction in the value of the residual). Values of RMS residual and changes in RMS residual are provided in thou- sandths of a g (i.e., mg) in Tables 18 and 19. For GCARS using a fixed simulation speed, the mid-sized sedan and SUV showed the greatest improvement in cor- relation at simulation speeds of 30 mi/hr (48 km/hr) and 35 mi/hr (56 km/hr). This reflects a shift in sensitivity of the test vehicles toward shorter wavelengths at lower test speeds. More than 90 percent of the test runs were performed at speeds from 25 mi/hr (40 km/hr) to 45 mi/hr (72 km/hr), and more than half of the test runs were performed at 30 mi/hr (48 km/hr) or 35 mi/hr (56 km/hr). However, correlation was highest for the full-sized van at a simulation speed of 40 mi/hr (64 km/hr), and was not improved for all discomfort quantities at any speed below the simulation speed used for the IRI of 49.7 mi/hr (80 km/hr). This is because the full- sized van was more sensitive to low-frequency (i.e., longer- wavelength) input than the other vehicles. For GCARSV, which uses a simulation speed equal to the test speed for each run, correlation compared to the IRI was improved for the mid-sized sedan and SUV, and about equal to the IRI for the full-sized van. Use of the actual travel speed in the Golden Car simulation helped match the frequency response of the index to the test vehicles in each run. How- ever, the correlation still compared temporal intensity of measured vehicle response in terms of RMS acceleration to spatial intensity of roughness in terms of inches per mile. GCARVV, which reports roughness in terms of input veloc- ity (e.g., inches per second) rather than slope (e.g., inches per mile), improved correlation compared to the IRI for the SUV and the full-sized van. RMS residual was reduced by 1 mg for the full-sized van compared to all GCARS variations and the IRI. However, GCARVV only improved correlation com- pared to the IRI for weighted RMS acceleration at the floor/ foot interface (rmsawzff) for the mid-sized sedan. Note that the three other discomfort quantities (rmsawzsbt, PVTsbt, and OVT) are influenced by the dynamic properties of the seat and driver, which are not included in the quarter-car model. Correlation of rmsawzff to GCARVV produced R2 values of 0.90, 0.87, and 0.88 for the mid-sized sedan, the SUV, and the full-sized van, respectively. GCRMSS49.7 and GCRMSSV exhibited reduced correla- tion to measured discomfort compared to their counterparts that used the average rectified slope value to accumulate a Discomfort mid-sized sedan SUV full-sized van Quantity RMS Resid. (g) R2 RMS Resid. (g) R2 RMS Resid. (g) R2 rmsawzff 0.0059 0.832 0.0065 0.838 0.0075 0.772 rmsawzsbt 0.0035 0.874 0.0044 0.891 0.0047 0.710 PVTsbt 0.0040 0.846 0.0053 0.849 0.0073 0.554 OVT 0.0057 0.842 0.0069 0.849 0.0105 0.576 Table 15. Correlation of vibration discomfort to RN, left wheel path. Discomfort mid-sized sedan SUV full-sized van Quantity RMS Resid. (g) R2 RMS Resid. (g) R2 RMS Resid. (g) R2 rmsawzff 0.0066 0.790 0.0063 0.852 0.0063 0.840 rmsawzsbt 0.0049 0.757 0.0046 0.881 0.0046 0.719 PVTsbt 0.0047 0.788 0.0050 0.868 0.0069 0.600 OVT 0.0066 0.787 0.0066 0.863 0.0097 0.634 Table 16. Correlation of vibration discomfort to RN, both wheel paths.
58 summary index (i.e., IRI and GCARSV, respectively.) Using RMS velocity in place of average rectified velocity for GCARVV improved correlation for the SUV, reduced correlation for the full-sized van, and caused mixed results for the mid-sized sedan. These results do not support the use of RMS in place of the average rectified value for estimating measured discom- fort using indices based on quarter-car suspension response. Modification of the IRI to use RMS sprung mass accel- eration (GCRMSA49.7) in place of average rectified suspen- sion stroke rate reduced correlation to measured discomfort for all three vehicles. This is because (1) use of 49.7 mi/hr (80 km/hr) as the simulation speed emphasized longer wave- lengths relative to the travel speeds used during the measure- ment, and (2) prediction of sprung mass acceleration further R-squared, Linear Fit of Discomfort to Roughness Index mid-sized sedan SUV full-sized van Roughness Index rmsawzff rmsawzsbt PVTsbt OVT rmsawzff rmsawzsbt PVTsbt OVT rmsawzff rmsawzsbt PVTsbt OVT IRI 0.796 0.866 0.891 0.897 0.778 0.820 0.827 0.821 0.798 0.699 0.618 0.643 GCARS15 0.887 0.876 0.857 0.855 0.847 0.873 0.834 0.807 0.785 0.653 0.526 0.547 GCARS20 0.888 0.885 0.868 0.867 0.851 0.879 0.842 0.815 0.804 0.663 0.537 0.562 GCARS25 0.892 0.905 0.891 0.890 0.859 0.891 0.857 0.832 0.822 0.686 0.559 0.585 GCARS30 0.886 0.916 0.909 0.908 0.858 0.894 0.866 0.845 0.831 0.706 0.582 0.607 GCARS35 0.874 0.915 0.916 0.917 0.850 0.888 0.868 0.851 0.832 0.716 0.599 0.625 GCARS40 0.853 0.904 0.914 0.917 0.831 0.870 0.860 0.848 0.826 0.715 0.609 0.635 GCARS45 0.824 0.886 0.904 0.910 0.805 0.845 0.845 0.836 0.813 0.707 0.615 0.641 GCARSV 0.867 0.906 0.911 0.911 0.840 0.880 0.862 0.842 0.829 0.714 0.599 0.624 GCARVV 0.901 0.833 0.875 0.895 0.870 0.845 0.880 0.874 0.879 0.812 0.756 0.772 GCRMSS49.7 0.763 0.846 0.844 0.849 0.757 0.808 0.789 0.802 0.738 0.691 0.574 0.593 GCRMSSV 0.784 0.866 0.840 0.834 0.793 0.849 0.800 0.799 0.725 0.654 0.505 0.522 GCRMSVV 0.888 0.879 0.882 0.894 0.889 0.894 0.883 0.894 0.833 0.795 0.674 0.685 GCRMSA 0.672 0.761 0.784 0.796 0.676 0.726 0.741 0.759 0.708 0.655 0.584 0.606 GCRMSAV 0.857 0.844 0.877 0.899 0.857 0.853 0.889 0.909 0.858 0.842 0.771 0.782 *Bolded numbers indicate the highest value in each column within each grouping. Table 17. Correlation of vibration discomfort to Golden Car indices, coefficients of determination. RMS Residual (mg), Linear Fit of Discomfort to Roughness Index mid-sized sedan SUV full-sized van Roughness Index rmsawzff rmsawzsbt PVTsbt OVT rmsawzff rmsawzsbt PVTsbt OVT rmsawzff rmsawzsbt PVTsbt OVT IRI 6.5 3.6 3.3 4.6 7.7 5.7 5.7 7.5 7.1 4.8 6.8 9.6 GCARS15 4.8 3.5 3.8 5.4 6.4 4.7 5.6 7.8 7.3 5.1 7.5 10.8 GCARS20 4.8 3.4 3.7 5.2 6.3 4.6 5.5 7.6 7.0 5.0 7.5 10.7 GCARS25 4.7 3.1 3.3 4.7 6.1 4.4 5.2 7.3 6.7 4.8 7.3 10.4 GCARS30 4.8 2.9 3.1 4.3 6.1 4.3 5.0 7.0 6.5 4.7 7.1 10.1 GCARS35 5.1 2.9 2.9 4.1 6.3 4.5 5.0 6.9 6.5 4.6 6.9 9.9 GCARS40 5.5 3.1 3.0 4.1 6.7 4.8 5.1 6.9 6.6 4.6 6.9 9.7 GCARS45 6.0 3.3 3.1 4.3 7.2 5.2 5.4 7.2 6.8 4.7 6.8 9.7 GCARSV 5.3 3.0 3.0 4.2 6.5 4.6 5.1 7.1 6.5 4.6 6.9 9.9 GCARVV 4.5 4.0 3.6 4.6 5.9 5.2 4.8 6.3 5.5 3.8 5.4 7.7 GCRMSS49.7 7.0 3.9 4.0 5.5 8.0 5.8 6.3 7.9 8.1 4.8 7.2 10.3 GCRMSSV 6.7 3.6 4.1 5.8 7.4 5.2 6.1 8.0 8.3 5.1 7.7 11.1 GCRMSVV 4.8 3.4 3.5 4.6 5.4 4.3 4.7 5.8 6.5 3.9 6.3 9.0 GCRMSA 8.2 4.8 4.7 6.4 9.3 7.0 7.0 8.7 8.5 5.1 7.1 10.1 GCRMSAV 5.4 3.9 3.5 4.5 6.2 5.1 4.6 5.4 6.0 3.4 5.2 7.5 Table 18. Correlation of vibration discomfort to Golden Car indices, RMS residuals.
59 shifted the emphasis on longer wavelength content relative to suspension response. GCRMSAV, which reports simulated sprung mass acceleration at the travel speed from each test run, improved correlation compared to the IRI for the SUV and the full-sized van. GCRMSAV also improved correlation to rmsawzff for the mid-sized sedan, but slightly reduced cor- relation to rmsawzsbt and PVTsbt. 4.3.5 Discussion Section 4.3.4 provided results for correlation of measured ride discomfort to several variations on the IRI, which are based on the Golden Car model. The IRI exhibited accept- able correlation to measured discomfort. This is because, in terms of wavelength, the response of the IRI overlaps a large portion of the range of interest, even when the speed is reduced to 25 mi/hr (40 km/hr). However, Tables 17 through 19 demonstrate that shifting the sensitivity of the Golden Car model toward shorter wavelengths improves the relevance of the resulting index relative to the IRI for vehicle responses experienced at lower travel speeds. Roughness index options with higher correlation are pos- sible by customizing the input parameters to better match each test vehicle. However, the resulting index for each vehicle may not be appropriate for the others. Further improvement is possible using models with more detail than the quarter-car model. For example, a five degree-of-freedom model includ- ing pitch and bounce of the vehicle body, vertical vibration of both axles, and seat-occupant dynamics predicted acceleration at the seat/buttock interface on the full-sized van with an R2 value of 0.94 and RMS residual of 2.2 mg. However, use of the full-sized van index on runs from the SUV reduced correlation to an R2 value of 0.78 and an increased RMS residual of 6.2 mg. The results of this experiment justify the use of a Golden Car index with a simulated speed below 49.7 mi/hr (80 km/hr) on low-speed roads. However, further adjustment to the Golden Car model by selecting a different output quantity or adjusting the component parameters would reduce its gener- ality. As described below, the sensitivity of Golden Car model uniformly covers the frequency range of interest for a broad range of vehicle types and vehicle responses of interest. In this regard, the Golden Car model should be regarded as a filter designed to pass features that excite vehicle dynamics response, and exclude features that do not. 188.8.131.52 Golden Car Parameters The parameter values used in the Golden Car model were selected to provide relevance to as much of the prevailing vehicle fleet as possible. To do this, the researchers that devel- oped the Golden Car model used a high value for the suspen- sionâs damping coefficient. This flattened out the peaks in the frequency response relative to a typical vehicle, which created a more uniform gain response and prevented the model from âtuning inâ to specific frequencies that affect only a subset of the vehicles on the road (Gillespie et al. 1980). Figure 77 provides an example. The figure compares the gain response of a quarter-car simulator in use at the time the IRI was developed to the gain response of the Golden Car model. The quarter-car simulator used parameters corresponding Reduction in RMS Residual (mg) Relative to IRI, Linear Fit of Discomfort to Roughness Index mid-sized sedan SUV full-sized van Roughness Index rmsawzff rmsawzsbt PVTsbt OVT rmsawzff rmsawzsbt PVTsbt OVT rmsawzff rmsawzsbt PVTsbt OVT GCARS15 1.7 0.1 â0.5 â0.9 1.3 0.9 0.1 â0.3 â0.2 â0.4 â0.8 â1.2 GCARS20 1.7 0.3 â0.3 â0.6 1.4 1.0 0.3 â0.1 0.1 â0.3 â0.7 â1.0 GCARS25 1.8 0.6 0.0 â0.2 1.6 1.3 0.5 0.2 0.4 â0.1 â0.5 â0.8 GCARS30 1.6 0.8 0.3 0.3 1.5 1.3 0.7 0.5 0.6 0.1 â0.3 â0.5 GCARS35 1.4 0.7 0.4 0.5 1.4 1.2 0.7 0.7 0.6 0.1 â0.2 â0.2 GCARS40 1.0 0.6 0.4 0.5 1.0 0.9 0.6 0.6 0.5 0.1 â0.1 â0.1 GCARS45 0.5 0.3 0.2 0.3 0.5 0.4 0.3 0.3 0.3 0.1 0.0 0.0 GCARSV 1.2 0.6 0.3 0.3 1.2 1.0 0.6 0.5 0.6 0.1 â0.2 â0.3 GCARVV 2.0 â0.4 â0.2 0.0 1.8 0.4 1.0 1.2 1.6 1.0 1.4 1.9 GCRMSS49.7 â0.5 â0.3 â0.7 â1.0 â0.4 â0.2 â0.6 â0.4 â1.0 â0.1 â0.4 â0.7 GCRMSSV â0.2 0.0 â0.7 â1.2 0.3 0.5 â0.4 â0.4 â1.2 â0.3 â0.9 â1.5 GCRMSVV 1.7 0.2 â0.1 â0.1 2.3 1.3 1.0 1.7 0.6 0.8 0.5 0.6 GCRMSA â1.7 â1.2 â1.4 â1.9 â1.6 â1.3 â1.3 â1.2 â1.4 â0.3 â0.3 â0.5 GCRMSAV 1.1 â0.3 â0.2 0.0 1.5 0.6 1.1 2.2 1.1 1.3 1.5 2.1 Table 19. Improvement in coefficient of determination relative to IRI, linear fit of discomfort to roughness.
60 to a 1968 Chevrolet Impala (Burchett et al. 1977). The reso- nance peaks for the simulated Impala are much more local- ized because of the lowerâand more representativeâvalue of damping coefficient used in the simulation. Likewise, measured frequency responses confirm that the three test vehicles used in this research have higher, more localized peaks (i.e., a lower damping ratio) than the Golden Car. An index with high, localized peaks in its gain response may provide a superior prediction of the response of a par- ticular vehicle. However, its relevance to vehicles or classes of vehicles with resonant responses at other frequencies is diminished. 184.108.40.206 Vehicle Response Types Although the IRI is based on suspension stroke rate pre- dicted by the Golden Car model, it was designed to relate to other dynamic responses to the extent possible. Potential outputs from the Golden Car model include vertical position, velocity, and acceleration of each mass; relative vertical position, velocity, and acceleration of the two masses to each other; and relative vertical position, velocity, and acceleration of the unsprung mass to the input received from the road profile. For example, the quarter-car model is often used early in the vehicle development process to examine design trade-offs between (1) sprung mass verti- cal acceleration, which relates to comfort; (2) tire deflection, which is the vertical position of the unsprung mass relative to the road and relates to road holding and dynamic load fluc- tuations experienced by the pavement; and (3) suspension stroke, which is the relative vertical position of the sprung and unsprung masses and relates to durability and packag- ing to accommodate suspension travel space (Dahlberg 1979; Chalasani 1986; Hrovat 1988). Figure 78 shows the frequency content of multiple responses from a quarter-car model. The response plots were calculated using parameters from the Golden Car model and white noise slope as a spectral model for the road profile. Note that, since the model is linear and response plots are provided in terms of temporal frequency (i.e., in Hz), the figure is valid for any (finite) speed (this does not account for tire envelopment). The plot for suspension stroke rate corresponds to the IRI. Its appearance is different than the usual representation, such as that in Figure 73, because both axes have linear scaling. With linear scaling, the contribution of response within each range of frequencies to the mean square of the overall response is proportional to the area under the curve for that range. Comparisons of the response plot for suspension stroke rate to the others shows that sprung mass acceleration and sus- pension stroke are more sensitive to low frequencies, and dynamic tire load and unsprung mass acceleration are more sensitive to high frequencies. In terms of wavelength, sprung mass acceleration and suspension stroke are more sensitive to longer wavelengths, and dynamic tire load and unsprung mass acceleration are more sensitive to shorter wavelengths. In this regard, an index based on suspension stroke rate is the response âin the middle,â which helps maximize its relevance to the other responses of interest to the extent possible for a single index. For the ride experiment performed in this research, exten- sion of GCRMSAV to include the discomfort weighting func- tion applied to the measured accelerations and, for response at the seat/buttock interface, a dynamic model of the seat and driver would have improved correlation to measured discom- fort. However, the resulting index would be less relevant to vehicle responses other than passenger acceleration. 220.127.116.11 Thresholds GCARVV is recommended as a scale for estimating the functional status of urban and low-speed roads. This option maintains the relevance of the underlying IRI algorithm to a broad range of vehicle types and to a broad range of vehicle responses. However, GCARVV produces roughness on an unfamiliar scale and requires reporting of both the index value and the speed used to produce it. (Note that the simu- lation speed is indicated by the subscript âV,âwhich is used generically here.) Field experience and further research are needed to establish thresholds for various applications. It is anticipated that, since GCARVV estimates temporal intensity of response (i.e., response per second, rather than response per time), threshold values may be less sensitive to speed. Establishment of threshold values will require a broader set of field measurements than those collected for this research for several reasons. First, the change in sensitivity of the index to changes in speed depends heavily on the properties of the road surface, particularly when roads with high long-wavelength content Figure 77. Quarter-car response gain, Golden Car and a 1968 Impala.
61 (i.e., wavy) and short-wavelength content (i.e., choppy) roads are compared (Perera and Kohn 2004, Karamihas 2012). Second, as speed changes, the relative importance of various vehicle response types changes (Karamihas 2012). For example, two studies of simulated sensitivity of passen- ger vibration to road roughness related roughness to speed differently because they each selected a different objective method of quantifying ride quality (Yu et al. 2006; Cantisani and Loprencipe 2010). MÃºcka (2017) addresses these issues in a thorough review of road roughness limits. The review showed that various studies quantified the changes in sen- sitivity of vehicles to changes in speed depending on test conditions and the primary vehicle response under examina- tion (e.g., passenger acceleration versus dynamic tire loads). Lastly, user expectations must be considered (Shafizadeh et al. 2002, Poister et al. 2003). 4.4 Results, Localized Roughness Figures 79â81 show values of MTV/rmsawz for the seat/but- tock interface for each test vehicle, and Figures 82â84 show values of RMQ/RMS weighted acceleration (rmqawz/rmsawz) at the seat/buttock interface for each test vehicle. For both measures, a ratio of 1.5 indicates the presence of transient vibration. Using MTV/rmsawz at the seat/buttock interface, 453 of the 497 runs included transient vibration. Using MTV/rmsawz at the floor/foot interface, 471 of the 497 runs included tran- sient vibration. On 21 of the 29 test sections, all passes by all of the vehicles included transient vibration for both vehicle/ human interfaces. For RMQ/rmsawz at the seat/buttock interface, 289 of the 497 runs included transient vibration. Of the 29 test sections, (1) 8 test sections excited transient vibration in all passes by all vehicles, (2) an additional ten test sections excited tran- sient vibration in at least half of the passes, and (3) only two test sections did not cause transient vibration in any of the vehicles. For RMQ/rmsawz at the floor/foot interface, 391 of the 497 runs included transient vibration. Of the 29 test sections, (1) 16 test sections excited transient vibration in all passes by all vehicles, (2) an additional eight test sections excited transient vibration in at least half of the passes, and (3) only two test sections did not cause transient vibration in any of the vehicles. Figures 79â84 demonstrate that, collectively, these test sec- tions include roughness that causes transient vibration. Per ISO 2631-1 and SAE J2834, the RMS vibration level over the entire section may underestimate user discomfort, and some measure of transient vibration is required. Similarly, repre- senting the functional performance, in terms of ride quality, of Figure 78. Golden Car model responses (adapted with permission from Gillespie 1992, p. 86).
62 Figure 79. Ratio of MTV to RMS seat/buttock vertical acceleration, mid-sized sedan. Figure 80. Ratio of MTV to RMS seat/buttock vertical acceleration, SUV. Figure 81. Ratio of MTV to RMS seat/buttock vertical acceleration, full-sized van.
63 Figure 82. Ratio of RMQ to RMS seat/buttock vertical acceleration, mid-sized sedan. Figure 83. Ratio of RMQ to RMS seat/buttock vertical acceleration, SUV. Figure 84. Ratio of RMQ to RMS seat/buttock vertical acceleration, full-sized van.
64 these test sections requires reporting a measure of localized roughness in addition to the average roughness level. Figures 85â87 show the relationship between MTV at the seat/buttock interface and peak localized roughness for the left wheel path for each test vehicle. The figures include a value of MTV for any run that included transient vibration (i.e., any run where the MTV was greater than 1.5 times the RMS acceleration level). In this case, âpeak localized rough- nessâ refers to the peak value in a roughness profile using a base length of 25 ft (7.62 m). For each value of MTV, a peak localized roughness value was paired with it that occurred within a half-second of travel time of the maximum transient acceleration value. Table 20 lists the coefficient of determination and RMS residual for linear correlation of MTV for vertical vibration at the seat/buttock interface to peak localized roughness using various values of base length. The row listed for a base length of 25 ft (7.62 m) corresponds to a linear fit on the data in Figures 85â87. For the mid-sized sedan, the best correlation occurs using base lengths of 20 ft (6.10 m) to 35 ft (10.67 m). For the SUV, the best correlation occurs using base lengths of 25 ft (7.62 m) and 30 ft (9.14 m). For the full-sized van, the best correlation occurs using base lengths of 20 ft (6.10 m) and 25 ft (7.62 m). Note that the RMS residuals listed in Table 20 for a 25-ft (7.62-m) base length are approximately 10 percent of the range of MTV for each vehicle. As such, the peak localized roughness values using a base length of 25 ft (7.62 m) are only an estimate of the severity of transient vibration. However, the roughness profile provides a reliable method of identify- ing locations where transient vibration is likely to occur in passing vehicles. Figure 85. MTV versus roughness profile peak value, mid-sized sedan. Figure 86. MTV versus roughness profile peak value, SUV.
65 For example, Figure 88 shows the RMS weighted accel- eration at the seat/buttock interface averaged over 1-second intervals for a test run on West Grand River (Section 23) at 26 mi/hr (42 km/hr) by the mid-sized sedan. The high response 145 ft (44 m) from the start of the section occurred at the trailing end of a crowned intersection. A protruding strip of concrete at the leading edge of a textured pedestrian crossing caused the response 420 ft (128 m) from the start of the section. The high response 545 ft (166 m) from the start of the section occurred at a distressed area of pavement Figure 87. MTV versus roughness profile peak value, full-sized van. in the left wheel path. Figure 89 shows the short-interval profile for the left wheel path measured in the same pass. Although the peak values in the roughness profile are not proportional to the peak values of RMS acceleration, the peaks do occur in the same locations. For this test section, all three of the areas of high response described above qualify as âtransientâ relative to the overall response. The roughness profile registers a high value in all three locations, both in terms of absolute magnitude and as a multiple of the overall IRI value. Base Length (ft) mid-sized sedan SUV full-sized van RMS Resid. R2 RMS Resid. R2 RMS Resid. R2 10 0.0088 0.842 0.0167 0.753 0.0115 0.744 15 0.0083 0.858 0.0157 0.781 0.0104 0.791 20 0.0083 0.860 0.0150 0.800 0.0099 0.807 25 0.0084 0.854 0.0145 0.814 0.0098 0.814 30 0.0081 0.866 0.0144 0.816 0.0106 0.781 35 0.0084 0.856 0.0149 0.804 0.0112 0.756 40 0.0085 0.852 0.0149 0.803 0.0115 0.744 45 0.0085 0.851 0.0152 0.794 0.0117 0.734 50 0.0086 0.849 0.0153 0.792 0.0117 0.732 Table 20. Correlation of peak localized roughness to transient vibration using MTV.
66 Figure 88. RMS weighted acceleration, pass over West Grand River. Figure 89. Short-interval roughness profile, test section on West Grand River.