1、Designation: E 1170 97 (Reapproved 2007)Standard Practices forSimulating Vehicular Response to Longitudinal Profiles ofTraveled Surfaces1This standard is issued under the fixed designation E 1170; the number immediately following the designation indicates the year oforiginal adoption or, in the case
2、 of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 These practices cover the calculation of vehicular re-sponse to longitudinal profiles of tr
3、aveled surface roughness.1.2 These practices utilize computer simulations to obtaintwo vehicle responses: (1) axle-body (sprung mass) motion or(2) body (sprung mass) acceleration, as a function of time ordistance.1.3 These practices present standard vehicle simulations(quarter, half, and full car) f
4、or use in the calculations.1.4 The values stated in SI units are to be regarded as thestandard.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health pr
5、actices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E 950 Test Method for Measuring the Longitudinal Profileof Traveled Surfaces with an Accelerometer EstablishedInertial Profiling Reference2.2 ISO Standard:2631 Guide for the Eva
6、luation of Human Exposure toWhole-Body Vibration33. Summary of Practices3.1 These practices use a measured profile (see Test MethodE 950) or a synthesized profile as part of a vehicle simulationto obtain vehicle response.3.2 The first practice for obtaining vehicle response usessimulation of a quart
7、er-car or half-car model. The output is theaccumulated relative motion between the sprung and unsprungvehicle masses, of the simulated vehicle, for a predetermineddistance. The units are accumulated relative motion per unit ofdistance traveled (m/km or in./mile). For example, the quarter-car simulat
8、ion is used when a Bureau of Public RoadsBPR/roadmeter is to be simulated, and the half-car model (orthe quarter car with the average of the left and right elevationprofile input) is used when a road meter is to be simulated.3.3 The second practice uses either a quarter-car, half-car, orfull-car sim
9、ulation to obtain vehicle body acceleration. Theacceleration history can be computed as a function of time ordistance, or both. One application of this practice is to use theacceleration history in a ride quality evaluation, such as theISO Guide 2631.3.4 For all calculations, a vehicle test speed is
10、 selected andmaintained throughout the calculation. Pertinent informationaffecting the results must be noted.4. Significance and Use4.1 These practices provide a means for evaluating traveledsurface-roughness characteristics directly from a measuredprofile. The calculated values represent vehicular
11、response totraveled surface roughness.4.2 These practices provide a means of calibrating response-type road-roughness measuring equipment.45. Apparatus5.1 ComputerThe computer is used to calculate accelera-tion and displacement of vehicle response to a traveled surfaceprofile, using a synthesized pr
12、ofile or a profile obtained inaccordance with Test Method E 950 as the input. Filtering shallbe provided to permit calculation, without attenuation, atfrequencies as small as 0.1 Hz at speeds of 15 to 90 Km/h (10to 55 mph). Computation may be analog or digital. Noisewithin the computer shall be no m
13、ore than one quarter of theintended resolution. It is recommended that a 16-bit or betterdigital computer be used.5.2 Data-Storage DeviceA data-storage device shall beprovided for the reading of profiles and the recording andlong-term storage of computed data. Profile data shall be scaled1These prac
14、tices are under the jurisdiction of ASTM Committee E17 on Vehicle- Pavement Systems and are the direct responsibility of Subcommittee E17.33 onMethodology for Analyzing Pavement Roughness.Current edition approved Dec. 1, 2007. Published January 2008. Originallyapproved in 1987. Last previous edition
15、 approved in 2006 as E 1170 97 (2006).2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from America
16、n National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.4Gillespie, T. D., Sayers, M. W., and Segel, L., “Calibration and Correlation ofResponse-Type Road Roughness Measuring Systems,” NCHRP Report 228, 1980.1Copyright ASTM International, 100 Barr Harb
17、or Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.to maintain resolution of 0.025 mm (0.001 in.) and to accom-modate the full range of amplitudes encountered during normalprofile-measuring operations. The device shall not contributeto the recorded data any noise amplitude larger
18、 than 0.025 mm(0.001 in.).5.3 Digital Profile RecordingsRoad-roughness profilesshall be obtained in accordance with Test Method E 950 orsynthesized. The profile must be recorded at intervals nogreater than one third of the wavelength required for accuraterepresentation of the traveled surface for th
19、e intended use ofthe data. For most applications a sample interval of 600 mm (2ft) will give a valid representation for all types of road surfacesexcept where the roughness is extremely localized and there-fore could be missed, in which case a sample interval of 150mm (6 in.) should be used. When mo
20、re than one path of atraveled surface is measured, the recorded profile data for thepaths shall be at the same longitudinal location along themeasured profiles. The recorded profile shall include all of thenoted field data described in the Procedure (Data Acquisition)and Report sections of Test Meth
21、od E 950. The length of theroad-roughness profile must be reported with the results;however, caution must be exercised to ensure that transients inthe simulation do not influence the results. It is recommendedthat at least 160 m (0.1 miles) of profile, preceding the testsection, plus the desired tes
22、t section be used as input insimulation to eliminate the effects of transients.6. Vehicle Simulation Programs6.1 These practices use one of four vehicle simulations:5aquarter car, a half car, a full car with four-wheel independentsuspension, and a full car with a solid rear axle. Althoughseveral met
23、hods for solving the differential equations areavailable, the Runge-Kutta is described in NCHRP Report228.4. The parametric models in Figs. 1-4 (such as the lumpedparameter model) and the coordinate system defined constitutethe standard practice. The analytic representation of the modeland the metho
24、ds of implementation need not be the same asoutlined in the appendix.6.1.1 Quarter-Car Simulation Model:6.1.1.1 The quarter car is modeled as shown in Fig. 1, withz1, as the vehicle-body (sprung mass) displacement, z2as thetire (unsprung mass) displacement, and the zpas the longitu-dinal profile.6.1
25、.1.2 The relative motion between the body and the axle,Z8, is defined as:Z8 5 z12 z2(1)The equation of motion for the quarter-car model is given inX1.1. The parameters used for the quarter-car model arenormalized by the body mass, M1. The other vehicle param-eters are: the vehicle spring constant, K
26、1; the damper value, C1;the axle-wheel mass, M2; the tire stiffness, K2; and the tiredamping constant, C2. Values for these parameters are given inTable 1.6.2 Half-Car Simulation ModelThe half-car model isconstructed by using one half of a rigid vehicle and is made upof two quarter cars at the right
27、 and left tracks. The model forthe half car is shown in Fig. 2, and the associated parametersare given in Table 2. The equation of motion is given in X1.2.The relative motion between the body and the axle, Z8,is5Wambold, J. C., Henry, J. J., and Yeh, E. C., “Methodology for AnalyzingPavement Conditi
28、on Data” (Volume I and II, Final Report), Report No. FHWA/RD-83/094 and FHWA/RD-83/095, Federal Highway Administration, January 1984.FIG. 1 Quarter-Car Simulation ModelFIG. 2 Half-Car ModelFIG. 3 Full-Car With Independent SuspensionE 1170 97 (2007)2defined as Z8 = z312 (z1+ z2). The mass of the axle
29、, Maandthe moment of inertia of the axle, Iamust be set to zero whenthe half car being modeled has an independent wheel suspen-sion. Ibrepresents the moment of inertia of the car body and brepresents the wheel track.6.3 Full-Car Simulation Model with Four-Wheel Indepen-dent Suspension:6.3.1 This mod
30、el is an expansion of the half-car simulationmodel. Two more wheel and pitch motions are added to makeit a seven-degree-of-freedom model. This model is shown inFig. 3 and the vehicle parameters are given in Table 3.6.3.2 The equation of motion is developed similarly to thatin the half-car model and
31、the tire damping is again taken aszero to simplify the equations. The equations are given in X1.3.6.4 Full-Car Simulation Model with a Rear Axle:6.4.1 This model is a modification of the full-car model tochange the rear suspension to a solid axle. The model is shownin Fig. 4. Again, the tire damping
32、 is taken as zero to simplifythe equations. The equations are given in X1.4.6.4.2 The values of the parameters Ix, Iw, and MFare thesame as in the model for the full car with independentsuspension, except that the additional parameter, axle momentof inertia, Iaxis used.7. Example Applications7.1 Dis
33、placement per Length of Travel:7.1.1 Inches per MileAn improved method of computinginches per mile (IPM) has been proposed by Gillespie, Sayers,and Segel.4Quantization, as used in current road meters, doesnot truly reflect the axle-body movement. Therefore, IPM isdefined as:IPM 5(i 5 1N| Z8i2 Z8i11|
34、/distance (2)where:Z8i= relative maximum or minimum value of the axle-body movement.7.1.2 International Roughness Index (IRI)The IRI comesfrom the 1982 World Bank International Road RoughnessExperiment in Brazil. The IRI is the measurement of thedisplacement of the sprung mass to unsprung mass of a
35、quarterFIG. 4 Full-Car Model With Solid Rear AxleTABLE 1 Quarter-Car Vehicle Physical ConstantsSimulated VehicleParameterBPRRoughometerRide Meter-VehicleMountedRide Meter-TrailerIRIK1/M1129 s263 s2125 s263.3K2/M1643 s2653 s2622 s2653M2/M10.16 0.15 0.26 0.15C1/M13.9 s16.0 s18.0 s16.0C2/M100 00TABLE 2
36、 Half-Car Vehicle Physical ConstantsAParameter Ride-Meter Vehicle MountedRide-MeterTrailerK1/MH32 s257.5 s2K2/MH326 s2311 s2M2/MH0.075 0.125C1/MH3 s14 s1C2/MH00Ma/MH0.30 0.50(for model with rear axle)0(for model with independent rear suspension)IH/(MHb2)Ia/IH0.420.360.420.6(for model with rear axle)
37、0(for model with independent rear suspension)b 1.8 m 1.8 mAThe values apply to the rear half of a vehicle.E 1170 97 (2007)3car model and is reported in units of displacement per length oftravel. The method uses a standard quarter car modelsresponse to longitudinal profile measurements.7.1.3 These IP
38、M values are calculated on a continuous basisrather than in increments, and are considerably different fromthose obtained by current road meters.7.2 Ride Quality Analysis:7.2.1 The most commonly used standard is ISO 2631, thathas a tabular format and uses human-body acceleration topredict the exposu
39、re time for human discomfort or fatigue. ISO2631 can be converted to an index system by calculating thetime-to-discomfort for every frequency interval from 1 Hz to80 Hz. For ISO 2631, the usual input to the program isvehicle-body (sprung mass) acceleration. The analysis uses aFast Fourier Transform
40、(FFT) to obtain the space frequencyspectrum of the acceleration history. The selected vehiclespecifications and speed produce the vehicle-body accelerationspectrum. The seat is considered as having negligible effect onthe human-body acceleration in the range of 1 Hz to 80 Hz.47.2.2 Ride Number (RN)D
41、uring the 1980s the ride num-ber concept for estimating pavement ride quality from surfaceprofile measurements was developed in a National CooperativeHighway research project. Various papers have compared theperformance of ride number transforms and found it to besuperior to other ride quality trans
42、forms, producing estimatesof pavement ride quality with the highest correlation to themeasured subjective ride quality and with he lowest Standarderror.7.2.3 After the acceleration frequency spectrum is calcu-lated, the model in ISO 2631 is applied. This model determinesthe exposure time of reduced-
43、comfort boundary or the fatigueof a human body from the frequency spectrum of the seatvertical acceleration (Fig. 5). The details for calculating theexposure times for reduced comfort or fatigue are given inNCHRP Report 228.4An alternative for calculating a rideindex, developed at the University of
44、Virginia,6is also pre-sented in NCHRP Report 228.48. Calibration8.1 If a digital analysis is used, calibration is required whenthe system is installed. If an analog computer is used, thesystem shall be calibrated on a periodic basis. At present, nostandard road profile is available for such a calibr
45、ation. It issuggested that each agency adopt a range of profile records foruse in calibrating its complete system.9. Report9.1 Report the following information for each practice:9.1.1 Data from profiles obtained in accordance with TestMethod E 950 including date, the time of day of the measure-ment,
46、 or the date of the synthesized profile,9.1.2 Vehicle simulation program used,9.1.3 Speed of simulations,9.1.4 Vehicle-parameter values used if other than thosespecified in these practices, and9.1.5 Results of the analysis.6Richards, L. G., Jacobson, I. D., and Pepler, R. D., “Ride Quality Models fo
47、rDiverse Transportation Systems,” Transportation Research Record 774 (1980), pp.3945.TABLE 3 Full-Car Vehicle Physical ConstantsParameter Value Parameter ValueK1/MF16 s2Ix/MFb20.14K2/MF163 s2Iy/MFL2 A0.19M2/MF0.038 b 1.8 mC1/MF1.5 s1L/bA1.44C2/MF0 h/bA0.5Iax/MFb2with axle 0.022without axle 0AThe whe
48、el base is L, and the body height (center of gravity (cg) abovesuspension) is h.NOTE 1Vertical (az) acceleration limits as a function of exposure timeand frequency (center frequency of a third-octave band): “fatigue-decreased proficiency boundary.” This graph was taken from ISO 2631.FIG. 5 Model for
49、 Ride Quality AnalysisE 1170 97 (2007)4APPENDIX(Nonmandatory Information)X1. EQUATIONS OF MOTION FOR VEHICLE RESPONSES TO LONGITUDINAL PROFILESX1.1 Quarter-Car ModelThe equation of motion for thismodel can be represented as follows.z10010 z10z201 z2C2M2w1=K1M1K1M1C1M1C1M1 w1+C1C2M1M2 zpw2K1M2(K1 + K2)M2C1M2(C1 + C2)M2 w2C1C2 C2 2 + K2M2M22where two new variables are introduced.w1=z1, andw2=z2C2M2 zp, so thatw1=z1, andw2=z2C2M2 zp.X1.1.1 The relative motion between body and axle (Z8)isdefined as:Z8 5 z12 z2(X1.1)X1.2 H
