1、Designation: E2034 99 (Reapproved 2017)Standard Practices forSimulating Truck Response to Longitudinal Profiles ofVehicular Traveled Surfaces1This standard is issued under the fixed designation E2034; the number immediately following the designation indicates the year oforiginal adoption or, in the
2、case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 These practices cover the calculation of truck responseto longitudinal profiles of trave
3、led surface roughness.1.2 These practices utilize computer simulations to obtaintwo truck responses including: sprung and unsprung massvertical displacement, velocity and acceleration, and sprungmass pitch angular displacement, velocity, and acceleration.1.3 These practices present standard truck si
4、mulations(quarter truck, half-single unit truck, and half-tractor semi-trailer) for 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 theresponsib
5、ility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.1.6 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in
6、the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Referenced Documents2.1 ASTM Standards:2E867 Terminology Relating to Vehicle-Pavement SystemsE950 Test Method for
7、 Measuring the Longitudinal Profile ofTraveled Surfaces with an Accelerometer EstablishedInertial Profiling Reference2.2 ISO Standard:3ISO 2631 Guide for the Evaluation of Human Exposure toWhole-Body Vibration3. Terminology3.1 See Terminology E867.4. Summary of Practice4.1 These practices use a meas
8、ured profile (see Test MethodE950) or a synthesized profile as a part of a computersimulation to obtain truck response.4.2 The first practice uses a standard truck simulation toobtain truck sprung mass vertical acceleration. The accelera-tion history can be computed as a function of time or distance
9、.One application of this practice is to use the accelerationhistory in ride quality evaluation, such as the ISO Guide 2631.Another application is to use the sprung mass vertical displace-ment history as input to a suspended seat model in ride qualityevaluation.4.3 The second practice uses a truck si
10、mulation model toobtain tire/pavement vertical forces as a function of time ordistance. One application of this practice is to use the tire/pavement history in pavement loading evaluation.44.4 For all calculations, a truck speed is selected andmaintained throughout the calculation. Pertinent informa
11、tionaffecting the results must be noted.5. Significance and Use5.1 These practices provide a means for evaluating truckride quality and pavement loading exerted by truck tires.6. Apparatus6.1 ComputerThe computer is used to calculate truckresponse to a traveled surface profile using a synthesizedpro
12、file or a profile obtained in accordance with Test Method1These practices are under the jurisdiction of ASTM Committee E17 onVehicle- Pavement Systems and are the direct responsibility of Subcommittee E17.33 onMethodology for Analyzing Pavement Roughness.Current edition approved July 1, 2017. Publis
13、hed July 2017. Orignally approvedin 1999. Last previous edition approved in 2012 as E2304 99 (2012). DOI:10.1520/E2034-99R17.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information,
14、refer to the standards Document Summary page onthe ASTM website.3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.4Todd, K. B., and Kulakowski, B. T., “Simple Computer Models for PredictingRide Quality and Pavement Loading
15、for Heavy Trucks,” Transportation ResearchRecord, Vol 1215, 1989, pp. 137150.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standard
16、ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1E950 as the input. It is recommended that a 16- or more-bitdigital computer be used.6.2 Data
17、 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 scaledto maintain resolution of 0.025 mm (0.001 in.) and to accom-modate the full range of amplitudes encountered during normalprofile-meas
18、uring operations. The devices shall not contributeto the recorded data any noise amplitude larger than 0.025 mm(0.001 in.)6.3 Simulation InputDigital profile recordings of road-roughness profiles shall be obtained in accordance with TestMethod E950 or synthesized. The profile must be recorded atinte
19、rvals no greater than one-third of the wavelength requiredfor accurate representation of the traveled surface for theintended use of the data. For most applications, a sampleinterval of 0.15 m (0.5 ft) will give a valid representation for alltypes of road surfaces. When more than one path of a trave
20、ledsurface is measured, the recorded profile data for the pathsshall be at the same longitudinal location along the measuredprofiles to avoid phase shift between the paths. The recordedprofile shall include all of the noted field data described in theProcedure (Data Acquisition) and Report sections
21、of TestMethod E950. The length of the road roughness profile must bereported with the results; however, caution must be exercisedto ensure that transients in the simulation do not influence theresults. It is recommended that at least 160 m (0.1 miles) ofprofile, preceding the test section, plus the
22、desired test sectionbe used as input in simulation to eliminate the effects oftransients.7. Truck Simulation Programs7.1 These practices use one of the three truck simulationmodels described in Footnote 4: a quarter truck, a half-singleunit truck, and a half-tractor semitrailer. To develop themathem
23、atical models, the following was assumed:7.1.1 Constant truck velocity,7.1.2 No body or axle roll,7.1.3 Rigid truck bodies,7.1.4 Linear suspension and tire characteristics,7.1.5 Point tire to road contact, and7.1.6 Small truck pitch angles.7.1.7 Although several methods for numerical solution ofdiff
24、erential equations are available, the fourth-order Runge-Kutta method is employed in Footnote 4. The parametricmodels, shown in Fig. 1, Fig. 2, and Fig. 3, constitute thestandard practice. The analytic representations of the modelsand the methods of implementation need not be the same asoutlined in
25、Appendix X1.7.2 Quarter-Truck Simulation ModelThe quarter-truckmodel is shown in Fig. 1, with q1as the truck-body (sprungmass) displacement, q2as the tire (unsprung mass)displacement, and u as the road profile. The state variableequations of motion are given in X1.1. Two sets of modelparameters, one
26、 for front axle and the other for rear axle, aregiven in Table 1. Front axle parameters should be used in ridecomfort studies and rear axle parameters in pavement loadingstudies. The numerical values of the model parameters repre-sent a fully loaded single unit, single-axle truck.7.3 Half-Single Uni
27、t TruckThe half-single unit truckmodel is shown in Fig. 2. This model includes both front andrear axles, resulting in both a pitch and a heave mode of thetruck motion being incorporated in the model. The statevariable equations are given in X1.2, and the associated modelparameters are listed in Tabl
28、e 2. The numerical values of themodel parameters represent a fully loaded single unit single-axle truck.TABLE 1 Quarter-Truck Model ParametersSymbolSingle Unit TruckFront AxleSingle Unit TruckRear AxleMs2447.5 kg (14.0 lb s2/in.) 4003.5 kg (22.9036 lb s2/in.)Mu279.7 kg (1.6 lb s2/in.) 524.5 kg (3.0
29、lb s2/in.)K 198251.1 N/m (1132. lb/in.) 1138367.4 N/m (6500. lb/in.)C 2627.0 Ns/m (15. lb s/in.) 2627.0 Ns/m (15. lb s/in.)K1788100.5 N/m (4500. lb/in.) 875667.3 N/m (5000. lb/in.)TABLE 2 Half-Single Unit Truck Model ParametersSymbol Description Numerical ValueMsOne-half vehicle sprung mass 6451.0 k
30、g (36.9 lb s2/in.)IyOne-half sprung mass pitch moment 46249.0 Nms2(410876.4lb s2/in.)Mu1One-half front axle unsprung mass 279.7kg (1.6 lb s2/in.)Mu2One-half rear axle unsprung mass 524.5kg (3.0 lb s2/in.)K1Front suspension spring constant 198251.1 N/m (1132. lb/in.)K2Rear suspension spring constant
31、1138367.4 N/m (6500. lb/in.)C1Front suspension damping constant 2627.0 Ns/m (15.lb s/in.)C2Rear suspension damping constant 2627.0 Ns/m (15. lb s/in.)Kt1Front tire spring constant 788100.5 N/m (4500. lb/in.)Kt2Rear tire spring constant 875667.3 N/m (5000. lb/in.)A Horizontal distance from front axle
32、 tosprung mass center of gravity3.79 m (149.2 in.)B Horizontal distance from rear axle tosprung mass center of gravity2.31 m (90.9 in.)FIG. 1 Quarter-Truck ModelE2034 99 (2017)27.4 Half-Tractor Semitrailer ModelThe half-tractor semi-trailer model is shown in Fig. 3. This model expands thehalf-single
33、 unit truck model to include tandem axles and asemitrailer. The fifth wheel connecting the tractor to thesemitrailer is modeled with a stiff spring and damper. The statevariable equations are given in X1.3, and the associated modelparameters are listed in Table 3. The numerical values of themodel pa
34、rameters represent a fully loaded 18-wheel tractorsemitrailer with the payload evenly distributed.8. Calibration8.1 There is no calibration involved in the use of thesepractices.9. Report9.1 Report the following information for this practice:9.1.1 Description of the input profile data used in thesim
35、ulation,9.1.2 Truck simulation model used,9.1.3 Speed of truck in simulations,9.1.4 Truck parameter values used if other than thosespecified in these practices, and9.1.5 Results of the analysis.FIG. 2 Half-Single Unit Truck ModelFIG. 3 Half-Tractor Trailer ModelE2034 99 (2017)3APPENDIX(Nonmandatory
36、Information)X1. EQUATIONS OF MOTION FOR TRUCK RESPONSES TO LONGITUDINAL PROFILESX1.1 Quarter-Truck ModelThe state variable equationsfor this model are as follows:q15 q3(X1.1)q25 q4q35 1/Ms! Cq42 q3!1K q22 q1!#q45 1/Mu! Cq32 q4!1K q12 q2!1K1u 2 q2!#where:q1= vertical displacement of sprung mass,q2= v
37、ertical displacement of unsprung mass,q3= vertical velocity of sprung mass,q4= vertical velocity of unsprung mass, andu = road elevation profile.X1.2 Half-Single Unit TruckThe state variable equationsfor this model are as follows:q15 q5(X1.2)q25 q6q35 q7q45 q8q 5 5 1/Ms! $C1q72 q52 Aq6! 1 C2q82 q51B
38、q6!$ 1K1q32 q12 Aq2!1K2q42 q11Bq2!%q65 1/Iy! $C1A q72 q52 Aq6! 1 C2B q82 q51Bq6!$ 1K1A q32 q12 Aq2!1K2B q42 q11Bq2!%q75 1/Mu1! $C1q52 q71Aq6!1K1q12 q31Aq2!1Kt1u12 q3!%q85 1/Mu2! $C2q52 q82 Bq6!1K2q12 q41Bq2!1Kt2u22 q4!%where:q1= vertical displacement of sprung mass,q2= pitch angular displacement of
39、sprung mass,q3= vertical displacement of front unsprung mass,q4= vertical displacement of rear unsprung mass,q5= vertical velocity of sprung mass,q6= pitch angular velocity of sprung mass,q7= vertical velocity of front unsprung mass,q8= vertical velocity of rear unsprung mass,u1= elevation profile o
40、f road under front wheel, andu2= elevation profile of road under rear wheel.X1.3 Half-Tractor Semitrailer ModelThe state variableequations for this model are as follows:q15 q10q45 q13q75 q16(X1.3)q25 q11q55 q14q85 q17q35 q12q65 q15q95 q18q105 1/MS1! $C1q142 q101A1q11! 1 C2q151q162 2 q101B1TABLE 3 Mo
41、del ParametersSymbol Description Numerical ValueMs1One-half tractor sprung mass 1818.2 kg (10.4 lb s/2/in.)Iy1One-half tractor sprung mass pitch moment 22655.4 Nm s2(200490. lb s2in.)Mu1One-half front axle unsprung mass 279.7 kg (1.6 lb s2/in.)Mu2One-half tractor rear tandem axle unsprung mass (per
42、axle) 524.5 kg (3.0 lb s2/in.)K1Tractor front suspension spring constant 198251.1 N/m (1132. lb/in.)K2Tractor rear suspension spring constant 1260960.8 N/m (7200. lb/in.)C1Tractor front suspension damping constant 2627.0 Ns/m (15. lb s/in.)C2Tractor rear suspension damping constant 2627.0 Ns/m (15.
43、lb s/in.)Kt1Tractor front tire spring constant 788100.5 N/m (4500. lb/in.)Kt2Tractor rear tire spring constant 1576201.1 N/m (9000. lb/in.)A1Horizontal distance from tractor front axle to tractor sprung mass center of gravity 1.53 m (60.1 in.)B1Horizontal distance from tractor leading tandem axle to
44、 tractor sprung mass center of gravity 3.21 m (126.3 in.)B2Horizontal distance from tractor trailing tandem axle to tractor sprung mass center of gravity 4.51 m (177.4 in.)B5Horizontal distance from fifth wheel to tractor sprung mass center of gravity 3.01 m (188.7 in.)Ms2One-half trailer sprung mas
45、s 14283.2 kg (81.7 lb s2/in)Iy2One-half trailer sprung mass pitch moment 10235.0 Nm s2(90575.5 lb s2/in.)Mu3One-half trailer tandem axle unsprung mass (per axle) 58071.3 kg (1.9 lb s2/in.)K3Trailer suspension spring constant 1313500.9 N/m (7500. lb/in.)C3Trailer suspension damping constant 2627.0 Ns
46、/m (15 lb s/in.)Kt3Trailer tire spring constant 1751334.5 N/m (10000 lb/in.)A2Horizontal distance from fifth wheel to trailer sprung mass center of gravity 5.98 m (235.6 in.)B3Horizontal distance from trailer leading tandem axle to trailer sprung mass center of gravity 5.60 m (220.4 in.)B4Horizontal
47、 distance from trailer trailing tandem axle to trailer sprung mass center of gravity 6.82 m (268.4 in.)C5Fifth wheel damping constant 175133.5 Ns/m (1000 lb s/in.)K5Fifth wheel spring constant 17513345 N/m (100000. lb/in.)E2034 99 (2017)41B2! q11#1C5q122 q101B5q111A2q13!1K1q52 q12 A1q2!$ 1K2q61q72 2
48、q11B11B2! q2#1K5q32 q11B5q21A2q4!%q115 21/Iy1! $C1A1q102 q141A1q11! 1 K1A1q52 q12 Aq2!1C2B1q151B2q162 B11B2! q101B121B22! q11#1C5B5q122 q101B5q111A2q13!1K2B1q61B2q72 B11B2! q11B121B22! q2#$ 1K5B5q32 q11B5q21A2q4!%q125 1/MS2! $C3q171q182 2q121B31B4! q13# 1 C5q102 q122 B5q112 A2q13!$ 1K3q81q92 2q31B31
49、B4! q4#1K5q12 q32 B5q22 A2q4!%q135 21/Iy2! $C3B3q171B4q182 B31B4! q121B321B42! q13!1C5A2q122 q101B5q11A2q13!1K3B3q81B4q92 B31B4!q31B321B42!q4!$ 1K5A2q12 q31B5q21A2q4!%q145 1/Mu1! $C1q102 q141A1q11!1K1q12 q51A1q2!1Kt1u12 q5!%q155 1/Mu2! $C2q102 q152 B1q11!1K2q12 q62 B1q2!1Kt2u22 q6!%q165 1/Mu2! $C2q102 q162 B2q11!1K2q12 q72 B2q2!1Kt2u32 q7!%q175 1/Mu3! $C3q122 q172 B3q13!1K3q32 q82 B3q4!1Kt3u42 q8!%q185 1/Mu3! $C3q122 q182 B4q13!1K3q32 q92 B4q4!1Kt3u52 q9!%w
