1、Designation: E2034 99 (Reapproved 2012)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 stimulations 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.2. Referenced Documents2.1 ASTM Standards:2E867 Terminology Relating to Vehicle-Pavement SystemsE950 Test Method for Measuring the Longitud
6、inal Profileof Traveled Surfaces with an Accelerometer EstablishedInertial Profiling Reference2.2 ISO Standard:32631 Guide for the Evaluation of Human Exposure toWhole-Body Vibration3. Terminology3.1 See Terminology E867.4. Summary of Practice4.1 These practices use a measured profile (see Test Meth
7、odE950) 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.One application of this pr
8、actice 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 simulation model toobtain tir
9、e/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 informationaffecting the results m
10、ust 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 synthesizedprofile or a profile obtained
11、in accordance with Test MethodE950 as the input. It is recommended that a 16 or more-bitdigital computer be used.6.2 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 scaledto maintain
12、resolution of 0.025 mm (0.001 in.) and to accom-modate the full range of amplitudes encountered during normalprofile-measuring operations. The devices shall not contributeto the recorded data any noise amplitude larger than 0.025 mm(0.001 in.)1These practices are under the jurisdiction of ASTM Commi
13、ttee E17 onVehicle- Pavement Systems and are the direct responsibility of Subcommittee E17.33 onMethodology for Analyzing Pavement Roughness.Current edition approved June 1, 2012. Published June 2012. Orignally approvedin 1999. Last previous edition approved in 2007 as E2304 99 (2007). DOI:10.1520/E
14、2034-99R12.2For 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 American National Standards Instit
15、ute (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 for Heavy Trucks,” Transportation ResearchRecord 1215, 1989, pp. 137150.1Copyright ASTM International, 100 Barr Harb
16、or Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.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 atintervals no greater than one third of the wavelength r
17、equiredfor 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 traveledsurface is measured, the recorded profile data f
18、or 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 of TestMethod E950. The length of the road-roughnes
19、s profile mustbe reported with the results; however, caution must be exer-cised to ensure that transients in the simulation do not influencethe results. It is recommended that at least 160 m (0.1 miles) ofprofile, preceding the test section, plus the desired test sectionbe used as input in simulatio
20、n 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 themathematical models, the following was assumed:7.1.1 Co
21、nstant 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 ofdifferential equations are available, the fourth-orde
22、r Runge-Kutta method is employed in Footnote 4. The parametricmodels, shown in Figs. 1- 3 constitute the standard practice.The analytic representations of the models and the methods ofimplementation need not be the same as outlined in AppendixX1.7.2 Quarter Truck Simulation ModelThe quarter truckmod
23、el is shown in Fig. 1, with q1as the truck-body (sprungmass) displacement, q2as the tire (unsprung mass) displace-ment, and u as the road profile. The state variable equations ofmotion are given in X1.1. Two sets of model parameters, onefor front axle and the other for rear axle, are given in Table
24、1.Front axle parameters should be used in ride comfort studiesand rear axle parameters in pavement loading studies. Thenumerical values of the model parameters represent a fullyloaded single unit, single-axle truck.7.3 Half-Single Unit TruckThe half-single unit truckmodel is shown in Fig. 2. This mo
25、del 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 Table 2. The numerical values of themodel parameters represent a fully
26、 loaded single unit single-axle truck.7.4 Half-Tractor Semitrailer ModelThe half-tractor semi-trailer model is shown in Fig. 3. This model expands thehalf-single unit truck model to include tandem axles and asemitrailer. The fifth wheel connecting the tractor to thesemitrailer is modeled with a stif
27、f 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 parameters represent a fully loaded 18-wheel tractorsemitrailer with the payload evenly distributed.TABLE 1 Quarter-Truck Model ParametersSy
28、mbolSingle 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 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.
29、 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 kg (36.9 lb s2/in.)IyOne half sprung mass pitch moment 46249.0 Nms2(410876.4 lb s2/in.)Mu1One half front axle unsprung mass 279.7kg (1.6 lb s2/in
30、.)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 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
31、 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 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 Q
32、uarter-Truck ModelE2034 99 (2012)28. 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 thesimulation,9.1.2 Truck simulation model used,9.1.3 Speed of truck i
33、n 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 (2012)3APPENDIX(Nonmandatory Information)X1. EQUATIONS OF MOTION FOR TRUCK RESPONSES TO LONGI
34、TUDINAL PROFILESX1.1 Quarter Truck ModelThe state variable equationsfor this model are as follows:q15 q3(X1.1)q25 q4q35 1/Ms! Cq42 q3! 1 K q22 q1!#q45 1/Mu! Cq32 q4! 1 K q12 q2! 1 K1u 2 q2!#where:q1= vertical displacement of sprung mass,q2= vertical displacement of unsprung mass,q3= vertical velocit
35、y 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 q8q5 5 1/Ms! $C1q72 q52 Aq6! 1 C2q82 q51 Bq6!1 K1q32 q12 Aq2! 1 K2q42 q11 Bq2!%q65 1/Iy! $C1A q72 q5
36、2 Aq6! 1 C2B q82 q51 Bq6!1 K1A q32 q12 Aq2! 1 K2B q42 q11 Bq2!%q75 1/Mu1! $C1q52 q71 Aq6! 1 K1q12 q31 Aq2! 1 Kt1u12 q3!%q85 1/Mu2! $C2q52 q82 Bq6! 1 K2q12 q41 Bq2! 1 Kt2u22 q4!%where:q1= vertical displacement of sprung mass,q2= pitch angular displacement of sprung mass,q3= vertical displacement of f
37、ront 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 of road under front wheel, andu2= elevation
38、 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 q101 A1q11! 1 C2q151 q162 2 q101 B11 B2! q11#1 C5q122 q101 B5q111 A2q13! 1 K1q52 q12
39、 A1q2!1 K2q61 q72 2q11 B11 B2! q2# 1 K5q32 q11 B5q21 A2q4!%q115 21/Iy1! $C1A1q102 q141 A1q11! 1 K1A1q52 q12 Aq2!1 C2B1q151 B2q162 B11 B2! q101 B121 B22! q11#1 C5B5q122 q101 B5q111 A2q13! 1 K2B1q61 B2q72 B1TABLE 3 Model ParametersSymbol Description Numerical ValueMs1One half tractor sprung mass 1818.
40、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 axle) 524.5 kg (3.0 lb s2/in.)K1Tractor front suspension spring constant 198251.1 N/m
41、 (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. lb s/in.)Kt1Tractor front tire spring constant 788100.5 N/m (4500. lb/in.)Kt2Tractor
42、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 tractor sprung mass center of gravity 3.21 m (126.3 in.)B2Horizontal distance from t
43、ractor 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 mass 14283.2 kg (81.7 lb s2/in)Iy2One half trailer sprung mass pitch moment 10235.0 Nm s
44、2(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/m (15 lb s/in.)Kt3Trailer tire spring constant 1751334.5 N/m (10000 lb/in.)A2Horizon
45、tal 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 distance from trailer trailing tandem axle to trailer sprung mass center of gravity
46、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 (2012)41 B2! q11 B121 B22! q2#1 K5B5q32 q11 B5q21 A2q4!%q125 1/MS2! $C3q171 q182 2q121 B31 B4! q13# 1 C5q102 q122 B5q112 A2q13!1 K3q81 q92 2q31 B31 B4! q4
47、# 1 K5q12 q32 B5q22 A2q4!%q135 21/Iy2! $C3B3q171 B4q182 B31 B4! q121 B321 B42! q13!1 C5A2q122 q101 B5q11 A2q13!1 K3B3q81 B4q92 B31 B4!q31 B321 B42!q4!1 K5A2q12 q31 B5q21 A2q4!%q145 1/Mu1! $C1q102 q141 A1q11! 1 K1q12 q51 A1q2! 1 Kt1u12 q5!%q155 1/Mu2! $C2q102 q152 B1q11! 1 K2q12 q62 B1q2! 1 Kt2u22 q6
48、!%q165 1/Mu2! $C2q102 q162 B2q11! 1 K2q12 q72 B2q2! 1 Kt2u32 q7!%q175 1/Mu3! $C3q122 q172 B3q13! 1 K3q32 q82 B3q4! 1 Kt3u42 q8!%q185 1/Mu3! $C3q122 q182 B4q13! 1 K3q32 q92 B4q4! 1 Kt3u52 q9!%where:q1= vertical displacement of tractor sprung mass,q2= pitch angular displacement of tractor sprung mass,
49、q3= vertical displacement of trailer sprung mass,q4= pitch angular displacement of trailer sprung mass,q5= vertical displacement of tractor front unsprung mass,q6= vertical displacement of tractor leading tandem axle,q7= vertical displacement of tractor trailing tandem axle,q8= vertical displacement of trailer leading tandem axle,q9= vertical displacement of trailer trailing tandem axle,q10= vertical velocity of tractor sprung mass,q11= pitch angular veloci
