1、 6$(7HFKQLFDO6WDQGDUGV%RDUG5XOHVSURYLGHWKDW7KLVUHSRUWLVSXEOLVKHGE6$(WRDGYDQFHWKHVWDWHRIWHFKQLFDO and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising tKHUHIURPLVWKHVROHUHVSRQVL
2、ELOLWRIWKHXVHU SAE reviews each technical report at least every five years at which time it may be revised, reaffirmed, stabilized, or cancelled. SAE invites your written comments and suggestions. Copyright 2014 SAE International All rights reserved. No part of this publication may be reproduced, st
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4、0 Email: CustomerServicesae.org SAE WEB ADDRESS: http:/www.sae.org SAE values your input. To provide feedback on this Technical Report, please visit http:/www.sae.org/technical/standards/J2812_201402 SURFACE VEHICLE RECOMMENDED PRACTICE J2812 FEB2014 Issued 2014-02 Road Load Tire Model Validation Pr
5、ocedures for Dynamic Behavior RATIONALE This SAE Recommended Practice was developed to provide a standard procedure to validate tire models that are used for calculating dynamic spindle loads from road surface profiles. 1. SCOPE This SAE Recommended Practice describes an evaluation procedure for val
6、idating tire models for use in road load simulations and assesses the relevant dynamic behavior of tires. 7KHODERUDWRUWHVWXWLOLHGLVDFOHDWWHVWZKHUHDUROOLQJWLUHRQDGUXPHQFRXQWHUVDFOHDWDQGWKHUHVXOWLQJGQDPLFforces and moments are measured. This test is described in 6$(-QDPLF at 0.1 m/s at 50% rated load
7、when the wheel is locked. Handbook or estimated values may be used and shall be noted as such. - cleat surface sliding friction coefficient (optional) Friction coefficient for the tire sliding on a flat surface made of the same material as the cleat surface; at 0.1 m/s at 50% rated load when the whe
8、el is locked. - SAE INTERNATIONAL J2812 Issued FEB2014 Page 6 of 14 5.2.2 Nominal Tire Operating Conditions TABLE 4 TIRE OPERATING CONDITIONS Name Definition/notes Units inflation pressure Tire inflation pressure, unloaded at 20C ambient temp. kPa inclination angle Nominal tire inclination angle rel
9、ative to the rig surface as specified in SAE J2047 deg slip angle Nominal tire slip angle as specified in SAE J2047 deg 5.3 Required Measurements Report pre-test tire inflation pressure and post-test inflation pressure for each testing session, or every four hours, whichever is shorter. For this pur
10、pose, measure the inflation pressure of the unloaded tire immediately before and immediately after running a series of tests (a test session). Table 5 lists the time-domain signals that must be recorded during the test according to SAE J2730. The validation report shall contain graphs of these signa
11、ls versus time. TABLE 5 REPORTED TIME-DOMAIN SIGNALS Symbol Name Definition/notes Units VStest surface speed Drum surface velocity drum angular velocity multiplied by the mean drum surface radius m/s Z wheel spin velocity Angular velocity of wheel derived from RPM or angular position measurement rad
12、/s aXwheel center longitudinal acceleration Translational acceleration of the wheel center in the Xwdirection m/s2aYwheel center lateral acceleration Translational acceleration of the wheel center in the Ywdirection m/s2aZwheel center vertical acceleration Translational acceleration of the wheel cen
13、ter in the Zw direction m/s2FXlongitudinal force Longitudinal spindle force at the wheel center N FYlateral force Lateral spindle force at the wheel center N FZvertical force Vertical spindle force at the wheel center N MXoverturning moment Moment about the longitudinal axis at the wheel center N-m
14、MYrolling moment (optional) Moment about the wheel spin axis N-m MZaligning moment Moment about the vertical axis at the wheel center N-mNOTE 4: Although it is desired to measure the accelerations at the wheel center, in practice, this is generally not possible. Accelerometers are usually placed on
15、the spindle housing of the test machine, as close to the wheel center as possible. In such a case, the distances of the accelerometer to the wheel center should be measured and reported with respect to the wheel coordinate system. These measurements are required to gage the stiffness of the test mac
16、hine as described in SAE J2730 section 6. The first natural frequency of the test machine spindle should ideally be at least three times the first natural frequency of the tire being tested. 5.4 Computation of Single Cleat Test Simulation Accuracy 5.4.1 Steady-State Offset Elimination The force and
17、moment signals may include all, only part, or none of the total steady-state load component, depending on measurement equipment and procedures. In order to focus on the dynamic properties of the time signals, any steady-state load component is identified and eliminated by the procedure defined in th
18、is section. Perform this procedure for both the simulated and measured signals individually. The calculations require an estimate of steady-state vertical force (FZSS(EST) for the measured and simulated case. This will typically be the product of the rated maximum load and the wheel load indicator.
19、See Table 2.) SAE INTERNATIONAL J2812 Issued FEB2014 Page 7 of 14 Search the global vertical force trace for the maximum value. Designate the corresponding time as t3and the force value as FZ(t3). Seek the instant when the vertical force first surpasses a quarter of its rise above the estimated ste
20、ady state value: t1= mint; FZ(t) FZSS(EST)+ (FZ(t3) FZSS(EST)/4 (Eq. 3)and half of the its rise above the estimated steady state value: t2= mint; FZ(t) FZSS(EST)+ (FZ(t3) FZSS(EST)/2 (Eq. 4) Estimate the start of the dynamic response: t0= t2 2(t2 t1) (Eq. 5)Figure 4 illustrates the process. Calculat
21、e the steady-state value of vertical force by averaging over a 0.1-s interval, ending 0.01 s in advance of t0. For example: 01.0t11.0tZZSS00dt)t(Fsec1.01F (Eq. 6) Figure 5 provides an example of this process. Calculate FXSS, FYSS, MXSS, and MZSSby averaging over the same time interval. Repeat this c
22、alculation for both the measured and simulated signals, store the 10 calculated steady-state values, and remove the steady-state component from each time-domain signal. The steady-state values for the measured signals appear in 5.4ZLWK0DSSHQGHGWRWKHVXEVFULSW All subsequent calculations in this secti
23、on assume that the steady-state component has been removed. FIGURE 4 STEADY-STATE OFFSET ELIMINATION START OF DYNAMIC RESPONSE SAE INTERNATIONAL J2812 Issued FEB2014 Page 8 of 14 FIGURE 5 STEADY-STATE OFFSET ELIMINATION - AVERAGING 5.4.2 Time of First Cleat Contact After elimination of the steady-st
24、ate offset in the time domain signals (5.4.1), the time of first cleat contact (tCC) for measurement and simulation is defined by re-evaluating the vertical force signals. Search the global vertical force trace for the maximum value. Designate the corresponding time as tMand the force value as FZ(tM
25、). Seek the instant when the vertical force first surpasses a quarter of its rise: tQ= mint; FZ(t) FZ(tM)/4 (Eq. 7)and half of its rise: tH= mint; FZ(t) FZ(tM)/2 (Eq. 8) As shown in Figure 6, this procedure is very similar to the procedure in 5.4.1, with the exception that the steady-state value has
26、 been calculated and eliminated, rather than estimated. Time of first cleat contact is calculated by extrapolating backward in time from tQ, and assuming a rise to FZ(tQ) with the same slope leading to tQas occurred between tQand tH: )t(F)t(F)t(FttttHZQZHZQHHCC (Eq. 9)If any of the above values cann
27、ot be determined uniquely, the cleat test is not to be used for validation. SAE INTERNATIONAL J2812 Issued FEB2014 Page 9 of 14 FIGURE 6 TIME OF FIRST CLEAT CONTACT 5.4.3 Cleat Test Phases A single cleat test is divided into three phases. Simulation and measurement are compared separately in the on-
28、cleat phase and after-cleat phase. 5.4.3.1 Before-Cleat Phase The before-cleat phase begins 0.1 s before first cleat contact and ends at the instant immediately before first cleat contact. 5.4.3.2 On-Cleat Phase (O) The on-cleat phase (O) includes contact between the tire and the cleat and the short
29、 time interval immediately following contact defined as follows. This is the time interval, tObetween tCCand the first time FX(t) crosses zero after it has reached its maximum value. (See Figure 7.) Derive the value of this interval for the measured signal (tOM) and the simulated signal (tOS). 5.4.3
30、3 After-Cleat Phase (A) During the after-cleat, or post-pulse oscillation phase, cleat-induced vibrations die out. The after-cleat phase is defined as the 0.2-s interval immediately after the on-cleat phase. (See Figure 7.) 5.4.4 Cleat Contact Synchronization Prior to comparing measured and simulat
31、ed tire forces, the signals have to be synchronized. SAE INTERNATIONAL J2812 Issued FEB2014 Page 10 of 14 5.4.4.1 Synchronization Using Measured Cleat Position The preferred method for performing synchronization is by using the measured cleat position. The cleat position is defined by the drum posit
32、ion at which the center of the cleat passes directly below the wheel center. If cleat position is to be used for synchronization, it is necessary to determine the location of the cleat within +/-1 mm. ,QWKHPHDVXUHGVLJQDOVWKHFOHDWSRVLWLRQLVGHWHUPLQHGEXVLQJWKHWLPHWCLEATZKLFKFRUUHVSRQGVWRWKHPRPHQWDWwhi
33、ch the cleat passes the wheel center. Since the method to perform the cleat position measurement is not defined in SAE J2730, a recommended practice is proposed in section 6 of this document. Simulation results must also include a time indication of cleat position so that measurement and simulation
34、results can be aligned in time. FIGURE 7 CLEAT TEST PHASES SAE INTERNATIONAL J2812 Issued FEB2014 Page 11 of 14 5.4.4.2 Synchronization Using Alternative Method When no cleat position measurement is available, an alternative method may be used in which the simulation results are shifted along the ti
35、me axis for consistency with the measured signal. This shift is performed by aligning the point in time of first cleat contact of the simulation (tCCS) with the respective point in time of the measurement (tCCM). Without further refinement, both times coincide after the shift, this common point in t
36、ime is called tCC, and tOis the larger of tOMand tOS.As a refinement of this alignment, a second alignment can be performed by maximizing the cross correlation of the vertical force between tCCand tCCR, where tCCRis calculated by: VCOBDHDHRWttCCCCR)tan(/)()(222 (Eq. 10) Where the following definitio
37、ns apply: V: Surface speed W: Maximum cleat width H: Maximum cleat height R: Nominal tire radius B: Nominal tire width D: Tire deflection CO: Cleat orientation angle (see Table 2) After this refinement of the alignment the points in time of first cleat contact of measurement and of simulation, as we
38、ll as the estimated points in time of end of cleat contact, will not coincide anymore. The common points in time of first cleat contact (tCC) and the interval of cleat contact (tO) are thus defined as: tCC= mintCCS, tCCM (Eq. 11)tO = maxtCCS+tOS, tCCM+tOM - tCC(Eq. 12) 5.4.5 Assessment of Variabilit
39、y of Measured Data The run to run variations of the 16 impact events that are recorded for each test condition per SAE J2730 are evaluated for both the before-cleat phase and for the total event (all phases). The before-cleat phase is analyzed separately to focus on tire non-uniformities. 5.4.5.1 Fo
40、rce and Moment Variation During the Before-Cleat Phase For each of the 16 impacts, calculate the RMS difference between the measured longitudinal force and the steady state longitudinal force, which was determined using Equation 6. Use the same before-cleat time interval as was used in Equation 6. R
41、epeat the calculations for the vertical force, lateral force, overturning moment, and steer moment. Report the FX, FY, FZ, MXand MZ RMS variations for each of the 16 impacts during the before-cleat phase. 5.4.5.2 Force Variation During All Phases As described in SAE J2730, calculate a sample by samp
42、le average time trace of longitudinal force for the 16 cleat impacts. Calculate the RMS difference between each the 16 measured longitudinal force traces and the average of the 16 impacts. Repeat the calculations for the vertical force, lateral force, overturning moment, and steer moment. Report the
43、 FX, FY, FZ, MXand MZ RMS variations for each of the 16 impacts for the complete event (all phases). SAE INTERNATIONAL J2812 Issued FEB2014 Page 12 of 14 5.4.6 Quality Measure for Comparison of Simulation to Measurement for the On-Cleat Phase During the on-cleat phase, force and moment signals are c
44、ompared by using fourth-power deviation measures. Equation 13 provides an example for longitudinal force: 4ttt4XM4ttt4XMXSOFXOCCCCOCCCCdt)t(Fdt)t(F)t(FQ (Eq. 13) Where QOFXis a quality measure for longitudinal force. Calculate QOFY, QOFZ, QOMXand QOMZaccordingly. These five values appear in a compos
45、ite quality measure after the application of weighting factors. The weighting method requires a set of intermediate variables that depend on the peak value of each signal over the on-cleat interval. Equation 14 provides an example for longitudinal force: OCCCCXSSMXMOFXtt,tt,F)t(FmaxW (Eq. 14) Calcul
46、ate WOFY, WOFZ, WOMX, and WOMZaccordingly. Combine the individual quality measured into a single weighted quality measure as follows: OMZOMXOMZOMZOMXOMXOFZOFYOFXOFZOFZOFYOFYOFXOFXOWWQWQWWWWQWQWQW21Q (Eq. 15) Report QO.This is the composite quality measure of agreement between measurement and simulation for the on-cleat phase.5.4.7 Quality Measure for Comparison of Simulation to Measurement for the Post-Pulse Oscillation Phase Compare measured and simulated force traces during the after-cleat time interval based on dominant vibration frequency, maximum amplitude, and decay constant. To this en
