10 Special Issue Modeling, Analysis and Control Methods for Improving Vehicle Dynamic Behavior

Modeling of Overturning Moment Characteristics and Research the Analysis of Their Influence on Vehicle Rollover Behavior Report Toshimichi Takahashi, Masatoshi Hada

Abstract A newly developed tire model for the vertical loads, angles and camber angles. Overturning Moment (OTM) characteristics and The influence of tire OTM on the vehicle the analysis of the influence of OTM on vehicle rollover behavior was also investigated by means rollover behavior are presented. The new OTM of a full vehicle simulation in which a rather large model was developed based on the so-called steering angle was input. The results obtained Magic Formula tire model. The concept of the from the vehicle models with three different tire new model involves identifying the difference models (model without OTM, simple model, and between the simple model used previously and new model) were compared with experimental actual measurements to the newly defined results. It was found that the calculated result functions. The new model agrees very well with obtained with the new OTM model agreed best the measured data over a wide range of tire with the experiment.

Keywords Tire model, Overturning moment, , Rollover, Simulation

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1. Introduction longitudinal axis. The cause of the generation of OTM may be understood as the lateral shift of the It is well recognized that play an essential acting center of the tire vertical load during vehicle role in all aspects of vehicle behavior. Therefore, a cornering (see Fig. 2). The amount of that lateral huge number of studies to analyze and model tire shift is called a pneumatic scrub. properties have been undertaken to understand and simulate vehicle behavior. Among those studies, the 3. Comparison of simple OTM model with tire longitudinal force, the side force and the measurements aligning torque characteristics have been studied Considering the generation of OTM as noted thoroughly from various points of view to improve above, the measured pneumatic scrub can be vehicle dynamics analysis, but very few studies have calculated using Eq. (1) from the measured OTM considered the tire overturning moment (abbreviated and the vertical load. On the other hand, the simple to OTM, below) characteristics. treatment of the pneumatic scrub (Eq. (2) below) has The authors also have been studying the modeling been proposed with the following assumptions, of the tire characteristics as they relate to improving which is named the "Simple Model" in this study. the accuracy of vehicle dynamics simulations by 1) The tire contacts the road surface at a point. using the so-called Magic Formula (abbreviated to 2) The cross section of the is circular. 1-3) MF, below) tire model. In this paper, a new tire 3) The tire contact point moves laterally under the OTM model is presented, which was developed as a tire side force and the lateral stiffness. final part of our studies relating to the modeling of Ps, m = Mx / Fz • • • • • • • • • • • • • • (1) tire steady-state characteristics. In addition, the P = 1 / K • F − R tan γ • • • • • • • • • • • • • • (2) influence of OTM on vehicle rollover behavior is s, s L y L analyzed by comparing the results obtained by Here, experiment and those obtained by simulation. Fy : Side force Fz : Vertical load 2. Definition of tire coordinate system and KL : Lateral stiffness cause of OTM generation Mx : Overturning moment The coordinate system used for defining the tire Ps, m : Pneumatic scrub by direct measurement force and moment characteristics is shown in Fig. 1. Ps, s : Pneumatic scrub by simple model The OTM is the moment acting around the RL : Tire static radius γ : The two different pneumatic scrubs, namely, the Z measured value (Eq. (1)), and the value calculated Vertical Load

Self Aligning Torque Z

Y Side Force Camber Longitudinal X Angle Force e Slip Angl Moment Tire Vertical Load Direction of Wheel Travel Spin Axis Overturning Moment Side Force Y Direction of Wheel Heading Pneumatic Scrub Vertical Load Overturning Moment Distribution

Fig. 1 The tire coordinate system. Fig. 2 Schematic sketch of OTM generation.

R&D Review of Toyota CRDL Vol. 38 No. 4 12 from Eq. (2), were compared as shown in Fig. 3. type tire test machine. From Fig. 3, we can see that

The side force Fy in Eq. (2) was calculated by using there are rather large disagreements between the the MF tire model,3) while the values of the lateral measured results and those calculated using the stiffness and the static radius of two tires are simple model, especially in the region of large slip listed in Table 1. The tire force and moment angles and camber angles. 4) characteristics were measured by using a flat belt In the literature, a similar equation was used, but

the parameters, KL and RL , were determined by identifying the measured data of OTM instead of the

100 actual values, so the same trial was performed, as Measurement shown in Fig. 4 (named the "Simple Identified -9 deg Model" here). It is thought that the degree of 50 Simple Model agreement can be improved, but that disagreements 0deg will still exist in the region of large slip angles and 0 camber angles. This shows that the simple treatment of OTM generation agrees poorly with the actual tire -50 Camber Angle behavior, which may be caused by a change in the Pneumatic Scrub (mm) Scrub Pneumatic 9 deg

-100 -20 -10 0 10 20 Slip Angle (deg) 60 MeasurementMeasurement (a) Tire size : 215/70R16, Vertical load : 7.3 kN 40 SimpleSimple IdentifiedIdentified ModelModel 150 -9 deg 20 -9 Measurement 100 Simple Model -9 deg 0 50 0deg -20-20 Camber Angle Angle 0 0 degdeg 99 degdeg Pneumatic Scrub (mm) Scrub Pneumatic Pneumatic Scrub (mm) -40-40 -50 Camber Angle -60-60 9 deg -20-20 -10 -10 0 0 10 10 20 20 Pneumatic Scrub (mm) Scrub Pneumatic -100 Slip AngleAngle (deg)(deg)

-150 (a) Tire size : 215/70R16, Vertical load : 7.3 kN -20 -10 0 10 20 Slip Angle (deg) (b) Tire size : 265/70R16, Vertical load : 9.8 kN 60 Measurement

40 Simple Identified Model 20 Fig. 3 Comparison of pneumatic scrub between -9 deg measurement and Simple Model. 0

-20 Camber Angle 9 deg

Pneumatic Scrub (mm) Scrub Pneumatic -40 0 deg Table 1 Lateral stiffness and static radius. -60 -20 -10 0 10 20

Tire 215/70R16 265/70R16 Slip Angle (deg)

Lateral Stiffness 129 135 (b) Tire size : 265/70R16, Vertical load : 9.8 kN (N/mm) 350 Static Radius (mm) 319 Fig. 4 Comparison of pneumatic scrub between measurement and Simple Identified Model.

R&D Review of Toyota CRDL Vol. 38 No. 4 13 vertical load distribution of the tire and 4. 2 Model identification procedure and results from an error in the simple assumptions noted To successfully establish the MF tire model, the above. Then, the new tire OTM model was optimum values of the MF coefficients and developed to obtain better agreement with the parameters have to be determined. The authors have measurements. been developing a software system to identify those coefficients and parameters by using various types 4. Development of new OTM model of measured data and identification methods (see 4. 1 Model description Reference 3 for details). First, we observed the difference between the The calculations for establishing the New OTM pneumatic scrub obtained from measurement and Model shown in Fig. 6 were added to the former that obtained with the simple model, as shown in software. As shown in Fig. 6, the residual Fig. 5. This difference is called a "Residual pneumatic scrub is calculated first, after which the Pneumatic Scrub" in this paper. The shape of a MF coefficients and parameters are identified. residual pneumatic scrub depending on the slip angle Finally, by using the values obtained for the seems to be similar to that of the side force. Then, coefficients and parameters as initial values, all the the new term for the residual pneumatic scrub, Pr , coefficients and parameters are again simultaneously was added to Eq. (2) and the modified pneumatic optimized by using the measured data. scrub, Ps , was newly defined. For the residual Examples of calculated results obtained by the use pneumatic scrub, the same expression for the side 3) force of MF was used as below because of the similarity in the shape. The following model is 60 named the "New Model". 40 − γ − -9 deg Ps = 1 / KL • Fy RL tan Pr • • • • • • • • • • • • • (3) 20 0 deg Pr = D sin −(Ε + ∆Ε − [C arctan{Bx 0 sgn (x))(Bx arctan Bx)}] + Sv 0 • • • • • • • • • • • • • (4) Camber Angle 20 α + 9 deg x = Sh • • • • • • • • • • • • • (5)

40-40 KL = m18 • • • • • • • • • • • • • (6) Residual Pneumatic Scrub (mm) Pneumatic Residual • • • • • • • • • • • • • 60 RL = m19 (7) -20 -10 0 10 20 Slip Angle (deg) C = m0 • • • • • • • • • • • • • (8) 2 + − γ 2 (a) Tire size : 215/70R16, Vertical load : 7.3 kN D = ( m1 Fz m2 Fz )( 1 m15 ) • • • • • • • • (9) − γ BCD = m3 sin [2 arctan ( Fz / m4 )]( 1 m5| |) 60 -9 deg • • • • • • • • • • • • • (10) 40 B = BCD / CD • • • • • • • • • • • • • (11) 20 Ε 2 + 0 deg 0 = m6 Fz m7 Fz • • • • • • • • • • • • • (12) Ε − 2 + γ + α + 0 d = ( m6 Fz m7 Fz )(m16 m17 ) sgn ( Sh ) • • • • • • • • • • • • • (13) 20 2 + + γ Sh = m8 Fz m9 Fz m10 Fz • • • • • • • • • (14) Camber Angle 9 deg 2 + + 2+ γ 40 Sv = m11 Fz m12 Fz ( m13 Fz m14 Fz ) Residual Pneumatic Scrub (mm) Pneumatic Residual • • • • • • • • • • • • • (15) 60 -20 -10 0 10 20 α Where, is the slip angle, and B to Sv in Eqs. (4) Slip Angle (deg) and (5) are called the Magic Formula coefficients, (b) Tire size : 265/70R16, Vertical load : 9.8 kN which are functions of the vertical load and the camber angle. In Eqs. (6) to (15), m to m are 0 19 Fig. 5 Residual Pneumatic Scrub. called the Magic Formula parameters.

R&D Review of Toyota CRDL Vol. 38 No. 4 14 of the New Model and the newly developed For the vehicle description, a full vehicle model identification system are compared with the was developed using ADAMS with the parameter measured results in Fig. 7. It is clear that the New values for the vehicle used for the experiment. A OTM Model agrees very well with the measurements over a wide range up to a large slip angle, camber angle and vertical load. 300 Measurement 200 Fz 7.3 kN 5. Influence of tire OTM on vehicle rollover New Model behabior 100 5.4 kN 2.5 kN Finally, to observe the influence of tire OTM on 0 vehicle behavior, the vehicle rollover behavior was -100 investigated, because it is easy to imagine that the

influence of OTM appears more clearly with a large (Nm) Moment Overturning -200 Camber Angle -6 deg slip angle and vertical load by considering the cause -300 of OTM generation (Fig. 2). To precisely analyze -20 -10 0 10 20 Slip Angle (deg) the influence of OTM on the vehicle rollover (a) Tire size : 215/70R16, Camber angle : -6 deg behavior, three tire models were used in the vehicle simulation and the calculated results were compared 600 with vehicle experimental results. In vehicle Measurement 400 Fz 9.8 kN dynamics simulations, the tire OTM has normally New Model been disregarded (without OTM). The three tire 200 7.5 kN models are, 0 a) Without OTM 4.4 kN -200 b) Simple Model c) New Model -400 Overturning Moment (Nm) Moment Overturning Camber Angle 0 deg -600 -20 -10 0 10 20 Slip Angle (deg) Lateral Stiffness K L (b) Tire size : 265/70R16, Camber angle : 9 deg Side Force Fy Static Radius R L

Calculation of Fig. 7 Comparison of overturning moment between Measured Residual Pneumatic Scrub measurement and New Model. Data

Identification of Slip Angle Dependency ( MF Coefficients ) 400

200 Identification of Vertical Load and Camber Angle Dependency 0 ( MF Parameters )

-200 Identification of all Coefficients Steering Angle (deg) Angle Steering

and Parameters simultaneously Steering Angle (deg) -400

-600 New OTM Model 0 1 2 3 4 5 Time ((sec)sec)

Fig. 6 Procedure of identification of New OTM Model. Fig. 8 The steering angle input for vehicle simulation.

R&D Review of Toyota CRDL Vol. 38 No. 4 15 relatively large steering angle input was applied as rollover are compared with the value obtained from shown in Fig. 8 for the simulation run, during which the experiment, which was performed in the same the vehicle forward speed was held constant. way as the calculation. We can see that the effect of We used three vehicle models, each with a OTM on the tire reduces the lateral acceleration for different tire model. The simulation run was rollover. We can also see that the result calculated repeated starting from a low forward speed which with the New OTM Model agrees best with the was increased in steps of 1 km/h. As the vehicle result by experiment and that the inclusion of the tire behavior, the roll angle response was observed. As OTM characteristics into the vehicle dynamics the forward speed increased, the roll angle response simulation improves the accuracy of the calculation. was altered as shown in Fig. 9. At the forward 6. Conclusion speed denoted as V+2 km/h in Fig. 9, the roll angle response diverged. Then, the maximum value of The findings presented in this paper are lateral acceleration in the simulation run of V+1 summarized below. km/h was defined as the lateral acceleration for (1) A new model for the tire overturning moment rollover. In Fig. 10, the lateral accelerations for characteristics was developed based on the Magic Formula by adding a new term for the residual pneumatic scrub. 10 (2) To find the optimal values for the coefficients 8 and parameters of the new OTM model, a 6 calculation program was developed and added to the 4 existing software system. 2 0 (3) It was found that the new OTM model agrees -2 very well with the measured results.

Roll Angle (deg) Roll -4 V km/h V+1 km/h (4) The influence of tire OTM on the vehicle Roll Angle (deg) -6 V+2 km/h rollover behavior was investigated. Three tire -8 -10 models were introduced to the vehicle simulation 0 1 2345 model and the calculated results were compared with TimeTime (sec) those obtained by experiment. The effect of OTM on the tire reduces the lateral acceleration for Fig. 9 The response of roll angle. rollover. The result calculated using the new OTM model agreed best with the experiment. (5) The introduction of the new OTM model into ) 2 9.0 vehicle dynamics simulation is thus highly recommended for improving the accuracy of the (m/sec calculation. 8.0 References Rollover Rollover 1) Mizuno, M., et al. : "Magic Formula Tire Model Using the Measured Data of a Vehicle Running on 7.0 Actual Roads", Proc. of 4th Int. Symp. Advanced Vehicle Control (AVEC '98), Nagoya, (1998), 329-334 2) Hada, M., et al.: "Development of Tire Side Force

Lateral AccelerationLateral for 6.0 Model by use of Measured Data on Actual Roads" (in Japanese), Proc. of JSAE Autumn Meet., No. 9941223, 101-99(1999), 5-8 New Model Experiment Without OTM Simple Model 3) Takahashi, T., et al. : "The Modeling of Tire Force Characteristics of Passenger and Commercial Fig. 10 Comparison of lateral acceleration for rollover Vehicles on Various Road Surfaces", Proc. of 5th Int. between calculated results and experiment. Symp. Advanced Vehicle Control (AVEC 2000),

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Michigan, (2000), 785-792 4) Pacejka, H. B. and Besselink, I. J. M. : "Magic Formula Tyre Model with Transient Properties", Supplement to Vehicle System Dynamics, 27(1997), 234-249 (Report received on Sept. 26, 2003)

Toshimichi Takahashi Year of birth : 1953 Division : Vehicle Control Lab. Research fields : Vehicle Dynamics, Tire Dynamics, Man-Machine System Academic society : Soc. Autom. Eng. Jpn., Jpn. Soc. Mech. Eng. Awards : Outstanding Paper Award, 26th FISITA Congress, 1996

Masatoshi Hada Year of birth : 1967 Division : Research-Domain 16 Research fields : Tire Modeling, Man-Machine Sytem Academic society : Soc. Autom. Eng. Jpn., Jpn. Soc. Mech. Eng.

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