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Modeling, Analysis and Control Methods for Improving Vehicle 1 Special Issue Modeling, Analysis and Control Methods for Improving Vehicle Dynamic Behavior Modeling, Analysis and Control Methods for Improving Vehicle Dynamic Behavior (Overview) Review Toshimichi Takahashi Abstract So-called vehicle dynamics (or controllability behavior, the vehicle dynamics control and state and stability) refer to the "running, cornering and estimation, and the analysis of driver-vehicle stopping" of automobiles, which are the most system, are briefly summarized. Also, the important and basic performance of automobiles. purpose and background of these studies are Therefore, many studies have been undertaken mentioned. Moreover, a brief introduction to the from several points of view all over the world. In three technical papers included in this special this paper, our former studies, which focused on issue is presented. the analysis and modeling of vehicle and tire Keywords Vehicle dynamics, Modeling, Simulation, Control system, State estimation, Tire model, Optimum control, Driver-vehicle system R&D Review of Toyota CRDL Vol. 38 No. 4 2 1. Introduction Chapter 5. Finally, the purpose and outline of the three Among the many points of view and stages in technical papers included in this special issue are research and development in the vehicle dynamics briefly explained. field, we have been studying fundamental subjects focusing on the following concepts and purposes, 2. Tire modeling mainly in the three following categories for In addition to the analysis and modeling of tire improving vehicle dynamic behavior and safety. transient properties,1, 2) we have also been Here, it should be also noted that the "tire" is one of developing a software system to model a tire steady the key factors influencing our research activities, state characteristics using the so-called Magic either directly or indirectly, because the tire plays an Formula3-5) which has frequently been employed in essential role in all aspects of vehicle behavior. This vehicle dynamics simulation in recent years. The paper provides a brief summary and background of goal is to describe the tire force and moment our studies. The layout of this paper is as follows. properties very accurately over wide ranges of input (1) Analysis and modeling of vehicle and tire behavior variables including combined slip cases, this being Considering the importance of the tire to vehicle very important to the analysis of vehicle dynamic maneuvering, we have been studying and modeling behavior with multi-body dynamics simulation tire characteristics, especially from the viewpoint of software like ADAMS or DADS, as well as by in- developing accurate tire models for use in vehicle house development. simulation calculations. In Chapter 2, we To establish the Magic Formula (abbreviated to summarize the models we have developed to MF) tire model, the optimum values for many MF describe the tire steady state characteristics. parameters and coefficients have to be decided by In the analysis of vehicle dynamic behavior, the using measured data for each tire. Figure 1 shows road surface has been assumed to be flat and even in the structure of our software system,7) which can most cases, even though actual roads inevitably have handle the tire side force, the longitudinal force, and some undulations and unevenness. Our trial for the self aligning torque. The software was analyzing the braking performance of a vehicle on developed in a Matlab/Optimization toolbox uneven roads is briefly explained in Chapter 3. environment to support the use of a wide range of (2) Vehicle dynamics control and state estimation tires and test facilities.6, 7) In recent years, various kinds of control systems Examples of established MF models are shown in have been offered in vehicles on the market to Figs. 2 and 3. These figures show that the models improve the vehicle dynamic behavior and safety. The control algorithms of these systems and the state estimation techniques, which estimate the state variables of vehicle motion and tire characteristics Flat Belt M/C Trailer Vehicle Measurement . etc., are the key technologies used in the development of all these control systems. Chapter 4 Interface and Pre-Processing discusses some of our former studies in this < with/without Constrained Conditions > category. Measured Data One Step (3) Analysis of driver-vehicle system MF Coefficients Identification One of the most pressing and important problems Coefficients facing automobile manufacturers is the reduction of Identification MF Pure Slip Parameters Parameters the number of traffic accidents while increasing Identification MF Combined Slip < with/without Parameters traffic safety. Given that almost accidents are Constrained Conditions > caused by human-related factors, the study of driver- vehicle closed-loop systems is extremely important. Our recent study in this field is introduced in Fig. 1 Structure of tire model identification system. R&D Review of Toyota CRDL Vol. 38 No. 4 3 identified by our system agree with the measured vehicle chassis elements on braking performance data very well. Figure 2 shows the so-called have rarely been reported. Then, analytical and friction circle or friction ellipse, and Fig. 3 shows experimental studies were performed, in which the the braking force characteristics of a passenger braking performance of straight-running vehicles on vehicle tire (PV tire) and a commercial vehicle tire uneven roads and the influence of chassis elements (CV tire) on ice road. From Fig. 3, we can see that on that performance were investigated.8) there are rather large differences between the two For the analysis, a model for simulating of vehicle kinds of tires, namely, the maximum braking force behavior was developed based on the half car model, divided by the vertical load of the CV tire is smaller as shown in Fig. 4. The tire braking force than that of the PV tire, and the decrease in the characteristics that depend on the vertical load and braking force after the peak of the CV tire is much the wheel slip ratio were described by the Magic larger than that of PV tire. These differences may be Formula explained in a former chapter. In the caused by the difference in the inflation pressure, simulation, vehicle responses such as the which relates to the vertical load distribution per unit deceleration of the vehicle, the stopping distance area in the contact patch, and therefore a difference after braking and the tire vertical load can be in the generation of water between the tire and the icy road may be induced. In this case, the pressure 1500 was set to 220 kPa for the PV tire and 705 kPa for Camber angle 0 deg the CV tire. Plots : measurements Curves : MF model 3. Braking performance on uneven roads 6 kN 1000 Although vehicle behavior during steering and/or braking has been studied very widely for many 4 kN years, most studies have assumed the road surface to be even and flat. The analysis of vehicle behavior 500 Braking Force (N) Force Braking Vertical Load 2 kN on uneven roads is thought to be very important, however, when considering actual roads. On the other hand, it seems that many studies of brake Slip Ratio 0 systems and their performance have been 0 0.2 0.4 0.6 0.81 undertaken, but that analyses of the influence of (a) Passenger vehicle tire : 195/65R15 5.0 6000 Camber angle 0 deg Vertical Load 5 kN Camber angle 0 deg Plots : measurements 10 deg 4.0 Plots : measurements Curves : MF model 40 kN Curves : MF model 4000 6 deg 3.0 4 deg 2.0 26 kN Braking Force (kN) Force Braking Side Force (N) 2000 Slip Angle 2 deg 1.0 Vertical Load 14 kN Slip Ratio Braking Force (N) 0 deg 0.0 0 0 0.2 0.4 0.6 0.8 1 0 2000 4000 6000 (b) Commercial vehicle tire : 11R22.5 Fig. 2 Combined slip characteristics on dry road (Passenger vehicle tire : 195/65R15). Fig. 3 Pure braking force characteristics on ice road. R&D Review of Toyota CRDL Vol. 38 No. 4 4 calculated, provided the vehicle initial speed, the (C) Harder suspension bush ( kxf = 330 kN/m, time history of the brake fluid pressure and the cxf = 800 Nsec/m ) longitudinal road profile are given as inputs. (D) Higher tire inflation pressure + Larger damping Figure 5 shows the calculated and measured of shock absorber + harder suspension bush values for the influence of the chassis elements' In Fig. 5, the difference in the stopping distance characteristics on the braking performance, in which between each vehicle and the standard vehicle is the parameters of the chassis elements were changed indicated as a ratio (%) relative to the stopping from those of a standard vehicle (see Table 1) as distance of the standard vehicle both for calculated shown below. and measured results. Positive values indicate a (A) Higher tire inflation pressure ( ktf = 215 kN/m ) shorter stopping distance than the standard. (B) Higher tire inflation pressure + Larger damping Although some differences can be seen in the figure, of shock absorber ( cf = 1350 Nsec/m ) overall we can say that the tendency for the chassis elements to influence the braking performance as calculated agrees rather well with the experiments. In addition, the influences of the longitudinal 8.0 Experiment 6.0 4.0 Calculation 2.0 (A) 0.0 (B) (C) (D) -2.0 -4.0 Difference Ratio of Difference Stopping Distance (%) -6.0 Fig. 5 Comparison of stopping distance between Fig. 4 Vehicle model and symbol notation. calculation and experiments. Table 1 Parameter values of standard vehicle. R&D Review of Toyota CRDL Vol. 38 No. 4 5 suspension characteristics and the road profile on the developed, in which a very simple tire model ("two- braking performance were investigated by straight-line" model) was introduced and the simulation.
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