Study Of On-Center Handling Behaviour Of A Vehicle

Transcription

1 Study Of On-Center Handling Behaviour Of A Vehicle Rohit Vaidya, P Seshu 1 and G Arora Tata Technologies Limited Pune rohitvaidya@tatatechnologies.com 1 Mechanical Engineering Department. IIT Bombay. seshu@iitb.ac.in Tata Motors Limited. Pune gar938@tatamotors.com ABSTRACT On-Center Handling refers to the steering behaviour on and about the straight ahead driving position, and is important at high speeds. It is important to know early in the vehicle design process, the influential parameters that affect the OCH behaviour. Knowledge of these influential parameters helps to design-in good OCH behaviour. In the present work, a fourteen degrees of freedom mathematical model is used to simulate the OCH behaviour and perform a parametric study. The results of the study help identify the influential design parameters. INTRODUCTION Passenger cars and commercial vehicles spend large percentage of their life under state and national highway conditions. The speeds on the highways are high (of the order of 100 Kmph). High speeds raise concern for safety. The ability of the vehicle to respond to driver commands comes into focus. Much research has been directed towards understanding vehicle behavior under emergency conditions. However, vehicle spends large percentage of its life under non-emergency conditions. During non-emergency conditions, there are specific critical conditions that affect driver s confidence of his control over the vehicle. It is therefore equally important to understand the vehicle behavior under non-emergency conditions. One of the common driving situations is driving along a straight section (no lane change) of a highway at a very highspeed characterized by low lateral acceleration. The ease and confidence with which a vehicle can be driven in such a situation is important. The vehicle behavior on and about the straight-ahead driving position is referred to as On-Center Handling (OCH). A vehicle having poor OCH behavior requires continuous

2 steering inputs. Such a situation prevents the driver from getting true bearing of the vehicle and is not desirable. Limited literature is available on OCH. OCH studies were performed by Norman [1. He described tests to measure handling characteristics under straight-ahead driving conditions. Parameters relating to steering feel such as steering wheel torque, steering wheel angle, yaw rate and speed were measured during the tests. The test has provided a data-base from which general attributes of different classes of vehicles can be compared. Farrer [ described parameters that subjectively define OCH. Further, he deduced a test technique to evaluate the OCH performance. Additionally, he tried to establish a objective performance criteria. Peppler et al. [3 studied the effect of steering system on OCH performance for commercial vehicles. They found that steering system stiffness determined at the steering wheel is key discriminator among different steering systems. Higuchi and Sakai [4 presented a data processing method to study vehicle performance characteristics, yaw velocity, lateral acceleration, steering wheel angle and steering wheel torque. They use special functions to fit the raw data. Vehicle parameters or their combinations are coefficients of these special functions. This helps to identify the measures to improve OCH performance. Momiyama et al. [5 studied heavy vehicle performance improvement through utilising compliance steer at the front and rear suspension. Earlier research was directed to formulate test method to evaluate OCH, and to establish relation between subjective and objective parameters. Work is in progress to identify the governing design parameters especially for heavy vehicles. In the present work a fourteen degrees of freedom (dof) model is developed to study OCH of a typical passenger car. The weave test is used to simulate the OCH behaviour. Hysteresis on the graph of steering wheel torque versus steering wheel angle and that on the graph of lateral acceleration versus steering wheel torque is used as criteria for judging OCH. Results of a parameteric study, performed to identify the influential design parameters, are presented. MODEL DESCRIPTION There are five bodies represented in this model, viz., the sprung mass, and the four un-sprung masses representing the wheel assemblies. The sprung mass has six dof and the un-sprung masses have two dof each, translation along vehicle z axis and rotation about the vehicle y-axis. Figure 1 shows a vehicle model explaining the fourteen dof.. The model is divided into two parts. 1. model of translational and rotational states of the wheel assemblies (unsprung mass)

3 Sprung mass Z Translation along x, y and z axes Rotation about x,y and z axes Y X Unsprung mass Z Translation along z axis Rotation about y axis (axis of spin) Figure 1 Vehicle model with 14 dof. sprung mass model a. model of translational states of the sprung mass b. model of the rotational states of the sprung mass The model for the un-sprung mass requires inputs about suspension parameters, drive torque, braking torque, and longitudinal force. The outputs of this model are the unsprung mass states i.e. z, z&, ω. The equations of motion for the un-sprung mass are m F & z us us w ( C + C ) z& + ( K + K ) z C z K z = 0 USij + SUSi t USij SUSi t USij SUSi SFij SUSj SFij J ZWω& ij T Dij + T Bij + F Xij tlr = 0 where i = F(front)orR(rear) j = L(left)orR(right) (1) () The model for sprung mass requires inputs about the tire forces, sprung mass parameters and steering angle. The tire forces require un-sprung mass states as inputs. Magic Formula [6 empirical model is used to calculate the tyre forces. Magic Formula model provides the advantage of modelling the measured tire properties in a simple manner. Tyre lateral force is a function of normal load and slip angle. The magic formula is written as 1 1 = Dsin[ C tan { Bα E( Bα tan Bα)} (3) F Y

4 where B : stiffness C : shape factor D : peak value factor E : curvature factor The magic formula parameters were obtained through fitting experimental data. The output of the sprung mass model is the sprung mass states. The equations of motion for the six dof are && xin FXFL + FXFR + FXRL + FXRR mcog yin T InCoG FYFL FYFR FYRL F && = YRR z && In FZFL + FZFR + FZRL + F ZRR + FGZ (4) cosψ sinψ 0 where T InCoG = sinψ cosψ 0 is the transformation matrix from CoG coordinate system to Inertial coordinate system br bf J Zψ& & = ( FYFR + FYFL ) lf ( FYRL + FYRR ) lr + ( FXRR FXRL ) + ( FXFR FXFL ) (5) J & Yφ = ( FZFL + FZFR ) lf ( FZRL + FZRR ) lr + mcogaxhcog (6) bf br J & Xθ = ( FZFL FZFR ) + ( FZRL FZRR ) + mcoga yhcog (7) SIMULATIONS OCH behaviour of a vehicle is significantly influenced by the steering system characteristics [3,4,7. The present work aims to identify vehicle parameters which significantly influence the OCH, considering the steering system to be ideal i.e. without friction, no backlash and no compliance. Therefore, steering system dynamics is not modelled. The highway driving, during which OCH is an issue, can be simulated under test conditions using a weave test. Therefore, the weave manoeuvre is useful for judging vehicle characteristics. The international working group ISO/TC/SC9 WG 7 has formulated a proposal for the standardization of the description of steering around the central position [8.

5 The steering wheel is moved Weave Test 15 sinusoidally with a steering wheel angle lateral acceleration frequency of 0. Hz ±10% yaw rate 10 at a constant vehicle longitudinal speed of 100 kmph ±3 %. The steering wheel amplitude must be determined to produce 5 0 lateral acceleration of m/s^ ±10%. Figure -5 shows the time history of the weave test. In the present -10 work, the weave test is simulated using the mathematical model. The equations of motion (Eqs. Time [s Figure. Time history of the weave test. (1), (), (4)-(7)) are solved numerically using Runge-Kutta integrator in MATLAB. Steering Wheel Angle [deg, Lateral acceleration [m/s^, Yaw rate [degs/s RESULTS AND DISCUSSIONS The weave manoeuvre test is used to judge the OCH. A parametric study (±10 % about the nominal values listed in Appendix) is performed to identify the most influential vehicle parameters. Six vehicle parameters listed in Table 1 were studied in the exercise. All of the vehicle parameters except the tyre cornering stiffness have contribution from various independent Table 1. Vehicle parameters for Parametric study S.No. Vehicle Parameter 1 Mass of Vehicle (m CoG ) Yaw moment of inertia (J z ) 3 Roll moment of inertia (J x ) 4 Tyre cornering stiffness (C ) α 5 Wheel base (l F +l R ) 6 Distance of CoG from front axle (l F ) vehicle aggregates, like the power-train, body trims, wheel assembly, battery etc. Therefore these parameters are very difficult to modify late in the vehicle design process. Hence it is very important to know the influential design parameter. Figure 3 shows the graph of lateral acceleration plotted against steering wheel torque. Hysteresis width (H l ) when steering wheel torque is zero was noted for comparison. Figure 4 shows the graph of steering wheel torque plotted against steering wheel angle. Hysteresis width (H t ) when steering wheel angle is zero was noted for comparison.

6 8 Lateral acceleration H l Steering Torque H t Steering Torque Steering Wheel Angle (deg) Figure 3. Lateral acceleration versus Figure 4. Steering Torque versus Steering Steering Torque angle The hysteresis width H l and Ht correlate well with subjective feel [1, and have been used by several researchers to quantify OCH. Therefore, these two metrics have been used in the present study. Figures 5 though 10 show the graphs of effect of the design parameters on hysteresis torque H t. Figures 11 through 16 show the graphs of effect of the design parameters on lateral acceleration hysteresis H l. Steering Torque Hysteresis Steering Torque Hysteresis Vehicle Mass (Kgs) Figure 5 Effect of Vehicle Mass Vehicle Roll Inertia (Kg-m^) Figure 7 Effect of Vehicle Roll Inertia Steering Torque Hysteresis Vehicle Yaw Inetia (Kg-m^) Figure 6 Effect of Vehicle Yaw Inertia Steering Torque Hysteresis Tyre Cornering Stiffness (N/rad) Figure 8. Effect of Tyre Cornering Stiffness

7 Steering Torque Hysteresis Steering Torque Hysteresis Wheel Base (m) a (m) Figure 9 Effect of Vehicle Wheel Base Figure 10. Effect of distance of front axle from CoG Vehicle Mass (Kgs) Vehicle Yaw Inetia (Kg-m^) Figure 11 Effect of Vehicle Mass Figure 1 Effect of Vehicle Yaw Inertia Vehicle Roll Inertia (Kg-m^) Tyre Cornering Stiffness (N/rad) Figure 13 Effect of Vehicle Roll Inertia Figure 14. Effect of Tyre Cornering Stiffness Wheel Base (m) a (m) Figure 15 Effect of Vehicle Wheel Base Figure 16. Effect of distance of front axle from CoG

8 Table shows the effects on H t and H l for specific change in the vehicle design parameters. Figures 7 and 13 show the effect of roll moment of inertia in graphical form. It can be observed that roll moment of inertia is the least influential of the design parameters under study. Therefore, placement of vehicle aggregates at a distance from vehicle x axis should affect OCH the least. Figures 6 and 1 show the effect of yaw moment of inertia in graphical form. Yaw moment of inertia has a small influence on H t but has major effect on H l. Therefore, it is beneficial to have yaw moment of inertia as low as possible. Hence vehicle aggregates should be placed close to the vehicle CoG. Figures 5 and 11 show the effect of vehicle mass in graphical form. Vehicle mass has no effect on H l but has small effect on H t. Vehicle mass therefore has small overall influence on OCH. Figures 8 and 14 show the effect of tyre cornering stiffness in graphical form. Tyre cornering stiffness has considerable influence on H t but small effect on H l. Therefore the tyre cornering stiffness should be high. In this respect vehicles having radial tyres should have better OCH behaviour. Figure 9 and 15 show the effect of wheel base in graphical form. Wheel base has a significant influence on both H t and H l. Higher the wheel base, higher is the hysteresis value. Hence, the vehicle wheel base should be low to the best possible extent. This observation leads to the inference that longer buses and large car (limousines) may be prone to poor OCH behaviour. Figures 10 and 16 show the effect of distance of front wheel from CoG. The distance of front wheels from CoG has significant effect on both H t and H l. Higher the distance of front wheels from CoG, higher is the hysteresis. Larger distance of the front wheels from CoG makes the vehicle rear heavy and therefore having oversteering characteristics. This observation emphasises that weight balance between front end and rear end of the vehicle is significantly influential for OCH behaviour and that a front heavy vehicle should have better OCH behaviour. Table. Effect on H t and H l S.No. Vehicle Parameter Change Ht Hl 1 Mass of Vehicle (m CoG ) 8 % 7 % 0 % Yaw moment of inertia (J z ) 6 % % 13 % 3 Roll moment of inertia (J x ) 10 % 0 % - % 4 Tyre cornering stiffness ( Cα ) 10 % -1 % 5 % 5 Wheel base (l F +l R ) 4 % -7 % -19 % 6 Distance of CoG from front axle (l F ) 8 % 34 % 3 % CONCLUSIONS A fourteen dof model was used to study the OCH behaviour. A parametric study was performed to evaluate the effect of six design parameter on OCH. A weave test was used to simulate highway driving wherein OCH is an issue. Hysteresis torque (H t ) and lateral acceleration hysteresis (H l ) were used as metrics to judge OCH.

9 The findings of the parametric study indicate that the wheel base and the distance of front wheel from CoG are very influential parameters. Smaller wheel base and shorter distance between the front wheels from CoG would improve the OCH behaviour. Vehicle roll moment of inertia and mass of the vehicle are the least influential parameters. NOMENCLATURE h CoG - height of CoG from ground k t, C t - tire radial stiffness and damping l F, l R - distance between CoG and front wheels and rear wheels respectively along x-axis m - mass of the wheel assembly (unsprung mass) m CoG - mass of the vehicle except the unsprung mass tlr - tire laden radius x, y, z - displacement of sprung mass along x, y and z-axis in inertial co-ordinate system z z& US US - displacement and velocity of unsprung mass (wheel) along Wheel z-axis C sus, K sus - Suspension damping and stiffness along z-axis in CoG co-ordinate system F x, F y, F z - Tire Force along x, y, and z-axis in the tyre co-ordinate system J x, J y, J z - Moment of inertia about the x, y and z-axis in CoG co-ordinate system T b, T d - Brake torque, drive torque T CoGIn - transformation matrix from CoG to inertial co-ordinate system α - Slip angle δ W - Steering wheel angle φ, θ, ψ - pitch, roll and yaw displacement of sprung mass along in CoG co-ordinate system ω - angular speed of the wheel REFERENCES 1. Norman, K. D., Objective Evaluation of On-Center Handling Performance, SAE Paper Farrer, D. G., An Objective Measurement Technique for the Quantification of On-Centre Handling Quality, SAE Paper 93087

10 3. Peppler, S. A., Johnson, J. R. and Williams, D. E., Steering System Effects on On-Center Handling and Performance, SAE Paper Higuchi, A., and Sakai, H., Objective Evaluation Method of On-Center Handling Characteristics, SAE Paper Momiyama, F., Yuhara, N. and Tajima, J., Performance Improvement of On- Center Regulation for Large Sized Vehicles, SAE Paper Pacejka, H. B., Besselink, I. J. M., Magic Formula Tyre Model with Transient Properties., Vehicle System Dynamics, Supplement 7 (1997). pp Kim, H. S., The Investigation of Design Parameters Influencing on On-Center Handling Using AUTOSIM, SAE Paper Dettki, F., A test method for the quantification of on-centre handling with respect to cross-wind, Proc Institution of Mechanical Engineers, Vol. 16 Part D, pp , 00 APPENDIX Typical Vehicle Parameters Wheel Base [l 350 Mm Distance of Front wheels from CoG [l F 1190 Mm Front wheels track [b F 1300 Mm Rear wheels track [b R 180 Mm Height of CoG from ground [ hcog 60 Mm Sprung Mass [ mcog 1335 Kgs Moment of Inertia about z-axis [ J Z 1500 Kg-m^ Moment of Inertia about y-axis [ JY 1300 Kg-m^ Moment of Inertia about x-axis [ J X 800 Kg-m^ Unsprung Mass (per wheel assembly) [ mf 30 Kgs (Front) Suspension Stiffness [K SUS N/m (Front) Suspension Damping [C SUS 183 N-s/m (Front)