Vehicle dynamic simulation using multibody vehicle model has been very useful in reducing time and cost in the development stages. Using computer simulation the engineer may understand the dynamic behavior of the vehicle in different operating conditions.

In this paper, the main objective is the validation of the multibody vehicle model in handling maneuvres. In this kind of analysis tire dynamics dominate the handling behavior. So, it is very important to have a good characterization of tire characteristics.

In order to validate the multibody model, experimental measurements were carried out with steering wheel imposed motion and the results were compared to simulation results, with the same motion.

Figure 1 shows the bus multibody model that was built in ADAMS/Car version 10.1 The model was divided into eight subsystems: front suspension, rear suspension, front wheel and tire, rear wheel and tire, steering system, brake system, powertrain and car body (comprised of seats, chassis and all the agregate elements).

The air spring was modeled using an adiabatic curve since only transient analysis has been performed (in this type of analysis the process is adiabatic, without heat transfer). The front and rear axle were modeled as rigid bodies . The shock absorbers were modeled using non linear curves. The non linearities of the bushings stiffnesses were also included. The car body was modeled as rigid body because the type of chassis used in this bus is very stiff .

The steering system model is shown in Figure 2. The steering compliance and damping were included in this model. The steering compliance was obtained from experimental results.

To setup tire parameters experimental measurementes were made by Pirelli. With these parameters, a wheel and tire susbsystem was built using the Delft Tyre Model. It is based on Magic Formula. Magic Formula calculates the longitudinal and lateral forces and aligning moment acting on the tire under pure and combined slip conditions, using longitudinal and lateral slips, wheel camber and the vertical force as input quantities. In a handling analysis, it is very important a good tire characterization, because tire dynamics has a strong influence in vehicle dynamics.

In order to perform closed-loop simulations (imposing steering wheel angle and maintaining the logitudinal velocity), the brake and powertrain systems were modeled. The ADAMS/Car Driving Machine needs these subsystems to perform closed-loop maneuvres. Figure 3 shows the engine curve of the bus.

Open-loop and closed-loop manouvers were carried out. The open-loop manouvers have been performed using experimental steering wheel angle imposed at steer wheel at the bus model. Closed-loop manouvers were performed using ADAMS/Car Driving Machine. In these manouvers, the Driving Machine attempts to perform a ISO lane change manouver at 60 km/h at prescribed path and velocity.

The experimental validation was carried out with experimental steering wheel angle imposed at the ADAMS/Car model and comparing the model results to experimental measurements (Figure 4).

Figure 4: The experimental steering wheel angle was imposed and the results were compared to experimental measurements.

Double lane change at 80 km/h

The double lane change at 80 km/h was performed according to ISO Technical Report 3888 [8] with experimental steering wheel imposed motion (Figure 5).

Figure 6 shows the power spectral density (PSD) of the steering wheel angle. It can be seen that the band-width is limited and the frequency-dependent behavior of the vehicle coul not be determined.

Figure 7 shows the experimental and simulated results of the lateral acceleration. It can be seen that the simulation results are very close to experimental results.

Yaw rate response is shown in Figure 8. The peaks of experimental results were higher than simulation. Figure 8 shows that the bus model has more damping in yaw mode than the real vehicle.

Sweep steer at 40 km/h.

The sweep steer maneuvre was performed. Figure 9 shows the steering wheel imposed motion.

Figure 10 shows the PSD of the steering wheel angle It can be seen from Figure 10 that the band-width of this maneuvre is limited and it is not possible to obtain much information about the frequency-dependent behavior of the vehicle from this test.

Figure 11 shows the lateral acceleration. The correlation of the simulation was very close.

The yaw rate response is shown in Figure 12. The correlation of the simulation was very close for low frequencies. However, with increasing frequency, the simulation began to deviate from experimental results. This behavior was due to yaw damping of the bus model.

FREQUENCY DOMAIN ANALYSIS

In order to investigate the vehicle frequency-dependent behavior, the sweep steer maneuvre at 70 km/h was carried out in ADAMS/Car model. The steering wheel angle is shown in Figure 13.

The PSD of the steering wheel angle is shown in Figure 14. The band-width of this maneuvre was large enough to analize the frequency-dependent behavior of the vehicle.

Figure 15 shows the lateral acceleration gain due to steering wheel angle. The shape of the lateral acceleration response is explained by the fact that the lateral acceleration is composed of the centrifugal acceleration caused by yawing velocity and a linear acceleration along the lateral axis [1].

The phase angle between lateral acceleration and steering wheel angle is shown in Figure 16.

Figure 17 shows the yaw rate gain due to steering wheel angle. At low frequencies, the yaw rate remains nearly constant. As frequency increases beyond 0.5 Hz, the inertia of the vehicle begins to predominate and the yawing velocity response tends to decrease. A high frequency steering input produces very little response [1].

Figure 18 shows the phase angle between yaw rate and steering wheel angle.

One of the maneuvres that is avaliable in ADAMS/Car Driving Machine is the ISO Lane Change Maneuvre. In this maneuvre, the Driving Machine attempts to perform a double lane change maneuvre at prescribed path and velocity.

Driving Machine defines the driving style with one parameter called Lateral Preview Time (LPT), representing the time the drivers knows in advance the desired trajectory [3]. Low values of LPT represents nervous driver reactions and high values of LPT represents very smoothing driving styles.

ISO double lane change maneuvrer using machine control has been performed using different values of LPT.

Figure 19 shows the steering wheel angle of the ISO double lane change maneuvrer at 60 km/h with different values of LPT compared to experimental steering wheel angle.

Figure 20 shows the bus trajectory with different values of LPT and with experimental steering wheel imposed motion.

Figure 21 shows the lateral acceleration with different values of LPT and with experimental steering wheel imposed motion.

Figure 22 shows the yaw rate at different values of LPT and with experimental steering wheel imposed motion.

It can be seen from Figure 19 to 22 that the LPT strongly influences the behavior of the vehicle during the maneuvres. The experimental result compared to simulation results were shown that the real driver has low value of LPT.

The bus model has been validated for transient maneuvrers (the experimental results were very close to simulation results). The bus model was not validated in steady-state maneuvres because the air spring model was not modeled with height and roll control valves

The influence of driver styles in bus handling behavior was analyzed and the results were shown that driver styles has a strong influence in bus handling behavior.

For future investigations, the air spring will be modeled with height and roll control valves in order to perform steady-state analysis.

1. Segel, L. , Theoretical prediction and experimental substantiation of the response of the automobile to steering control, IMechE proceedings, 1956

2. Whitcomb, D. W.; Milliken, W. F. , Design implications of a general theory of automobile stability and control, IMechE proceedings, 1956.

3. Mancosu, F. ;Savi, C., Vehicle sensitivity to tyre characteristics both in open and closed loop manouvres, Pirelli Pneumatici, 2000 ADAMS Conference – Rome, November 15^th –16^th .

4. Pacejka, H.B; Bakker E., The magic formula tyre model, 1^st International Colloquium on Tyre Models for Vehicle Dynamics Analysis, Delft, The Netherlands, 1991.

5. Bernard, J. E.; Clover, C. L. , Tire modeling for low-speed and high-speed calculations, Iowa State Univ., SAE paper 950311.

6. Xia, X.; Willis, J. N., The effects of tire cornering stiffness on vehicle linear handling performance, General Tire, Inc, SAE paper 950313

5. Shröder, C., Chung, S., Influence of tire characteristic properties on the vehicle lateral transient response, Tire Science and Technology, TSTA, Vol 23, No 2, April-June 1995, pp 72-95.

6. Gillespie, T., Fundamentals of vehicle dynamics, Society of Automotive Engineers, second print, 1992.

7. Experimental measurements Pirelli and DCBR, Campo de provas Pirelli, Sumaré – SP, 15 june 2000.

8.  "Road Vehicles – Lateral Transient Response Test Methods".International Standards Organization, Ref. No. ISO 7401: 1988