For dynamic car simulators, it is obvious that the longitudinal motion cannot be fully reproduced, the possibility to simulate longitudinal motions being generally reduced to less than 1m. In our case, a four post shaker is intended to be built as dynamic car simulator. Each post shaker, one under each car wheel, is aimed to generate mainly vertical vibrations and lateral motion. Since the displacements/motion in the longitudinal direction can only be partially reproduced, our problem was how to compensate the impossibility of fully reproducing the longitudinal motion by at least taking into account the influence of the longitudinal motion on the vertical vibrations.
In this paper a simplified 4 DOF “bicycle” model is used for vertical dynamics, instead of a 7 DOF full car vertical dynamics model, which will be considered in a further study.
On the other hand, the vertical vibrations are different for the same car riding on the same road, but for different acceleration regimes: 1) null acceleration (e.g., 60km/h constant speed); 2) uniform acceleration from 10 to 110 km/h (during 8 seconds), followed by uniform deceleration from 110 to 10 km/h (during another 8 sec), then uniform acceleration from 10 to 60 km/h (during the last 4 sec of the simulation).
In order to reproduce in the dynamic car simulator the vertical vibrations of the above-mentioned longitudinal motion regimes (involving displacements of tens of meters), the following steps are proposed: a) direct dynamics CARSIM computer simulations of the car motion and its interaction with the road; b) inverse dynamics of car vertical model (4 degrees of freedom), using as input the following parameters computed in step a): the vertical displacements and velocities of the sprung mass and of the front and rear wheel centers as well as the pitch angle of the sprung mass and its rate. These inverse dynamics computer simulations are performed using an in-house Matlab software programming only the 4-DOF vertical car/road interaction (2D “bicycle” model in the pitch plane, no roll motion considered), without considering any longitudinal motion.
The output of these inverse dynamics computer simulations, using the in-house Matlab software, is the “modified/distorted road profile”. Thus, the modifications brought to the real road profile are aimed to compensate the lack of the longitudinal degree of freedom in the dynamic car simulator, in order to reproduce the vertical vibrations of the above-mentioned longitudinal motion regimes (so that to encounter the same car vertical displacements and accelerations for the in-house Matlab simulation, as for the CARSIM simulation).
Results are presented in order to show how the real road profile is modified/distorted in order to cope with this impossibility to simulate the road profile in dynamic car simulators, without huge costs.