The paper presents a quarter car model two degrees of freedom (wheel and body), with vertical guiding system, the model being equipped with suspension stroke limiters and with excitation by wheel and/ or by body. The model reproduces elastic and damping characteristics of wheel and of rebound and compression stopper bumpers, the spring elastic characteristic and the shock absorber damping characteristic on rebound and compression, function piston speed. The road profile is generated with simple or summation of harmonic functions, or by reproducing real roads. The forces acting on full vehicle body e.g. aerodynamic and inertial forces are reproduced in the proposed quarter model by vertical forces reduced to the analysed quarter part. Thus, the model can be used for evaluation the vertical and horizontal stability at acceleration, deceleration, pitch and roll, at aerial forces, the body ground clearance and the comfort. The model can evaluate the influence of the damping and elastic characteristics of suspension and wheel, of the static position, of the vehicle load state, of the road profile and of the external forces, to the vehicle behaviour
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