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This paper presents analysis of dynamie properties of a car, based on a hybrid sky-hook and ground-hook model. Apart from a classical damper, which is located between sprung and unsprung masses, a ąuarter car model mcludes two abstract dampers. The first, so called sky-hook is placed between yehicle's sprung mass and an imaginary point in the sky. This yirtual damper is used to minimize acceleration of sprung mass. The second abstract ground-hook damper, is located between vehicle's unsprung mass and an imaginary point in the ground. This damper increases a level of a yehicle ride safety by reducing oscillations of force acting on the ground. The hybrid model comprises both the sky-hook and ground-hook. This model is tested in selected papers, but in the literature there are no results which define its optimal properties. Optimization of the hybrid model is presented in this paper. Acceleration of sprung mass is used to determine the performance index of ride comfort. The performance index of ride safety of the abstract model is based on the force acting on the ground. The ground force is considered in two variants: (I) the only elastic force of a tire, (II) eJastic force of a tire and damping force in the ground-hook. The performance index of ride safety has been also calculated takmg into account tota! force acting on the enyironment: force in a tke and also sky and ground forces in the abstract model. Properties of the model with abstract dampers are compared with the reference model with a traditionally placed viscous element.
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