Abstrakt

The this paper focus on the behaviour of a “rigid” body biting into another “rigid” body, with some nonzero relative velocity. In the presently considered case, the introduced collision appears between a selected element of a multibody structure and its reference body being interpreted as the motionless ground. Instead of the classic case, described in a number of dissertations, where a single impacting contact is considered, three unilateral contacts are considered simultaneously. Impacting bodies are considered as rigid (non-deformable). According to it, all impact periods are considered as infinitesimally short. As a consequence, some simplifications are possible in integrations performed during the impact period. Position can be considered as constant. Non-impact forces (gravity, joint actuation forces) can be neglected. Velocity quadratic inertia terms can be neglected, too. Only the velocity changes have to be evaluated. It can be done with use of the mass matrix and the contact forces, only. As it is detailed in the paper, in some of the considered cases, solution of a linear system of equations can be used instead of the integration. In the present test, a three unilateral contact points are considered, simultaneously. The main body of the system is at rest and it is supported at two unilateral contact points. As the mass of the main body is relatively high, these two contacts are preserved during all the pre-impact period of calculation. An additional arm is attached to the main body and it rotates at a high speed. It impacts the ground. It effects in a third contact point that appears simultaneously with the two previous contacts. Extending the classic conclusion formulated for the single impact cases, post impact velocities can be calculated with use of the linear system of equations. Such hypothesis is taken under verification in the paper. The numerical tests have disproved this hypothesis. Performed calculations have verified that classic method formulated for a single impact does not give the correct results, now. Post impact velocities of the system elements depend not only on the initial velocities of the impacting elements, but on the characteristics of the elastic and the damping properties of the contacting regions, too.

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