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Stable periodic motions of an impact-pair. (English) Zbl 0556.70019

Clearances occur commonly in kinematic pairs of mechanisms such as linkages, gear trains, and joints. Collisions or impacts happen when the mechanism’s vibrations are greater than a clearance. Then high but transient impact stresses will result which may lead to hammer hardening, scoring, pitting wear and high noise levels. Intuition suggests that wear and noise increase generally with the rate, number, and severity of impacts. More easily formulated relationship between the latter characteristics and known properties of the structure may be a useful indicator therefore of the practically important wear and noise. The authors develop such a dependency for certain structures called ”impact pairs”. The asymptotically stable motion of an impact pair is formulated most generally when the masses collide periodically. Predictions are shown to agree with previous but more limited calculations and to correlate quite well with experimental results. Difficulties encountered in the practical application of the stability theory used are discussed with the help of empirical data.

MSC:

70K20 Stability for nonlinear problems in mechanics
70B15 Kinematics of mechanisms and robots
70F35 Collision of rigid or pseudo-rigid bodies
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