Time-Domain Modeling and Simulation of Rolling Objects

Author： Stoelinga Christophe Chaigne Antoine

ISSN： 1610-1928

Source： Acta Acustica united with Acustica, Vol.93, Iss.2, 2007-03, pp. : 290-304

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Abstract

A model previously developed for simulating a single impact of a ball on a damped plate has been adapted to simulate the sound of a ball rolling over a plate. The original model has the advantage of being well tested and showing good agreement between measurements and time-domain simulations of various impacted plates. The main changes for its adaptation to rolling sounds were made in the ball-plate contact. Instead of an impact point that is fixed in space and short in time the model now incorporates an interacting contact point that is continuously moving in space. To allow for the variable position of the contact point, we use a special spatial window that is optimized for this purpose. Furthermore, a model for the surface roughness of the plate was added. The model is validated by means of three different types of simulations. The numerical results are either compared with experiments or with analytical calculations. The first type of simulation is that of a ball that rolls over a surface with some random asperities. The main observation is that the ball looses contact with the plate at some speed. The second simulation is that of a sinusoidally time-varying source that moves over the plate. Here the characteristic Doppler effect is identified. The third set of simulations are of a ball that is dropped on a plate. The ball bounces back to some height that is lower than the original release height. This fraction of height, also called the restitution coefficient, was measured and compared with simulated data.Following the validation procedure, the model is used to simulate rolling objects. It is shown that different kinds of contact exist between ball and plate. Four different types of rolling with different plate/ball contact parameters are identified: amplitude modulations, periodic bouncing, chaotic bouncing and continuous contact. Comparisons are made between measured and simulated accelerations of a fixed point on a aluminum plate with a sinusoidal waviness profile, which is set into vibrations by rolling spheres of various sizes, stiff nesses and densities.