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We develop a dynamic model for a spur gear system with backlash. This model is circular and is geometrically different from the rectilinear gear model of Azar and Crossley. By taking advantage of involute tooth profile, we are able to take material compliance and energy dissipation into account. Furthermore, the complicated phenomenon of contact tooth pairs alternation between one and two during meshing is also included in the model. This model is believed to be closer to reality than the existing model and hopefully is useful in studying gears in high-speed and intermittent motions.
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Yang et al. (1985) studied this question.
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