On the dynamics of gear shifting

Continuously or discretely variable transmissions are used in a variety of machines to match prime mover characteristics to varying loads. In most cas es, the transmissions provide a fairly rigid constraint on the motions of i nertial elements associated with the prime mover and the load although comp liance will allow some high frequency oscillatory behavior. In this paper, compliance effects are neglected and the emphasis is on correct representat ions of impulsive forces associated with rapid gear ratio changes. The aim is to represent jumps in speeds, momenta and energy at the shifting times. This allows an efficient computer model of the overall system dynamics to b e made without the necessity of representing the high frequency dynamics of the transmission itself. Bond graph models of automotive systems will be u sed to illustrate some of the pitfalls associated with models of various ty pes of shiftable transmissions but the concepts apply to a wide variety of machines.