Abstract
A theoretical model of multistep gear transmission dynamics is presented. This model is based on the assumption that the connection between the teeth of the gears is with properties within the range from ideal clasic to viscoelastic so that a new model of connection between the teeth was expressed by means of derivative of fractional order. For this model a two-step gear transmision with three degrees of freedom of motion has been used. The obtained solutions are in the analytic form of the expansion according to time. As boundary cases this model gives results for the case of ideally elastic connection of the gear teeth and for the case of viscoelastic connection of the gear teeth, as well. Eigen fractional modes are obtained and a vizualization is done.
Highlights
Gear transmissions have a long history dating back since the time of the first engineering systems
By using knowledge of nonlinear mechanics see 37, 45, as well as by using introduced mass moments vectors and vector rotators in the series of the published papers 8, 19, 23–25, 34, 36, 46–49 phase portrait of gyrorotor dynamics with analysis of static and dynamical equilibrium positions depending on system kinetic parameters are presented in new light and new approach
Gear transmissions are very often exposed to action of forces that change with time dynamic load
Summary
Gear transmissions have a long history dating back since the time of the first engineering systems. Their practical usage in the present day modern engineering systems is enormous. Operate under nonstationary conditions so that the loads of the elements of these gear transmissions are variable. Abrupt accelerations and abrupt decelerations of machine parts, that is, masses of the gear transmissions cause inertial forces which, in addition to the conditions of operation, influence the magnitude of actual leads of the elements of gear transmissions. Behaviours of the complete system, and so forth, lead to the simulation where the stresses in the gears are higher than critical stresses; after certain time this may result in breakage of the teeth
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