Dynamics Modeling of Gear Transmissions with Asymmetric Load-Dependent Friction

This is the author's final version of the work. The final version of record is published in the journal Mechanism and Machine Theory and is available from:

https://doi.org/10.1016/j.mechmachtheory.2022.105116

This paper proposes a new concise mathematical model of gear transmission dynamics with asymmetric load-dependent friction. It is built only upon the rigid-contact mechanics and the Coulomb friction law, but provides a new theoretical perspective on dynamic and static characteristics of gear transmissions. The presented model is of the form of a differential-algebraic inclusion (DAI) characterized by some parameters, including input-side and output-side asymmetry coefficients. The presented model properly captures the static friction and even the non-backdrivability. It is applicable to different classes of transmissions, such as leadscrew transmissions, worm gear transmissions, and spur gear transmissions. The DAI representation is extended into a multi-dimensional representation for articulated rigid-body systems driven through joint transmissions. Moreover, simulation algorithms are derived through the implicit Euler discretization. Some simulation examples illustrate the capability of the presented simulation algorithm to reproduce load-dependent asymmetric frictional behaviors, which cannot be reproduced by conventional load-independent joint friction models.