# Dynamic modeling of a gear transmission system containing damping particles using coupled multi-body dynamics and discrete element method

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## Abstract

The reduction in vibration in gear transmission systems is an engineering task. Particle damping technology attenuates vibration by means of friction and inelastic collisions between damping particles. This study proposes a dynamic model for a spur gear transmission system that contains damping particles inside the holes on gear bodies, using two-way coupling with multi-body dynamics and discrete element method. The equations of motion for the multi-body system are derived using Euler–Lagrange formalism. The discrete element method with a soft contact approach is used to model the dynamic behavior of damping particles. Hertzian contact theory and Coulomb friction theory are applied to modeling contacts. The effects of particle radius, coefficient of friction and restitution coefficient on the dynamic characteristics are explored. Numerical results show that vibration in the transmission is appreciably attenuated by the particle damping mechanism and that the contact friction, and not contact damping, dominates the energy dissipation of the multi-body system in such a centrifugal scenario.

## Keywords

Gear transmission Damping particles Coupled MBD–DEM method Dynamic characteristics## Notes

### Acknowledgements

The authors are very grateful to the ministry of science and technology (MOST) of Taiwan for financial support under Project Numbers: MOST 107-2221-E-008-052-MY2 and MOST 105-2221-E-008-048-MY2. The authors also greatly appreciate the valuable discussion with Professor W. Q. Xiao at Xiamen University in China and the technical support of Professor C. K. Lin at National Central University in Taiwan.

### Funding

The study was funded by the ministry of science and technology (MOST) of Taiwan (Grant Numbers: 105-2221-E-008-048-MY2 and 107-2221-E-008-052-MY2). The authors also greatly appreciate the valuable discussion with Professor W. Q. Xiao at Xiamen University in China and the technical support of Professor C. K. Lin at National Central University in Taiwan.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflicts of interest.

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