Zhiwei You, Yuankui Luo, Lixin Xu
The idler gear is a transitional component in a gear transmission system. By meshing with two non-contacting gears, it changes the rotation direction of the driven gear while maintaining the original transmission ratio. Based on the theories of contact dynamics and multibody dynamics, this paper establishes a contact dynamics model for a three-gear system, which consists of two components: a tooth profile mathematical model and a contact dynamics model. In the tooth profile mathematical model, the meshing phase angle must be calculated to satisfy the initial assembly relationships. In the contact dynamics model, a 9DoF dynamic differential equation for the three-gear system needs to be established, and a contact model for the three-gear system should be constructed based on the mathematical contact judgment method derived from previous research. Based on the established model, this paper investigates the dynamic responses of two-gear and three-gear systems under varying input speeds and load torques. By comparing these results, the influence of the idler gear on the vibration characteristics of the three-gear system is analyzed. The proposed model and findings provide useful reference for the design of idler gears in gear transmission systems.