Analysis of the influence of phase angle on the motion characteristics of two-stage elliptical gear transmission system

Elliptical gears are widely used in the fields of aerospace and automation equipment due to their excellent variable speed characteristics and compact structure. To reveal the control mechanism of phase angle on the motion characteristics of two-stage elliptical gear transmission system (TSEGTS) and improve its stability under variable speed loading, this paper proposes a modeling method that integrates two-dimensional tooth profile envelope method and image processing technology to extract tooth profile and analyze system motion characteristics. By introducing the fluctuation coefficient as a stability indicator, the system studied the effects of phase angle, input speed, and load torque on angular velocity, angular acceleration, and torque. The results indicate that the phase angle has a significant periodic modulation effect on the motion characteristics of the system. The angular velocity and acceleration of intermediate shaft B and output shaft C, as well as the torque of output shaft C, exhibit a distribution with 90° as the axis of symmetry within the range of 0°–180°. The average torque fluctuation coefficients of input shaft A and intermediate shaft B in the range of 0°–90° are 4.02 and 3.03, respectively, which are significantly higher than the 3.46 and 1.99 coefficients in the range of 90°–180°. As the input speed increases from 5π to 20π rad/s, the torque fluctuation coefficients of shafts A, B, and C increase from 2.87, 1.37, and 0.53 to 22.54, 14.19, and 8.43, respectively. When the load torque increases from 2 to 8 N·m, the fluctuation coefficients of the three axes decrease from 11.33, 7.12, and 4.22 to 3.51, 1.91, and 1.05, respectively. The increase in load torque effectively suppresses fluctuations and improves meshing stability. The experimental and simulation results are consistent, verifying the effectiveness of the model. The research results can provide theoretical basis for parameter optimization and dynamic performance control of TSEGTS.