Nonlinear Dynamics of Three-Ring Reducer with Dynamic Tooth-side Clearance

Abstract Reduction gears, especially those with fewer gears similar to the three-ring reducer, can cause changes in the gap between gear teeth due to wear of the tooth surfaces during the application process. The dynamic variation of the gear tooth gap adds nonlinear factors to the dynamic behavior of the engagement process, thus complicating its dynamic behavior and leading to increased vibration and wear, which affects the expansion of the application of fewer gears in the aerospace field. To solve this problem, the aeronautical three-ring gear reducer with fewer gears is taken as the research object, the tooth surface state at different wear stages is considered, the Weierstrass-Mandelbor function is introduced to describe the tooth surface morphology and the time-varying tooth flank gap is calculated, a bending-torsion coupled Six-degree-of-freedom nonlinear vibration model is established. Using the fractal dimension of the Weierstrass-Mandelbor function to describe the state of the tooth surface at different wear stages and the dynamics of aviation three-ring reducer with small tooth difference is analyzed, with the increase of fractal dimension under the same initial conditions, the gear transmission system changes from quasi-periodic motion state to chaotic motion state. By considering the influencing factors of torque and rotational speed, the nonlinear dynamic behaviors at different wear stages are analyzed. The results show that as the rotational speed increases, the system response cycle exhibits a chaotic-proposed cycle-chaotic law of motion. As the torque increases, the system responds to periodic processes now chaotic-hypothetical periodic laws of motion. The findings of the study can effectively support the vibration and noise reduction of the three-ring reducer and provide a theoretical basis for the expansion of its application in the aerospace field.