The investigation of nonlinear dynamic characteristics of spur gear with angular misalignment error based on an improved dynamic model

Abstract

Angular misalignment error is a prevalent occurrence in gear systems, mainly caused by manufacturing and installation errors in gearbox components. This significantly impacts the meshing characteristics of the system, making it necessary to carry out the nonlinear dynamic analysis of spur gear pairs with angular misalignment errors. In this study, a meshing stiffness model for a spur gear pair with angular misalignment error is established based on the Load Teeth Contact Analysis (LTCA) method. The effect of misalignment errors on the distribution of tooth surface stiffness are analyzed. Additionally, an improved dynamic model considering angular misalignment errors and variable backlash along the tooth width direction was proposed based on the lumped mass method and the slicing method. The effects of angular misalignment errors parallel and perpendicular to the meshing plane on the nonlinear dynamics of the system were studied. Frequency domain diagrams, Poincaré diagrams, and bifurcation diagrams were employed to comprehensively analyze the nonlinear characteristics of the system. The results indicate that with light loads, the system experiences a sequence of periodic and chaotic motions as θa increases, eventually returning to periodic motion. Conversely, θv shows minimal influence on the gear backlash, with the system exhibiting periodic motion when θv is small. As θv increases, the system transitions to chaotic motion before ultimately returning to periodic motion. Under heavy load conditions, as θa increases, the system transitions gradually from chaotic to periodic motion. However, regardless of the variations in θv, the system consistently remains in periodic motion.