Nonlinear dynamics analysis of high contact ratio gears system with multiple clearances

Abstract

A brief research status on high contact ratio gears (HCRG) is first conducted to obtain a basic understanding. Subsequently, a nonlinear dynamic model of HCRG with multiple clearances is established by the lumped mass method, in which timevarying mesh stiffness (TVMS), static transmission error, gear backlash, and bearing radial clearance are taken into consideration as well. The TVMS of HCRG is calculated based on an improved potential energy model and then fitted into a Fourier series form. After the dimensionless treatment, the system differential equations of motion are solved using Runge-Kutta numerical integration method. With the help of bifurcation diagrams, largest Lyapunov exponent charts, time-domain waveforms, FFT spectra, Poincaré maps, and phase diagrams, the influence of excitation frequency, gear backlash, mesh damping ratio, error fluctuation, and bearing radial clearance on the nonlinear dynamic characteristics of the system is investigated in detail. The results show that with the changes of these analysis parameters, the system exhibits different types of nonlinear behaviors and dynamic evolution mechanism, including period-one, multi-periodic, quasi-periodic, chaotic motions, and jump discontinuity phenomenon. Meanwhile, three typical routes to chaos, namely period-doubling bifurcation to chaos, quasi-period to chaos, and crisis to chaos, are also demonstrated. Additionally, it is found that the bearing radial clearance produces a weaker nonlinear coupling effect when compared to gear backlash. The research results can provide a certain theoretical support for the dynamic design and vibration control of the HCRG.

Influence of Pitch Error on Vibration, Bifurcation, and Chaos Characteristics of the Helical Gear Pair System

“…In equations ( 8)- (12), ω h , f, k m , and m e are the natural frequency, meshing frequency, average meshing stiffness, and equivalent mass of the helical gear pair system, respectively.…”

“…To facilitate the storage of lubricating oil and prevent the tooth surface from being stuck by thermal expansion, gear in the assembly process along the direction of the meshing line to leave a specific tooth side clearance. e tooth side clearance function can be expressed as follows [12]:…”

“…Han and Qi [11] studied the influence of tooth spalling and local fracture on the meshing stiffness and vibration characteristics of the helical gear pair system. Huang et al [12] studied the effects of excitation frequency, backlash, meshing damping ratio, and bearing radial clearance on bifurcation and chaos characteristics of the high contact ratio gear system. Zhang et al [13] investigated the impact of bearing clearance on the vibration characteristics of the spur gear transmission system.…”

Review and Comparison of Clearance Control Strategies

“…Thus, the mechanical transmission structure is an important component of servo systems. Considering the manufacturing and assembly errors of the servo system, as well as the hinge connection or screw connection between the transmission mechanisms, kinematic pair clearance is inevitably generated [5][6][7][8]. The nonlinearity of the clearance is destructive, and the clearance of the kinematic pair causes the actual motion trajectory of the mechanism to deviate from the expected trajectory, significantly affecting the response speed, control accuracy, and motion performance of the system.…”

Calculating the Load Distribution and Contact Stress of the Disposable Harmonic Drive under Full Load

“…Compared to the traditional structure, the drive led to significant reductions in the contact stress and bending stress. Considering the time-varying mesh stiffness, gear backlash, static transmission error, and other parameters, Huang et al [15] established a nonlinear dynamic model of a high contact ratio gear with multiple clearances. Jia et al [16] proposed a tooth-profile modification scheme to reduce the contact stress and transmission error.…”