A computer model for simulation of the wear behaviour in helical gears has been developed. The method used can deal with tooth modifications and different profiles. The authors have studied the effects of wear previously but only in a two-dimensional perspective. The objective of the paper is to compare the wear behaviour of gears using different approaches. The gear teeth in this model are regarded as thin uncoupled slices, the slicing method is valid when the contact area is slender in the rolling direction, which is the case for contacting gear teeth. The pressure distribution on each slice is calculated using the well-known theories of Hertz assuming an infinitely wide line-contact. When the pressure and velocity on the surfaces are known, a modified Archard's wear equation is applied to calculate wear depths on the teeth. The simulation then becomes an initial value problem since a complete mesh cycle is repeated a number of times with gradually changing surfaces due to the wear that is being integrated over each time step.

Simulation of Mild Wear in Helical Gears

Relationship between the contact force strength and numerical inaccuracies in piecewise-smooth systems

Investigation on planetary gearbox fault mechanism under variable speed conditions based on rigid-flexible coupling dynamics model

There exists a kind of complex periodic motion caused by the short-period error such as the pitch deviation, tooth surface crack, and so on, in the gear transmission system. It affects the transmission stationary of the system. This complex periodic motion is defined as the neighboring periodic motion in this paper. Its identification methods are proposed by using the multi-time scale Poincare mapping sections. The nonlinear dynamics model of spur gear pair considering pitch deviation under multi-state meshing is introduced. The neighboring periodic motion of the system under different parameters is analyzed according to the proposed identification methods. The multi-stable motion of the spur gear pair with short-period error is explored by analysis methods of nonlinear dynamics. Results show that the short-period error leads to the nonstationary transmission of spur gear pair. The periodic motion of the system shows a long-period motion in the micro-time scale due to the effect of the short-period error. The actual periodic number of the system motion is the number of mapping points obtained in the macro-time scale. The number of mapping points in micro-time scale illustrates point clusters. The number of phase trajectory in micro-time scale displays lines clusters. The short-period error affects the range of parameters for multi-stable motion in spur gear pair. These identification and analysis methods provide a theoretical basis for investigation of the neighboring periodic motion in nonlinear systems.

Neighboring periodic motion in spur gear pair and its identification methods

\n Nonlinear vibration, a main factor affecting the dynamic stability, widely exists in the transmission system. In addition, geometric eccentricities caused by the manufacturing errors are inevitable in the gear transmission system, which may lead to the excessive nonlinear vibration. In order to suppress the nonlinear vibration under the excitation of the geometric eccentricities, a rigid–flexible gear pair consisting of the ring gear, the composite material, and the hub is proposed in this study. A dynamic model with nine degrees-of-freedom which considers geometric eccentricities is proposed to analyze the nonlinear dynamic characteristics of the rigid–flexible gear pair. Furthermore, the dynamic characteristics of the rigid–flexible gear pair and the rigid gear pair are compared within a wide range of operating conditions. The comparative analysis demonstrates that the rigid–flexible gear pair has better vibration suppression effect on the system.

Nonlinear Dynamic Analysis of a Rigid–Flexible Gear Transmission Considering Geometric Eccentricities

\n At present, the mean value of the meshing stiffness and the gear backlash is a fixed value in the nonlinear dynamic model. In this study, wear is considered in the model of the gear backlash and time-varying stiffness. With the increase of the operating time, the meshing stiffness decreases and the gear backlash increases. A six degrees-of-freedom nonlinear dynamic model of a new rigid-flexible gear pair is established with time-varying stiffness and time-varying gear backlash. The dynamic behaviors of the gear transmission system are studied through bifurcation diagrams with the operating time as control parameters. Then, the dynamic characteristics of the gear transmission system are analyzed using excitation frequency as control parameters at four operating time points. The bifurcation diagrams, Poincaré maps, fast Fourier transform (FFT) spectra, phase diagrams, and time series are used to investigate the state of motion. The results can provide a reference for the gear transmission system with wear.

Investigation on Nonlinear Dynamic Characteristics of a New Rigid-Flexible Gear Transmission with Wear

\n In this study, a nonlinear dynamic model of a spur gear transmission system with non-uniform wear is proposed to analyze the interaction between surface wear and nonlinear dynamic characteristics. A quasi-static non-uniform wear model is presented, with consideration of the effects of operating time on mesh stiffness and gear backlash. Furthermore, a nonlinear dynamic model with six degrees-of-freedom is established considering surface friction, time-varying gear backlash, time-varying mesh stiffness, and eccentricity, and the Runge–Kutta method applied to solve this model. The bifurcation and chaos in the proposed dynamic model with the change of the operating time and the excitation frequency are investigated by bifurcation and spectrum waterfall diagrams to analyze the bifurcation characteristics and the dimensionless mesh force. It is found that surface wear is generated with a change in operating time and affects the nonlinear dynamic characteristics of the spur gear system. This study provides a better understanding of nonlinear dynamic characteristics of gear transmission systems operating under actual conditions.

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

In this study, a new rigid–flexible gear with metal rubber is proposed to reduce the vibration of the gear transmission system. A nonlinear dynamic model with nine degrees of freedom considering be...

Zhibo Geng

Papers

Investigation on Nonlinear Dynamic Characteristics of a New Rigid-Flexible Gear Transmission with Wear

Bifurcation and Chaos of a Spur Gear Transmission System With Non-Uniform Wear

Nonlinear Dynamic Analysis of a Rigid–Flexible Gear Transmission Considering Geometric Eccentricities

Analysis on the vibration reduction for a new rigid–flexible gear transmission system:

Modelling and analysis of a spur gear pair with the effect of bearing clearances