Zehua Hu

Effect of Mesh Stiffness on the Dynamic Response of Face Gear Transmission System

The effect of mesh stiffness on the dynamic response of face gear transmission system combining with backlash nonlinearity is studied. First, a nonlinear time-varying (NLTV) and a nonlinear time-invariant (NLTI) dynamic models of face gear transmission system with backlash nonlinearity are formulated. The 6DOF motion equations of the face gear pair considering the mesh stiffness, backlash, contact damping and supporting stiffness are proposed. Second, the effect of mesh stiffness on the dynamic response of the face gear drive system is analyzed with the numerical method, where the mesh stiffness is expressed in two patterns as time-varying form and time-invariant form. According to the comparative study, some significant phenomena as bifurcation, chaos, tooth separation and occurrence of multijump are detected. The results show that different forms of mesh stiffness generate an obvious change on the dynamic mesh force.

Modal Analysis of Double-Helical Planetary Gears With Numerical and Analytical Approach

The vibration modal properties of double-helical planetary gear (DHPG) system with three-dimensional motion are investigated with a combined use of numerical and analytical approach in this paper. The lumped-parameter model of the DHPG considering stiffness coupled between the left gear and the right gear is developed. Load-sharing with journal bearings is accepted in this planetary gear system, so that four stiffness coefficients can be applied to describe the dynamic behavior between the planet gear and the carrier. The model has three planar degrees of freedom for the carrier and an added axial degree of freedom for all gears, considering the effect of axial dynamic forces. The vibration equations are obtained according to Lagrange equation. A modal type distribution map is plotted initially to simplify modal classification. With the application of this modal type distribution map, all vibration modes are categorized distinctly into three essentially different types of modes including planet mode (PM), rotational-axial mode (RAM), and planer-translational mode (PTM). Unique characteristics of these vibration modes, such as, eigenvalue number, multiplicity of natural frequencies and deflection relations, are deduced and proved analytically. For each type of vibration modes, the reduced-order eigenvalue problems are derived.

Effects of directional rotation radius and transmission error on the dynamic characteristics of face gear transmission system

The effects of directional rotation radius and transmission error excitation on the nonlinear dynamic characteristics of face gear transmission system are analyzed. First, the accurate time-varying mesh stiffness is calculated using finite element method, and the nonlinear motion equation of the system under static transmission error excitation is proposed. The frequency response curve, time history curve, dynamic mesh force curve and dynamic factor curve are given, and the phenomena of jump, multiple solutions and tooth impact are observed. The numerical results show that the effect of amplitude variation of directional rotation radius on the dynamic characteristics of face gear pair is less conspicuous than that of transmission error but actually existing. The amplitude of the dynamic response of face gear pair reduces to some extent with the uniform distribution of the loading area through enlarging the amplitude variation of directional rotation radius. The static transmission error excitation should be reduced to perfect the transmission property. The system is in periodic motion most of the time, and tooth impact occurs only near ω = 1 . Since its dynamic property at low velocity and high velocity is good, the system should get through the resonant area quickly in work.

Analysis of coupled lateral-torsional vibration response of a geared shaft rotor system with and without gyroscopic effect

A torsional gear dynamic model and a coupled lateral-torsional geared shaft rotor dynamic model are developed considering the time-varying mesh stiffness, backlash, and static transmission error excitation. The torsional dynamic transmission error responses gained from the torsional gear dynamic model and coupled lateral-torsional geared shaft rotor dynamic model are compared. The natural frequencies and mode shapes of the geared shaft rotor system are given and the frequency whirling behaviors are analyzed based on the Campbell diagram. The influences of gyroscopic effects of rotating shafts and meshing gear rotors on the lateral-torsional vibration responses of the geared shaft rotor system are talked about and some conclusions are drawn. (1) The coupled lateral-torsional geared shaft rotor dynamic model could reflect the jump phenomenon of dynamic responses near the critical speed of the gear pair as well as the pure torsional gear dynamic model and it can give more vibration features caused by geared shaft and bearings than the torsional gear dynamic model. (2) When the gear pair is set in the midpoint of the shaft, the influences of the gyroscopic effects on the gear pair’s lateral vibration responses are light and only can be observed near the high critical speeds. However, when the displacements from the gear body to the bearings are not the same, the influences of the gyroscopic effects on the lateral and torsional vibration responses are obvious and can be located both near the low critical speeds and the high critical speeds corresponding to the forward and backward whirling frequency. (3) The influences of the gyroscopic effects on the lateral and torsional vibration responses of the pinion are more obvious than those on the vibration responses of the gear. In addition, relative to the torsional vibration, the lateral vibration of the gear pair is more easily affected by the gyroscopic effect.