Jinyuan Tang

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.

Simulation and optimization of computer numerical control-milling model for machining a spiral bevel gear with new tooth flank

Distinguished with the traditional tooth flank of spiral bevel gears, an accurate spherical involute tooth profile is of obvious advantages for the design and manufacture. For obtaining the gear model with enough tooth flank accuracy, simulation and optimization methodologies of computer numerical control-milling model are proposed. Initially, it gives an identification of the spherical involute tooth flank based on an improved formation theory. A universal simulation machining of the universal multi-axis computer numerical control-milling center is proposed to obtain an initial model. Then, in order to get/for getting improved tooth flank accuracy of the initial gear model, it presents some optimization methods included in the applications which are (1) non-uniform rational B-spline reconstruction by the Skinning method and (2) an overall interpolation based on Energy method. Finally, some given numerical examples are utilized to verify the form error of tooth flank. In addition, a closed-loop experiment scheme is provided to verify the validity of proposed methods.

Accurate modification methodology of universal machine tool settings for spiral bevel and hypoid gears

Universal machine tool settings with higher-order motion coefficients are developed to make accurate modification considering the actual machine geometric error compensation for spiral bevel and hypoid gears. First, the universal machine tool settings are exploited for the identification of the real tooth flank form error. Furthermore, the error sensitivity analysis method and an improved Levenberg–Marquardt algorithm with a trust-region strategy are utilized to obtain the solution of modification amount. Finally, a higher-order modification methodology for the universal machine tool settings is proposed which mainly covers three vital parts: (a) optimized selection of the modification settings, (b) modification of universal machine tool settings, and (c) machine geometric error compensation. Especially, a higher-accuracy fitting method for the form error tooth flank is investigated. Some numerical examples verify that the tooth flank form error after higher-order modification can reach less than 0.5 µm or even a smaller one, and the position error after compensating process spindle can be reduced from 0.0044861° to 0.0009232°. In addition, given experimental result can validate the feasibility of the proposed methodology.

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.

An advanced CAD/CAE integration method for the generative design of face gears

Abstract The conventional generative design of face gears involves CAD modeling and stress analysis by finite element analysis (FEA), which is usually performed repeatedly by optimizing design parameters until acceptable stress result is obtained. An integration of computer-aided design (CAD) and computer-aided engineering (CAE) can significantly reduce both time and labor costs to this generative design. However, this idea has not been adopted by any commercial software in designing face gears due to the complicated tooth surface geometry. The main problem is that the isoparametric discretization points of the tooth surface are non-equidistant. In this work, we derive an advanced method, based on the geometry characteristic of the tooth surface, to calculate the points as an even distribution on the tooth surface. In this method, sample points are discretized according to gear blank geometry and then a mapping between sample point and tooth surface point is established; according to which a comprehensive algorithm is proposed to recalculate the tooth surface points. Subsequently, the calculated tooth surface model is input to the proposed CAD/CAE integration method to implement the finite element analysis (FEA). The proposed method is validated by a series of face gear drives with varying shaft angles.