Dynamic Analysis Of Face Gear Drive Based On Meshing Characteristics

Abstract:As a new type of gear transmission system, face gear drive pair is widely used in the aerospace field with many advantages including high transmission ratio, compact structure and torque splitting. In order to improve and expand its advantages, the stability, vibration and noise have been become the keys of the theoretical research of face gear transmission system. Based on the theory of the nonlinear vibration, this paper studied the meshing characteristic, method of modeling and nonlinear dynamic responses including bifurcation and chaos. The main contents and conclusions are listed as follows:(1) Based on the meshing theory and tooth surface equation, the meshing points, corresponding principle direction and line of action of face gear were obtained applying with numerical method. The real accurate meshing stiffness and time-varying meshing parameters were gained applying the quasi-static tooth contact analysis of face gear pair with finite element approach.(2) Taking single face gear and pinion pair as object, a single-degree-of-freedom torsional vibration dynamic model considering the time-varying meshing stiffness and nonlinear backlash was proposed. The dynamic equation of face gear pair was solved by the Runge-Kutta numerical method and the dynamic responses including the bifurcation diagram, poincare map and spectrum were obtained. The stability of face gear transmission system dynamic responses were analyzed with the Floquet theory and Lyapunov exponent and the effects of transmission error excitation and directional rotation radius on the dynamic responses were investigated.(3) Taking the structure of shafts, supporting bearings, engine and load into account, a multi-degree-of-freedom dynamic system coupled the lateral and torsional vibration effect was developed. The dynamic responses including the bifurcation and chaos behaviors of face gear transmission system were obtained and analyzed. The periodic motion, chaotic motion and nonlinear jump phenomenon were observed and a path from periodic motion to chaotic motion through doubling-bifurcation was discovered.(4) The phase diagram, bifurcation diagram, PPV curves and RMS curves of dynamic responses were obtained. The effects of meshing stiffness, load and backlash on the dynamic behaviors in the multi-degree-of-freedom face gear dynamic system were investigated.(5) A rolling contact test of face gear drive pair was made and the contact area of face gear pair was obtained. The results of the test and tooth contact analysis and theoretical calculation were compared and the accuracy of the finite element model was proved. Based on the test results of input shaft angle and output shaft angle of face gear pair and the definition of dynamic transmission error, the dynamic transmission error of face gear was obtained and compared with the results of the dynamic analysis, the form and amplitude of the dynamic transmission error were coincident.