Dynamic Study Of Periodic Time-Varying Cam-Follower Systems

In engineering practice, cam-follower system is used widely because of its easily achieving the special rule. At the case of cam-follower system at high speed, the inertia of kinetic components is bound to increase to a leap compared with the system at low speed, the elastic deformation of these components will affect the precision of the driven parts at special position, so the dynamic departure is inevitable. Hence, more and more consideration is been focused on the high-speed cam-follower system, or flexible cam-follower system. However, most of the previous studies have been limited entirely to just the linear cam-follower system with time invariable coefficients. There is little attention paid to the dynamic analysis of the time periodic coefficeints response, the clearance and the response of the high-speed cam-follower system with the clearance, etc.The focus of this paper is on the dynamic analysis of the high-speed cam-follower system with time periodic coefficeints. The main contributions are as following: the dynamic modeling, the solution of the linear and nonlinear differential equations, the dynamic response of the system, and so on.On account of the influence of the model of the high-speed cam-follower system on the dynamic character, the two modelings, the modeling with consideration of the clearance between the cam and the follower and the modeling without consideration of the clearance, were been addressed firstly. The cam-follower system is reduced to a multi-degree-freedom system similar to the practice, by ignoring of some accidental parts. Based on the method of equivalent energy, the multi-degree-freedom system will then be simplified to a single-degree- freedom system which can be analyzed more expediently.In this paper, dynamic stability of parametrically excited flexible cam-follower system on the weakly nonlinear condition is investigated by using the combination of both the method of multiple scales and the technique of Fourier series expansion. The equations of approximate transition curves in the plane of the dimensionless frequency and excitation (amplitude) parameter that separate stable from unstable solution are derived. The results show that the types of time distribution of follower motion events dominate the stability diagram and the existence of damping reduces the instability regimes effectively.In this paper, dynamic response of parametrically excited flexible cam-follower system on universal condition is investigated by using the method of the expansion of the system equation based on Chebyshev polynomials. The state vector and the periodic matrix of the system are expanded in terms of Chebyshev polynomials over the principal period at first. Such an expansion reduces the original problem to a set of linear algebraic equations from which the solution in the interval of one period can be obtained. Then, the transition matrix at the end of one period with Flouquet theory is obtained, which can provide the stability conditions via an eigen-analysis procedure.The two kind of harmonic balance methods, analytical HBM and DFT Numerical HBA, are used for the analysis of the parametrically excited flexible cam-follower system with consideration of the clearance between cam and follower. Through the two methods, the system equation is reduced to a series of nonlinear algebraic equations. The resulting equations are finally solved by using Broyden algorithm.At last, progress and shortcoming of studies presented in this paper is concluded, and ongoing research work is proposed.