关键词: 铰链, 间隙, 非线性系统, 动力学

Abstract: Dynamical modeling and simulation of a symmetric rigid flexible coupling system with hinge backlashes are studied.The rigid beam is simplified as a thin cantilever with a lumped mass in the free end.A new concept——bi rigidity of a thin beam is put forward at first.Then,based on the analyzing of the kinematic relationship,the dynamical model with five degrees of freedom of the coupling system is derived by using d'Alambert principle.The anti symmetric initial value response of the system is discussed in detail.It shows that there are one kind of vibration with low frequency and two kinds of vibrations with high frequencies in the response.Because of the vibrations,a small enough step must be used in simulation to obtain reliable numerical solutions.Simulations show that the frequency of the former would decrease with the backlash angles appearing and increasing.