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A general approach to the dynamic analysis of planar geared linkage mechanisms (GLMs) is presented based on their structural topological characteristics and the theory of type transformation. First, the geared linkage Assur group (GLAG) turned out to be not only a kinematical determinate system but also a force determinate system. A method of force analysis for multiple joints is proposed. A systematic method for the dynamic analysis of GLAGs is obtained through decomposing a GLAG into a series of sequential independent kinematic units, such as simple links and dyads. Then, the unity and mutual reversibility between kinematic and dynamic analysis of GLAGs are revealed. The dynamic analysis models and explicit solutions for the basic kinematic units are derived from force determination and the process of dynamic analysis of GLMs is established in an algorithmic fashion. Finally, an application program has been developed through which the complete process from kinematic analysis to dynamic analysis can be accomplished automatically for any GLM. An example is given to illustrate the process.
This paper presents a three-dimensional model of a helical two-stage gear system. Excitation is induced by periodic variation of the mesh stiffness. This case describes the real working of the gearing. The mesh phasing variation is related to the number of teeth and also to the location of the gears. First, dynamic response is calculated using Newmark's step-by-step time integration method. The numerical results are presented in both the frequency and time domains. The dynamic behaviour of a defect-free gear system and a defective one are compared in both the time domain and frequency domain. Two types of defect are considered: a cracked tooth and misalignment. The cracked tooth produces an amplitude modulation with the mesh frequency and its first harmonics on the dynamic response. An amplitude modulation also occurs when a misalignment is introduced. The Wigner–Ville distribution method is used to show the dynamic behaviour in the joint time–frequency domain and to localise the cracked teeth.