| The cycloid ball planetary transmission is a precise planetary transmission mechanism, and the vibration caused in working process will influence the precision, the production efficiency and the operating life of mechanical devices, so the higher requirements are present to improve the dynamic characteristics. By investigating the dynamic problems of the cycloid ball planetary transmission system, it has an important significance to the dynamic characteristics optimization, and offers a general scientific reference to the other planetary transmission systems in practical engineering applications.Firstly, the nonlinear mechanical model of the cycloid ball engagement pair is established using the hyperstatic method. The load of the engagement pair is present by solving the energy equilibrium equation. The central deformation and the central pressure of the engagement pair in contact zone are calculated by the Hertz contact formula, and the engagement positions of the parameter extremes in transmission process are obtained. The deformed deflection surface equation of contact zone, the stress distribution under contact surface, and the depth of the maximum shear stress are presented using the superposition method. The finite element models of the engagement pair are established, and the loads are applied to the models according to the load distribution of the engagement pair. The stress distribution states are present by the finite element simulation of the engagement process, and the alternate variation regularity of the loading contact pairs as well as the stress variation regularity of the engagement points is analyzed.Secondly, the translational-torsional coupling dynamic model of the cycloid ball planetary transmission system is established in the following coordinate system of the eccentric shaft, and the model includes some key factors such as the time-variant engagement rigidity, the bearing rigidity and the gyroscopic effect. The governing differential equations and the dynamic equations of system are derived to investigate the natural characteristics. The engagement rigidity excitation is analyzed in time-domain and frequency-domain. The frequency spectrum components of the engagement rigidity excitation are present, and the influences of the different system parameters to the engagement rigidity excitation are analyzed. The natural frequencies and the principal modes of system are present by solving the eigenvalues and the eigenvectors. The sensitivities of the natural frequencies are analyzed, and the influence of the system parameters as well as the transmission structures to the natural frequencies is discussed.Thirdly, the parametric vibration analytic model of the cycloid ball planetary transmission system is established by transformation and uncoupling of the dynamic equations. The combination resonance frequencies of system are calculated using the multi-scale method, and the dynamic stability of system is analyzed. The characteristic functions of system of the internal resonance are derived using the Lindstedt-Poincaréperturbation method, the boundary curves of the stability zones are obtained, the stability diagrams are drawn, and the influence of the generalized mass and the engagement rigidity to the dynamic stability is analyzed. The linear damping is added in the dynamic equations, and the influence of the damping to the dynamic stability is analyzed. The steady-state response of the parametric vibration of system is solved using the perturbation method.Finally, the parametric models and the simulated assembly of the cycloid ball planetary transmission mechanism are completed using the three-dimensional design software Pro/E. According to the accurate engagement conditions of the cycloid ball engagement pair, the design criterions for the sectional profile, the angle and the depth of the cycloid groove are present, and the design formula for the cycloid curtate coefficient of the compact arrangement structure of balls is also present. The numerical control manufacture process is designed using the module of Pro/NC. The manufacture process of the cycloid groove is simulated by the locus manufacture method, and the procedure of the numerical control milling is programmed. The design process of the cycloid ball planetary transmission mechanism is summarized, and the prototype is manufactured successfully.
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