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Dynamics of nonlinear parametric planetary systems with kinematic constraints
 Hortel, Milan ; Škuderová, Alena
The report thoroughly discusses the theory of dynamics of planar mathematical-physical models of planetary differential and special cases of pseudoplanetary transmission systems. Due to the existence of the tooth backlashes, the system is seen as a discrete nonconservative strongly nonlinear parametric and multifrequency excited system with many degrees of freedom. The equations of motion are derived and compiled on the basis of the Lagrangian theory in a compact form and express the three areas of the gear mesh, ie. the range of normal gear mesh, gear backlash area and the area of the inverse gear mesh. After the rebound meshing gear profiles in the region of the side gear backlash, the impact effects occur when re contacting tooth flanks in both normal as well as during the eventual inverse mesh, depending on the size of the dynamic forces in the gearing.
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