A parametric solution domain structure based on cell mapping theory and a control method based on radial basis function neural network are proposed to solve the dynamic characteristic transition and control problem of bevel gear system with backlash. The dynamics model of 7-degree-of-freedom spiral bevel gear was established by using the concentrated mass method. Then, the frequency and load parameter plane is constructed based on cell mapping theory, and the pseudo-fixed point continuous tracking algorithm is used to solve the transition rule of bifurcation, tooth surface impact, tooth no-meshing, tooth back contact and dynamic load characteristics of the straight bevel gear system. It is found that frequency and tooth impact are the main factors affecting the periodic bifurcation. With the increase of load, the tooth no-meshing and impact weaken, and the dynamic load coefficient increases. For the chaotic phenomena of the system in the plane, a parametric feedback controller is designed, and the fitness function is constructed based on Poincaré cross section Euclidean distance. The adaptive gravity search algorithm is used to optimize the controller parameters, so as to realize the effective control of chaos, quasi-period and periodic motions to periodic orbit.
Key words
nonlinear vibration /
spiral bevel gear system /
bifurcation /
tooth impact /
RBF neural network
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