Analysis for the nonlinear primary resonance behavior and bifurcation characteristics of the hydrostatic spindle - Zhang, Han Wen; Rong, You Min; Cui, Hai Long; Hu, Hai Dong; Huang, Yu (Nonlinear dynamics, 2025)
In order to effectively reduce or avoid the abnormal vibration of the hydrostatic spindle caused by the nonlinear oil film force, it is particularly important to grasp the vibration behavior mechanism. Therefore, the analytical mechanics combined with the elastic mechanics method-assumed modal method is applied to establish the nonlinear dynamics model and the average method is introduced to solve the amplitude-frequency response equation of the primary resonance. Based on amplitude-frequency response equations and singularity theory, a transfer-set root-finding algorithm is proposed to solve the primary resonance bifurcation boundary solution problem of the amplitude-frequency and parameter coupling system. The correctness of the dynamics model and the average solution results are verified by experiments. The effects of spindle stiffness, excitation force and oil film gap on the nonlinear primary resonance behavior of hydrostatic spindle and the bifurcation characteristics of the two-parameter variables are investigated. The results show that: due to the nonlinearity of the supporting oil film force, the nonlinear primary resonance behaviors of oil film oscillation phenomenon, jump phenomenon, multi-solution phenomenon, unstable solution and whirl will appear in the range of dimensionless frequency ratios w = [0.6, 0.8]. The spindle stiffness suppresses the nonlinear phenomena, the excitation force and oil film gap promote the nonlinear phenomena. When the structural parameter combination points fall within the range of the root-finding algorithm of the transfer set, there will be different degrees of bifurcated nonlinear dynamic behavior, and when the structural parameter combination points fall outside, there is basically no nonlinear dynamic behavior.