Analysis for the nonlinear primary resonance behavior and bifurcation characteristics of the hydrostatic spindle

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 metho...

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Bibliographic Details
Published in:Nonlinear dynamics Vol. 113; no. 15; pp. 19451 - 19474
Main Authors: Zhang, Han Wen, Rong, You Min, Cui, Hai Long, Hu, Hai Dong, Huang, Yu
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.08.2025
Subjects:
Accuracy
Algorithms
Amplitudes
Bifurcations
Dynamical systems
Excitation
Frequency response
Journal bearings
Mathematical models
Mechanics (physics)
Nonlinear dynamics
Nonlinear phenomena
Nonlinearity
Parameters
Resonance
Stiffness
Thrust bearings
Vibration
ISSN:0924-090X, 1573-269X
Online Access:Get full text
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Summary: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.
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ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-025-11186-0