Chatter stability analysis in internal grinding of bearing rings
CHI Yulun
CAO Tianyi
ZHU Wenbo
YING Xiao'ang
Abstract：[Objective]To effectively suppress regenerative chatter during the lateral internal grinding of bearing rings and avoid workpiece surface degradation,a two-degree-of-freedom dynamic model incorporating a nonlinear grinding force relation was established to formulate the explicit mathematical correlation between processing parameters and self-excited vibration boundaries.[Methods]Firstly,governed by the fundamental laws of force balance,the nonlinear delay differential equations coupling the elastic contact effects of the grinding wheel and the workpiece were constructed.Secondly,an additional chatter frequency constraint was introduced to substitute critical eigenvalues into the transcendental quasi-polynomial characteristic equations.The resulting boundary equations were then solved numerically via a continuation algorithm tracking system combined with the Newton-Raphson iteration to comprehensively separate the stable and unstable cutting zones within the three-dimensional parameter space(Sf-τ1-τ2).Finally,modal impact testing was executed to extract the exact natural frequencies in the feed direction,which were subsequently substituted into the parameterized models to execute time-domain simulations and empirical grinding quality validations.[Results]Modal test results show that the 1st-order natural frequencies of the grinding wheel shaft and the bearing ring in the X-feed direction are 355 Hz and 200 Hz,respectively.Sensitivity evaluations reveal that below a critical workpiece speed of 40 rad/s,the stability boundary exhibits an extremely high sensitivity,triggering rapid alternations between stable and unstable cuts within minor velocity fluctuations.Conversely,operating above 40 rad/s dampens this sensitivity,allowing the grinding system to remain monotonous over wider velocity spans.Scaling down the grinding wheel speed or increasing the initial feed rate markedly suppresses the sensitivity of the system to workpiece speed adjustments.Empirically,bearing rings machined within the defined stable parameter intervals yield a superior surface roughness Ra of 0.35 μm and an inner roundness error Rn of 1.03 μm with completely clean surfaces,outperforming those processed within the unstable interval(Ra=0.47 μm,Rn=1.89 μm).
Keywords：ChatterGrindingNonlinear grinding force modelBearing ringLinear stability
Publication Date：2026-06-30
Online Publishing Date：2026-09-12(First online date of this platform, not the publication date of the document)
Pages：13( 78-90 )