Chatter stability analysis in internal grinding of bearing rings

CHI Yulun; CAO Tianyi; ZHU Wenbo; YING Xiao'ang

doi:10.16579/j.issn.1001.9669.2026.06.009

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Chatter stability analysis in internal grinding of bearing rings

·Vibration·Noise·Monitoring·Diagnosis· | 更新时间：2026-06-16

- Chatter stability analysis in internal grinding of bearing rings
- Journal of Mechanical Strength Vol. 48, Issue 6, Pages: 78-90(2026)
- 作者机构：
  
  上海理工大学机械工程学院，上海 200093
- 作者简介：
  
  ZHU Wenbo, E-mail: teacherzwb@163.com
- 基金信息：
- DOI：10.16579/j.issn.1001.9669.2026.06.009
  CLC： TH161
- Received：13 October 2024，
  
  Published：15 June 2026
- 稿件说明：
移动端阅览
迟玉伦，曹天熠，朱文博，等. 轴承套圈内圆磨削颤振稳定性分析［J］. 机械强度，2026，48（6）：78-90.

CHI Yulun，CAO Tianyi，ZHU Wenbo，et al. Chatter stability analysis in internal grinding of bearing rings［J］. Journal of Mechanical Strength，2026，48（6）：78-90.
迟玉伦，曹天熠，朱文博，等. 轴承套圈内圆磨削颤振稳定性分析［J］. 机械强度，2026，48（6）：78-90. DOI： 10.16579/j.issn.1001.9669.2026.06.009.

CHI Yulun，CAO Tianyi，ZHU Wenbo，et al. Chatter stability analysis in internal grinding of bearing rings［J］. Journal of Mechanical Strength，2026，48（6）：78-90. DOI： 10.16579/j.issn.1001.9669.2026.06.009.

摘要

目的

针对轴承套圈磨削加工过程中由于双再生效应极易引发加工颤振并严重恶化套圈表面质量的问题，基于非线性磨削力模型建立双时滞二自由度机械磨削系统动力学模型，用以精确求解并定量建立加工工艺参数与自激振动稳定性边界之间的映射关系。

方法

首先，考虑了砂轮与工件的弹性接触变形，依据力平衡基本定律构建了二自由度非线性时滞控制微分方程；其次，通过引入颤振频率附加约束，将超越特征方程转化为临界稳定性条件，并利用延拓算法，结合Newton-Raphson迭代法，对超越方程进行了全局数值解集搜索，从而在三维工艺参数空间（

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2.96333337

3.30200005

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403942&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403975&type=

2.45533323

3.21733332

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403953&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403952&type=

2.45533323

3.21733332

）中精细划分出轴承套圈磨削的绝对稳定区与非稳定区；最后，通过力锤敲击频响函数试验获取了系统进给方向的实际固有频率，并开展了多组加工参数的切削稳定性与表面形貌对比验证试验。

结果

模态试验结果表明，砂轮轴与轴承套圈在进给

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403955&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403991&type=

2.11666679

2.28600001

方向的1阶固有频率分别为355、200 Hz。动态特性与灵敏度分析表明，当工件转速低于40 rad/s时，系统稳定性对加工转速波动的灵敏度极高，转速在极小范围内即可引发稳定状态的频繁周期性交替；而高于40 rad/s时，系统灵敏度显著降低，可在较大的工件转速范围内保持单调稳定的磨削状态。在相同的初始进给量下，降低砂轮转速或增大初始进给量均能有效抑制系统对工件转速变化的灵敏度。采用稳定区参数加工的轴承套圈表面无振纹产生，其平均表面粗糙度

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403971&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403969&type=

2.96333337

3.21733332

（0.35 μm）、内圆圆度

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403987&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403986&type=

3.04800010

3.21733332

（1.03 μm）显著优于不稳定区参数（分别为0.47、1.89 μm）。

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 transc

endental 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 (

). 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

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2.53999996

2.37066650

-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

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110404007&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110403998&type=

3.30200005

3.21733332

of 0.35 μm and an inner roundness error

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3.38666677

3.21733332

of 1.03 μm with completely clean surfaces

outperforming those processed within the unstable interval (

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110404041&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110404040&type=

3.30200005

3.21733332

= 0.47 μm

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110404043&type=

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=110404002&type=

3.38666677

3.21733332

= 1.89 μm).

关键词

Keywords

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