基于概率分布与肘部法融合优化K-means聚类的弧齿铣齿机热误差建模

doi:10.3901/JME.260699

机械工程学报 ›› 2026, Vol. 62 ›› Issue (13): 322-334.doi: 10.3901/JME.260699

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基于概率分布与肘部法融合优化K-means聚类的弧齿铣齿机热误差建模

王徉扬^1,2, 景秀并^1,2, 郑泽辉^1,2, 陈永亮^1,2, 王福军^1,2, 张大卫^1,2, 邢侃^1,2

1. 天津大学机械工程学院天津 300354;
2. 天津大学先进制造技术与装备天津市重点实验室天津 300354

收稿日期:2025-07-06 修回日期:2025-12-19 发布日期:2026-08-28
作者简介:王徉扬，男，1999年出生。主要研究方向为精密数控加工工艺与装备。E-mail：wyy_0363@126.com;景秀并(通信作者)，女，1975年出生，博士，副教授，硕士研究生导师。主要研究方向为精密、超精密数控加工工艺与装备、振动辅助加工、激光加工技术及其应用。E-mail：jingxiuping@tju.edu.cn
基金资助:
天津市科技计划资助项目(24PTGTOY00100，21ZXJBGX00020)。

Thermal Error Modeling of Spiral Bevel Gear Milling Machines Using An Improved K-means Clustering Based on Probability Distribution and Elbow Method

WANG Yangyang^1,2, JING Xiubing^1,2, ZHENG Zehui^1,2, CHEN Yongliang^1,2, WANG Fujun^1,2, ZHANG Dawei^1,2, XING Kan^1,2

1. School of Mechanical Engineering, Tianjin University, Tianjin 300354;
2. Key Laboratory Equipment Design and Manufacturing Technology, Tianjin University, Tianjin 300354

Received:2025-07-06 Revised:2025-12-19 Published:2026-08-28

摘要/Abstract

摘要： 数控机床的热误差是影响加工精度的关键因素之一，由于弧齿铣齿机存在复杂的多轴误差传递链，其影响尤为显著。以YKH2235弧齿铣齿机为研究对象，提出一种基于概率分布与肘部法融合优化K-means聚类的方法，根据机床温度数据特征有效筛选信息差异大、相互独立的温度敏感点，降低温度敏感点之间的共线性。将动态温度下降速率引入模拟退火算法优化BP神经网络，自适应调整算法搜索空间以提高收敛性能，并基于该方法建立机床各轴的热误差模型，最后通过多体理论构建机床末端的热误差模型。与现有普遍使用的温度敏感点筛选方法和人工神经网络对比验证，所提出的方法预测结果具有更高的精度和更好的鲁棒性。现场试切实验数据表明，所提出的热误差模型能够预测弧齿锥齿轮齿面误差，对弧齿铣齿机的热误差预测补偿有一定的参考意义。

关键词: 热误差建模, K-means聚类, 模拟退火算法, 多体理论

Abstract: Thermal errors of CNC machine tools are one of the key factors affecting machining accuracy. Due to spiral bevel gears milling machine involved in complex multi-axis error transmission chains, the effect of thermal error is particularly significant. A thermal characteristic experiment is conducted on the YKH2235 bevel gear milling machine. To effectively screen temperature-sensitive points, a probability distribution and elbow method fused to optimize K-means clustering (PDE-KM) is proposed, which reduces collinearity among the points by selecting those with high information variability and independence based on the machine tool’s temperature data. Additionally, a dynamic temperature decline rate is integrated into the simulated annealing-optimized BP neural network (DTR-SA-BP), enabling adaptive search space adjustment to improve convergence. DTR-SA-BP is used to develop thermal error model for each axis, and multi-body theory is employed to devise thermal error model for the end-point of machine tool. Compared with commonly used temperature-sensitive point selection methods and artificial neural networks, the proposed method demonstrates higher prediction accuracy and better robustness. Experimental results from trial machining indicate that the proposed thermal error model can effectively predict surface errors in bevel gear teeth and provides a valuable reference for thermal error compensation in bevel gear milling machines.

Key words: thermal error modeling, K-means clustering, simulated annealing algorithm, multibody approach

中图分类号:

TG502

王徉扬, 景秀并, 郑泽辉, 陈永亮, 王福军, 张大卫, 邢侃. 基于概率分布与肘部法融合优化K-means聚类的弧齿铣齿机热误差建模[J]. 机械工程学报, 2026, 62(13): 322-334.

WANG Yangyang, JING Xiubing, ZHENG Zehui, CHEN Yongliang, WANG Fujun, ZHANG Dawei, XING Kan. Thermal Error Modeling of Spiral Bevel Gear Milling Machines Using An Improved K-means Clustering Based on Probability Distribution and Elbow Method[J]. Journal of Mechanical Engineering, 2026, 62(13): 322-334.

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http://www.cjmenet.com.cn/CN/Y2026/V62/I13/322

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基于概率分布与肘部法融合优化K-means聚类的弧齿铣齿机热误差建模

Thermal Error Modeling of Spiral Bevel Gear Milling Machines Using An Improved K-means Clustering Based on Probability Distribution and Elbow Method

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