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工程设计学报
Chinese Journal of Engineering Design  2025, Vol. 32 Issue (2): 208-219    DOI: 10.3785/j.issn.1006-754X.2025.04.140
Reliability and Quality Design     
Prediction of machining error of machine tool based on nonlinear statics model of feed system
Shengtao LI1(),Dawei ZHANG1(),Shuguo ZHENG2
1.School of Mechanical Engineering, Tianjin University, Tianjin 300354, China
2.Tianjin First Machine Tool Co. , Ltd. , China General Technology (Group) Holding, Ltd. , Tianjin 300380, China
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Abstract  

In order to improve the machining accuracy of machine tools, the target of guide rail error is determined during the machine tool design stage, and the mapping relationship between guide rail errors and workpiece errors was studied. Firstly, based on Hertz contact theory, the coordination relationship between rolling element deformation and load was constructed, as well as the static equilibrium equation of the guide rail pair considering the structural stiffness of the slider. On this basis, the potential energy function for the guide rail pair was constructed. The equivalent stiffness model of the guide rail pair was established through the potential energy decomposition, and the finite element simulation verification was carried out. Then, based on the finite element model of the slider fastener, a stiffness matrix of the slider fastener facing the slider position nodes was constructed. Based on the principle of minimum potential energy and combined with the equivalent stiffness model of the guide rail pair, the error mapping relationship between the guide rail and the motion pair in the multi-slider system considering the structural stiffness of the slider fastener was established, and the finite element simulation verification was also carried out. Next, based on the multi-body system theory, a geometric error transfer model for machine tools was established to obtain the tool pose error. Finally, by employing the principle of geometric kinematics, a prediction model for workpiece machining errors was established by performing Boolean operations on the three-dimensional discrete points of the workpiece and the geometric boundaries of the tool, thereby establishing a mapping model between guide rail errors and workpiece errors. Taking a certain type of machine tool as an example, the influence of guide rail error and turntable error on workpiece error was compared and analyzed, which verified the feasibility of the proposed method. The research results can provide theoretical guidance for the precision design of machine tools.

Key words： guide rail error      workpiece error      mapping model      multi-slider system      motion pair error     
Received: 20 May 2024      Published: 06 May 2025
CLC:  TH 122  
Corresponding Authors: Dawei ZHANG     E-mail: shengtao_li@tju.edu.cn;medzhang@tju.edu.cn
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Shengtao LI
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Cite this article:

Shengtao LI,Dawei ZHANG,Shuguo ZHENG. Prediction of machining error of machine tool based on nonlinear statics model of feed system. Chinese Journal of Engineering Design, 2025, 32(2): 208-219.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2025.04.140     OR     https://www.zjujournals.com/gcsjxb/Y2025/V32/I2/208


基于进给系统非线性静力学模型的机床加工误差预测

为提高机床的加工精度，在机床设计阶段即确定导轨误差的目标，并对导轨误差与工件误差之间的映射关系进行了研究。首先，基于赫兹接触理论，构建了滚动体变形与载荷间的协调关系以及考虑滑块结构刚度的导轨副静力平衡方程；在此基础上，构造了导轨副势能函数，通过势能分解建立了导轨副的等效刚度模型，并开展了有限元仿真验证。然后，基于滑块固定件有限元模型，构建了面向滑块位置节点的滑块固定件刚度矩阵，并基于最小势能原理，结合导轨副等效刚度模型建立了考虑滑块固定件结构刚度的多滑块系统中导轨与运动副间的误差映射关系，同样进行了有限元仿真验证。接着，基于多体系统理论建立了机床几何误差传递模型，得到了刀具的位姿误差。最后，借助几何运动学原理，开展工件三维离散点与刀具几何边界的布尔运算，构建了工件加工误差预测模型，从而建立了导轨误差与工件误差间的映射模型。以某型号机床为例，对比分析了导轨误差与转台误差对工件误差的影响，验证了所提出方法的可行性。研究结果可为机床的精度设计提供理论指导。


关键词： 导轨误差,  工件误差,  映射模型,  多滑块系统,  运动副误差 
Fig.1 Size of slider and arrangement of rolling elements
Fig.2 Statics analysis of single-slider guide rail pair
Fig.3 Simulation model of single-slider guide rail pair
Fig.4 Comparison of simulation value and theoretical calculation value of equivalent stiffness of single-slider guide rail pair
Fig.5 Structure diagram of multi-slider system
Fig.6 Construction of coordinate system for multi-slider system
Fig.7 Force diagram of slider fastener
Fig.8 Deformation diagram of guide rail and slider
Fig.9 Comparison between calculation results and simulation results of motion pair errors
Fig.10 Topology structure of machine tool
Fig.11 Schematic diagram of tool machining position
Fig.12 Calculation process of workpiece surface contour
Fig.13 Structure of vertical coordinate grinder
Fig.14 Prediction results of workpiece surface contour under influence of guide rail error
Fig.15 Workpiece roundness error under influence of guide rail error
Fig.16 Prediction results of workpiece surface contour under influence of comprehensive error
Fig.17 Workpiece roundness error under influence of comprehensive error
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