Similar articles

Abstract: accuracy allocation is crucial in the accuracy design of machining tools. Current accuracy allocation methods primarily focus on positional deviation, with little consideration for tool direction deviation. To address this issue, we propose a geometric error cost sensitivity-based accuracy allocation method for five-axis machine tools. A geometric error model consisting of 41 error components is constructed based on homogeneous transformation matrices. Volumetric points with positional and tool direction deviations are randomly sampled to evaluate the accuracy of the machine tool. The sensitivity of each error component at these sampling points is analyzed using the Sobol method. To balance the needs of geometric precision and manufacturing cost, a geometric error cost sensitivity function is developed to estimate the required cost. By allocating error components affecting tool direction deviation first and the remaining components second, this allocation scheme ensures that both deviations meet the requirements. We also perform numerical simulation of a BC-type (B-axis and C-axis type) five-axis machine tool to validate the method. The results show that the new allocation scheme reduces the total geometric error cost by 27.8% compared to a uniform allocation scheme, and yields the same positional and tool direction machining accuracies.

基于几何误差成本灵敏度和姿态偏差先行的五轴机床精度分配方法

[1]ArmillottaA, 2020. Selection of parameters in cost-tolerance functions: review and approach. The International Journal of Advanced Manufacturing Technology, 108(1-2):167-182.

[2]ChanK, SaltelliA, TarantolaS, 1997. Sensitivity analysis of model output: variance-based methods make the difference. Proceedings of the Winter Simulation Conference, p.261-268.

[3]ChenGD, LiangYC, SunYZ, et al., 2013. Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool. The International Journal of Advanced Manufacturing Technology, 68(9-12):2525-2534.

[4]ChenQD, HuXL, LinM, et al., 2023. Research review of error compensation technology for ultra-precision machining. China Mechanical Engineering, 34(3):253-268 (in Chinese).

[5]ChengQ, ZhaoHW, ZhangGJ, et al., 2014. An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis. The International Journal of Advanced Manufacturing Technology, 75(1-4):107-121.

[6]ChengQ, DongLF, LiuZF, et al., 2018. A new geometric error budget method of multi-axis machine tool based on improved value analysis. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(22):4064-4083.

[7]Díaz-SaldañaG, Osornio-RíosRA, Zamudio-RamírezI, et al., 2023. Methodology for tool wear detection in CNC machines based on fusion flux current of motor and image workpieces. Machines, 11(4):480.

[8]DingS, ChenZW, ZhangH, et al., 2023. Gear evaluation deviations-based crucial geometric error identification of five-axis CNC gear form grinding process. Journal of Manufacturing Processes, 99:663-675.

[9]FanJW, TaoHH, PanR, et al., 2020. An approach for accuracy enhancement of five-axis machine tools based on quantitative interval sensitivity analysis. Mechanism and Machine Theory, 148:103806.

[10]FanYC, FanKC, HuangYB, 2024. Modeling and compensation of enhanced volumetric error of machine tools containing crosstalk errors. Precision Engineering, 86:252-264.

[11]ISO (International Organization for Standardization), 2012a. Test Code for Machine Tools–Part 1: Geometric Accuracy of Machines Operating under No-Load or Quasi-Static Conditions, ISO 230-1:2012. ISO, Geneva, Switzerland.

[12]ISO (International Organization for Standardization), 2012b. Test Code for Machine Tools–Part 7: Geometric Accuracy of Axes of Rotation, ISO 230-7:2012. ISO, Geneva, Switzerland.

[13]JiangXG, CrippsRJ, 2015. A method of testing position independent geometric errors in rotary axes of a five-axis machine tool using a double ball bar. International Journal of Machine Tools and Manufacture, 89:151-158.

[14]LiZH, FengWL, YangJG, et al., 2018. An investigation on modeling and compensation of synthetic geometric errors on large machine tools based on moving least squares method. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 232(3):412-427.

[15]LinMQ, YuanPJ, TanHJ, et al., 2015. Improvements of robot positioning accuracy and drilling perpendicularity for autonomous drilling robot system. IEEE International Conference on Robotics and Biomimetics, p.1483-1488.

[16]LiuJ, TuLW, LiuGZ, et al., 2019. An analytical structural global sensitivity analysis method based on direct integral. Inverse Problems in Science and Engineering, 27(11):1559-1576.

[17]NiuP, ChengQ, LiuZF, et al., 2021. A machining accuracy improvement approach for a horizontal machining center based on analysis of geometric error characteristics. The International Journal of Advanced Manufacturing Technology, 112(9-10):2873-2887.

[18]NiuP, ChengQ, LiuZF, et al., 2025. Multi-objective optimal tolerance allocation design of machine tool based on NSGA-II algorithm and thermal characteristic analysis. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2025:09544054241310330.

[19]SaltelliA, AleksankinaK, BeckerW, et al., 2019. Why so many published sensitivity analyses are false: a systematic review of sensitivity analysis practices. Environmental Modelling & Software, 114:29-39.

[20]SobolIM, 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55(1-3):271-280.

[21]SongLQ, SunT, JiaRY, et al., 2024. An error allocation method for five-axis ultra-precision machine tools. The International Journal of Advanced Manufacturing Technology, 130(5-6):2601-2616.

[22]TianWJ, 2014. Investigation into Accuracy Design and Error Compensation of High-Precision Horizontal Machining Centers. PhD Thesis, Tianjin University, Tianjin, China(in Chinese).

[23]WangYH, MinYX, YuGY, et al., 2023. Parameters coordinated optimization of subsynchronous oscillation of doubly fed induction generator system based on impedance sensitivity analysis with Sobol method. High Voltage Engineering, 49(4):1703-1713 (in Chinese).

[24]WeiXY, YeHH, WangG, et al., 2024. Adaptive thermal error prediction for CNC machine tool spindle using online measurement and an improved recursive least square algorithm. Case Studies in Thermal Engineering, 56:104239.

[25]WuHR, ZhengHL, LiXX, et al., 2020a. A geometric accuracy analysis and tolerance robust design approach for a vertical machining center based on the reliability theory. Measurement, 161:107809.

[26]WuHR, ZhengHL, LiXX, et al., 2020b. Robust design method for optimizing the static accuracy of a vertical machining center. The International Journal of Advanced Manufacturing Technology, 109(7-8):2009-2022.

[27]XiaCJ, WangSL, SunSL, et al., 2019. An identification method for crucial geometric errors of gear form grinding machine tools based on tooth surface posture error model. Mechanism and Machine Theory, 138:76-94.

[28]XiaCJ, WangSL, MaC, et al., 2020. Crucial geometric error compensation towards gear grinding accuracy enhancement based on simplified actual inverse kinematic model. International Journal of Mechanical Sciences, 169:105319.

[29]XiangST, WuCY, 2021. Application of sensitivity analysis in precision optimization of CNC machine tools: a state-of-the-art review. Aeronautical Manufacturing Technology, 64(22):40-47 (in Chinese).

[30]XingKL, AchicheS, MayerJRR, 2019. Five-axis machine tools accuracy condition monitoring based on volumetric errors and vector similarity measures. International Journal of Machine Tools and Manufacture, 138:80-93.

[31]XiongG, DingY, ZhuLM, 2019. Stiffness-based pose optimization of an industrial robot for five-axis milling. Robotics and Computer-Integrated Manufacturing, 55:19-28.

[32]YuJB, ChengX, LuL, et al., 2021. A machine vision method for measurement of machining tool wear. Measurement, 182:109683.

[33]YuanPJ, WangQS, ShiZY, et al., 2014. A micro-adjusting attitude mechanism for autonomous drilling robot end-effector. Science China Information Sciences, 57(12):1-12.

[34]ZhangHN, XiangST, WuC, et al., 2024. Optimal proportion compensation method of key geometric errors for five-axis machine tools considering multiple-direction coupling effects. Journal of Manufacturing Processes, 110:447-461.

[35]ZhangK, ZhangLQ, YanYC, 2016. Single spherical angle linear interpolation for the control of non-linearity errors in five-axis flank milling. The International Journal of Advanced Manufacturing Technology, 87(9-12):3289-3299.

[36]ZhangZ, JiangF, LuoM, et al., 2024. Geometric error measuring, modeling, and compensation for CNC machine tools: a review. Chinese Journal of Aeronautics, 37(2):163-198.

[37]ZhangZL, LiuZF, ChengQ, et al., 2017. An approach of comprehensive error modeling and accuracy allocation for the improvement of reliability and optimization of cost of a multi-axis NC machine tool. The International Journal of Advanced Manufacturing Technology, 89(1-4):561-579.

[38]ZhongXM, LiuHQ, MaoXY, et al., 2019. Influence and error transfer in assembly process of geometric errors of a translational axis on volumetric error in machine tools. Measurement, 140:450-461.

[39]ZhuMR, YangY, FengXB, et al., 2023. Robust modeling method for thermal error of CNC machine tools based on random forest algorithm. Journal of Intelligent Manufacturing, 34(4):2013-2026.