Abstract
Accuracy design constitutes an important role in machine tool designing. It is used to determine the permissible level of each error parameter of a machine tool, so that any criterion can be optimized. Geometric, thermal-induced, and cutting force-induced errors are responsible for a large number of comprehensive errors of a machine tool. These errors not only influence the machining accuracy but are also of great importance for accuracy design to be performed. The aim of this paper is the proposal of a general approach that simultaneously considered geometric, thermal-induced, and cutting force-induced errors, in order for machine tool errors to be allocated. By homogeneous transformation matrix (HTM) application, a comprehensive error model was developed for the machining accuracy of a machine tool to be acquired. In addition, a generalized radial basis function (RBF) neural network modeling method was used in order for a thermal and cutting force-induced error model to be established. Based on the comprehensive error model, the importance sampling method was applied for the reliability and sensitivity analysis of the machine tool to be conducted, and two mathematical models were presented. The first model predicted the reliability of the machine tool, whereas the second was used to identify and optimize the error parameters with larger effect on the reliability. The permissible level of each geometric error parameter can therefore be determined, whereas the reliability met the design requirement and the cost of this machining was optimized. An experiment was conducted on a five-axis machine tool, and the results confirmed the proposed approach being able to display the accuracy design of the machine tool.
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Cai LG, Zhang ZL, Cheng Q, Liu ZF, Gu PH (2015) A geometric accuracy design method of multi-axis NC machine tool for improving machining accuracy reliability. Eksploatacja i Niezawodnosc-Maintenance and Reliability 17(1):143–155
Cai LG, Zhang ZL, Cheng Q, Liu ZF, Gu PH, Qi Y (2016) An approach to optimize the machining accuracy retainability of multi-axis NC machine tool based on robust design. Int. J. Precis Eng 43:370–386
António CC, Hoffbauer LN (2009) An approach for reliability-based robust design optimisation of angle-ply composites. Compos Struct 90:53–59
Chen ZJ (2008) Real-time compensation of cutting forces induced error on CNC machine tools. Dissertation, Shanghai Jiao Tong University
Cheng Q, Feng QN, Liu ZF, Gu PH, Zhang GJ (2016) Sensitivity analysis of machining accuracy of multi-axis machine tool based on POE screw theory and Morris method. Int J Adv Manuf Technol 84(9–12):2301–2318
Cheng Q, Qi Z, Zhang GJ, Zhao YS, Sun BW, Gu PH (2015) Robust modeling and prediction of thermally induced positional error based on grey rough set theory and neural network. Int J Adv Manuf Technol 83(5–8):753–764
Cheng Q, Zhao HW, Zhang GJ, Gu PH, Cai LG (2014) An analytical approach for crucial geometric errors identification of multi-axis machine tool based on global sensitivity analysis. Int J Adv Manuf Technol 75(1–4):107–121
Choi JH, Lee WH, Park JJ, Youn BD (2008) A study on robust design optimization of layered plate bonding process considering uncertainties. Struct Multidiscip Optim 35:531–540
Dong Z, Hu W, Xue D (1994) New production cost-tolerance models for tolerance synthesis. ASME J Eng Ind 116:199–206
Dorndorf U, Kiridena VSB, Ferreira PM (1994) Optimal budgeting of quasistatic machine tool errors. J Eng Ind 116(1):42–53
Dufour P, Groppetti R. (2006) Computer aided accuracy improvement in large NC machine-tools. In Proceedings of the 2006 International Conference on the MTDR 22: 611–618.
Fu GQ, Fu JZ, Shen HY, Xu YT, Jin Y (2015) Product-of-exponential formulas for precision enhancement of five-axis machine tools via geometric error modeling and compensation. Int J Adv Manuf Technol 81(1–4):289–305
Fu GQ, Fu JZ, Xu YT, Chen ZC (2014) Product of exponential model for geometric error integration of multi-axis machine tools. Int J Adv Manuf Technol 71(9–12):1653–1166
Geng JH (2015) Research on error modeling of cutting force and analysis and application of threedimensional heat critical point of CNC machine tools. Dissertation, Anhui University of Science and Technology
Guo QJ, Yang JG, Wu H (2010) Application of ACO-BPN to thermal error modeling of NCmachine tool. Int J Adv Manuf Technol 50:667–675
Hocken RJ, Simpson JA, Borchardt B, Lazar J, Reeve C, Stein P (1977) Three dimensional metrology. Journal of Ann. CIRP 26(2):403–408
Huang X, Ding W, Hong R (2006) Research on accuracy design for remanufactured machine tools. In Proceedings of the 2006 International Conference on Technology and Innovation 1403–1410
Krishna AG, Rao KM (2006) Simultaneous optimal selection of design and manufacturing tolerances with different stack-up conditions using scatter search. Int J Adv Manuf Technol 30(3–4):328–333
Kiridena V, Ferreira PM (1993) Mapping the effects of positioning errors on the volumetric accuracy of five-axis CNC machine tools. Int J Mach Tools Manuf 33(3):417–437
Jin S, Zheng C, Yu K, Lai X (2010) Tolerance design optimization on cost-quality trade-off using the Shapley value method. J Manuf Syst 29(4):142–150
Li SY, Dai YF, Yin ZQ, Zheng ZW, Wang GL, Peng ZQ (2007) Accuracy modeling technology of precision and ultra-precision machine tool. National University of Defense Technology Press, Changsha
Liu H, Li B, Wang X, Tan G (2011) Characteristics of and measurement methods for geometric errors in CNC machine tools. Int J Adv Manuf Technol 54(1–4):195–201
Liu YW, Zhang Q, Zhao XS, Zhang ZF (2002) Multi-body system based technique for compensating thermal errors in machining centers. Chin J Mech Eng 38(1):127–130
Lu ZY, Song SF, Li HS, Yuan XK (2009) Structural reliability and reliability sensitivity analysis organization. Sciences Press, Beijing
Lv C, Liu ZY, Liu ZJ, Yu ZM (2015) Application of generalized radial basis function neural network to thermal error modeling. Opt Precis Eng 23(6):1705–1713
Portman VT (1982) A universal method for calculating the accuracy of mechanical devices. J Sov Eng Res 1(7):11–15
Raksiri C, Parnichkun M (2004) Geometric and force errors compensation in a 3-axis CNC milling machine. Int J Mach Tools Manuf 44(12/13):1283–1291
She CS, Huang ZH (2008) Postprocessor development of a five-axis machine tool with mutating head and table configuration. Int J Adv Manuf Technol 38(7):728–740
Shi XL, Liu HL, Li H, Liu C, Tan GY (2016) Comprehensive error measurement and compensation method for equivalent cutting forces. Int J Adv Manuf Technol 85(1–4):149–156
Shi YG, Zhao XY, Zhang HJ, Nie YX, Zhang DW (2016) A new top-down design method for the stiffness of precision machine tools. Int J Adv Manuf Technol 83(9–12):1887–1904
Wang HT, Wang LP, Li TM, Han J (2013) Thermal sensor selection for the thermal error modeling of machine tool based on the fuzzy clustering method. Int J Adv Manuf Technol 69:121–126
Wang SX, Yun JT, Zhang ZF (2003) Modeling and compensation technique for the geometric errors of five-axis CNC machine tools. Chin J Mech Eng 16(2):197–201
Wu H, Jiliweisi ZHT, Yang JG (2005) Cutting force error modeling of NC machine tool and real-time compensation based on the current measurement. Chin J Mech Manuf 43(492):13–15
Wu H, Yang JG, Zhao HT (2008) Synthetically modeling for the thermal error and cutting force induced error on a CNC Turning Center. J Sichuan Univ (Engineering science edition) 40(2):165–169
Yang JG, Wang XS, Zhao HT (2005) Temperature measurement points optimization selection of machine tools. Chinese Mechanical Engineering Society annual conference 627–632
Yu ZM, Liu ZJ, Ai YD, Xiong M (2013) Geometric error model and precision distribution based on reliability theory for large CNC gantry guideway grinder. Chin J Mech Eng 49(17):142–151
Zhang Y, Yang JG, Jiang H (2012) Machine tool thermal error modeling and prediction by grey neural network. Int J Adv Manuf Technol 59:1065–1072
Zou HB, Chen XD, Wang SJ (2015) A study of single kinematic errors accurate fitting for ultra-precision micro v-groove machine tools. Int J Adv Manuf Technol 77(5–8):1345–1351
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Zhang, Z., Liu, Z., Cai, L. et al. An accuracy design approach for a multi-axis NC machine tool based on reliability theory. Int J Adv Manuf Technol 91, 1547–1566 (2017). https://doi.org/10.1007/s00170-016-9824-5
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DOI: https://doi.org/10.1007/s00170-016-9824-5