This paper presents one automatic modeling method of position-dependent geometric error components based on F test in statistics and one error compensation method of five-axis machine tools to ensure textures of the workpiece. At first, according to the definition of error components, the polynomials with zero constant term are chosen as the expressions. The calculation of corresponding coefficients is presented in details. Then, F test is introduced to evaluate the overall significance of polynomials. The automatic modeling of position-dependent geometric error components is expressed as seeking the polynomial with the best overall significance among a series of the polynomials with different orders. It is automatic and programmatic to improve the efficiency and precision of modeling. It can overcome the difficulty in determining the order of the polynomials. Next, geometric error compensation by limiting ideal tool positions of tool poses is proposed to ensure machining requirements of textures of the workpiece. The rotation angles of two rotary axes are optimized by particle swarm optimization (PSO) with the mathematical expressions of integrated geometric errors of five-axis machine tools. The movements of linear axes are calculated with inverse kinematics of the machine tool by inputting ideal tool positions and optimized rotation angles. Finally, the experiments are carried out on one SmartCNC500_DRTD five-axis machine center to testify the precision of the automatic modeling and the effectiveness of the error compensation.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Shen H, Fu J, He Y, Yao X (2012) On-line asynchronous compensation methods for static/quasi-static error implemented on CNC machine tools. Int J Mach Tools Manuf 60:14–26
Schwenke H, Knapp W, Haitjema H, Weckenmann A, Schmitt R, Delbressine F (2008) Geometric error measurement and compensation of machines—an update. CIRP Ann Manuf Technol 57(2):660–675
Zhu S, Ding G, Qin S, Lei J, Zhuang L, Yan K (2012) Integrated geometric error modeling, identification and compensation of CNC machine tools. Int J Mach Tools Manuf 52(1):24–29
Cai L, Zhang Z, Cheng Q, Liu Z, Gu P, Qi Y (2016) An approach to optimize the machining accuracy retainability of multi-axis NC machine tool based on robust design. Precis Eng 43:370–386
Khan A, Chen W (2011) A methodology for systematic geometric error compensation in five-axis machine tools. Int J Adv Manuf Technol 53(5–8):615–628
Fu GQ, Fu JZ, Xu YT, Chen ZC, Lai JT (2015) Accuracy enhancement of five-axis machine tool based on differential motion matrix: geometric error modeling, identification and compensation. Int J Mach Tool Manu 89:170–181
Fu G, Fu J, Shen H, Xu Y, Ya J (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 G, Fu J, Xu Y, Chen Z (2014) Product of exponential model for geometric error integration of multi-axis machine tools. Int J Adv Manuf Technol 71(9–12):1653–1667
Tang H, J-a D, Lan S, Shui H (2015) A new geometric error modeling approach for multi-axis system based on stream of variation theory. Int J Mach Tools Manuf 92:41–51
Chen J, Lin S, He B (2014) Geometric error compensation for multi-axis CNC machines based on differential transformation. Int J Adv Manuf Technol 71(1–4):635–642
Peng FY, Ma JY, Wang W, Duan XY, Sun PP, Yan R (2013) Total differential methods based universal post processing algorithm considering geometric error for multi-axis NC machine tool. Int J Mach Tools Manuf 70:53–62
Ding S, Huang X, Yu C, Wang W (2016) Actual inverse kinematics for position-independent and position-dependent geometric error compensation of five-axis machine tools. Int J Mach Tools Manuf 111:55–62
Zhou X, Jiang Z, Song B, Tang X, Zheng S (2016) A compensation method for the geometric errors of five-axis machine tools based on the topology relation between axes. Int J Adv Manuf Technol 88:1–15
Yao X, Fu J, Xu Y, He Y (2013) Synthetic error modeling for NC machine tools based on intelligent technology. Proc CIRP 10:91–97
Zhang Y, Yang J, Xiang S, Xiao H (2013) Volumetric error modeling and compensation considering thermal effect on five-axis machine tools. Proc Inst Mech Eng C J Mech Eng Sci 227(C5):1102–1115
Slamani M, Mayer R, Balazinski M, Zargarbashi SH, Engin S, Lartigue C (2010) Dynamic and geometric error assessment of an XYC axis subset on five-axis high-speed machine tools using programmed end point constraint measurements. Int J Adv Manuf Technol 50(9–12):1063–1073
Jung JH, Choi JP, Lee SJ (2006) Machining accuracy enhancement by compensating for volumetric errors of a machine tool and on-machine measurement. J Mater Process Technol 174(1–3):56–66
Lee KI, Lee DM, Yang SH (2012) Parametric modeling and estimation of geometric errors for a rotary axis using double ball-bar. Int J Adv Manuf Technol 62(5–8):741–750
Fan K, Yang J, Yang L (2014) Unified error model based spatial error compensation for four types of CNC machining center: part II—unified model based spatial error compensation. Mech Syst Signal Process 49(1–2):63–76
Fan K, Yang J, Yang L (2013) Orthogonal polynomials-based thermally induced spindle and geometric error modeling and compensation. Int J Adv Manuf Technol 65(9–12):1791–1800
Mir YA, Mayer JRR, Fortin C (2002) Tool path error prediction of a five-axis machine tool with geometric errors. Proc Inst Mech Eng B J Eng Manuf 216(5):697–712
Li Z, Yang J, Fan K, Zhang Y (2015) Integrated geometric and thermal error modeling and compensation for vertical machining centers. Int J Adv Manuf Technol 76(5–8):1139–1150
He Z, Fu J, Zhang X, Shen H (2016) A uniform expression model for volumetric errors of machine tools. Int J Mach Tools Manuf 100:93–104
Xiang S, Yang J, Zhang Y (2014) Using a double ball bar to identify position-independent geometric errors on the rotary axes of five-axis machine tools. Int J Adv Manuf Technol 70(9–12):2071–2082
Lin ZW, Fu JZ, Shen HY, Gan WF (2014) On the workpiece setup optimization for five-axis machining with RTCP function. Int J Adv Manuf Technol 74(1–4):187–197
Lin Z, Fu J, Sun Y, Gao Q, Xu G, Wang Z (2017) Non-retraction toolpath generation for irregular compound freeform surfaces with the LKH TSP solver. Int J Adv Manuf Technol 92:1–15
This work was financially supported by the National Natural Science Foundation of China (No. 51575483), the National Natural Science Foundation of China (No. 51605253), and Zhejiang Provincial Natural Science Foundation of China (LY16E050011).
About this article
Cite this article
Fu, G., Zhang, L., Fu, J. et al. F test-based automatic modeling of single geometric error component for error compensation of five-axis machine tools. Int J Adv Manuf Technol 94, 4493–4505 (2018). https://doi.org/10.1007/s00170-017-1143-y
- Geometric error components
- Automatic modeling
- F test
- Error compensation
- Five-axis machine tools