Abstract
This paper presents one novel model of squareness errors using the D-H matrix to improve the accuracy of integrated geometric errors of the machine tools. It considers the motion of the axis and reflects the geometric meaning of the squareness errors. Firstly, analysis of the existing squareness error models is proposed. It helps to find the improvements of the modeling. Secondly, squareness error modeling is represented by integrating the kinematic property of the axes. The influences of squareness errors are to change the translational direction of translational axes and to deflect the axial line of rotary axes. The squareness error model of translational axes is expressed as the translational homogeneous matrix along the real movement direction. And, the model of rotary axes is expressed as the rotational homogeneous matrix around the real axial line. The unit vector of the real direction is established based on the geometric definition of squareness errors. The models are available for different axes with the property of the axes. Finally, experiments are conducted on one SmartCNC500 five-axis machine tool. The virtual large squareness errors of translational axes and C-axis are simulated by the motion of axes. The positions of the target are measured by laser tracker when moving the axes. The comparisons of measured points and calculated points with the proposed model and one existing model are proposed. The results show that the novel models are precise.
Similar content being viewed by others
References
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(0):14–26
Fu G, Fu J, Shen H, Yao X, Chen Z (2015) NC codes optimization for geometric error compensation of five-axis machine tools with one novel mathematical model. Int J Adv Manuf Technol 80(9–12):1879–1894
Fu G, Fu J, Shen H, Sha J, Xu Y (2016) Numerical solution of simultaneous equations based geometric error compensation for CNC machine tools with workpiece model reconstruction. Int J Adv Manuf Technol: 1–14
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 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
Uddin MS, Ibaraki S, Matsubara A, Matsushita T (2009) Prediction and compensation of machining geometric errors of five-axis machining centers with kinematic errors. Precision Engineering-Journal of the International Societies for Precision Engineering and Nanotechnology 33(2):194–201
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
Li J, Xie F, Liu X-J, Li W, Zhu S (2016) Geometric error identification and compensation of linear axes based on a novel 13-line method. Int J Adv Manuf Technol:1–15
Kong LB, Cheung CF, To S, Lee WB, Du JJ, Zhang ZJ (2008) A kinematics and experimental analysis of form error compensation in ultra-precision machining. International Journal of Machine Tools & Manufacture 48(12–13):1408–1419
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
Chen GS, Mei XS, Li HL (2013) Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes. Int J Adv Manuf Technol 69(9–12):2583–2592
Lin Y, Shen Y (2003) Modelling of five-Axis machine tool metrology models using the matrix summation approach. Int J Adv Manuf Technol 21(4):243–248
Khan AW, Wuyi C (2010) Systematic geometric error modeling for workspace volumetric calibration of a 5-axis turbine blade grinding machine. Chin J Aeronaut 23(5):604–615
Wang J, Guo J (2012) Research on volumetric error compensation for NC machine tool based on laser tracker measurement. SCIENCE CHINA Technol Sci 55(11):3000–3009
Kong LB, Cheung CF (2012) Prediction of surface generation in ultra-precision raster milling of optical freeform surfaces using an integrated kinematics error model. Adv Eng Softw 45(1):124–136
Chen G, Liang Y, Sun Y, Chen W, Wang B (2013) Volumetric error modeling and sensitivity analysis for designing a five-axis ultra-precision machine tool. Int J Adv Manuf Technol 68(9–12):2525–2534
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
Cui G, Lu Y, Li J, Gao D, Yao Y (2012) Geometric error compensation software system for CNC machine tools based on NC program reconstructing. Int J Adv Manuf Technol 63(1–4):169–180
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
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
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
Fan K, Yang J, Yang L (2015) Unified error model based spatial error compensation for four types of CNC machining center: part I—singular function based unified error model. Mech Syst Signal Process 60–61(0):656–667
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. International Journal of Machine Tools & Manufacture 89(0):170–181
Okafor AC, Ertekin YM (2000) Derivation of machine tool error models and error compensation procedure for three axes vertical machining center using rigid body kinematics. Int J Mach Tools Manuf 40(8):1199–1213
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fu, G., Fu, J., Gao, H. et al. Squareness error modeling for multi-axis machine tools via synthesizing the motion of the axes. Int J Adv Manuf Technol 89, 2993–3008 (2017). https://doi.org/10.1007/s00170-016-9259-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-016-9259-z