Abstract
This paper presents geometric error compensation of CNC machine tools based on workpiece model modification and the numerical solution of equation set. Firstly, the nominal cutter position is introduced to the geometric error model of machine tool as the compensation goal according to the kinematics of three-axis machine tools. With the polynomials of basic error components, the polynomials of the geometric error model are established, which are the functions about movements of all axes and nominal NC code. The accurate compensation is represented as solution of corresponding simultaneous equations. The high-efficiency numerical calculation can obtain the compensated NC code. Secondly, the polynomial equations about points of workpiece are established based on the simple relationship between workpiece model and NC codes. The compensated points are calculated using numerical solution. STL is chose as the format of reconstructed workpiece model. In order to obtain the precise workpiece model with compensated points, one conversion approach from CAD model to STL model is proposed. The number of points calculated with isoparametric method can control the precision of STL. The reconstructed STL model is inputted to CAM software to generate processing file for machining. The input of the proposed compensation is CAD model of workpiece rather than NC codes and CL data. It makes the compensation convenient and suitable for different three-axis machine tools. Finally, the experiments are carried out on Carver800T CNC machine tool to testify the effectiveness of proposed geometric error compensation.
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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
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
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
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
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 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
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
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 33(2):194–201
Hsu YY, Wang SS (2007) A new compensation method for geometry errors of five-axis machine tools. Int J Mach Tools Manuf 47(2):352–360
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
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
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
Habibi M, Arezoo B, Vahebi Nojedeh M (2011) Tool deflection and geometrical error compensation by tool path modification. Int J Mach Tools Manuf 51(6):439–449
Nojedeh MV, Habibi M, Arezoo B (2011) Tool path accuracy enhancement through geometrical error compensation. Int J Mach Tool Manuf 51(6):471–482
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
Lei WT, Hsu YY (2003) Accuracy enhancement of five-axis CNC machines through real-time error compensation. Int J Mach Tools Manuf 43(9):871–877
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
Fu G, Fu J, Xu Y, Chen Z, Lai J (2015) Accuracy enhancement of five-axis machine tool based on differential motion matrix: geometric error modeling, identification and compensation. Int J Mach Tools Manuf 89:170–181
Lei WT, Sung MP (2008) NURBS-based fast geometric error compensation for CNC machine tools. Int J Mach Tools Manuf 48(3–4):307–319
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
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. Int J Mach Tools Manuf 48(12–13):1408–1419
Fan JW, Guan JL, Wang WC, Luo Q, Zhang XL, Wang LY (2002) A universal modeling method for enhancement the volumetric accuracy of CNC machine tools. J Mater Process Technol 129(1–3):624–628
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 216(5):697–712
Wang J, Guo J (2012) Research on volumetric error compensation for NC machine tool based on laser tracker measurement. Sci China Technol Sci 55(11):3000–3009
Bohez ELJ, Ariyajunya B, Sinlapeecheewa C, Shein TMM, Lap DT, Belforte G (2007) Systematic geometric rigid body error identification of 5-axis milling machines. Comput Aided Des 39(4):229–244
Chen Y, Gao J, Deng H, Zheng D, Chen X, Kelly R (2013) Spatial statistical analysis and compensation of machining errors for complex surfaces. Precision Engineering 37(1):203–212
Sortino M, Belfio S, Motyl B, Totis G (2014) Compensation of geometrical errors of CAM/CNC machined parts by means of 3D workpiece model adaptation. Comput Aided Des 48:28–38
Huang N, Bi Q, Wang Y, Sun C (2014) 5-Axis adaptive flank milling of flexible thin-walled parts based on the on-machine measurement. Int J Mach Tools Manuf 84:1–8
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
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Fu, G., Fu, J., Shen, H. et al. Numerical solution of simultaneous equations based geometric error compensation for CNC machine tools with workpiece model reconstruction. Int J Adv Manuf Technol 86, 2265–2278 (2016). https://doi.org/10.1007/s00170-015-8175-y
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DOI: https://doi.org/10.1007/s00170-015-8175-y