A novel evaluation approach based on invariants is proposed to deal with the discrete error motion of the prismatic pair. The approach reflects the global property of the discrete error motion, which does not depend on the measurement coordinate system. The new 6D high-precision measurement instrument is used to investigate the six error terms. The evaluation model for directrix and spherical image curve is set up to study the geometry property of the moving body compared with the ideal one. The density of directrix error space and spherical envelope circle error surface are selected as the global evaluation indicators, while the minimal directrix error and the minimal spherical image curve error as the characteristic indicators. Three contrast tests are presented to illustrate the consistency and objectivity of the invariant indicators, which can evaluate the accuracy of the prismatic pair comprehensively and objectively.
WANG Delun
,
WU Yu
,
WANG Zhi
,
DONG Huimin
. Evaluation Based on Invariants for Discrete Error Motion of Prismatic Pair[J]. Journal of Mechanical Engineering, 2018
, 54(23)
: 1
-9
.
DOI: 10.3901/JME.2018.23.001
[1] ASME B5.54:2005. Methods for performance evaluation of computer numerically controlled machining centers[S]. New York:ASME,2005.
[2] ISO 230-1:2012. Test code for machine tools -Part 1:Geometric accuracy of machines operating under no-load or quasi-static conditions[S]. Geneva ISO,2012.
[3] FAN K C,CHEN M J. A 6-degree-of-freedom measurement system for the accuracy of X-Y stages[J]. Precision Engineering,2000,24(1):15-23.
[4] GAO W,ARAI Y,SHIBUYA A,et al. Measurement of multi-degree-of-freedom error motions of a precision linear air-bearing stage[J]. Precision Engineering,2006,30(1):96-103.
[5] LIN C C,HER J L. Calibrating the volumetric errors of a precision machine by a laser tracker system[J]. International Journal of Advanced Manufacturing Technology,2005,26(11-12):1255-1267.
[6] OKUYAMA S,YANO H,WATANABE S. Effect of floating capacity on the measurement error of the CBP method[J]. Journal-Japan Society for Precision Engineering,1997,63:1427-1431.
[7] ZIEGERT J C,MIZE C D. The laser ball bar:A new instrument for machine tool metrology[J]. Precision Engineering,1994,16(4):259-267.
[8] 刘又午,刘丽冰,赵小松,等. 数控机床误差补偿技术研究[J]. 中国机械工程,1998(12):48-52. LIU Youwu,LIU Libing,ZHAO Xiaosong,et al. Research for the error compensation of the NC machine tool[J]. China Mechanical Engineering,1998(12):48-52.
[9] TIAN Wenjie. Research on geometric error tracing of NC machine tools[J]. Journal of Mechanical Engineering,2014,50(7):128-135.
[10] CHEN G,YUAN J,NI J. A displacement measurement approach for machine geometric error assessment[J]. International Journal of Machine Tools & Manufacture,2001,41(1):149-161.
[11] 黄天喜. 10线法辨识三轴数控机床几何误差及误差补偿研究[D]. 长沙:中南大学,2008. HUANG Tianxi. A new method for error parameter identification based on ten displacement measurement line[D]. Changsha:Central South University,2008.
[12] BRYAN J B. The Abbé principle revisited:An updated interpretation[J]. Precision Engineering,1979,1(3):129-132.
[13] WANG Delun,WANG Wei. Kinematic differential geometry and saddle synthesis of linkages[M]. John Wiley & Sons Singapore Pte. Ltd,2015.
[14] WU Yu,WANG Delun,WANG Wei,et al. Kinematic geometry for the saddle line fitting of planar discrete positions[J]. Chinese Journal of Mechanical Engineering,2015,28(4):763-768.
[15] 唐焕文,秦学志. 实用最优化方法[M]. 大连:大连理工大学出版社,2004. TANG Huanwen,QIN Xuezhi. Practical methods of optimization[M]. Dalian:Dalian University of Technology Press,2004.
[16] WANG W,WANG D L. Curvature theory for point-path and plane-envelope in spherical kinematics by new adjoint approach[J]. Chinese Journal of Mechanical Engineering,2014,27(6):1157-1168.
[17] WANG Zhi,WANG Delun,WU Yu,et al. Error calibration of controlled rotary pairs in five-axis machining centers based on the mechanism model and kinematic invariants[J]. International Journal of Machine Tools & Manufacture,2017,120:1-11.
[18] WANG Delun,WANG Zhi,WU Yu,et al. Invariant errors of discrete motion constrained by actual kinematic pairs[J]. Mechanism and Machine Theory,2018,119:74-90.
