Precision Engineering 41 (2015) 86–95 Contents lists available at ScienceDirect Precision Engineering jo ur nal homep age: www.elsevier.com/locate/precision Stage error calibration for coordinates measuring machines based on self-calibration algorithm Daodang Wang a,b , Xixi Chen a , Yangbo Xu a , Tiantai Guo a,∗ , Ming Kong a , Jun Zhao a , Baowu Zhang a , Baohua Zhu c,d,e a College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018, China b State Key Laboratory of Precision Measuring Technology and Instrumentation, Tianjing University, Tianjing 300072, China c Guilin University of Electronic Technology, Guilin 541004, China d Guangxi Colleges and Universities Key Laboratory of Optoelectronic Information Processing, Guilin 541004, China e Guangxi Key Laboratory of Automatic Detecting Technology and Instruments (Guilin University of Electronic Technology), Guilin 541004, China a r t i c l e i n f o Article history: Received 25 June 2014 Received in revised form 5 January 2015 Accepted 27 February 2015 Available online 7 March 2015 Keywords: Self-calibration Coordinate measuring machines Stage error Grid plate Least squares method a b s t r a c t The stage error of coordinate measuring machines (CMM) can significantly influence the measurement results, and it places ultra-high requirement on the measurement and calibration tools. A calibration technique based on self-calibration algorithm is presented to calibrate the two-dimensional stage error of CMM, and it can be carried out with a grid plate of the accuracy no higher than test stage. With the proposed self-calibration algorithm based on least squares method, the measurements at various position combinations of rotation and translation are carried out to separate the stage error from measurement results. Both the accuracy and feasibility of the proposed calibration method have been demonstrated by computer simulation and experiments, and the measurement accuracy RMS better than 1 m is achieved. The proposed calibration method has a good anti-noise ability and provides a feasible way to lower the accuracy requirement on standard parts. It is of great practicality for high-accuracy calibration of the stage error of CMM and manufacturing machines in the order of submicron. © 2015 Elsevier Inc. All rights reserved. 1. Introduction With the development of ultra-precise machining technique, coordinate measuring machines (CMM) have become a power- ful measurement tool in the field of high-accuracy measurement. However, there is generally a deviation of measured stage posi- tion from the ideal position in Cartesian coordinates of CMM, which is mainly introduced by the errors including the sys- tematic measurement error and random noise. The systematic measurement error, that is stage error, could introduce signifi- cant error in the measurement results [1,2]. Thus, it is necessary to measure and compensate the stage error to realize the high- accuracy measurement with CMM. Due to the limitation of practical problems such as technical and economic difficulties in the man- ufacture of precise test artifacts, the traditional CMM calibration method with an absolute standard artifact (with higher accu- racy than the stage to be calibrated) is limited in application ∗ Corresponding author at: College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018, China. Tel.: +86 571 86914563. E-mail address: teampaper209@cjlu.edu.cn (T. Guo). [3–5], especially not feasible in the case of high-accuracy measure- ment better than sub-microns. Though the high-accuracy method based with laser interferometer [2,6,7] has been widely applied in stage error calibration, it is high-cost and complex in the system. The self-calibration method, which realizes the calibration of stage error with a grid plate of the accuracy no higher than test stage, has been proposed to overcome the accuracy lim- itation of standard parts and achieve the required accuracy. It is generally realized by measuring the grid plate at differ- ent positions on test stage, and the stage error map could be reconstructed by comparing different measurement positions, in which the unknown marker positioning errors cancel. Various self-calibration algorithms have been proposed to separate stage error from the measured systematic error [8–12], and they are mostly based on discrete Fourier Transform (FT) method. The self-calibration algorithms have been applied in the motion accu- racy testing of two-dimensional stages [13–23], such as electron beam lithography. However, the existing algorithms are poor in noise suppression (the noise amplification factor is generally greater than 1) [9], and are difficult to be applied in practical measurement. http://dx.doi.org/10.1016/j.precisioneng.2015.02.002 0141-6359/© 2015 Elsevier Inc. All rights reserved.