Although there are some multi-sensor methods for measuring the straightness and tilt errors of a linear slideway, they need to be further improved in some aspects, such as suppressing measurement noise and reducing precondition. In this paper, a new four-sensor method with an improved measurement system is proposed to on-machine separate the straightness and tilt errors of a linear slideway from the sensor outputs, considering the influences of the reference surface profile and the zero-adjustment values. The improved system is achieved by adjusting a single sensor to different positions. Based on the system, a system of linear equations is built by fusing the sensor outputs to cancel out the effects of the straightness and tilt errors. Three constraints are then derived and supplemented into the linear system to make the coefficient matrix full rank. To restrain the sensitivity of the solution of the linear system to the measurement noise in the sensor outputs, the Tikhonov regularization method is utilized. After the surface profile is obtained from the solution, the straightness and tilt errors are identified from the sensor outputs. To analyze the effects of the measurement noise and the positioning errors of the sensor and the linear slideway, a series of computer simulations are carried out. An experiment is conducted for validation, showing good consistency. The new four-sensor method with the improved measurement system provides a new way to measure the straightness and tilt errors of a linear slideway, which can guarantee favorable propagations of the residuals induced by the noise and the positioning errors.
Lei Zhao
,
Kai Cheng
,
Hui Ding
,
Liang Zhao
. On-Machine Measurement of the Straightness and Tilt Errors of a Linear Slideway Using a New Four-Sensor Method[J]. Chinese Journal of Mechanical Engineering, 2019
, 32(2)
: 24
-24
.
DOI: 10.1186/s10033-019-0338-6
Although there are some multi-sensor methods for measuring the straightness and tilt errors of a linear slideway, they need to be further improved in some aspects, such as suppressing measurement noise and reducing precondition. In this paper, a new four-sensor method with an improved measurement system is proposed to on-machine separate the straightness and tilt errors of a linear slideway from the sensor outputs, considering the influences of the reference surface profile and the zero-adjustment values. The improved system is achieved by adjusting a single sensor to different positions. Based on the system, a system of linear equations is built by fusing the sensor outputs to cancel out the effects of the straightness and tilt errors. Three constraints are then derived and supplemented into the linear system to make the coefficient matrix full rank. To restrain the sensitivity of the solution of the linear system to the measurement noise in the sensor outputs, the Tikhonov regularization method is utilized. After the surface profile is obtained from the solution, the straightness and tilt errors are identified from the sensor outputs. To analyze the effects of the measurement noise and the positioning errors of the sensor and the linear slideway, a series of computer simulations are carried out. An experiment is conducted for validation, showing good consistency. The new four-sensor method with the improved measurement system provides a new way to measure the straightness and tilt errors of a linear slideway, which can guarantee favorable propagations of the residuals induced by the noise and the positioning errors.
[1] S J Zhang, S To, S J Wang, et al. A review of surface roughness generation in ultra-precision machining. International Journal of Machine Tools and Manufacture, 2015, 1(91):76-95.
[2] Chinese Mechanical Engineering Society. Technology roadmaps of Chinese mechanical engineering. 2nd ed. Beijing:Popular Science Press, 2016. (in Chinese)
[3] P Yang, T Takamura, S Takahashi, et al. Development of high-precision micro-coordinate measuring machine:multi-probe measurement system for measuring yaw and straightness motion error of XY linear stage. Precision Engineering, 2011, 35(3):424-430.
[4] K C Fan, F Cheng, H Y Wang, et al. The system and the mechatronics of a pagoda type micro-CMM. International Journal of Nanomanufacturing, 2012, 8:67-86.
[5] Q Huang, G B Zhang. Precision design for machine tool based on error prediction. Chinese Journal of Mechanical Engineering, 2013, 26(1):151-157.MathSciNet
[6] H Schwenke, W Knapp, H Haitjema, et al. Geometric error measurement and compensation of machines-an update. CIRP Annals-Manufacturing Technology, 2008, 57(2):660-675.
[7] The International Organization for Standardization. ISO 230-1-2012 Test code for machine tools-Part 1:geometric accuracy of machines operating under no-load or quasi-static conditions. Geneva:ISO Office, 2012.
[8] J Li, F G Xie, B Mei, et al. Analysis on the research status of volumetric positioning accuracy improvement methods for five-axis NC machine tools. Journal of Mechanical Engineering, 2017, 53(7):113-128. (in Chinese)
[9] S W Zhu, G F Ding, S F Qin, et al. Integrated geometric error modeling, identification and compensation of CNC machine tools. International Journal of Machine Tools and Manufacture, 2012, 52(1):24-29.
[10] D D Zhai, S Y Chen, Z Q Yin, et al. Review of self-referenced measurement algorithms:bridging lateral shearing interferometry and multi-probe error separation. Frontiers of Mechanical Engineering, 2017, 12:143-157.
[11] Z Q Yin. Research on ultra-precision measuring straightness and surface microtopography analysis. Changsha:National University of Defense Technology, 2003. (in Chinese)
[12] W Gao, S Kiyono. High accuracy profile measurement of a machined surface by the combined method. Measurement, 1996, 19(1):55-64.
[13] Z Liu, S Jiang, X Li, et al. Precision measurement of X-axis stage mirror profile in scanning beam interference lithography by three-probe system based on bidirectional integration model. Optics Express, 2017, 25(9):10312-10321.
[14] W Gao, S Kiyono. On-machine profile measurement of machined surface using the combined three-point method. JSME International Journal Series C:Mechanical Systems, Machine Elements and Manufacturing, 1997, 40(2):253-259.
[15] Z Q Yin, S Y Li. High accuracy error separation technique for on-machine measuring straightness. Precision Engineering, 2006, 30(2):192-200.
[16] Z Q Yin, S Y Li, F J Tian. Exact reconstruction method for on-machine measurement of profile. Precision Engineering, 2014, 38(4):969-978.
[17] I Fujimoto, K Nishimura, T Takatsuji, et al. A technique to measure the flatness of next-generation 450 mm wafers using a three-point method with an autonomous calibration function. Precision Engineering, 2012, 36(2):270-280.
[18] I Weingartner, C Elster. System of four distance sensors for high-accuracy measurement of topography. Precision Engineering, 2004, 28(2):164-170.
[19] A Wiegmann, C Elster, R D Geckeler, et al. Stability analysis for the TMS method:influence of high spatial frequencies. Optical Measurement Systems for Industrial Inspection V, Munich, Germany, June 17-21, 2007:661618-1-661618-9.
[20] E H K Fung, M Zhu. An improved Fourier five-sensor (IF5S) method for separating straightness and yawing errors of a linear slide based on multiple sensor parameter sets and least square regression technique. Measurement, 2012, 45(5):1323-1330.
[21] E H K Fung. An experimental five-sensor system for measuring straightness and yawing motion errors of a linear slide. Measurement Science and Technology, 2008, 19(7):075102.
[22] E H K Fung, M Zhu, X Z Zhang, et al. A novel Fourier-Eight-Sensor (F8S) method for separating straightness, yawing and rolling motion errors of a linear slide. Measurement, 2014, 47:777-788.
[23] C J Evans, R J Hocken, W T Estler, et al. Self-calibration:reversal, redundancy, error separation, and ‘absolute testing’. CIRP Annals, 1996, 45(2):617-634.
[24] W Gao, J Yokoyama, H Kojima, et al. Precision measurement of cylinder straightness using a scanning multi-probe system. Precision Engineering, 2002, 26(3):279-288.
[25] W Gao. Precision nanometrology:sensors and measuring systems for nanomanufacturing. London:Springer, 2010.
[26] D C Lay, S R Lay, J J McDonald. Linear algebra and its applications. 5th ed. New York:Pearson, 2015.
[27] A Uncini. Fundamentals of adaptive signal processing. Cham:Springer International Publishing, 2015.
[28] V K Ivanov, V V Vasin, V P Tanana. Theory of linear ill-posed problems and its applications. Berlin:Walter de Gruyter, 2013.zbMATH
[29] M Fuhry, L Reichel. A new Tikhonov regularization method. Numerical Algorithms, 2012, 59(3):433-445.MathSciNet
[30] K Ito, B Jin. Inverse problems:Tikhonov theory and algorithms. Singapore:World Scientific, 2014.
