Abstract The geometric position of probe is calibrated by a reference sphere on most of mainstream gear measuring instruments. Compared to the reference sphere, the reference mandrel is not only easy to be installed and operated, but also it can detect the static accuracy of the machine tool. So the probe calibration is conducted by the reference mandrel in the process of gear on-machine measurement on a new developed gear grinding. To improve the calibration accuracy of probe position, the calibration of probe geometric position is defined by the least squares method (LSM), which can fit the center of reference mandrel. Simultaneously, the algorithm based on Aitken Δ2 iteration, which is used on the basis of LSM, is built to compensate the error of position produced by LSM. This method replaces the nonlinear fitting iterative process with linear convergent numerical sequence, which not only has a faster convergence rate, but also tends to be stable. The effectiveness of this method can be validated through the experiment of tooth profile evaluation, and it can provide guidance for the geometric position calibration of other gear measurement.
WANG Fa,WANG Zhonghou,CHEN Mingzhi, et al. Position Error of Touch-Trigger Probe Based on Mandrel Calibration on the Process of Gear on-Machine Measurement[J]. Acta Metrologica Sinica, 2024, 45(9): 1291-1299.
LIN H, KELLER F, STEIN M. Influence and compensation of CMM geometric errors on 3D gear measurements［J］. Measurement, 2020, 151: 107110.
LI H L, CHEN S, HUA J. On-line measuring technique for total profile error in gear molding milling ［J］. Acta Metrologica Sinica, 2005, 26(2): 125-127.
［18］
YIN P, HAN F, WANG J, et al. Influence of coordinate system establishment error on tooth profile deviation measured by standard polar coordinate method on gear measuring center［J］. Measurement, 2022, 187: 110344.
［21］
GUO J, YANG J. An iterative procedure for robust circle fitting［J］. Communications in Statistics-Simulation and Computation, 2019, 48(6): 1872-1879.
［24］
LI S, FENG P, ZENG L, et al. A rigid-flexible coupling pretravel error model for a touch-trigger probe in an on-machine inspection system［J］. The International Journal of Advanced Manufacturing Technology, 2021, 114(9-10): 2991-3003.
［26］
VERZHBITSKII V M, YUMANOVA I F. On the quadratic convergence of the Aitken Δ2 process［J］. Computational Mathematics and Mathematical Physics, 2011, 51(10): 1659-1663.
［28］
CylindricalGears—ISO System of Flank Tolerance Classification Part 1: Definitions and Allowable Values of Deviations Relevant to Flanks of Gear Teeth:ISO 1328-1［S］. Geneva: International Organization for Standardization Geneva, 2013.
［27］
LE FERRAND H. The rational iteration method by Georges Lematre［J］. Numerical Algorithms, 2019, 80(1): 235-251.
TANG J, WEI J, SHI Z. An evaluation method of gear profile deviations based on the consideration of installation errors［J］. Measurement, 2019, 146: 806-814.
SHI Z Y, YU B, SONG H X, et al. Development of gear measurement technology during last 20 years［J］. China Mechanical Engineering, 2022, 33(9): 1009-1024.
［6］
DAI Z, LI T, ZHANG Y, et al. A model construction and measurement method for tooth surface deviation of spiral bevel gear based a on one-dimensional probe［J］. Measurement Science and Technology, 2023, 34(4): 045001.
［9］
METZ D, JANTZEN S, WESSEL D, et al. Integration of an isotropic microprobe and a microenvironment into a conventional CMM［J］. Measurement Science and Technology, 2019, 30(11): 115007.
［11］
CHEN Y T, MORE P, LIU C S. Identification and verification of location errors of rotary axes on five-axis machine tools by using a touch-trigger probe and a sphere［J］. The International Journal of Advanced Manufacturing Technology, 2019, 100(9-12): 2653-2667.
［14］
IBARAKI S, IRITANI T, MATSUSHITA T. Calibration of location errors of rotary axes on five-axis machine tools by on-the-machine measurement using a touch-trigger probe［J］. International Journal of Machine Tools and Manufacture, 2012, 58: 44-53.
［15］
KONDO Y, KONDO K, OSAWA S, et al. Evaluation of instruments for helix measurement using wedge artifact［J］. Precision engineering, 2010, 34(4): 667-674.
［17］
TAGUCHI T, KONDO Y. Evaluation of a high-precision gear measuring machine for helix measurement using helix and wedge artifacts［J］. Measurement Science and Technology, 2016, 27(8): 084008.
ZHAO D S, ZHANG J, JIA M Q, et al. Comparison of two methods for measuring the error of CNC machine tool［J］. Acta Metrologica Sinica, 2019, 40(6A): 33-35.
［22］
LIU X R, WANG Z H. Research on high-precision form grinding technology of gear based on ambient temperature adaptability［J］. Mathematical Problems in Engineering, 2018, 2018(2018): 1-13.
［25］
ABDUL-RAHMAN H, CHERNOV N. Fast and numerically stable circle fit［J］. Journal of mathematical imaging and vision, 2014, 49(2): 289-295.
GOLEBSKI R, STOIC A. Analysis of Outline Measurements Methods of Spur Gear Involute Profile［J］. Tehnicˇki vjesnik, 2021, 28(3): 1008-1011.
ZHOU W C, ZHU X C, DING W Z, et al. An efficient on-machine measuring method of gear tooth error［J］. Manufacturing Automation, 2018, 40(10): 14-18.
ZENG B, ZHOU Y S, WANG S H, et al. Tooth profile error measurement of face gear based on general coordinate measuring machine［J］. Journal of Aerospace Power, 2022 37(4): 856-868.
［8］
TANG J, JIA J, FANG Z, et al. Development of a gear measuring device using DFRP method［J］. Precision Engineering, 2016, 45: 153-159.
［10］
LI S, ZENG L, FENG P, et al. Accurate compensation method for probe pre-travel errors in on-machine inspections［J］. The International Journal of Advanced Manufacturing Technology, 2019, 103(5-8): 2401-2410.
LU Y, GE W Q, GUO B, et al. Calibration of industrial robot parameters based on standard ball distance constraints［J］. Acta Metrologica Sinica, 2020, 41(9): 1048-1054.
LING S Y, LING M, LIN H, et al. Research progress in high-precision gear involute artifacts and measuring instruments. ［J］. Optics and Precision Engineering, 2023, 31(23): 3457-3473.
YANG Y M, WANG Z H, LIU X R, et al. Modeling and compensation of geometric error chain of on-machine inspection mechanism for gear grinder［J］. Chinese Journal of Scientific Instrument, 2021, 42(6): 9-19.
2024, Vol. 45 
