Abstract
The randomness of the repeated positioning error of feed shaft is the main reason for the difficulty to address this error. The previous repeated loading and unloading suppression methods will easily do damages to parts. This paper sets out to investigate the probability distribution of all possible error values while feed shaft is at different positions, and determine the maximum value of probability error from the random errors. With feed axis at a certain position, first of all, we count the probability of each error based on a large number of random errors. We also draw the digital map of the repeated positioning error of this error with the error of positive and negative stroke measurement as the x-axis and y-axis coordinates and the probability of each error value as the z-axis coordinates. Secondly, based on the digital map of each position on the feed axis and combined with the dynamic optimization algorithm, we find the highest point on the map and take the coordinate point of this point as the starting point of each position compensation. Then, we set the error probability threshold to control the possibility of compensation errors and output the size and direction of the final compensation value. Finally, we start the compensation command and detect the compensated error. The error data that fail to meet the requirements will enter the probability statistics again, redraw the digital map and update the map. Through real-time detection and feedback, the digital map is dynamically improved to adapt to the changing environment. This probability compensation model of repeated positioning error can end the suppressing repeated positioning errors brought by repeatedly disassembling parts.
Similar content being viewed by others
References
Altintas Y, Verl A, Brecher C, Uriarte L, Pritschow G (2011) Machine tool feed drives[J]. CIRP Ann Manuf Technol 60(2):779–796
Li T, Zhao C, Zhang Y (2019) Adaptive on-line compensation model on positioning error of ball screw feed drive systems used in computerized numerical controlled machine tools[J]. Proc IMechE, Part B: J Engineering Manufacture 233:914–926
Chen GD, Sun YZ, An C, Zhang F, Sun Z, Chen WQ (2018) Measurement and analysis for frequency domain error of ultra-precision spindle in a fly cutting machine tool[J]. Proc IMechE, Part B: J Engineering Manufacture 232(9):1501–1507
Sun GM, He GY, Zhang DW, Ding BH (2019) Experimental study on the repeatability of positioning of linear axes of machine tools: [J]. Proceedings of the Institution of Mechanical Engineers, Part B: J Eng Manuf 234(4):739–751
Szipka K, Archenti A (2019) Utilization of multi-axis positioning repeatability performance in kinematic modelling[J]. Int J Autom Technol 13(1):149–156
Mori M, Ota K, Matsubara A, Mizuyamac H (2015) Design and formation of workforce skills for machine tool assembly[J]. CIRP Ann Manuf Technol 64(1):459–462
Lu C, Wang SL (2014) An approach to evaluating product assembly precision considering the effect of joint surface deformation[J]. ARCHIVE Proc Inst Mech Eng Part C J Mech Eng Sci 1989-1996 228(14):2604–2617 (vols 203-210)
Sun Y, Wang D, Dong H, Xue R, Yu SD (2014) Pre-deformation for assembly performance of machine centers[J]. Chin J Mech Eng-En 27(3):528–536
He GY, Guo LZ, Li SQ, Zhang DW (2017) Simulation and analysis for accuracy predication and adjustment for machine tool assembly process[J]. Adv Mech Eng (Sage Publications Inc) 9(11):168781401773447
Sun GM, He GY, Zhang DW, Sang YC, Zhang XL, Ding BH (2018) Effects of geometrical errors of guideways on the repeatability of positioning of linear axes of machine tools[J]. Int J Adv Manuf Technol 98(9–12):2319–2333
Shang P, Gao CJ, Han ZJ, Liu T, Gao WG, Zhang JJ, Zhang DW (2019) Simulation study on thermal balance-temperature rise characteristics of a precision ball screw-nut pair[J]. J Tianjin Univ (Science and Technology) 57(7):725–732
Zhu J, Ni J, Shih AJ (2008) Robust machine tool thermal error modeling through thermal mode concept[J]. J Manuf Sci E T ASME 130(6):0610061–0610069
Yang H, Ni J (2005) Dynamic neural network modeling for nonlinear, nonstationary machine tool thermally induced error[J]. Int J Mach Tools Manuf 45(4–5):455–465
Zhang J, Li B, Zhou CX, Zhao WH (2016) Positioning error prediction and compensation of ball screw feed drive system with different mounting conditions[J]. Proc Inst Mech Eng Part B-Journal of Engineering Manufacture 230(12):2307–2311
Shi H, Ma C, Yang J, Zhao L, Mei XS, Gong GF (2015) Investigation into effect of thermal expansion on thermally induced error of ball screw feed drive system of precision machine tools[J]. Int J Mach Tools Manuf 97:60–71
Liu W, Zhang Y, Fang H, Duan H, Liu B, Xu SD (2018) Assembly method and assembly error evaluation of machine tool linear rolling guide pair[J]. Mech Eng 08:74–76
Acknowledgements
It is great thankful to NEWAY CNC EQUIPMENT(SUZHOU)CO., LTD for providing experimental instruments.
Funding
This research is supported by Jiangsu Science and Technology Achievement Conversion Project (No.BA2018093).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Highlights
1. A description method of repeated positioning error of feed shaft is proposed.
2. The probability compensation model of repeated positioning error of feed shaft is constructed.
3. A dynamic modeling method of probability compensation model for repeated positioning error is described.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Wu, H., Zuo, D. Digital map and probability compensation model for repeated positioning error of feed axis. Int J Adv Manuf Technol 124, 2631–2643 (2023). https://doi.org/10.1007/s00170-022-10698-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-022-10698-y