Abstract
Laser pipe-cutting system, a special machine tool, has been widely used in the precision machining of metal pipe. The geometric errors remarkably affect the machining accuracy of products. Error modeling and sensitivity analysis are key issues to improve the product quality. In this paper, the geometric error model of the laser pipe-cutting system which contains 70 geometric errors is established based on multi-body theory and Lie group. The coupling effects caused by two chucks are considered as the spatial angular deviation in modeling. The sensitivity analysis for the geometric error model is conducted to identify the essential sensitivity errors based on an improved Sobol method with quasi-Monte Carlo algorithm. The results show that not only the linear positioning errors, but also the squareness errors and parallelism errors play crucial roles in the machining accuracy. Based on the result, the essential sensitivity errors are calibrated and the machining accuracy is improved.
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References
Abbaszadeh-Mir, Y., Mayer, J.R.R., Cloutier, G.: Theory and simulation for the identification of the link geometric errors for a five-axis machine tool using a telescoping magnetic ball-bar. Int. J. Prod. Res. 40(18), 4781–4797 (2002)
Zhu, S., Ding, G., Qin, S.: Integrated geometric error modeling, identification and compensation of CNC machine tools. Int. J. Mach. Tools Manuf 52(1), 24–29 (2012)
Murray R., Sastry, S., Li, Z.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Inc. (1994)
Cheng, Q., Feng, Q., Liu, Z., Gu, P., Zhang, G.: Sensitivity analysis of machining accuracy of multi-axis machine tool based on POE screw theory and Morris method. Int. J. Adv. Manuf. Technol. 84(9–12), 2301–2318 (2015). https://doi.org/10.1007/s00170-015-7791-x
Xiang, S., Altintas, Y.: Modeling and compensation of volumetric errors for five-axis machine tools. Int. J. Mach. Tools Manuf. 101, 65–78 (2016)
Sobol, I.M.: Sensitivity analysis for non-linear mathematical models. Math. Modeling Comput. Exp. 1 (1993)
Zou, X., Zhao, X., Li, G., Li, Z., Sun, T.: Sensitivity analysis using a variance-based method for a three-axis diamond turning machine. Int. J. Adv. Manuf. Technol. 92(9–12), 4429–4443 (2017). https://doi.org/10.1007/s00170-017-0394-y
Xia, C., Wang, S., Sun, S.: An identification method for crucial geometric errors of gear form grinding machine tools based on tooth surface posture error model. Mech. Mach. Theory 138, 76–94 (2019)
Liu, Y., Fei, D., Li, D.: Machining accuracy improvement for a dual-spindle ultra-precision drum roll lathe based on geometric error analysis and calibration. Precis. Eng. 66, 401–416 (2020)
Dai, J.: Screw Algebra and Kinematic Approaches for Mechanisms and Robotics. Springer, London (2019)
Sobol, I.M.: Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simul. 55(1–3), 271–280 (2014)
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Jiang, Y., Yang, W., Qin, L., Ding, T. (2021). Geometric Error Modeling and Sensitivity Analysis of a Laser Pipe-Cutting System Based on Lie Group and Sobol Method. In: Dolgui, A., Bernard, A., Lemoine, D., von Cieminski, G., Romero, D. (eds) Advances in Production Management Systems. Artificial Intelligence for Sustainable and Resilient Production Systems. APMS 2021. IFIP Advances in Information and Communication Technology, vol 633. Springer, Cham. https://doi.org/10.1007/978-3-030-85910-7_49
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DOI: https://doi.org/10.1007/978-3-030-85910-7_49
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