Abstract
A tensor-based general order full-discretization method which can be automated to preempt all manual case-by-case symbolic analyses associated with chatter stability identification is upgraded with the capacity for model order reduction of elastic thin-walled workpieces. The implemented method is then exploited for studying the sensitivity of the precision of stability lobes of a reduced elastic thin-walled workpiece to arbitrary variation of interpolation order of both the current and delayed regenerative chatter states. The studied system shows almost identical results for unidirectional and bidirectional models. It was further found that within the numerically stable interpolation orders which are usually from 0 to 9, stability lobes are mildly sensitive to the variation of the order of the current state but strongly sensitive to the variation of the order of the delayed state. Though no combination of orders of current and delayed states is seen to outperform the others in all spindle speed ranges, it is recommended to keep the order of the delayed state at 3 while the order of the current state is varied to get the best results. Error surfaces and time-domain simulations were instrumental in the deductions and discussions of results. The programmed method offers potential industrial benefit of making use of stability lobes for precise selection of productive chatter-free process parameters more user-friendly.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Altinta, Y., Budak, E.: Analytical prediction of stability lobes in milling. CIRP Ann. Manuf. Technol. 44(1), 357–362 (1995)
Insperger, T., Stépán, G.: Stability of the milling process. Period. Polytechn. Mech. Eng. 44(1), 47–57 (2000)
Ding, Y., Zhu, L., Zhang, X., Ding, H.: Numerical integration method for prediction of milling stability. J. Manuf. Sci. Eng. 133(3), 1–9 (2011)
Ozoegwu, C., Ofochebe, S., Omenyi, S.: A method of improving chatter-free conditions with combined-mode milling. J. Manuf. Process. 21, 1–13 (2016)
Altintas, Y., Montgomery, D., Budak, E.: Dynamic peripheral milling of flexible structures. Precis. Eng. 13(3), 137–145 (1991)
Bravo, U., Altuzarra, O., López De Lacalle, L.N., Sánchez, J.A., Campa, F.J.: Stability limits of milling considering the flexibility of the workpiece and the machine. Int. J. Mach. Tools Manuf. 45(15), 1669–1680 (2005)
Herranz, S., Campa, F.J., De Lacalle, L.N., Rivero, A., Lamikiz, A., Ukar, E., Sánchez, J.A., Bravo, U.: The milling of airframe components with low rigidity: a general approach to avoid static and dynamic problems. Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf. 219(11), 789–801 (2005)
Thevenot, V., Arnaud, L., Dessein, G., Cazenave-Larroche, G.: Integration of dynamic behaviour variations in the stability lobes method: 3D lobes construction and application to thin-walled structure milling. Int. J. Adv. Manuf. Technol. 27(7–8), 638–644 (2006)
Thevenot, V., Arnaud, L., Dessein, G., Cazenave-Larroche, G.: Influence of material removal on the dynamic behavior of thin-walled structures in peripheral milling. Mach. Sci. Technol. 10(3), 275–287 (2006)
Adetoro, O.B., Sim, W.M., Wen, P.H.: An improved prediction of stability lobes using nonlinear thin wall dynamics. J. Mater. Process. Technol. 210(6–7), 969–979 (2010)
Budak, E., Tunç, L.T., Alan, S., Özgüven, H.N.: Prediction of workpiece dynamics and its effects on chatter stability in milling. CIRP Ann. Manuf. Technol. 61(1), 339–342 (2012)
Song, Q., Liu, Z., Wan, Y., Ju, G., Shi, J.: Application of Sherman-Morrison-Woodbury formulas in instantaneous dynamic of peripheral milling for thin-walled component. Int. J. Mech. Sci. 96–97, 79–90 (2015)
Yang, Y., Zhang, W.H., Ma, Y.C., Wan, M.: Chatter prediction for the peripheral milling of thin-walled workpieces with curved surfaces. Int. J. Mach. Tools Manuf. 109, 36–48 (2016)
Ahmadi, K.: Finite strip modeling of the varying dynamics of thin-walled pocket structures during machining. Int. J. Adv. Manuf. Technol. 89(9–12), 2691–2699 (2017)
Song, Q., Shi, J., Liu, Z., Wan, Y.: A time-space discretization method in milling stability prediction of thin-walled component. Int. J. Adv. Manuf. Technol. 89(9–12), 2675–2689 (2017)
Shi, J., Song, Q., Liu, Z., Ai, X.: A novel stability prediction approach for thin-walled component milling considering material removing process. Chin. J. Aeronaut. 30(5), 1789–1798 (2017)
Song, Q., Ai, X., Tang, W.: Prediction of simultaneous dynamic stability limit of time-variable parameters system in thin-walled workpiece high-speed milling processes. Int. J. Adv. Manuf. Technol. 55(9–12), 883–889 (2011)
Zhang, L., Gao, W., Zhang, D., Tian, Y.: Prediction of dynamic milling stability considering time variation of deflection and dynamic characteristics in thin-walled component milling process. Shock Vib. 2016, 1–14 (2016)
Eksioglu, C., Kilic, Z.M., Altintas, Y.: Discrete-time prediction of chatter stability, cutting forces, and surface location errors in flexible milling systems. J. Manuf. Sci. Eng. 134(6), 1–13 (2012)
Wan, M., Dang, X.B., Zhang, W.H., Yang, Y.: Optimization and improvement of stable processing condition by attaching additional masses for milling of thin-walled workpiece. Mech. Syst. Signal Process. 103, 196–215 (2018)
Li, Z., Sun, Y., Guo, D.: Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece. Int. J. Adv. Manuf. Technol. 89(9–12), 2663–2674 (2017)
Zhang, Z., Li, H., Liu, X., Zhang, W., Meng, G.: Chatter mitigation for the milling of thin-walled workpiece. Int. J. Mech. Sci. 138–139, 262–271 (2018)
Hamann, D., Eberhard, P.: Stability analysis of milling processes with varying workpiece dynamics. Multibody Syst. Dyn. 42(4), 383–396 (2018)
Ma, Y.-C., Yang, Y., Wan, M., Zhang, W.-H., Dang, X.-B.: An efficient decomposition-condensation method for chatter prediction in milling large-scale thin-walled structures. Mech. Syst. Signal Process. 121, 58–76 (2019)
Dong, X., Zhang, W.: Stability analysis in milling of the thin walled part considering multiple variables of manufacturing systems. Int. J. Adv. Manuf. Technol. 89(1–4), 515–527 (2017)
Ozoegwu, C.G.: Polynomial tensor-based stability identification of milling process: application to reduced thin-walled workpiece. In: Fehr, J., Haasdonk, B. (eds.) IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, 22–25 May 2018, vol. 36, ch. 15, pp. 209–220. Springer International Publishing, Stuttgart, Germany (2020)
Tang, A., Liu, Z.: Three-dimensional stability lobe and maximum material removal rate in end milling of thin-walled plate. Int. J. Adv. Manuf. Technol. 43(1–2), 33–39 (2009)
Qu, S., Zhao, J., Wang, T.: Three-dimensional stability prediction and chatter analysis in milling of thin-walled plate. Int. J. Adv. Manuf. Technol. 86(5–8), 2291–2300 (2016)
Powałka, B., Jemielniak, K.: Stability analysis in milling of flexible parts based on operational modal analysis. CIRP J. Manuf. Sci. Technol. 9, 125–135 (2015)
Ozoegwu, C., Eberhard, P.: Tensor-based automatic arbitrary order computation of the full-discretization method for milling stability analysis. In: Altenbach, H., Irschik, H., Matveenko, V. (eds.) Contributions to Advanced Dynamics and Continuum Mechanics, ch. 11, pp. 179 – 205. Springer International Publishing (2019)
Ozoegwu, C.G., Omenyi, S.N., Ofochebe, S.M.: Hyper-third order full-discretization methods in milling stability prediction. Int. J. Mach. Tools Manuf. 92, 1–9 (2015)
Bayly, P.V., Mann, B.P., Peters, D.A., Schmitz, T.L., Stepan, G., Insperger, T.: Effects of radial immersion and cutting direction on chatter instability in end-milling. In: ASME International Mechanical Engineering Congress and Exposition, New Orleans, pp. 1–13 (2002)
Acknowledgements
The matrices for the elastic workpiece model were kindly provided by Dominik Hamann. This help is greatly appreciated. The described research was partially done while C.G. Ozoegwu visited the ITM at the University of Stuttgart in 2019. This stay was funded by the Priority Program SPP 1897 “Calm, Smooth, Smart” of the DFG (German Research Foundation). This support is highly appreciated.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Ozoegwu, C., Eberhard, P. (2021). Automated Upgraded Generalized Full-Discretization Method: Application to the Stability Study of a Thin-Walled Milling Process. In: Dixit, U., Dwivedy, S. (eds) Mechanical Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-15-5712-5_4
Download citation
DOI: https://doi.org/10.1007/978-981-15-5712-5_4
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-5711-8
Online ISBN: 978-981-15-5712-5
eBook Packages: EngineeringEngineering (R0)