Abstract
Chatter stability prediction is of great practical importance for stable machining because regenerative chatter in the milling process will result in poor surface quality and low machining efficiency. Full-discretization method and its variants have been demonstrated to be effective for the prediction of milling stability. However, the main shortcoming of such methods is that they can predict milling stability but involve inverse matrix calculation, which would lead to increases in computational complexity and reductions in numerical stability. In addition, there may not necessarily exist good inverse matrix for these methods. This study proposes a precise integration-based third-order full-discretization method that can be both accurate and efficient in milling stability prediction without the need of any inverse matrix calculation. The performance evaluation performed by the simulation demonstrates that the proposed method outperforms the conventional methods with respect to stability prediction accuracy and speed. Extensive simulation is also carried out to investigate the effects of interpolation order for the simplified state term on the performance of the proposed method. Three demonstrative examples are employed to demonstrate how the proposed method can function effectively in the prediction of milling chatter stability. Although a chatter stability prediction tool for the milling process is the particular application presented here, the proposed method can be applied to other machining processes, such as turning, boring, and drilling.
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References
Altintas Y, Weck M (2004) Chatter stability of metal cutting and grinding. CIRP Ann Manuf Technol 53(2):619–642
Kayhan M, Budak E (2009) An experimental investigation of chatter effects on tool life. Inst Mech Eng Part B J Eng Manuf 223(11):1455–1463
Wiercigroch M, Budak E (2001) Sources of nonlinearities, chatter generation and suppression in metal cutting. Philos Trans R Soc A-Math Phys Eng Sci 359(1781):663–693
Ismail F, Vadari VR (1990) Machining chatter of end mills with unequal modes. J Eng Ind 112(3):229–235
Wiercigroch M, Krivtsov AM (2001) Frictional chatter in orthogonal metal cutting. Philos Trans R Soc A Math Phys Eng Sci 359(1781):713–738
Merritt HE (1965) Theory of self-excited machine-tool chatter: contribution to machine-tool chatter research. J Eng Ind 87(4):447–454
Insperger T, Stépán G (2002) Semi-discretization method for delayed systems. Int J Numer Methods Eng 55(5):503–518
Ding H, Ding Y, Zhu LM (2012) On time-domain methods for milling stability analysis. Sci Bull 57(33):4336–4345
Qin CJ, Tao JF, Lin L, Liu CL (2017) An Adams-Moulton-based method for stability prediction of milling processes. Int J Adv Manuf Technol 89(9–12):3049–3058
Davies MA, Pratt JR, Dutterer BS, Burns TJ (2002) Stability prediction for low radial immersion milling. J Manuf Sci Eng-Trans ASME 124(2):217–225
Li ZQ, Liu Q (2008) Solution and analysis of chatter stability for end milling in the time-domain. Chin J Aeronaut 21(2):169–178
Altintaş Y, Budak E (1995) Analytical prediction of stability lobes in milling. CIRP Ann Manuf Technol 44(1):357–362
Merdol SD, Altintas Y (2004) Multi frequency solution of chatter stability for low immersion milling. J Manuf Sci Eng-Trans ASME 126(3):459–466
Bayly PV, Halley JE, Mann BP, Davies MA (2003) Stability of interrupted cutting by temporal finite element analysis. J Manuf Sci Eng-Trans ASME 125(2):220–225
Insperger T, Stépán G (2004) Updated semi-discretization method for periodic delay-differential equations with discrete delay. Int J Numer Methods Eng 61(1):117–141
Insperger T, Stépán G, Turi J (2008) On the higher-order semi-discretization for periodic delayed systems. J Sound Vib 313(1–2):334–341
Altintas Y, Chan PK (1992) In-process detection and suppression of chatter in milling. Int J Mach Tools Manuf 32(3):329–347
Insperger T, Stepan G (2004) Stability analysis of turning with periodic spindle speed modulation via semidiscretization. J Vib Control 10(12):1835–1855
Long XH, Balachandran B (2010) Stability of up-milling and down-milling operations with variable spindle speed. J Vib Control 16(7–8):1151–1168
Ding Y, Niu JB, Zhu LM, Ding H (2015) Numerical integration method for stability analysis of milling with variable spindle speeds. ASME J Vib Acoust 138(1):011010–011011
Altıntas Y, Engin S, Budak E (1999) Analytical stability prediction and design of variable pitch cutters. J Manuf Sci Eng 121(2):173–178
Sims ND, Mann B, Huyanan S (2008) Analytical prediction of chatter stability for variable pitch and variable helix milling tools. J Sound Vib 317(3–5):664–686
Wan M, Zhang WH, Dang JW, Yang Y (2010) A unified stability prediction method for milling process with multiple delays. Int J Mach Tools Manuf 50(1):29–41
Balachandran B (2001) Nonlinear dynamics of milling processes. Philos Trans R Soc A-Math Phys Eng Sci 359(1781):793–819
Long XH, Balachandran B, Mann BP (2007) Dynamics of milling processes with variable time delays. Nonlinear Dyn 47(1–3):49–63
Long XH, Balachandran B (2007) Stability analysis for milling process. Nonlinear Dyn 49(3):349–359
Liu XB, Vlajic N, Long XH, Meng G, Balachandran B (2014) Multiple regenerative effects in cutting process and nonlinear oscillations. Int J Dynam Control 2(1):86–101
Ding Y, Zhu LM, Zhang XJ, Ding H (2010) A full-discretization method for prediction of milling stability. Int J Mach Tools Manuf 50(5):502–509
Ding Y, Zhu LM, Zhang XJ, Ding H (2010) Second-order full-discretization method for milling stability prediction. Int J Mach Tools Manuf 50(10):926–932
Quo Q, Sun YW, Jiang Y (2012) On the accurate calculation of milling stability limits using third-order full-discretization method. Int J Mach Tools Manuf 62:61–66
Ozoegwu CG (2014) Least squares approximated stability boundaries of milling process. Int J Mach Tools Manuf 79:24–30
Ozoegwu CG, Omenyi SN, Ofochebe SM (2015) Hyper-third order full-discretization methods in milling stability prediction. Int J Mach Tools Manuf 92:1–9
Ding Y, Zhu LM, Zhang XJ, Ding H (2011) Numerical integration method for prediction of milling stability. J Manuf Sci Eng-Trans ASME 133(3):031005–031009
Li MZ, Zhang GJ, Huang Y (2013) Complete discretization scheme for milling stability prediction. Nonlinear Dyn 71(1–2):187–199
Xie QZ (2016) Milling stability prediction using an improved complete discretization method. Int J Adv Manuf Technol 83(5–8):815–821
Li ZQ, Yang ZK, Peng YR, Zhu F, Ming XZ (2016) Prediction of chatter stability for milling process using Runge-Kutta-based complete discretization method. Int J Adv Manuf Technol 86(1–4):943–952
Zhang Z, Li HG, Meng G, Liu C (2015) A novel approach for the prediction of the milling stability based on the Simpson method. Int J Mach Tools Manuf 99:43–47
Tang XW, Peng FY, Yan R, Gong YH, Li YT, Jiang LL (2017) Accurate and efficient prediction of milling stability with updated full-discretization method. Int J Adv Manuf Technol 88(9–12):2357–2368
Yan ZH, Wang XB, Liu ZB, Wang DQ, Jiao L, Ji YJ (2017) Third-order updated full-discretization method for milling stability prediction. Int J Adv Manuf Technol 92(5–8):2299–2309
Zhong WX, Williams FW (1994) A precise time step integration method. Proc Inst Mech Eng Part C J Eng Mech Eng Sci 208(6):427–430
Gu YX, Chen BS, Zhang HW, Guan ZQ (2001) Precise time-integration method with dimensional expanding for structural dynamic equations. AIAA J 39(12):2394–2399
Ding Y, Zhu LM, Zhang XJ, Ding H (2011) On a numerical method for simultaneous prediction of stability and surface location error in low radial immersion milling. J Dyn Syst Meas Control-Trans ASME 133(2):024503
Jiang SL, Sun YW, Yuan XL, Liu WR (2017) A second-order semi-discretization method for the efficient and accurate stability prediction of milling process. Int J Adv Manuf Technol 92(1–4):583–595
Dai YB, Li HK, Xing XY, Hao BT (2018) Prediction of chatter stability for milling process using precise integration method. Precis Eng-J Int Soc Precis Eng Nanotechnol 52:152–157
Li HK, Dai YB, Fan ZF (2018) Improved precise integration method for chatter stability prediction of two-DOF milling system. Int J Adv Manuf Technol 101(5–8):1235–1246
Farkas M (1994) Periodic motions. Springer, Berlin
Gradišek J, Kalveram M, Insperger T, Weinert K, Stépán G, Govekar E (2005) On stability prediction for milling. Int J Mach Tools Manuf 45(7):769–781
Insperger T, Stepan G (2011) Semi-discretization for time-delay systems: stability and engineering application. Springer, Berlin
Acknowledgments
This study is funded partially by the National Science Foundation of China (51775279, 51775277), National Defense Basic Scientific Research Program of China (JCKY201605B006), and Jiangsu Industry Foresight and Common Key Technology (SBE2018030858).
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Yang, WA., Huang, C., Cai, X. et al. Effective and fast prediction of milling stability using a precise integration-based third-order full-discretization method. Int J Adv Manuf Technol 106, 4477–4498 (2020). https://doi.org/10.1007/s00170-019-04790-z
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DOI: https://doi.org/10.1007/s00170-019-04790-z