Abstract
This paper proposes a novel approach with time-invariant transition matrix to predict surface location error (SLE) for low radial immersion milling. In considerations of regenerative and steady cutting thicknesses, the milling process is first concluded as a delay differential equation (DDE). Subsequently, ordinary differential theory is adopted to formulate the response of the machine tool system using the indirect integral scheme. According to Taylor series, the self- and forced-excited term is expanded by linear approximation in turn to deduce a discrete closed map. Taking advantage of this map, a novel transition matrix without any relation to the change of time is established in total tooth passing period to predict the SLE. To verify the effectiveness of the proposed approach, two experimentally validated examples are conducted. The results demonstrate that the method is of higher computational accuracy and efficiency.
This is a preview of subscription content, log in via an institution to check access.
References
Altintas Y (2000) Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. Cambridge University, Cambridge
Altintas Y, Budak E (1995) Analytical prediction of stability lobes in milling. CIRP Ann Manuf Technol 44(1):357–362
Altintas Y, Shamoto E, Lee P (1999) Analytical prediction of stability lobes in ball end milling. J Manuf Sci E-T ASME 121(4):586–592
Merdol S, Altintas Y (2004) Multi frequency solution of chatter stability for low immersion milling. J Manuf Sci Eng 126(3):459–466
Dai Y, Li H, Wei Z, et al (2018) Chatter stability prediction for five-axis ball end milling with precise integration method. J Manuf Process 32:20–31
Niu J, Ding Y, Zhu L, Ding H (2014) Runge–Kutta methods for a semi-analytical prediction of milling stability. Nonlinear Dynam 76(1):289–304
Dai Y, Li H, Hao B (2018) An improved full-discretization method for chatter stability prediction. Int J Adv Manuf Technol 96(9–12):3503–3510
Insperger T, Stépán G (2002) Semi-discretization method for delayed systems. Int J Numer Meth Eng 55(5):503–518
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
Dai Y, Li H, Xing X, Hao B (2018) Prediction of chatter stability for milling process using precise integration method. Precis Eng 52:152–157
Schmitz T, Mann B (2006) Closed-form solutions for surface location error in milling. Int J Mach Tools Manuf 46(12):1369–1377
Kiran K, Rubeo M, Kayacan MC, Schmitz T (2017) Two degree of freedom frequency domain surface location error prediction. Precis Eng 48:234–242
Mann B, Young K, Schmitz T, Bartow M, Bayly P (2003) Machining accuracy due to tool or workpiece vibrations. ASME Int Mech Eng Congress and Exposition, pp 55–62
Mann B, Young K, Schmitz T, David N (2005) Simultaneous stability and surface location error predictions in milling. J Manuf Sci Eng 127(3):446–453
Mann B, Edes B, Easley S, Young K, Ma K (2008) Chatter vibration and surface location error prediction for helical end mills. Int J Mach Tools Manuf 48(3):350–361
Bachrathy D, Insperger T, Stepan G (2009) Surface properties of the machined workpiece for helical mills. Mach Sci Technol 13(2):227–245
Insperger T, Gradišek J, Kalveram M, Govekar E (2006) Machine tool chatter and surface location error in milling processes. J Manuf Sci Eng 128(4):913–920
Ding Y, Zhu L, Zhang X, 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 133(2):024503
Eksioglu C, Kilic Z, Altintas Y (2012) Altintas. Discrete-time prediction of chatter stability, cutting forces, and surface location errors in flexible milling systems. J Manuf Sci Eng 134(6):061006
Zhang X, Xiong C, Ding Y, Huang X, Ding H (2014) A synthetical stability method for cutting parameter optimization to assure surface location accuracy in flexible part milling. Int J Adv Manuf Technol 75(5–8):1131–1147
Yuan L, Zeng S, Chen Z (2015) Simultaneous prediction of surface topography and surface location error in milling. Arch P I Mech Eng C 229(10):1805–1829
Honeycutt A, Schmitz T (2017) Surface location error and surface roughness for period-n milling bifurcations. J Manuf Sci Eng 139:061010–061011
Ding Y, Zhang X, Ding H (2015) Harmonic differential quadrature method for surface location error prediction and machining parameter optimization in milling. J Manuf Sci Eng 137(2):024501
Li Z, Jiang S, Sun Y (2017) Chatter stability and surface location error predictions in milling with mode coupling and process damping. P I Mech Eng B 095440541770822
Funding
This study was supported by the National Natural Science Foundation of China (51575075) and Collaborative Innovation Center of Major Machine Manufacturing in Liaoning.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dai, Y., Li, H., Yao, J. et al. A novel approach with time-invariant transition matrix for surface location error prediction in low radial immersion milling. Int J Adv Manuf Technol 101, 1267–1274 (2019). https://doi.org/10.1007/s00170-018-2910-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-018-2910-0