Abstract
The accurate evaluation of the instantaneous undeformed chip thickness (IUCT) plays a crucial role in the modeling of milling processes. However, the vibrations of the tool–workpiece system can make conventional IUCT models either inaccurate or not applicable. This paper introduces the concept of surface function to describe the milled surface, through which the IUCT can be readily computed. The evolution of this surface function is governed by a partial differential equation (PDE) in the form of a balance law, and the material removal process is characterized by discontinuous conditions at the cutters. A finite volume algorithm is adopted to solve the proposed PDE with discontinuous conditions at the cutters. Through a case study of the asymmetric cutting process, the surface function method demonstrates two main advantages over conventional methods: (i) a detailed description of IUCT evolution considering the influence of the initial shape of the workpiece and (ii) a general framework to accurately compute the IUCT. This method shows a promising potential for computing the IUCT in numerical simulations of chattering phenomenon in the milling process.
References
1.
Le
, B.
, Khaliq
, J.
, Huo
, D.
, Teng
, X.
, and Shyha
, I.
, 2020
, “A Review on Nanocomposites. Part 2: Micromachining
,” ASME J. Manuf. Sci. Eng.
, 142
(10
), p. 100802
. 2.
Lei
, S.
, Zhao
, X.
, Yu
, X.
, Hu
, A.
, Vukelic
, S.
, Jun
, M. B.
, Joe
, H.
, Yao
, Y. L.
, and Shin
, Y. C.
, 2020
, “Ultrafast Laser Applications in Manufacturing Processes: A State-of-the-Art Review
,” ASME J. Manuf. Sci. Eng.
, 142
(3
), p. 031005
. 3.
Shin
, Y. C.
, Wu
, B.
, Lei
, S.
, Cheng
, G. J.
, and Lawrence Yao
, Y.
, 2020
, “Overview of Laser Applications in Manufacturing and Materials Processing in Recent Years
,” ASME J. Manuf. Sci. Eng.
, 142
(11
), p. 110818
. 4.
McConaha
, M.
, Venugopal
, V.
, and Anand
, S.
, 2021
, “Design Tool for Topology Optimization of Self Supporting Variable Density Lattice Structures for Additive Manufacturing
,” ASME J. Manuf. Sci. Eng.
, 143
(7
), p. 071001
. 5.
Weiss
, B. M.
, Hamel
, J. M.
, Ganter
, M. A.
, and Storti
, D. W.
, 2021
, “Data-Driven Additive Manufacturing Constraints for Topology Optimization
,” ASME J. Manuf. Sci. Eng.
, 143
(2
), p. 021001
. 6.
Altintas
, Y.
, 2012
, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design
, Cambridge University Press
, Cambridge, UK
.7.
Zhang
, W.
, and Wan
, M.
, 2016
, Milling Simulation: Metal Milling Mechanics, Dynamics and Clamping Principles
, John Wiley & Sons
, Hoboken, NJ
.8.
Kiss
, A. K.
, Bachrathy
, D.
, and Stepan
, G.
, 2020
, “Effects of Varying Dynamics of Flexible Workpieces in Milling Operations
,” ASME J. Manuf. Sci. Eng.
, 142
(1
), p. 011005
. 9.
Insperger
, T.
, Stépán
, G.
, Bayly
, P.
, and Mann
, B.
, 2003
, “Multiple Chatter Frequencies in Milling Processes
,” J. Sound Vib.
, 262
(2
), pp. 333
–345
. 10.
Merdol
, S. D.
, and Altintas
, Y.
, 2004
, “Multifrequency Solution of Chatter Stability for Low Immersion Milling
,” ASME J. Manuf. Sci. Eng.
, 126
(3
), pp. 459
–466
. 11.
Afazov
, S.
, Ratchev
, S.
, and Segal
, J.
, 2010
, “Modelling and Simulation of Micro-Milling Cutting Forces
,” J. Mater. Process. Technol.
, 210
(15
), pp. 2154
–2162
. 12.
Ismail
, F.
, Elbestawi
, M. A.
, Du
, R.
, and Urbasik
, K.
, 1993
, “Generation of Milled Surfaces Including Tool Dynamics and Wear
,” J. Eng. Ind.
, 115
(3
), pp. 245
–252
. 13.
Insperger
, T.
, Gradišek
, J.
, Kalveram
, M.
, Stépán
, G.
, Winert
, K.
, and Govekar
, E.
, 2006
, “Machine Tool Chatter and Surface Location Error in Milling Processes
,” ASME J. Manuf. Sci. Eng.
, 128
(4
), pp. 913
–920
. 14.
Li
, H.
, Liu
, K.
, and Li
, X.
, 2001
, “A New Method for Determining the Undeformed Chip Thickness in Milling
,” J. Mater. Process. Technol.
, 113
(1–3
), pp. 378
–384
. 15.
Faassen
, R. P. H.
, van de Wouw
, N.
, Nijmeijer
, H.
, and Oosterling
, J. A. J.
, 2006
, “An Improved Tool Path Model Including Periodic Delay for Chatter Prediction in Milling
,” ASME J. Comput. Nonlinear Dyn.
, 2
(2
), pp. 167
–179
. 16.
Spiewak
, S.
, 1995
, “An Improved Model of the Chip Thickness in Milling
,” CIRP Ann.
, 44
(1
), pp. 39
–42
. 17.
Kumanchik
, L. M.
, and Schmitz
, T. L.
, 2007
, “Improved Analytical Chip Thickness Model for Milling
,” Precis. Eng.
, 31
(3
), pp. 317
–324
. 18.
Song
, G.
, Li
, J.
, and Sun
, J.
, 2013
, “Approach for Modeling Accurate Undeformed Chip Thickness in Milling Operation
,” Int. J. Adv. Manuf. Technol.
, 68
(5–8
), pp. 1429
–1439
. 19.
Bao
, W.
, and Tansel
, I.
, 2000
, “Modeling Micro-end-milling Operations. Part II: Tool Run-out
,” Int. J. Mach. Tools Manuf.
, 40
(15
), pp. 2175
–2192
. 20.
Li
, C.
, Lai
, X.
, Li
, H.
, and Ni
, J.
, 2007
, “Modeling of Three-Dimensional Cutting Forces in Micro-end-milling
,” J. Micromech. Microeng.
, 17
(4
), p. 671
. 21.
Chen
, W.
, Teng
, X.
, Huo
, D.
, and Wang
, Q.
, 2017
, “An Improved Cutting Force Model for Micro Milling Considering Machining Dynamics
,” Int. J. Adv. Manuf. Technol.
, 93
(9
), pp. 3005
–3016
. 22.
Rodríguez
, P.
, and Labarga
, J. E.
, 2013
, “A New Model for the Prediction of Cutting Forces in Micro-End-Milling Operations
,” J. Mater. Process. Technol.
, 213
(2
), pp. 261
–268
. 23.
Li
, K.
, Zhu
, K.
, and Mei
, T.
, 2016
, “A Generic Instantaneous Undeformed Chip Thickness Model for the Cutting Force Modeling in Micromilling
,” Int. J. Mach. Tools Manuf.
, 105
, pp. 23
–31
. 24.
Liu
, X.
, Vlajic
, N.
, Long
, X.
, Meng
, G.
, and Balachandran
, B.
, 2014
, “Multiple Regenerative Effects in Cutting Process and Nonlinear Oscillations
,” Int. J. Dyn. Control
, 2
(1
), pp. 86
–101
. 25.
Li
, X.
, and Li
, H.
, 2004
, “Theoretical Modelling of Cutting Forces in Helical End Milling With Cutter Runout
,” Int. J. Mech. Sci.
, 46
(9
), pp. 1399
–1414
. 26.
Li
, H.
, and Li
, X.
, 2005
, “A Numerical Study of the Effects of Cutter Runout on Milling Process Geometry Based on True Tooth Trajectory
,” Int. J. Adv. Manuf. Technol.
, 25
(5
), pp. 435
–443
. 27.
Long
, X.
, Balachandran
, B.
, and Mann
, B.
, 2007
, “Dynamics of Milling Processes With Variable Time Delays
,” Nonlinear Dyn.
, 47
(1
), pp. 49
–63
. 28.
Han
, X.
, and Tang
, L.
, 2015
, “Precise Prediction of Forces in Milling Circular Corners
,” Int. J. Mach. Tools Manuf.
, 88
, pp. 184
–193
. 29.
Montgomery
, D.
, and Altintas
, Y.
, 1991
, “Mechanism of Cutting Force and Surface Generation in Dynamic Milling
,” J. Eng. Ind.
, 113
(2
), pp. 160
–168
. 30.
Paris
, H.
, Peigne
, G.
, and Mayer
, R.
, 2004
, “Surface Shape Prediction in High Speed Milling
,” Int. J. Mach. Tools Manuf.
, 44
(15
), pp. 1567
–1576
. 31.
Jun
, M. B. G.
, Liu
, X.
, DeVor
, R. E.
, and Kapoor
, S. G.
, 2006
, “Investigation of the Dynamics of Microend Milling—Part I: Model Development
,” ASME J. Manuf. Sci. Eng.
, 128
(4
), pp. 893
–900
. 32.
Gupta
, S. K.
, and Wahi
, P.
, 2016
, “Global Axial–Torsional Dynamics During Rotary Drilling
,” J. Sound Vib.
, 375
, pp. 332
–352
. 33.
Zhang
, H.
, and Detournay
, E.
, 2020
, “An Alternative Formulation for Modeling Self-Excited Oscillations of Rotary Drilling Systems
,” J. Sound Vib.
, 474
, p. 115241
. 34.
Bale
, D. S.
, Leveque
, R. J.
, Mitran
, S.
, and Rossmanith
, J. A.
, 2003
, “A Wave Propagation Method for Conservation Laws and Balance Laws With Spatially Varying Flux Functions
,” SIAM J. Sci. Comput.
, 24
(3
), pp. 955
–978
. 35.
LeVeque
, R. J.
, 2002
, Finite Volume Methods for Hyperbolic Problems
, Cambridge University Press
, Cambridge, UK
.Copyright © 2022 by ASME
You do not currently have access to this content.
