Abstract
Fly cutting is widely used in manufacturing of large-scale, high-precision optical components. However, the discontinuity of fly cutting machining leads to significant relative vibrations between the tool and the workpiece. The cutting process generates periodic waves along the cutting direction, which will deteriorate the wavefront characteristics of optical components. Based on the machining dynamics, this paper proposes a direct integration method to predict the waviness error of the machined surface. The cutting force model of fly cutting is established. The multi-mode characteristics of the spindle-tool system are measured by the experimental method. Then, the influence of uncertainties on the calculation results is analyzed by the variance-based sensitivity analysis method. Finally, the plane cutting experiment verifies that the direct integration method effectively predicts the waviness error and its variation trend, and the waviness prediction research is important for optimization of the machining parameters.
Graphical Abstract Figure
References
1.
Zhang
, S. J.
, To
, S.
, Zhu
, Z. W.
, and Zhang
, G. Q.
, 2016
, “A Review of Fly Cutting Applied to Surface Generation in Ultra-Precision Machining
,” Int. J. Mach. Tools Manuf.
, 103
, pp. 13
–27
. 2.
Schönemann
, L.
, Riemer
, O.
, Karpuschewski
, B.
, Schreiber
, P.
, Klemme
, H.
, and Denkena
, B.
, 2022
, “Digital Surface Twin for Ultra-Precision High Performance Cutting
,” Precis. Eng.
, 77
, pp. 349
–359
. 3.
Liang
, Y.
, Chen
, W.
, Bai
, Q.
, Sun
, Y.
, Chen
, G.
, Zhang
, Q.
, and Sun
, Y.
, 2013
, “Design and Dynamic Optimization of an Ultraprecision Diamond Flycutting Machine Tool for Large KDP Crystal Machining
,” Int. J. Adv. Manuf. Technol.
, 69
(1–4
), pp. 237
–244
. 4.
Wang
, S.
, An
, C.
, Zhang
, F.
, Wang
, J.
, Lei
, X.
, and Zhang
, J.
, 2016
, “An Experimental and Theoretical Investigation on the Brittle Ductile Transition and Cutting Force Anisotropy in Cutting KDP Crystal
,” Int. J. Mach. Tools Manuf.
, 106
, pp. 98
–108
. 5.
Chen
, M.
, Li
, M.
, Jiang
, W.
, and Xu
, Q.
, 2010
, “Influence of Period and Amplitude of Microwaviness on KH2PO4 Crystal's Laser Damage Threshold
,” J. Appl. Phys.
, 108
(4
), p. 043109
. 6.
Fu
, P.
, Xue
, J.
, Zhou
, L.
, Wang
, Y.
, Lan
, Z.
, Zhan
, L.
, and Zhang
, F.
, 2019
, “Influence of the Heat Deformation of Ultra-Precision Fly Cutting Tools on KDP Crystal Surface Microstructure
,” Int. J. Adv. Manuf. Technol.
, 103
(1–4
), pp. 1009
–1018
. 7.
Zhang
, S. J.
, To
, S.
, Zhang
, G. Q.
, and Zhu
, Z. W.
, 2015
, “A Review of Machine-Tool Vibration and Its Influence upon Surface Generation in Ultra-Precision Machining
,” Int. J. Mach. Tools Manuf.
, 91
, pp. 34
–42
. 8.
An
, C. H.
, Zhang
, Y.
, Xu
, Q.
, Zhang
, F. H.
, Zhang
, J. F.
, Zhang
, L. J.
, and Wang
, J. H.
, 2010
, “Modeling of Dynamic Characteristic of the Aerostatic Bearing Spindle in an Ultra-Precision Fly Cutting Machine
,” Int. J. Mach. Tools Manuf.
, 50
(4
), pp. 374
–385
. 9.
An
, C.
, Deng
, C.
, Miao
, J.
, and Yu
, D.
, 2018
, “Investigation on the Generation of the Waviness Errors Along Feed-Direction on Flycutting Surfaces
,” Int. J. Adv. Manuf. Technol.
, 96
(1–4
), pp. 1457
–1465
. 10.
Ding
, Y.
, Rui
, X.
, Lu
, H.
, Chang
, Y.
, and Chen
, Y.
, 2020
, “Research on the Dynamic Characteristics of the Ultra-Precision Fly Cutting Machine Tool and Its Influence on the Mid-Frequency Waviness of the Surface
,” Int. J. Adv. Manuf. Technol.
, 106
(1–2
), pp. 441
–454
. 11.
Li
, J.
, Wei
, W.
, Huang
, X.
, and Liu
, P.
, 2020
, “Study on Dynamic Characteristics of Ultraprecision Machining and Its Effect on Medium-Frequency Waviness Error
,” Int. J. Adv. Manuf. Technol.
, 108
(9–10
), pp. 2895
–2906
. 12.
Wang
, M.
, Zhang
, Y.
, Guo
, S.
, and An
, C.
, 2018
, “Longitudinal Micro-Waviness (LMW) Formation Mechanism on Large Optical Surface During Ultra-Precision Fly Cutting
,” Int. J. Adv. Manuf. Technol.
, 95
(9–12
), pp. 4659
–4669
. 13.
Chen
, W.
, Liang
, Y.
, Sun
, Y.
, and Lu
, L.
, 2014
, “Investigation on the Influence of Machine Tool Dynamics on the Wavefront Gradient of KH2PO4 Crystals
,” ASME J. Manuf. Sci. Eng.
, 136
(5
), p. 051006
. 14.
Sun
, Y.
, Chen
, W.
, Liang
, Y.
, An
, C.
, Chen
, G.
, and Su
, H.
, 2015
, “An Integrated Method for Waviness Simulation on Large-Size Surface
,” Proc. Inst. Mech. Eng. B
, 229
(1
), pp. 178
–182
. 15.
Kiran
, K.
, Rubeo
, M.
, Kayacan
, M. C.
, and Schmitz
, T.
, 2017
, “Two Degree of Freedom Frequency Domain Surface Location Error Prediction
,” Precis. Eng.
, 48
, pp. 234
–242
. 16.
Schmitz
, T. L.
, and Mann
, B. P.
, 2006
, “Closed-Form Solutions for Surface Location Error in Milling
,” Int. J. Mach. Tools Manuf.
, 46
(12–13
), pp. 1369
–1377
. 17.
Mann
, B. P.
, Young
, K. A.
, Schmitz
, T. L.
, and Dilley
, D. N.
, 2005
, “Simultaneous Stability and Surface Location Error Predictions in Milling
,” ASME J. Manuf. Sci. Eng.
, 127
(3
), pp. 446
–453
. 18.
Ding
, Y.
, Zhu
, L.
, Zhang
, X.
, and Ding
, H.
, 2011
, “On a Numerical Method for Simultaneous Prediction of Stability and Surface Location Error in Low Radial Immersion Milling
,” ASME J. Dyn. Syst. Meas. Control
, 133
(2
), p. 024503
. 19.
Ding
, Y.
, Zhu
, L.
, Zhang
, X.
, and Ding
, H.
, 2010
, “A Full-Discretization Method for Prediction of Milling Stability
,” Int. J. Mach. Tools Manuf.
, 50
(5
), pp. 502
–509
. 20.
Ding
, Y.
, Zhu
, L.
, Zhang
, X.
, and Ding
, H.
, 2013
, “Stability Analysis of Milling Via the Differential Quadrature Method
,” ASME J. Manuf. Sci. Eng.
, 135
(4
), p. 044502
. 21.
Ding
, Y.
, Zhu
, L.
, Zhang
, X.
, and Ding
, H.
, 2011
, “Numerical Integration Method for Prediction of Milling Stability
,” ASME J. Manuf. Sci. Eng.
, 133
(3
), p. 031005
. 22.
Ding
, Y.
, Zhu
, L.
, Zhang
, X.
, and Ding
, H.
, 2012
, “Response Sensitivity Analysis of the Dynamic Milling Process Based on the Numerical Integration Method
,” Chin. J. Mech. Eng.
, 25
(5
), pp. 940
–946
. 23.
Wen
, Z.
, Ding
, Y.
, Liu
, P.
, and Ding
, H.
, 2017
, ““Direct Integration Method for Time-Delayed Control of Second-Order Dynamic Systems
,” AMSE J. Dyn. Syst. Meas. Contr.
, 139
(6
), p. 061001
. 24.
Sujuan
, W.
, Tao
, Z.
, Wenping
, D.
, Zhanwen
, S.
, and To
, S.
, 2022
, “Analytical Modeling and Prediction of Cutting Forces in Orthogonal Turning: A Review
,” Int. J. Adv. Manuf. Technol.
, 119
(3
), pp. 1407
–1434
. 25.
Zhao
, L.
, Zhang
, J.
, Zhang
, J.
, Dai
, H.
, Hartmaier
, A.
, and Sun
, T.
, 2023
, “Numerical Simulation of Materials-Oriented Ultra-Precision Diamond Cutting: Review and Outlook
,” Int. J. Extreme Manuf.
, 5
(2
), p. 022001
. 26.
Baday
, Ş
, Başak
, H.
, and Sönmez
, F.
, 2017
, “The Assessment of Cutting Force With Taguchi Design in Medium Carbon Steel–Applied Spheroidization Heat Treatment
,” Meas. Control
, 50
(4
), pp. 89
–96
. 27.
Sardiñas
, R. Q.
, Santana
, M. R.
, and Brindis
, E. A.
, 2006
, “Genetic Algorithm-Based Multi-Objective Optimization of Cutting Parameters in Turning Processes
,” Eng. Appl. Artif. Intell.
, 19
(2
), pp. 127
–133
. 28.
Sharma
, V. S.
, Dhiman
, S.
, Sehgal
, R.
, and Sharma
, S. K.
, 2008
, “Estimation of Cutting Forces and Surface Roughness for Hard Turning Using Neural Networks
,” Intell. Manuf.
, 19
(4
), pp. 473
–483
. 29.
Noordin
, M. Y.
, Venkatesh
, V. C.
, Sharif
, S.
, Elting
, S.
, and Abdullah
, A.
, 2004
, “Application of Response Surface Methodology in Describing the Performance of Coated Carbide Tools When Turning AISI 1045 Steel
,” J. Mater. Process. Technol.
, 145
(1
), pp. 46
–58
. 30.
Altintas
, Y.
, 2012
, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design
, Cambridge University Press
, New York
.31.
Hajdu
, D.
, Insperger
, T.
, and Stepan
, G.
, 2015
, “The Effect of Non-Symmetric FRF on Machining: A Case Study
,” Proceedings of the Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
, Boston, MA
, Aug. 2–5
.32.
Peeters
, B.
, Van der Auweraer
, H.
, Guillaume
, P.
, and Leuridan
, J.
, 2004
, “The PolyMAX Frequency-Domain Method: A New Standard for Modal Parameter Estimation?
,” Shock Vibr.
, 11
(3–4
), pp. 395
–409
. 33.
Yuan
, J.
, Li
, J.
, Wei
, W.
, and Liu
, P.
, 2022
, “Operational Modal Identification of Ultra-Precision Fly-Cutting Machine Tools Based on Least-Squares Complex Frequency-Domain Method
,” Int. J. Adv. Manuf. Technol.
, 119
(7–8
), pp. 4385
–4394
. 34.
Wen
, Z.
, Ding
, Y.
, Liu
, P.
, and Ding
, H.
, 2019
, “An Efficient Identification Method for Dynamic Systems With Coupled Hysteresis and Linear Dynamics: Application to Piezoelectric-Actuated Nanopositioning Stages
,” IEEE/ASME Trans. Mechatron.
, 24
(1
), pp. 326
–337
. 35.
Sauer
, T.
, 2012
, Numerical Analysis
, Pearson
, Boston, MA
.36.
Lei
, Y.
, Hou
, T.
, and Ding
, Y.
, 2023
, “Stability Analysis of Pocket Machining with the Spiral Tool Path Using the Discontinuous Galerkin Method
,” J. Manuf. Processes
, 92
, pp. 12
–31
. 37.
Saltelli
, A.
, Ratto
, M.
, Andres
, T.
, Campolongo
, F.
, Cariboni
, J.
, Gatelli
, D.
, Saisana
, M.
, and Tarantola
, S.
, 2007
, Global Sensitivity Analysis. The Primer
, Wiley
, New York
.38.
Saltelli
, A.
, Annoni
, P.
, Azzini
, I.
, Campolongo
, F.
, Ratto
, M.
, and Tarantola
, S.
, 2010
, “Variance Based Sensitivity Analysis of Model Output. Design and Estimator for the Total Sensitivity Index
,” Comput. Phys. Commun.
, 181
(2
), pp. 259
–270
. 
