메뉴 건너뛰기




Volumn 1, Issue 4, 2006, Pages 294-306

Analysis of the Chatter instability in a nonlinear model for drilling

Author keywords

Center manifold reduction; Chatter; Delay differential equations; Drilling

Indexed keywords

BIFURCATION (MATHEMATICS); DIFFERENTIAL EQUATIONS; DRILLING; MATHEMATICAL MODELS;

EID: 33751079600     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2338648     Document Type: Article
Times cited : (10)

References (27)
  • 1
    • 85024511543 scopus 로고
    • "The Dynamics of High-Speed Milling"
    • Tlusty, J., 1986, "The Dynamics of High-Speed Milling," J. Eng. Ind., 108, pp. 59-67.
    • (1986) J. Eng. Ind. , vol.108 , pp. 59-67
    • Tlusty, J.1
  • 2
    • 0029210691 scopus 로고
    • "Analytical Prediction of Stability Lobes in Milling"
    • Altintas, Y., and Budak, E., 1995, "Analytical Prediction of Stability Lobes in Milling," CIRP Ann., 44(1), pp. 357-362.
    • (1995) CIRP Ann. , vol.44 , Issue.1 , pp. 357-362
    • Altintas, Y.1    Budak, E.2
  • 3
    • 0001658506 scopus 로고    scopus 로고
    • "Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Comparison to Test"
    • Bayly, P. V., Metzler, S. A., Schaut, A. J., and Young, K. A., 2001, "Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Comparison to Test," ASME J. Manuf. Sci. Eng., 123, pp. 552-561.
    • (2001) ASME J. Manuf. Sci. Eng. , vol.123 , pp. 552-561
    • Bayly, P.V.1    Metzler, S.A.2    Schaut, A.J.3    Young, K.A.4
  • 4
    • 0000421939 scopus 로고    scopus 로고
    • "Analysis of Tool Oscillation and Hole Roundness Error in a Quasi-Static Model of Reaming"
    • Bayly, P. V., Young, K. A., and Halley, J. E., 2001, "Analysis of Tool Oscillation and Hole Roundness Error in a Quasi-Static Model of Reaming," ASME J. Manuf. Sci. Eng., 123, pp. 387-396.
    • (2001) ASME J. Manuf. Sci. Eng. , vol.123 , pp. 387-396
    • Bayly, P.V.1    Young, K.A.2    Halley, J.E.3
  • 6
    • 0003143423 scopus 로고    scopus 로고
    • "Delay-Differential Equation Models for Machine Tool Chatter"
    • in F. Moon, ed., Wiley, New York
    • Stépán, G., 1998, "Delay-Differential Equation Models for Machine Tool Chatter," in Dynamics and Chaos in Manufacturing Processes, F. Moon, ed., Wiley, New York, pp. 165-191.
    • (1998) Dynamics and Chaos in Manufacturing Processes , pp. 165-191
    • Stépán, G.1
  • 7
    • 0036523478 scopus 로고    scopus 로고
    • "Nonlinear Models of Chatter in Drilling Processes"
    • Stone, E., and Askari, A., 2002, "Nonlinear Models of Chatter in Drilling Processes," Dyn. Syst., 17(1), pp. 65-85.
    • (2002) Dyn. Syst. , vol.17 , Issue.1 , pp. 65-85
    • Stone, E.1    Askari, A.2
  • 8
    • 84867969858 scopus 로고    scopus 로고
    • "Stability and Bifurcation Analysis of a Nonlinear DDE Model for Drilling"
    • Stone, E., and Campbell, S. A., 2004, "Stability and Bifurcation Analysis of a Nonlinear DDE Model for Drilling," J. Nonlinear Sci., 14(1), pp. 27-57.
    • (2004) J. Nonlinear Sci. , vol.14 , Issue.1 , pp. 27-57
    • Stone, E.1    Campbell, S.A.2
  • 9
    • 0001414176 scopus 로고
    • "Analytical and Symbolically-Assisted Investigation of Hopf Bifurcations in Delay-Differential Equations"
    • Campbell, S. A., and Bélair, J., 1995, "Analytical and Symbolically-Assisted Investigation of Hopf Bifurcations in Delay-Differential Equations," Can. Appl. Math. Q., 3(2), pp. 137-154.
    • (1995) Can. Appl. Math. Q. , vol.3 , Issue.2 , pp. 137-154
    • Campbell, S.A.1    Bélair, J.2
  • 10
    • 0000840164 scopus 로고
    • "Normal Forms for Retarded Functional Differential Equations With Parameters and Applications to Hopf Bifurcation"
    • Faria, T., and Magalhães, L., 1995, "Normal Forms for Retarded Functional Differential Equations With Parameters and Applications to Hopf Bifurcation," JDE, 122, pp. 181-200.
    • (1995) JDE , vol.122 , pp. 181-200
    • Faria, T.1    Magalhães, L.2
  • 11
    • 84974185478 scopus 로고
    • "Flows on Center Manifolds for Scalar Functional Differential Equations"
    • Hale, J. K., 1985, "Flows on Center Manifolds for Scalar Functional Differential Equations," Proc. - R. Soc. Edinburgh, Sect. A: Math., 101A, pp, 193-201.
    • (1985) Proc. - R. Soc. Edinburgh, Sect. A: Math. , vol.101 A , pp. 193-201
    • Hale, J.K.1
  • 15
    • 0002644042 scopus 로고
    • "Stability Criteria for Second Order Dynamical Systems With Time Lag"
    • Bhatt, S. J., and Hsu, C. S., 1966, "Stability Criteria for Second Order Dynamical Systems With Time Lag," ASME J. Appl. Mech., 33, pp. 113-118.
    • (1966) ASME J. Appl. Mech. , vol.33 , pp. 113-118
    • Bhatt, S.J.1    Hsu, C.S.2
  • 16
    • 0000204399 scopus 로고    scopus 로고
    • "Stability and Bifurcation in the Harmonic Oscillator With Multiple Delayed Feedback Loops"
    • Campbell, S. A., 1999, "Stability and Bifurcation in the Harmonic Oscillator With Multiple Delayed Feedback Loops," Dyn. Cont. Disc. Impul. Sys., 5, pp. 225-235.
    • (1999) Dyn. Cont. Disc. Impul. Sys. , vol.5 , pp. 225-235
    • Campbell, S.A.1
  • 17
    • 34248352395 scopus 로고
    • "Limit Cycles, Tori, and Complex Dynamics in Second-Order Differential Equations With Delayed Negative Feedback"
    • Campbell, S. A., Bélair, J., Ohira, T., and Milton, J., 1995, "Limit Cycles, Tori, and Complex Dynamics in Second-Order Differential Equations With Delayed Negative Feedback," J. Dyn. Differ. Equ., 7(1), pp. 213-236.
    • (1995) J. Dyn. Differ. Equ. , vol.7 , Issue.1 , pp. 213-236
    • Campbell, S.A.1    Bélair, J.2    Ohira, T.3    Milton, J.4
  • 18
    • 0000209631 scopus 로고
    • "Discrete Delay, Distributed Delay and Stability Switches"
    • Cooke, K. L., and Grossman, Z., 1982, "Discrete Delay, Distributed Delay and Stability Switches," J. Math. Anal. Appl., 86, pp. 592-627.
    • (1982) J. Math. Anal. Appl. , vol.86 , pp. 592-627
    • Cooke, K.L.1    Grossman, Z.2
  • 19
    • 85024577148 scopus 로고
    • "Stability Charts for Second-Order Dynamical Systems With Time Lag"
    • Hsu, C. S., and Bhatt, S. J., 1966, "Stability Charts for Second-Order Dynamical Systems With Time Lag," ASME J. Appl. Mech., 33, pp. 119-124.
    • (1966) ASME J. Appl. Mech. , vol.33 , pp. 119-124
    • Hsu, C.S.1    Bhatt, S.J.2
  • 20
    • 36849140209 scopus 로고
    • "Mechanics of the Cutting Process. I. Orthogonal Cutting and a Type 2 Chip"
    • Merchant, M. E., 1945, "Mechanics of the Cutting Process. I. Orthogonal Cutting and a Type 2 Chip," J. Appl. Phys., 16, pp. 267-275.
    • (1945) J. Appl. Phys. , vol.16 , pp. 267-275
    • Merchant, M.E.1
  • 26
    • 33751096546 scopus 로고
    • "Classification and Unfoldings of Degenerate Hopf Bifurcation"
    • Golubitsky, M., and Langford, W. F., 1981, "Classification and Unfoldings of Degenerate Hopf Bifurcation," JDE, 41, pp. 525-546.
    • (1981) JDE , vol.41 , pp. 525-546
    • Golubitsky, M.1    Langford, W.F.2
  • 27
    • 0000857092 scopus 로고
    • "Unfoldings of Certain Singularities of Vector Fields: Generalized Hopf Bifurcations"
    • Takens, F., 1973, "Unfoldings of Certain Singularities of Vector Fields: Generalized Hopf Bifurcations," JDE, 14, pp. 476-493.
    • (1973) JDE , vol.14 , pp. 476-493
    • Takens, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.