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Extended Nonlinear Modeling and Stability Analysis of the Peripheral Milling Process

Moradi, Hamed | 2012

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 43383 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Vossoughi, Gholamreza; Movahhedy, Mohammad Reza
  7. Abstract:
  8. In this thesis, an extended nonlinear model of peripheral milling process (2D) is presented. For the first time, cutting forces are described through a complete third order polynomial function of the axial depth of cut. Also, cubic nonlinearity is considered for the structural stiffness as a function of tool tip displacement. To complete the model, process damping and tool wear effects are also considered. A set of experiments including modal tests to determine natural frequencies and structural damping ratios; and also cutting force measurements at different feed rates to determine nonlinear cutting force coefficients, are carried out. Also, measurement of critical axial depth of cut at different spindle speeds and stability lobes analysis are accomplished to determine coefficients of nonlinear stiffness (for the first time) and process damping. For analytical investigation of the nonlinear dynamics of self excited vibrations and internal resonance, perturbation analysis is performed through multiple scales approach. As another contribution, the mentioned perturbation analysis is used for the 2DOF milling process with coupled dynamic terms associated with time delay. After developing the frequency response function, jump phenomenon is studied. As the other contribution, the effects of nonlinear coefficients of cutting forces and structural stiffness on stability lobes diagram are investigated. In addition, the energy transfer between vibration modes (x/y) is studied. Through forced vibration analysis of the dynamic system, problem solution is obtained under primary and sub-harmonic resonances. For the first time, detuning parameter (the difference between tooth passing and chatter frequencies), damping ratio and tool wear length are introduced as the new bifurcation parameters. Occurrence of new kinds of bifurcation including Symmetry-Breaking (pitchfork), Period Doubling (flip), Secondary Hopf (Neimark) and Cyclic-Fold (tangent) bifurcations are investigated. Attractive behavior of periodic, quasi-periodic and chaotic limit cycles and their related Poincare sections are studied.

  9. Keywords:
  10. Stability ; Bifurcation ; Damping ; Perturbation Method ; Peripheral Milling ; Nonlinear Extended Model ; Tool Wear

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  • 1-s2.0-S0022460X12001988-main.pdf
    • Dynamics of regenerative chatter and internal resonance in milling process with structural and cutting force nonlinearities
      • Introduction
      • Extended nonlinear model of peripheral milling process
        • Classical model of cutting forces
        • Extended nonlinear model of cutting forces including regenerative chatter effect
      • Perturbation analysis of the regenerative chatter dynamics
        • Simulation results
        • Jump phenomenon and the effects of nonlinearities
        • The effects of structural and cutting force nonlinearities on the stability lobes diagram
      • Investigation of the internal resonance dynamics (mode coupling) in the milling process
        • Non-resonant condition
        • Internal resonance condition
      • Conclusions
      • Acknowledgement
      • Appendix A
      • Appendix B
      • References
  • fulltext.pdf
    • Bifurcation analysis of milling process with tool wear and process damping: regenerative chatter with primary resonance
      • Abstract
      • Introduction
      • Extended nonlinear model of the peripheral milling with tool wear and process damping
        • Extended nonlinear model of cutting forces with regenerative chatter effect
        • Modeling of the tool flank wear
        • Modeling of the process damping effect
      • Perturbation analysis of the extended nonlinear model under regenerative chatter
      • Results and discussion
      • Conclusions
      • Appendix
      • References
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