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  • 1
    Electronic Resource
    Electronic Resource
    A Mechanics Based Model for Study of Dynamics of Milling Operations (2000)
    Springer
    Meccanica 35 (2000), S. 89-109 
    Details
    ISSN: 1572-9648
    Keywords: Milling process ; Chatter ; Stability ; Bifurcation ; Machining dynamics ; Nonlinear dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A unified mechanics based model with multiple degrees of freedom is developed and numerically simulated to study workpiece-tool interactions during milling of ductile workpieces with helical tools. A refined orthogonal cutting model is used at each section of the tool, and the milling forces are determined by using a spatial integration scheme along the axis of the tool. Both regenerative and loss of contact effects are considered in determining the cutting forces, which makes the model well suited for a wide range of milling operations. The model also allows for partial engagement of a tool with a workpiece, which is an important feature needed for milling operations with helical tools. Time domain simulations are carried out by using the developed model to predict the stability boundaries in the space of the tool spindle speed and the axial depth of cut. Poincaré sections are used to determine loss of stability from period-one motions to other motions such as two-period quasiperiodic motions, as a control parameter is varied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004887301926
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  • 2
    Electronic Resource
    Electronic Resource
    Cyclic motions near a Hopf bifurcation of a four-dimensional system (1992)
    Springer
    Nonlinear dynamics 3 (1992), S. 19-39 
    Details
    ISSN: 1573-269X
    Keywords: Hopf bifurcation ; multiple scales ; limit cycles ; internal resonance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study motions near a Hopf bifurcation of a representative nonconservative four-dimensional autonomous system with quadratic nonlinearities. Special cases of the four-dimensional system represent the envelope equations that govern the amplitudes and phases of the modes of an internally resonant structure subjected to resonant excitations. Using the method of multiple scales, we reduce the Hopf bifurcation problem to two differential equations for the amplitude and phase of the bifurcating cyclic solutions. Constant solutions of these equations provide asymptotic expansions for the frequency and amplitude of the bifurcating limit cycle. The stability of the constant solutions determines the nature of the bifurcation (i.e., subcritical or supercritical). For different choices of the control parameter, the range of validity of the analytical approximation is ascertained using numerical simulations. The perturbation analysis and discussions are also pertinent to other autonomous systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00045469
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