Analysis of compliance between the cutting tool and the workpiece on the stability of a turning process

Chatter is a common vibration problem that limits productivity of machining processes, since its large amplitude vibrations causes poor surface finishing, premature damage and breakage of cutting tools, as well as mechanical system deterioration. This phenomenon is a condition of instability that has been classified as a self-excited vibration problem, which shows a nonlinear behavior characterized by the presence of limit cycles and jump phenomenon. In addition, subcritical Hopf and flip bifurcations are mathematical interpretations for loss of stability. Regeneration theory and linear time delay models are the most widely accepted explanations for the onset of chatter vibrations. On the other hand, models based on nonlinearities from structure and cutting process have been also proposed and studied under nonlinear dynamics and chaos theory. However, on both linear and nonlinear formulations usually the compliance between the workpiece and cutting tool has been ignored. In this work, a multiple degree of freedom model for chatter prediction in turning, based on compliance between the cutting tool and the workpiece, is presented. Hence, a better approach to the physical phenomenon is expected, since the effect of the dynamic characteristics of the cutting tool is also taken into account. In this study, a linear stability analysis of the model in the frequency domain is performed and a method to construct typical stability charts is obtained. The effect of the dynamics of the cutting tool on the stability of the process is analyzed as well.

[1]  D. W. Wu,et al.  An Analytical Model of Cutting Dynamics. Part 2: Verification , 1985 .

[2]  Gábor Stépán,et al.  Nonlinear Dynamics of High-Speed Milling—Analyses, Numerics, and Experiments , 2005 .

[3]  Yusuf Altintas,et al.  Analytical Prediction of Stability Lobes in Milling , 1995 .

[4]  Gábor Stépán,et al.  Stability of up-milling and down-milling, part 1: alternative analytical methods , 2003 .

[5]  Yusuf Altintas,et al.  Analytical Prediction of Chatter Stability in Milling—Part I: General Formulation , 1998 .

[6]  Tony L. Schmitz,et al.  Effects of Radial Immersion and Cutting Direction on Chatter Instability in End-Milling , 2002 .

[7]  Cha'o-Kuang Chen,et al.  A stability analysis of regenerative chatter in turning process without using tailstock , 2006 .

[8]  M. S. Fofana,et al.  Sufficient conditions for the stability of single and multiple regenerative chatter , 2002 .

[9]  Gábor Stépán,et al.  Multiple chatter frequencies in milling processes , 2003 .

[10]  Günter Radons,et al.  Nonlinear Dynamics of Production Systems , 2004 .

[11]  B. Mann,et al.  Limit cycles, bifurcations, and accuracy of the milling process , 2004 .

[12]  Tamás Kalmár-Nagy,et al.  Subcritical Hopf Bifurcation in the Delay Equation Model for Machine Tool Vibrations , 2001 .

[13]  Gábor Stépán,et al.  On stability prediction for milling , 2005 .

[14]  Jiří Tlustý,et al.  Manufacturing processes and equipment , 1999 .

[15]  M. S. Fofana,et al.  Effect of Regenerative Process on the Sample Stability of a Multiple Delay Differential Equation , 2000, Nonlinear Dynamics and Stochastic Mechanics.

[16]  Gábor Stépán,et al.  Stability Analysis of Turning With Periodic Spindle Speed Modulation Via Semidiscretization , 2004 .

[17]  Yusuf Altintas,et al.  Analytical Stability Prediction and Design of Variable Pitch Cutters , 1998, Manufacturing Science and Engineering.

[18]  Gábor Stépán,et al.  Nonlinear Dynamics of High‐Speed Milling Subjected to Regenerative Effect , 2005 .

[19]  Gábor Stépán,et al.  Stability of up-milling and down-milling, part 2: experimental verification , 2003 .

[20]  Brian P. Mann,et al.  Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration , 2005 .

[21]  M. S. Fofana,et al.  Parametric stability of non-linear time delay equations , 2004 .

[22]  Gábor Stépán,et al.  State Dependent Regenerative Delay in Milling Processes , 2005 .

[23]  André Preumont,et al.  Chatter reduction through active vibration damping , 2005 .

[24]  Marian Wiercigroch,et al.  Sources of nonlinearities, chatter generation and suppression in metal cutting , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  H. E. Merritt.  Theory of Self-Excited Machine-Tool Chatter: Contribution to Machine-Tool Chatter Research—1 , 1965 .

[26]  R N Arnold,et al.  Cutting Tools Research: Report of Subcommittee on Carbide Tools: The Mechanism of Tool Vibration in the Cutting of Steel , 1946 .

[27]  Yusuf Altintas,et al.  Analytical Prediction of Chatter Stability in Milling—Part II: Application of the General Formulation to Common Milling Systems , 1998 .

[28]  F. W. Taylor.  The Art of Cutting Metals , 1907 .

[29]  Yusuf Altintas,et al.  Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design , 2000 .

[30]  M. Wiercigroch,et al.  Frictional chatter in orthogonal metal cutting , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[31]  Gábor Stépán,et al.  Delay, Parametric Excitation, and the Nonlinear Dynamics of Cutting Processes , 2005, Int. J. Bifurc. Chaos.

[32]  M. Fofana.  Delay dynamical systems and applications to nonlinear machine-tool chatter , 2003 .

[33]  Francisco J. Campa,et al.  Stability limits of milling considering the flexibility of the workpiece and the machine , 2005 .

[34]  F. Moon,et al.  Nonlinear models for complex dynamics in cutting materials , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[35]  S. A. Tobias,et al.  A Theory of Nonlinear Regenerative Chatter , 1974 .

[36]  Gábor Stépán,et al.  Semi‐discretization method for delayed systems , 2002 .

[37]  Tony L. Schmitz,et al.  COMPARISON OF ANALYTICAL AND NUMERICAL SIMULATIONS FOR VARIABLE SPINDLE SPEED TURNING , 2003 .

[38]  Chun Liu,et al.  An Analytical Model of Cutting Dynamics. Part 1: Model Building , 1985 .

[39]  Keith A. Young,et al.  Simultaneous Stability and Surface Location Error Predictions in Milling , 2005 .

[40]  M. S. Fofana,et al.  Aspects of stable and unstable machining by Hopf bifurcation , 2002 .