On time-domain methods for milling stability analysis

As a basic and advanced machining technique, the high-speed milling process plays an important role in realizing the goal of high performance manufacturing. From the viewpoint of machining dynamics, obtaining chatter-free machining parameters is a prerequisite to guaranteeing machining accuracy and improving machining efficiency. This paper gives an overview on recent progress in time domain semi-analytical methods for chatter stability analysis of milling processes. The state of art methods of milling stability prediction in milling processes and their applications are introduced in detail. The bottlenecks involved are analyzed, and potential solutions are discussed. Finally, a brief prospect on future works is presented.

[1]  Haitao Ma,et al.  Stability of linear time‐periodic delay‐differential equations via Chebyshev polynomials , 2004 .

[2]  Tony L. Schmitz,et al.  Examination of surface location error due to phasing of cutter vibrations , 1999 .

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

[4]  T. Schmitz,et al.  Closed-form solutions for surface location error in milling , 2006 .

[5]  Bin Li,et al.  Time-frequency analysis and detecting method research on milling force token signal in spindle current signal , 2009 .

[6]  Eric A. Butcher,et al.  Analysis of Milling Stability by the Chebyshev Collocation Method: Algorithm and Optimal Stable Immersion Levels , 2009 .

[7]  A. Galip Ulsoy,et al.  Delay differential equations via the matrix Lambert W function and bifurcation analysis: application to machine tool chatter. , 2007, Mathematical biosciences and engineering : MBE.

[8]  Ye Ding,et al.  Variable-step integration method for milling chatter stability prediction with multiple delays , 2011 .

[9]  J. Tlusty,et al.  Basic Non-Linearity in Machining Chatter , 1981 .

[10]  Keith A. Young,et al.  Chatter vibration and surface location error prediction for helical end mills , 2008 .

[11]  He Li,et al.  Experimental investigation of three-dimensional mixed-mode fracture of a titanium alloy at room and elevated temperatures , 2011 .

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

[13]  Tony L. Schmitz,et al.  A Robust Semi-Analytical Method for Calculating the Response Sensitivity of a Time Delay System , 2008 .

[14]  Manfred Weck,et al.  Chatter Stability of Metal Cutting and Grinding , 2004 .

[15]  Yuwen Sun,et al.  Analytical modeling of geometric errors induced by cutter runout and tool path optimization for five-axis flank machining , 2011 .

[16]  Jon R. Pratt,et al.  Stability Prediction for Low Radial Immersion Milling , 2002 .

[17]  Lutfi Taner Tunc,et al.  Modeling and simulation of 5-axis milling processes , 2009 .

[18]  Chunya Wu,et al.  Research on the influence of machining introduced sub-surface defects and residue stress upon the mechanical properties of single crystal copper , 2010 .

[19]  L. Delves,et al.  Computational methods for integral equations: Frontmatter , 1985 .

[20]  Min Wan,et al.  A unified stability prediction method for milling process with multiple delays , 2010 .

[21]  I. E. Minis,et al.  A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling , 1993 .

[22]  F. Ismail,et al.  Machining chatter of end mills with unequal modes , 1990 .

[23]  Wenwu Cao,et al.  Applied Numerical Methods Using MATLAB®: Yang/Applied Numerical MATLAB , 2005 .

[24]  Martin Hosek,et al.  A new perspective and analysis for regenerative machine tool chatter , 1998 .

[25]  Nejat Olgac,et al.  Dynamics and Stability of Variable-pitch Milling , 2007 .

[26]  Zoltan Dombovari,et al.  Chatter stability of milling in frequency and discrete time domain , 2008 .

[27]  Tony L. Schmitz,et al.  Predicting High-Speed Machining Dynamics by Substructure Analysis , 2000 .

[28]  Han Ding,et al.  Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (II): Tool positioning strategy , 2010 .

[29]  Yusuf Altintas,et al.  Prediction of Milling Force Coefficients From Orthogonal Cutting Data , 1996 .

[30]  Balakumar Balachandran,et al.  Dynamics of milling processes with variable time delays , 2006 .

[31]  Zhen Huang,et al.  Type synthesis of the rotational decoupled parallel mechanism based on screw theory , 2011 .

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

[33]  J. Dai,et al.  Type synthesis of a class of spatial lower-mobility parallel mechanisms with orthogonal arrangement based on Lie group enumeration , 2010 .

[34]  Matthew A. Davies,et al.  Thermomechanical oscillations in material flow during high-speed machining , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[35]  Ryozo Nagamune,et al.  Double-loop robust tracking control for micro machine tools , 2011 .

[36]  B. Mann,et al.  Stability of Interrupted Cutting by Temporal Finite Element Analysis , 2003 .

[37]  Jon R. Pratt,et al.  The Stability of Low Radial Immersion Milling , 2000 .

[38]  Yingchun Liang,et al.  Molecular dynamics simulations of thermal effects in nanometric cutting process , 2010 .

[39]  Han Ding,et al.  Response sensitivity analysis of the dynamic milling process based on the numerical integration method , 2012 .

[40]  Yusuf Altintas,et al.  Multi frequency solution of chatter stability for low immersion milling , 2004 .

[41]  YiTong Zhang,et al.  New concept and new theory of mobility calculation for multi-loop mechanisms , 2010 .

[42]  Han Ding,et al.  Milling stability analysis using the spectral method , 2011 .

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

[44]  Brian P. Mann,et al.  Stability of Delay Equations Written as State Space Models , 2010 .

[45]  Luning Liu,et al.  Simulation and analysis of aerodynamics for high speed face milling cutters , 2010 .

[46]  Han Ding,et al.  Wholly smoothing cutter orientations for five-axis NC machining based on cutter contact point mesh , 2010 .

[47]  Meng Guang.  Stability analysis of milling process by semidiscretization method based on Magnus-Guassian truncation , 2009 .

[48]  Han Ding,et al.  Second-order full-discretization method for milling stability prediction , 2010 .

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

[50]  Han Ding,et al.  On a Numerical Method for Simultaneous Prediction of Stability and Surface Location Error in Low Radial Immersion Milling , 2011 .

[51]  Youlun Xiong,et al.  Kinematics constrained five-axis tool path planning for high material removal rate , 2011 .

[52]  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.

[53]  Wŏn-yŏng Yang,et al.  Applied Numerical Methods Using MATLAB , 2005 .

[54]  Han Ding,et al.  Numerical Integration Method for Prediction of Milling Stability , 2011 .

[55]  Gábor Stépán,et al.  On the higher-order semi-discretizations for periodic delayed systems , 2008 .

[56]  Chunyu Zhao,et al.  Synchronization of the four identical unbalanced rotors in a vibrating system of plane motion , 2010 .

[57]  Jian S. Dai,et al.  Orientation angle rotatability of planar serial n-link manipulators , 2010 .

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

[59]  Yusuf Altintas,et al.  An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions , 2003 .

[60]  Xiao-Shan Gao,et al.  High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining , 2011 .

[61]  Keith A. Young,et al.  Machining Accuracy Due to Tool or Workpiece Vibrations , 2003 .

[62]  Han Ding,et al.  Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (I): Third-order approximation of tool envelope surface , 2010 .

[63]  Huayong Yang,et al.  Piecewise model and experiment of power chuck’s gripping force loss during high speed turning , 2011 .

[64]  S. Smith,et al.  Efficient simulation programs for chatter in milling , 1993 .

[65]  R. Sridhar,et al.  A Stability Algorithm for the General Milling Process: Contribution to Machine Tool Chatter Research—7 , 1968 .

[66]  A. Galip Ulsoy,et al.  Analysis of a System of Linear Delay Differential Equations , 2003 .

[67]  Gábor Stépán,et al.  Machine Tool Chatter and Surface Location Error in Milling Processes , 2006 .

[68]  Gábor Stépán,et al.  SURFACE PROPERTIES OF THE MACHINED WORKPIECE FOR HELICAL MILLS , 2009 .

[69]  Xin-Jun Liu,et al.  A new solution for topology optimization problems with multiple loads: The guide-weight method , 2011 .

[70]  Richard E. DeVor,et al.  Mechanistic Modeling of the Ball End Milling Process for Multi-Axis Machining of Free-Form Surfaces , 2001 .

[71]  Caihua Xiong,et al.  A New Solution for Stability Prediction in Flexible Part Milling , 2011, ICIRA.

[72]  Yanwen Li,et al.  A new formula of mechanism mobility based on virtual constraint loop , 2011 .

[73]  Ye Ding,et al.  Milling stability analysis with simultaneously considering the structural mode coupling effect and regenerative effect , 2012 .

[74]  Tony L. Schmitz,et al.  Tool Point Frequency Response Prediction for High-Speed Machining by RCSA , 2001 .

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

[76]  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.

[77]  Caihua Xiong,et al.  Improved Full-Discretization Method for Milling Chatter Stability Prediction with Multiple Delays , 2010, ICIRA.

[78]  Hongqi Liu,et al.  On-line chatter detection using servo motor current signal in turning , 2011 .

[79]  Tao Sun,et al.  Dimensional synthesis of a 3-DOF parallel manipulator based on dimensionally homogeneous Jacobian matrix , 2010 .

[80]  Han Ding,et al.  A full-discretization method for prediction of milling stability , 2010 .

[81]  B. Mann,et al.  Stability of a Time-Delayed System With Parametric Excitation , 2007 .

[82]  Liu Qiang,et al.  Solution and Analysis of Chatter Stability for End Milling in the Time-domain , 2008 .

[83]  J. Tlustý,et al.  Special Aspects of Chatter in Milling , 1983 .

[84]  Dinh Van Huynh,et al.  Algebra and Its Applications , 2006 .

[85]  B. Balachandran,et al.  Stability of Up-milling and Down-milling Operations with Variable Spindle Speed , 2010 .

[86]  Gábor Stépán,et al.  Updated semi‐discretization method for periodic delay‐differential equations with discrete delay , 2004 .