An efficient decomposition-condensation method for chatter prediction in milling large-scale thin-walled structures

Abstract In this work, an efficient decomposition-condensation method is developed to predict the in-process workpiece (IPW) dynamics for chatter prediction in finishing and semi-finishing large-scale thin-walled structures. Considering the fact that the IPW dynamics is time-varying during the milling process, the IPW is decomposed into three components, namely the machined workpiece, the initial material to be removed and the removed material. The first component is kept unchanged, while the third component is subtracted from the second one. The initial material to be removed is updated by the structural dynamic modification technique to efficiently reveal the effect of material removal. Finite element models of the first two components are further condensed and coupled using component mode synthesis method to calculate the IPW dynamics. In this way, the model order of IPW is significantly reduced and the material removal can be simulated efficiently. The proposed method is finally integrated into a dynamic model for chatter prediction of the milling process. Two thin-walled pockets with planes and curved surfaces are investigated as typical cutting tests to verify the proposed method. It is shown that numerical results agree well with the experimental ones. For the same computing accuracy, the proposed method is observed to reduce the computational burden twice more than the existing methods for chatter prediction.

[1]  József Kövecses,et al.  Development of a New Model for the Varying Dynamics of Flexible Pocket-Structures During Machining , 2011 .

[2]  O. B. Adetoro,et al.  An improved prediction of stability lobes using nonlinear thin wall dynamics , 2010 .

[3]  Yuwen Sun,et al.  Predictive modeling of chatter stability considering force-induced deformation effect in milling thin-walled parts , 2018, International Journal of Machine Tools and Manufacture.

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

[5]  Yusuf Altintas,et al.  Frequency Domain Updating of Thin-Walled Workpiece Dynamics Using Reduced Order Substructuring Method in Machining , 2017 .

[6]  M. Friswell,et al.  Model reduction using dynamic and iterated IRS techniques , 1995 .

[7]  Krzysztof J. Kaliński,et al.  Optimal spindle speed determination for vibration reduction during ball-end milling of flexible details , 2015 .

[8]  Kenan Y. Sanliturk,et al.  Elimination of transducer mass loading effects from frequency response functions , 2005 .

[9]  Yusuf Altintas,et al.  Time-Domain Modeling of Varying Dynamic Characteristics in Thin-Wall Machining Using Perturbation and Reduced-Order Substructuring Methods , 2018 .

[10]  Christian Brecher,et al.  Chatter suppression techniques in metal cutting , 2016 .

[11]  Weihong Zhang,et al.  Chatter prediction for the peripheral milling of thin-walled workpieces with curved surfaces , 2016 .

[12]  Andrew J. Kurdila,et al.  『Fundamentals of Structural Dynamics』(私の一冊) , 2019, Journal of the Society of Mechanical Engineers.

[13]  Yao-Lin Jiang,et al.  A multi-point parameterized model reduction for large parametric systems by using Krylov-subspace techniques , 2018 .

[14]  K. B. Elliott,et al.  Structural modification utilizing beam elements , 1987 .

[15]  Keivan Ahmadi,et al.  Finite strip modeling of the varying dynamics of thin-walled pocket structures during machining , 2017 .

[16]  Jia Feng,et al.  Mechanism of process damping in milling of thin-walled workpiece , 2018, International Journal of Machine Tools and Manufacture.

[17]  Han Ding,et al.  Note on a novel method for machining parameters optimization in a chatter-free milling process , 2013 .

[18]  Gábor Stépán,et al.  Operational stability prediction in milling based on impact tests , 2018 .

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

[20]  Min Wan,et al.  Efficient prediction of varying dynamic characteristics in thin-wall milling using freedom and mode reduction methods , 2019, International Journal of Mechanical Sciences.

[21]  Nan-Chyuan Tsai,et al.  On milling of thin-wall conical and tubular workpieces , 2016 .

[22]  Min Wan,et al.  Working mechanism of helix angle on peak cutting forces together with its design theory for peripheral milling tools , 2017 .

[23]  Erhan Budak,et al.  Mechanics and dynamics of milling thin walled structures , 1994 .

[24]  Dirk Biermann,et al.  A general approach to simulating workpiece vibrations during five-axis milling of turbine blades , 2010 .

[25]  L. Taner Tunç,et al.  Prediction of workpiece dynamics and its effects on chatter stability in milling , 2012 .

[26]  Francisco J. Campa,et al.  Chatter avoidance in the milling of thin floors with bull-nose end mills: Model and stability diagrams , 2011 .

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

[28]  Min Wan,et al.  Optimization and improvement of stable processing condition by attaching additional masses for milling of thin-walled workpiece , 2018 .

[29]  B. K. Wada,et al.  Matrix Perturbation for Structural Dynamic Analysis , 1977 .

[30]  Yi Wan,et al.  A time-space discretization method in milling stability prediction of thin-walled component , 2017 .

[31]  József Kövecses,et al.  Dynamics Modeling and Analysis of Thin-Walled Aerospace Structures for Fixture Design in Multiaxis Milling , 2008 .

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

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

[34]  Yuwen Sun,et al.  Chatter prediction utilizing stability lobes with process damping in finish milling of titanium alloy thin-walled workpiece , 2017 .

[35]  Grégoire Peigné,et al.  Simulation of low rigidity part machining applied to thin-walled structures , 2011 .

[36]  Gilles Dessein,et al.  INFLUENCE OF MATERIAL REMOVAL ON THE DYNAMIC BEHAVIOR OF THIN-WALLED STRUCTURES IN PERIPHERAL MILLING , 2004 .

[37]  Hilde Pérez,et al.  Dynamic analysis of a piezoelectric system to compensate for workpiece deformations in flexible milling , 2017 .

[38]  Ming Luo,et al.  A wireless instrumented milling cutter system with embedded PVDF sensors , 2018, Mechanical Systems and Signal Processing.

[39]  Daniel Rixen,et al.  Updating component reduction bases of static and vibration modes using preconditioned iterative techniques , 2013 .

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

[41]  Yusuf Altintas,et al.  Discrete-Time Prediction of Chatter Stability, Cutting Forces, and Surface Location Errors in Flexible Milling Systems , 2012 .

[42]  H. Nevzat Özgüven,et al.  Structural modifications using frequency response functions , 1990 .

[43]  Min Wan,et al.  Study on the construction mechanism of stability lobes in milling process with multiple modes , 2015 .

[44]  Min Wan,et al.  Effect of cutter runout on process geometry and forces in peripheral milling of curved surfaces with variable curvature , 2011 .

[45]  Yusuf Altintas,et al.  Unified cutting force model for turning, boring, drilling and milling operations , 2012 .

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

[47]  Yao-Lin Jiang,et al.  A parameterised model order reduction method for parametric systems based on Laguerre polynomials , 2018, Int. J. Control.

[48]  Guang Meng,et al.  Dynamics and stability of milling thin walled pocket structure , 2018, Journal of Sound and Vibration.

[49]  Balakumar Balachandran,et al.  Impact Dynamics in Milling of Thin-Walled Structures , 1996, Nonlinear Dynamics and Controls.

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

[51]  Dragos Axinte,et al.  Novel ancillary device for minimising machining vibrations in thin wall assemblies , 2014 .

[52]  Jia Feng,et al.  On improving chatter stability of thin-wall milling by prestressing , 2019, Journal of Materials Processing Technology.