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Research Papers

Time-Domain Modeling of Varying Dynamic Characteristics in Thin-Wall Machining Using Perturbation and Reduced-Order Substructuring Methods

[+] Author and Article Information
Oguzhan Tuysuz

Manufacturing Automation Laboratory (MAL),
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: oguzhan.tuysuz@alumni.ubc.ca

Yusuf Altintas

Professor
Fellow ASME
Manufacturing Automation Laboratory (MAL),
Department of Mechanical Engineering,
The University of British Columbia,
2054-6250 Applied Science Lane,
Vancouver, BC V6T 1Z4, Canada
e-mail: altintas@mech.ubc.ca

1Corresponding author.

Manuscript received April 3, 2017; final manuscript received September 13, 2017; published online November 17, 2017. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 140(1), 011015 (Nov 17, 2017) (15 pages) Paper No: MANU-17-1221; doi: 10.1115/1.4038000 History: Received April 03, 2017; Revised September 13, 2017

The dynamic response of thin-walled parts becomes time and tool position dependent due to material removal along the toolpath. This article proposes a new reduced-order workpiece dynamic parameters update model using substructuring and perturbation methods. The removed volumes between discrete locations along the toolpath are defined as substructures of the initial global workpiece. The dynamically reduced-order initial workpiece structure and the removed substructures are obtained with model order reduction techniques. Equations of motion of the workpiece are updated in time-domain by rigidly coupling fictitious substructures having the negative mass and stiffness of the removed material. Instead of solving the generalized eigenvalue problem repeatedly along the toolpath, the mode shapes of the in-process workpiece are perturbed using the mass and stiffness of the removed substructures. Convergence of the perturbation is improved by integrating a vector sequence convergence accelerating algorithm. The corresponding updated mode frequencies are evaluated using Rayleigh Quotient with the perturbed mode shapes. The proposed reduced-order time-domain dynamics update model is verified in five-axis ball-end milling tests on a thin-walled twisted fan blade, and its predictions are also compared against the authors’ previously developed frequency-domain reduced-order model. It is shown that the newly introduced model is ∼4 times more computationally efficient than the frequency-domain model.

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Figures

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Fig. 1

Overall organization of the article

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Fig. 2

(a) Dynamic substructuring of the initial thin-walled global workpiece structure B0 and (b) DOF partitioning and coupling of fictitious substructure −Ai with the in-process workpiece Bi−1

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Fig. 3

Time-dependent mode frequencies and dynamic displacements in the cutting region

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Fig. 4

Flow chart of the detailed simulation algorithm

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Fig. 5

(a) Initial workpiece geometry, machining sequence, and four segments of each operation and (b) FE mesh of the initial thin-walled workpiece

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Fig. 6

(a) Experimental setup and (b) measurement (comparison) locations (points 1–9) and removed four segments in R1

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Fig. 7

Comparison of the measured and predicted direct FRFs along x-direction at points #1, #2, #6, and #7 in operation R1

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Fig. 8

Comparison of the measured and predicted direct FRFs along x-direction at points #19, #20, #24, and #25 in operation SF1

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Fig. 9

Comparison of the measured and predicted direct FRFs along x-direction at points #37, #38, #42, and #43 in operation F1

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Fig. 10

(a) Variation of the first bending mode frequency with material removal in experiment and simulation. (b) Comparison of the prediction error in the reduced-order time-domain and frequency-domain models for the first bending mode.

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Fig. 11

(a) Variation of the first torsional mode frequency with material removal in experiment and simulation. (b) Comparison of the prediction error in the reduced-order time-domain and frequency-domain models for the first torsional mode.

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Fig. 12

Effect of number of the perturbed modes on the computation time and mode prediction error

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Fig. 13

Comparison of the experimentally measured and predicted static stiffness of the twisted blade in x-direction with tool position along the toolpath

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