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Research Papers

Frequency Domain Updating of Thin-Walled Workpiece Dynamics Using Reduced Order Substructuring Method in Machining

[+] 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 October 16, 2016; final manuscript received February 20, 2017; published online April 10, 2017. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 139(7), 071013 (Apr 10, 2017) (16 pages) Paper No: MANU-16-1551; doi: 10.1115/1.4036124 History: Received October 16, 2016; Revised February 20, 2017

The structural dynamics of thin-walled parts vary as the material is removed during machining. This paper presents a new, computationally efficient reduced order dynamic substructuring method to predict the frequency response function (FRF) of the workpiece as the material is removed along the toolpath. The contribution of the removed mass to the dynamics of the workpiece is canceled by adding a fictitious substructure having the opposite dynamics of the removed material. The equations of motion of the workpiece are updated, and workpiece FRFs are evaluated by solving the hybrid set of assembled equations of motion in frequency domain as the tool removes the material between two consecutive dynamics update steps. The orders of the initial workpiece structure and the removed substructures are reduced using a model order reduction method with a newly introduced automatic master set selection criterion. The reduced order FRF update model is validated with peripheral milling tests and FRF measurements on a plate-shaped workpiece. It is shown that the proposed model provides ∼20 times faster FRF predictions than the full order finite element (FE) model.

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References

Figures

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Fig. 1

Time invariant tool dynamics and varying workpiece dynamics at different stages of machining

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Fig. 2

Equivalent dynamics removal from a blank by coupling of a fictitious substructure

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Fig. 3

(a) Machined workpiece Bi−1 at machining step (i – 1), (b) the interaction between the substructure Ai and in-process workpiece Bi−1 by interface coupling forces, fictitiously added substructure −Ai, and the associated opposite interface coupling forces, and (c) interface force equilibrium after addition of the fictitious substructure

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Fig. 4

Flow chart of the overall simulation scheme

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Fig. 5

(a) Initial workpiece geometry 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 1–6) and removed nine segments in roughing

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Fig. 7

Comparison of the measured and predicted direct FRFs along the x-direction at points #1, #2, #4, and #5 in roughing

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Fig. 8

Comparison of the measured and predicted direct FRFs along the x-direction at points #7, #8, #10, and #11 in semifinishing

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Fig. 9

Comparison of the measured and predicted direct FRFs along the x-direction at points #13, #14, #16, and #17 in finishing

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Fig. 10

(a) Variation of the first bending mode frequency at all FRF comparison points in experiment and simulation and (b) comparison of the prediction error in full and reduced order dynamics decoupling for the first bending mode

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Fig. 11

(a) Variation of the first torsional mode frequency at all FRF comparison points in experiment and simulation and (b) comparison of the prediction error in full and reduced order dynamics decoupling for the first torsional mode

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Fig. 12

Schematic illustration of the master DOF selected due to (a) the first bending (shaded region) and (b) the first torsional (shaded region) modes of the initial workpiece

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Fig. 13

Comparison of the experimentally measured and predicted static stiffness of the plate in the x-direction at all FRF measurement points

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