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Research Papers

Position-Dependent Multibody Dynamic Modeling of Machine Tools Based on Improved Reduced Order Models

[+] Author and Article Information
Mohit Law

Ph.D. Candidate

A. Srikantha Phani

Assistant Professor

Yusuf Altintas

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

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received January 31, 2012; final manuscript received October 19, 2012; published online March 22, 2013. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 135(2), 021008 (Mar 22, 2013) (11 pages) Paper No: MANU-12-1033; doi: 10.1115/1.4023453 History: Received January 31, 2012; Revised October 19, 2012

Dynamic response of a machine tool structure varies along the tool path depending on the changes in its structural configurations. The productivity of the machine tool varies as a function of its frequency response function (FRF) which determines its chatter stability and productivity. This paper presents a computationally efficient reduced order model to obtain the FRF at the tool center point of a machine tool at any desired position within its work volume. The machine tool is represented by its position invariant substructures. These substructures are assembled at the contacting interfaces by using novel adaptations of constraint formulations. As the tool moves to a new position, these constraint equations are updated to predict the FRFs efficiently without having to use computationally costly full order finite element or modal models. To facilitate dynamic substructuring, an improved variant of standard component mode synthesis method is developed which automates reduced order determination by retaining only the important modes of the subsystems. Position-dependent dynamic behavior and chatter stability charts are successfully simulated for a virtual three axis milling machine, using the substructurally synthesized reduced order model. Stability lobes obtained using the reduced order model agree well with the corresponding full-order system.

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Figures

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Fig. 1

Overview of the proposed modeling scheme

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Fig. 2

Substructural assembly by enforcing continuity constraints, (a) compatible substructures, (b) incompatible substructures

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Fig. 3

Flow chart for determining mode cut-off number

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Fig. 4

NRFD and MAC comparison for standard component mode synthesis scheme (left) and iterated improved component mode synthesis scheme (right)

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Fig. 5

Substructural assembly of the spindle-spindle housing substructure with the column substructure through constraint formulations

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Fig. 6

Comparison of TCP FRFs for solution: with different constraint formulations (top), and with different numerical methods (bottom)

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Fig. 7

Comparison of full order model and reduced order model TCP FRFs at three different positions: top position (top), mid position (middle), and bottom position (bottom)

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Fig. 8

Stability boundaries at two distinct positions (left) and the corresponding chatter frequencies (right) for machining AISI 1045 common steel

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Fig. 9

Stability boundaries at two distinct positions (left) and the corresponding chatter frequencies (right) for machining Al 7075-T6

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