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Research Papers

Substructure Coupling of a Machine Tool in Arbitrary Axis Positions Considering Local Linear Damping Models

[+] Author and Article Information
Thomas Semm

Institute for Machine Tools and Industrial Management,
Department of Mechanical Engineering,
Technical University of Munich (TUM),
Boltzmannstr. 15,
85748 Garching, Germany
e-mail: Thomas.Semm@iwb.mw.tum.de

Michael B. Nierlich

Institute for Machine Tools and Industrial Management,
Department of Mechanical Engineering,
Technical University of Munich (TUM),
Boltzmannstr. 15,
85748 Garching, Germany
e-mail: m.nierlich@gmx.net

Michael F. Zaeh

Institute for Machine Tools and Industrial Management,
Department of Mechanical Engineering,
Technical University of Munich (TUM),
Boltzmannstr. 15,
85748 Garching, Germany
e-mail: Michael.Zaeh@iwb.mw.tum.de

1Corresponding author.

Manuscript received February 3, 2019; final manuscript received May 9, 2019; published online May 30, 2019. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 141(7), 071014 (May 30, 2019) (8 pages) Paper No: MANU-19-1075; doi: 10.1115/1.4043767 History: Received February 03, 2019; Accepted May 10, 2019

Virtual prototypes, e.g., finite element models, are commonly used to reduce the development times of a new machine tool generation. However, the accuracy of these models is often limited by their representation of damping effects and the possibility to efficiently simulate the dynamic behavior in different axis positions. This paper shows the changing local damping distribution within a single-axis machine tool configuration for different axis positions. Based on this investigation, an approach to accurately model the position-dependent dynamics, while keeping the calculation times small, is presented. The virtual model of the machine is divided in several substructures, which consider the local damping behavior of each dissipation source. The reduced mass, stiffness, and damping matrices are coupled in the desired machine position by using multipoint constraints, which are generated at the desired machine position after the reduction of the substructures. Four different approaches to apply multipoint constraints on reduced substructures are compared, followed by an investigation of their influencing parameters. The most promising approach is compared with a model without local damping representation as well as a model without substructuring. By considering the local damping effects within the finite element model and coupling the reduced models of each component in arbitrary axis positions, an efficient analysis and optimization of the dynamic behavior of a machine tool over the whole workspace can be conducted.

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Figures

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Fig. 1

Test object: basic mechanical structure of a single-axis machine tool configuration

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Fig. 2

Linear damping distribution for two positions of the workpiece table: position z0 (left bar) and position z1 (right bar)

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Fig. 3

Model of a coupling point including the considered DOF (a) with RBE and (b) without RBE to allow a position independent coupling

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Fig. 4

Example of a depended MPC

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Fig. 5

Connection of two components with springs

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Fig. 6

(a) Fine-discretized model (BSD5:PRS0) with 4364 DOF compared with (b) the rough-discretized model (BSD40:PRS2) with 1238 DOF

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Fig. 7

Parameter variation of the penalty parameter α

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Fig. 8

Comparison of the NFD value for the rigid- and parameter-based methods in the rear position z1

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Fig. 9

FRF of the substructured system at the workpiece table DP1 for positions z0 and z5 compared with the reference system

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Fig. 10

FRF of the substructured system at the workpiece table DP1 for position z0 and different damping models: local damping models, constant damping, and modal damping evaluated in position z5

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Fig. 11

FRF of the linear-substructured model at the workpiece table DP1 for positions z0 and z5 compared with the measurements of the real system

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