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Research Papers

Multipoint Constraints for Modeling of Machine Tool Dynamics

[+] Author and Article Information
Christian Brecher, Marcel Fey, Christian Tenbrock

Laboratory for Machine Tools and
Production Engineering,
RWTH Aachen University,
Aachen 52074, Germany

Matthias Daniels

Laboratory for Machine Tools and
Production Engineering,
RWTH Aachen University,
Aachen 52074, Germany
e-mail: m.daniels@wzl.rwth-aachen.de

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June 15, 2015; final manuscript received September 23, 2015; published online November 18, 2015. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 138(5), 051006 (Nov 18, 2015) (8 pages) Paper No: MANU-15-1292; doi: 10.1115/1.4031771 History: Received June 15, 2015; Revised September 23, 2015

The dynamic properties of machine tools are frequently calculated by means of finite-element (FE) models. Usually, in a first step, the structural components, such as machine bed, slides, columns, spindle housing, spindle, and work piece, are meshed. In a second step, these components are positioned relatively to each other and are connected by joints. Usually, the joints comprise a three-dimensional spring–damper element (SDE) and constraints that connect the SDE to adjacent structural components. Commercial FE programs do rarely offer insight into the underlying constraint equations. Rather, the constraints are realized by selecting the faces or nodes to connect and the type of constraint over a graphical user interface. Moreover, when insight into the underlying equations is offered, it is normally difficult to implement user-defined constraint equations. So far, literature lacks a coherent and in-depth description of constraints that are used for assembly of machine tool FE components. This drawback is addressed here. Different common constraints are revisited while particular focus is put on simulating moving machine axes. Common multipoint constraints (MPC) are supplemented by a shape function based node weighting. Thus, two new MPC are introduced, which improve model quality for ball screw joints (named node-to-beam (NB)-constraint) and linear guides (named RBE4-constraint). A three-axis milling machine serves as an application example for the different constraints. Simulation results are compared to experimentally derived results. Both, frequency response functions (FRF) and time-domain forced responses are considered. Showing reasonable correlation, the comparison of simulation and experiment indicates the validity of the constraints that have been introduced.

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References

Figures

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Fig. 1

(a) Typical joint elements and (b) the conventional joint model

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Fig. 2

(a) Picture of a machine tool foundation and (b) model for the machine tool foundation

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Fig. 3

(a) Conforming and nonconforming meshes, (b) exemplary planar element and exemplary shape function, and (c) picture of surface-to-surface contact

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Fig. 4

(a) Exemplary condensation node-to-face constraint and (b) nomenclature for deflections at condensation and coupling nodes

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Fig. 5

(a) Screw joint model, (b) picture of ball screw joint, and (c) linear shape functions for beam element

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Fig. 6

(a) Linear guide model and (b) picture of linear guide

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Fig. 7

(a) Test assembly for RBE3/RBE4 comparison and (b) position-dependent eigenfrequencies

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Fig. 8

FE model of three axes milling machine and adopted constraint types

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Fig. 10

Simulated FRF Gxx for many different y-positions

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Fig. 9

Measured (a) and simulated (b) FRF Gxx for seven different y-positions

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Fig. 11

Forced response to harmonic excitation—measurement and simulation

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