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RESEARCH PAPERS

Effect of a Nonlinear Joint on the Dynamic Performance of a Machine Tool

[+] Author and Article Information
Jaspreet S. Dhupia1

NSF Engineering Research Center for Reconfigurable Manufacturing Systems, University of Michigan, Ann Arbor, 2250 GGBL, 2350 Hayward Street, Ann Arbor, MI 48109-2125jdhupia@umich.edu

Bartosz Powalka

 Technical University of Szczecin, Piastow 19, 70-310 Szczecin, Poland

A. Galip Ulsoy, Reuven Katz

Research Center for Reconfigurable Manufacturing Systems, University of Michigan, Ann Arbor, 2250 GGBL, 2350 Hayward Street, Ann Arbor, MI 48109-2125

1

Corresponding author.

J. Manuf. Sci. Eng. 129(5), 943-950 (Apr 17, 2007) (8 pages) doi:10.1115/1.2752830 History: Received September 12, 2006; Revised April 17, 2007

This paper presents the effect of experimentally evaluated nonlinearities in a machine joint on the overall machine tool dynamic performance using frequency response functions and stability lobe diagrams. Typical machine joints are very stiff and have weak nonlinearities. The experimental evaluation of the nonlinear joint parameters of a commercial translational guide has been discussed in Dhupia, 2007, J. Vibr. Control, accepted. Those results are used in the current paper to represent the connection between the column and the spindle of an idealized column-spindle machine structure. The goal is to isolate and understand the effects of such joints on the machine tool dynamic performance. The nonlinear receptance coupling approach is used to evaluate the frequency response function, which is then used to evaluate the stability lobe diagrams for an idealized machine structure. Despite the weak nonlinearities in the joint, significant shifts in the natural frequency and amplitudes at resonance can be observed at different forcing amplitudes. These changes in the structural dynamics, in turn, can lead to significant changes in the location of chatter stability lobes with respect to spindle speed. These variations in frequency response function and stability lobe diagram of machine tools due to nonlinearities in the structure are qualitatively verified by conducting impact hammer tests at different force amplitudes on a machine tool.

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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Nonlinear estimation test for translational guide (12)

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Figure 2

Experimentally determined nonlinear restoring force relationship for translational guide (12)

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Figure 3

(a) Arch-type RMT, and (b) column-spindle machine structure

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Figure 4

Representation of column-spindle machine structure as a mass-spring-damper system in: (a) feed direction, and (b) cross-feed direction

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Figure 5

Schematic for machine connection showing internal and connection coordinates

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Figure 6

Feed and cross-feed measured cutting force during full immersion milling operation with four inserts at depth of cut, αp=5.6mm and spindle speed: (a)N=1500rpm, and (b)N=1450rpm

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Figure 7

FFT of the feed and cross-feed measured cutting force during full immersion milling operation with four inserts at depth of cut, αp=5.6mm and spindle speed: (a)N=1500rpm; and (b)N=1450rpm

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Figure 8

FRFs of column-spindle machine structure in: (a) feed direction; and (b) cross-feed direction

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Figure 9

Stability lobe diagrams generated for various input excitations for the spindle column machine structure

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Figure 10

Variations in FRF obtained from impact hammer test on arch type RMT at different peak impact levels

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Figure 11

Stability lobe diagrams generated from the various FRFs obtained from the arch-type RMT

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