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Research Papers

Theoretical and Experimental Studies of Chatter in Turning for Uniform and Stepped Workpieces

[+] Author and Article Information
S. D. Yu

Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2K3, Canadasyu@ryerson.ca

V. Shah

Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, ON, M5B 2K3, Canadavipul.shah@messier-dowty.com

J. Vib. Acoust 130(6), 061005 (Oct 15, 2008) (18 pages) doi:10.1115/1.2948384 History: Received January 29, 2007; Revised January 07, 2008; Published October 15, 2008

This paper presents a method for predicting regenerative chatter onset conditions for uniform and stepped workpieces. The lateral deflections of flexible workpieces are modeled using the Timoshenko beam theory and three-node beam finite elements. The modal summation method is employed in conjunction with an adaptive remeshing scheme to determine the varying natural frequencies and varying mode shapes of workpieces during a cutting process, and to reduce the system equations of motion in terms of nodal variables to coupled equations of motion in terms of the modal coordinates. Various simulations were conducted and presented in this paper for understanding the gyroscopic and cross-coupling effect, and effects of other system and cutting process parameters on chatter onset conditions. Six experiments were carried out on an engine lathe for three uniform and three stepped workpieces to verify the theoretical chatter onset conditions. Good agreement in chatter onset conditions was observed between the simulations and the experiments.

Copyright © 2008 by American Society of Mechanical Engineers
Topics: Chatter , Cutting , Force
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References

Figures

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Figure 1

Components of cutting force acting on the tool in an orthogonal cutting process

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Figure 2

Two types of workpieces used in experiments: (a) uniform and (b) stepped

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Figure 3

Cutting tool geometry and coordinate system

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Figure 4

Comparisons of cutting parameters between the original data of Rao and Shin (14) and fifth order polynomials

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Figure 5

Sketch of an orthogonal cutting process and the inertial coordinate system

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Figure 6

Division of workpieces into uniform segments to account for the instant material removal

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Figure 7

Variations of the fundamental natural frequency for different depths of cut: uniform workpiece

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Figure 8

Variations of the fundamental natural frequency for different depths of cut: stepped workpiece

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Figure 9

Critical values of cutting coefficient versus spindle rate for various damping ratios

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Figure 10

Chatter frequency versus spindle rate for various damping ratios

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Figure 11

Gyroscopic effect on chatter onset conditions for small damping: (a) chatter frequency versus spindle rate; (b) cutting coefficient versus spindle rate

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Figure 12

Gyroscopic effect on chatter onset conditions for large damping: (a) chatter frequency versus spindle rate; (b) cutting coefficient versus spindle rate

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Figure 13

Cross-coupling effect on chatter onset conditions: (a) chatter frequency versus spindle rate; (b) cutting coefficient versus spindle rate

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Figure 14

Combined gyroscopic and cross-coupling effects on chatter onset conditions under experimental conditions: (a) chatter frequency versus spindle rate; (b) cutting coefficient versus spindle rate

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Figure 15

Experimental sound level data recorded before and after chatter (Experiment WP1-1)

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Figure 16

Critical values of cutting parameter versus tool locations for uniform workpieces: (a) Experiment WP1-1, (b) Experiment WP1-2, and (c) Experiment WP1-3

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Figure 17

Critical values of cutting parameter versus tool locations for stepped workpieces: (a) Experiment WP2-1, (b) Experiment WP2-2, and (c) Experiment WP2-3

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Figure 18

Photographs of machined surfaces of uniform workpieces: (a) Experiment WP1-1, (b) Experiment WP1-2, and (c) Experiment WP1-3

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Figure 19

Photographs of machined surfaces of stepped workpieces: (a) Experiment WP2-1, (b) Experiment WP2-2, and (c) Experiment WP2-3

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Figure 20

Effect of tailstock on natural frequency of a uniform workpiece

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Figure 21

Effect of tailstock on natural frequency of a stepped workpiece

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Figure 22

Effect of tailstock on cutting process stability for a uniform workpiece

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Figure 23

Effect of tailstock on cutting process stability for a stability workpiece

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Figure 24

Effect of spin rate on cutting process stability

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