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TECHNICAL PAPERS

Machine Tool Chatter and Surface Location Error in Milling Processes

[+] Author and Article Information
Tamás Insperger, Gábor Stépán

Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest H-1521, Hungary

Janez Gradišek, Edvard Govekar

Faculty of Mechanical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia

Martin Kalveram

Department of Mining Technology, University of Dortmund, D-44227 Dortmund, Germany

Klaus Winert

Department of Machining Technology, University of Dortmund, D-44227 Dortmund, Germany

J. Manuf. Sci. Eng 128(4), 913-920 (Mar 08, 2006) (8 pages) doi:10.1115/1.2280634 History: Received December 07, 2004; Revised March 08, 2006

A two degree of freedom model of the milling process is investigated. The governing equation of motion is decomposed into two parts: an ordinary differential equation describing the periodic chatter-free motion of the tool and a delay-differential equation describing chatter. The stability chart is derived by using the semi-discretization method for the delay-differential equation corresponding to the chatter motion. The periodic chatter-free motion of the tool and the associated surface location error (SLE) are obtained by a conventional solution technique of ordinary differential equations. It is shown that the SLE is large at the spindle speeds where the ratio of the dominant frequency of the tool and the tooth passing frequency is an integer. This phenomenon is explained by the large amplitude of the periodic chatter-free motion of the tool at these resonant spindle speeds. It is shown that large stable depths of cut with a small SLE can still be attained close to the resonant spindle speeds by using the SLE diagrams associated with stability charts. The results are confirmed experimentally on a high-speed milling center.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic mechanical model of the milling process

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Figure 2

Schematic of down-milling (a) and up-milling (b)

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Figure 3

Cutting force model

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Figure 4

Chip thickness model

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Figure 5

Surface location error defined by the desired and the actual milled surfaces

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Figure 6

Tooth path for 10% immersion down-milling (a) and 10% immersion up-milling (b). Dotted lines denote the desired tooth pass, continuous lines denote the actual tooth pass. Thick lines denote contact of the tool and the workpiece, thin lines denote free oscillation of the tool.

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Figure 7

(a) Theoretical and experimental stability chart for 10% immersion down-milling. Thick lines denote theoretical stability boundary, circles denote stable cutting, crosses denote quasi-periodic chatter, diamonds denote period doubling chatter. (b), (c) Theoretical and experimental surface location errors for ap=0.4mm(b) and ap=0.8mm(c). Dotted lines denote the theoretical SLE for unstable cutting, continuous lines denote the theoretical SLE for stable cutting, crosses denote the experimental SLE.

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Figure 8

Theoretical periodic chatter-free tool trajectories for 10% immersion down-milling with ap=0.4mm and different spindle speeds. Thick lines denote contact of the tool and the workpiece, thin lines denote free oscillation of the tool.

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Figure 9

Theoretical and experimental tool trajectories for 10% immersion down-milling with ap=0.4mm. Thick lines denote contact of the tool and the workpiece, thin lines denote free oscillation of the tool.

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Figure 10

(a) Theoretical stability chart for 10% immersion down-milling in the high-speed domain. (b) Theoretical surface location error for ap=0.8mm.

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