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Research Papers

Smooth Tool Path Optimization for Flank Milling Based on the Gradient-Based Differential Evolution Method

[+] Author and Article Information
YaoAn Lu

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: luyaoan028@163.com

Ye Ding

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: y.ding@sjtu.edu.cn

LiMin Zhu

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: zhulm@sjtu.edu.cn

1Corresponding author.

Manuscript received August 10, 2015; final manuscript received March 3, 2016; published online April 7, 2016. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 138(8), 081009 (Apr 07, 2016) (11 pages) Paper No: MANU-15-1399; doi: 10.1115/1.4032969 History: Received August 10, 2015; Revised March 03, 2016

Flank milling is one of the most important technologies for machining of complex surfaces. A small change of the tool orientation in the part coordinate system (PCS) may produce a great rotation of the rotary axes of the machine tool. Therefore, this paper proposes a tool path optimization model for flank milling in the machine coordinate system (MCS). The tool path is computed to smooth the variation of the rotary axes while controlling the geometric deviation. The geometric deviation is measured by the signed distance between the design surface and the tool envelope surface in the PCS. The geometric accuracy is not an objective but a constraint in the proposed optimization model. Given a prescribed geometric tolerance, the tool path smoothness optimization model is reformulated as a constrained nonlinear programming problem. The ε constrained differential evolution with gradient-based mutation (εDEg) is adopted to solve this constrained problem. The validity of the proposed approach is confirmed by numerical examples.

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References

Figures

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Fig. 1

C axis values according to i and j

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Fig. 2

Two different tool paths

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Fig. 3

Geometric model of a conical cutter

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Fig. 4

A conical cutter in five-axis motion

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Fig. 5

The table-tilting machine tool

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Fig. 6

Schematic diagram of the geometric deviations

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Fig. 8

Distribution of the geometric deviations of the initial tool path

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Fig. 9

Angles between the tool orientations

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Fig. 10

Distribution of the geometric deviations of the optimized tool path

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Fig. 11

Evolutions of the A axis

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Fig. 12

Evolutions of the C axis

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Fig. 13

The CLs of the (a) initial tool path, (b) tool path optimized in the PCS, and (c) tool path optimized in the MCS

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Fig. 14

Evolutions of A axis of the machine tool

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Fig. 15

Evolutions of C axis of the machine tool

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Fig. 16

C axis values along the tool paths

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Fig. 17

Distribution of the geometric deviations of the optimized tool path

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