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Research Papers

Smoothing Rotary Axes Movements for Ball-End Milling Based on the Gradient-Based Differential Evolution Method

[+] Author and Article Information
Yao-An Lu

School of Electromechanical Engineering,
Guangdong University of Technology,
Guangzhou 510006, China
e-mail: luyaoan@gdut.edu.cn

Cheng-Yong Wang, Jian-Bo Sui, Li-Juan Zheng

School of Electromechanical Engineering,
Guangdong University of Technology,
Guangzhou 510006, China

1Corresponding author.

Manuscript received February 13, 2018; final manuscript received September 9, 2018; published online October 5, 2018. Assoc. Editor: Sam Anand.

J. Manuf. Sci. Eng 140(12), 121008 (Oct 05, 2018) (10 pages) Paper No: MANU-18-1086; doi: 10.1115/1.4041478 History: Received February 13, 2018; Revised September 09, 2018

Ball-end milling is widely used in five-axis high-speed machining. The abrupt change of tool orientations or rotary axes movements will scrap the workpiece. This research presents a smoothing method of rotary axes movements within the feasible domains of the rotary-axes space. Most existing smoothing methods of tool orientation or rotary axes movements employ the Dijkstra's shortest path algorithm. However, this algorithm requires extensive computations if the number of the cutter locations is large or the sampling resolution in the feasible regions is high. Moreover, jumps in the results obtained with the Dijkstra's shortest path algorithm may occur, because the optimization problem has to be converted from a continuous problem into a discrete problem when using this algorithm. The progressive iterative approximation (PIA) method incorporating smoothness terms is established as a gradient-based optimization method to smooth the rotary axes movements in this research. Then a gradient-based differential evolution (DE) algorithm, combining the global exploration feature of the DE algorithm and the local searching ability of the gradient-based optimization method, is developed to solve the smoothing model. The validity and effectiveness of the proposed approach are confirmed by numerical examples.

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Figures

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Fig. 2

Cutter coordinate frame and local coordinate frame setup at a CC point

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Fig. 1

Illustration of the Dijkstra's shortest path algorithm

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Fig. 4

The schematic diagram of the classical PIA method

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Fig. 3

Potential collision points: (a) potential collision points for cutter flute and (b) potential collision points for cutter shank

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Fig. 9

The feasible regions and the Dijkstra's algorithm results

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Fig. 11

Comparison of the results obtained with different methods: (a) evolutions of the A axis and (b) evolutions of the C axis

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Fig. 12

The results of the A axis positions obtained with different maximal number of iterations

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Fig. 13

The C axis movements along the CC curve before and after optimization

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Fig. 14

The machining simulation in vericut: (a) setup for machining, (b) before milling, and (c) after milling

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Fig. 7

The cutter model and its parameters

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Fig. 8

The three CC curves: (a) the CC curve with 40 CC points, (b) the CC curve with 120 CC points, and (c) the CC curve with 2087 CC points

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Fig. 10

The Dijkstra's algorithm results: (a) evolutions of the A axis and (b) evolutions of the C axis

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Fig. 5

The 3D model of a dental crown: (a) front side view and (b) back side view

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Fig. 6

Point cloud for collisions detection

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