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Research Papers

A Five-Axis Dual NURBS Interpolator With Constant Speed at Feedrate-Sensitive Regions Under Axial Drive Constraints

[+] Author and Article Information
Jian-wei Ma

Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: mjw2011@dlut.edu.cn

Zhen-yuan Jia

Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: jzyxy@dlut.edu.cn

Feng-ze Qin

Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: a649362567@qq.com

De-ning Song

Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: deningsong@163.com

Wen-wen Jiang

Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: 2501394555@qq.com

Si-yu Chen

Key Laboratory for Precision and Non-Traditional Machining Technology of the Ministry of Education, School of Mechanical Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: 1124933288@qq.com

1Corresponding author.

Manuscript received November 9, 2018; final manuscript received March 15, 2019; published online April 12, 2019. Assoc. Editor: Sam Anand.

J. Manuf. Sci. Eng 141(6), 061002 (Apr 12, 2019) (17 pages) Paper No: MANU-18-1783; doi: 10.1115/1.4043256 History: Received November 09, 2018; Accepted March 15, 2019

In the five-axis machining, the dual nonuniform rational B-spline (NURBS) interpolator performs better than the conventional linear interpolator in improving machining efficiency and quality. However, a successful dual NURBS interpolator faces with two aspects of issues. First, the feedrate should be reasonably scheduled according to axial drive constraints. Furthermore, the axial trajectories should be precisely and rapidly calculated according to the scheduled feedrate. To schedule the feedrate, existing methods use either overall constant speed or frequent time-varying speed. However, the former one is adverse to the motion efficiency, while the latter one is adverse to the motion stability. To deal with these issues, this study schedules feedrate-sensitive and nonsensitive regions and plans constant speed at the sensitive regions and smooth transition speed within the nonsensitive regions, thus balancing the motion stability and the efficiency. In addition, to calculate the axial trajectories, existing methods, using inverse kinematics, result in multiple solutions due to the existence of antitrigonometric functions, and this requires complicated selection of the solutions, otherwise the axial positions will be discontinuity. To deal with this issue, this study proposes a Jacobi matrix-based Adams prediction–correction numerical algorithm, which uses the incremental value of the tool pose to calculate the consecutive unique solution of the five-axis positions directly. By integrating above techniques, a systematic five-axis dual NURBS interpolator with the constant speed at feedrate-sensitive regions under axial drive constraints is presented. Experimental tests are conducted to evaluate the effectiveness of the proposed method.

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Figures

Grahic Jump Location
Fig. 1

Overview of the presented five-axis dual NURBS interpolator

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Fig. 2

Five-axis machine kinematics

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Fig. 3

Schematic diagram of the bidirectional scanning for sensitive regional speed updating

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Fig. 4

Schematic diagram for determination of acceleration/deceleration start point parameters and their corresponding feedrates: (a) both acceleration and deceleration are executed and (b) merely acceleration/deceleration is executed

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Fig. 5

Testing parts with blade features: (a) geometry model of testing parts and (b) dual NURBS toolpath of testing parts

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Fig. 6

Scheduled feedrate for testing parts with blade features: (a) tool tip feedrate profile and (b) feedrate on the toolpath

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Fig. 7

Generated axial positions for testing parts with blade features: (a) positions of translational axes, (b) position of A-axis, and (c) position of C-axis

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Fig. 8

Calculation deviations of tool tip and tool orientation for testing parts with blade features: (a) tool tip calculation deviation and (b) tool orientation calculation error

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Fig. 9

Obtained axial kinematics parameters for testing parts with blade features: (a) translational axis velocities, (b) A-axis velocity, (c) C-axis velocity, (d) translational axis acceleration, (e) A-axis acceleration, (f) C-axis acceleration, (g) translational axis jerk, (h) A-axis jerk, and (i) C-axis jerk

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Fig. 10

Machining result of testing parts with blade features using proposed dual NURBS interpolation method

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Fig. 11

W-shape dual NURBS testing toolpath

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Fig. 12

Scheduled feedrate for testing W-shape toolpath: (a) tool tip feedrate profile and (b) feedrate on the toolpath

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Fig. 13

Generated axial positions for testing W-shape toolpath: (a) positions of translational axes, (b) position of A-axis, and (c) position of C-axis

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Fig. 14

Calculation deviations of tool tip and tool orientation for testing W-shape toolpath: (a) tool tip calculation deviation and (b) tool orientation calculation error

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Fig. 15

Obtained axial kinematics parameters for testing W-shape toolpath: (a) translational axis velocities, (b) A-axis velocity, (c) C-axis velocity, (d) translational axis acceleration, (e) A-axis acceleration, (f) C-axis acceleration, (g) translational axis jerk, (h) A-axis jerk, and (i) C-axis jerk

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Fig. 16

Linear interpolation machining feedrate for testing W-shape toolpath

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Fig. 17

Comparison of machining results: (a) linear interpolation machining results and (b) proposed dual NURBS interpolation machining results

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