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Research Papers

An Analytical C3 Continuous Local Corner Smoothing Algorithm for Four-Axis Computer Numerical Control Machine Tools

[+] Author and Article Information
Qin Hu, Youping Chen, Dailin Zhang

School of Mechanical Science and Engineering,
State Key Lab of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, Hubei, China

Jixiang Yang

School of Mechanical Science and Engineering,
State Key Lab of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, Hubei, China
e-mail: yangjixiang1002@gmail.com

1Corresponding author.

Manuscript received September 3, 2017; final manuscript received December 24, 2017; published online March 1, 2018. Editor: Y. Lawrence Yao.

J. Manuf. Sci. Eng 140(5), 051004 (Mar 01, 2018) (15 pages) Paper No: MANU-17-1550; doi: 10.1115/1.4039116 History: Received September 03, 2017; Revised December 24, 2017

Linear motion commands of multi-axis computer numerical control (CNC) machine tools need to be smoothed at the transition corners, because the velocity discontinuities at corners can result in fluctuations on machine tool motions and lead to poor surface quality. However, no research has been reported on local corner smoothing algorithm for four-axis CNC machine tools with two rotary axes by considering their special kinematic characteristics. To this end, this paper proposes an analytical C3 continuous local corner smoothing algorithm for four-axis CNC machines with two rotary axes. After coordinates transformation, the tool tip positions and tool orientations are smoothed by locally inserting specially designed three-dimensional (3D) quintic B-splines and one-dimensional (1D) quintic B-splines into the corners between linear motion segments, respectively. The smoothing algorithm guarantees C3 continuity of the tool tip position and C3 continuous synchronization of the tool orientation related to the tool tip position, through analytically evaluating control points of the inserted microsplines. The maximum error tolerances of the tool tip position and tool orientation are mathematically constrained. Experiments on an in-house developed four-axis machine verify the efficacy of the proposed algorithm, where maximal errors caused by the local corner smoothing algorithm are constrained, the synchronization of the tool orientation and the tool tip position are achieved, and the proposed C3 continuous corner smoothing algorithm has lower jerk and jounce but higher tracking and contour accuracy than C2 continuous algorithm.

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Figures

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Fig. 4

Flow chart of the proposed four-axis corner smoothing algorithm

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Fig. 3

Kinematics of the four-axis welding machine: (a) kinematic chain analysis and (b) coordinates transformation from the Cartesian frame to the cylindrical frame [15]. Permission granted by Elsevier.

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Fig. 2

Four-axis kinematics configuration: (a) laser carving machine and (b) welding machine [15]. Permission granted by Elsevier.

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Fig. 1

Illustration of the multi-axis corner smoothing with rotary axes: (a) discrete G01 commands without corner smoothing and (b) after corner smoothing [25]. Permission granted by Elsevier.

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Fig. 5

Corner smoothing of the tool tip position in the workpiece coordinate system [22]. Permission granted by Elsevier.

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Fig. 6

Corner smoothing of the tool orientation

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Fig. 8

Four-axis welding machine used in experiments [15]. Permission granted by Elsevier.

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Fig. 9

Tool path geometry used in experiments

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Fig. 10

The maximum error caused by corner smoothing under error tolerances: εpw=0.8 mm,εow=0.01 rad

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Fig. 11

The maximum error caused by corner smoothing under error tolerances: εpw=0.06 mm,εow=0.002 rad

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Fig. 14

Comparison of the C2 and C3 reference jounce under error tolerances: εpw=0.06 mm, εow=0.002 rad

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Fig. 7

Flow chart of the proposed corner smoothing algorithm

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Fig. 12

Synchronization errors at junctions under error tolerances: εpw=0.06 mm, εow=0.002 rad

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Fig. 15

Block-diagram of the single drive using Lead-lag controller in experiments

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Fig. 16

Illustration of multi-axis tracking error and contour error

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Fig. 13

Comparison of the C2 and C3 reference jerk under error tolerances: εpw=0.06 mm,εow=0.002 rad

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