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Research Papers

Geometric Error Modeling, Separation, and Compensation of Tilted Toric Wheel in Fewer-Axis Grinding for Large Complex Optical Mirrors

[+] Author and Article Information
Zhenhua Jiang

State Key Laboratory of Mechanism System
and Vibration,
Institute of Robotics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: jzh0401@gmail.com

Yuehong Yin

State Key Laboratory of Mechanism System
and Vibration,
Institute of Robotics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: yhyin@sjtu.edu.cn

Xing Chen

State Key Laboratory of Mechanism System
and Vibration,
Institute of Robotics,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: sing@sjtu.edu.cn

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received March 20, 2014; final manuscript received January 22, 2015; published online February 16, 2015. Assoc. Editor: Allen Y. Yi.

J. Manuf. Sci. Eng 137(3), 031003 (Jun 01, 2015) (10 pages) Paper No: MANU-14-1125; doi: 10.1115/1.4029703 History: Received March 20, 2014; Revised January 22, 2015; Online February 16, 2015

In ultraprecision grinding, especially for large complex optical mirrors, the geometric accuracy of grinding wheel plays a vital role and almost dominates the success of the entire grinding process. In this paper, a complete set of geometric error modeling, separation, and compensation methods of tilted toric wheel is established for fewer-axis grinding of large complex optical mirrors. Based on the kinematic equations with the assumptions of virtual axes for toric wheel, a mirror surface error model including all wheel error components is established, providing an error prediction for mirror surface. By linearizing the mirror surface error model and using the error information of mirror surface, solving and separating wheel error components are achieved. Then, the mirror surface with highly improved accuracy is obtained after the compensation of wheel trajectories with calculated wheel error components. Finally, the above method is well verified by the simulation.

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Figures

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Fig. 1

Geometric parameters of tilted toric wheel

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Fig. 2

Toric wheel and its corresponding virtual axes

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Fig. 3

The change of {S} caused by noncircular generating line

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Fig. 4

The change of {S} caused by tilted-shaft angle error

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Fig. 5

Normal error of mirror surface

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Fig. 6

Trajectories for acquisition of error assessment points

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Fig. 7

The actual wheel generating line generated based on an arc

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Fig. 8

Curves of wheel error components with given generating line in case 2; (a) Error curve of Rc; (b) Error curve of β; (c) Error curve of ds; (d) Error curve of a

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Fig. 9

Mirror surface error for case 1: (a) dRc = −0.2 mm; (b) dβ = 0.05 deg; (c) dds = −0.1 mm; (d) dRc = −0.2 mm, dβ = 0.05 deg, and dds = −0.1 mm

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Fig. 10

Integrated mirror surface error for case 2

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Fig. 11

Curves of wheel error components calculated by the algorithm in case 2: (a) Error curve of Rc; (b) error curve of β; (c) error curve of ds; and (d) error curve of a

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Fig. 12

Trajectories of GP and trajectories of CP

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Fig. 13

Error compensation curves for trajectories of CP

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Fig. 14

Error distribution of mirror surface after compensation: (a) case 1 and (b) case 2

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