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Research Papers

Predictive Modeling of Grinding Force Considering Wheel Deformation for Toric Fewer-Axis Grinding of 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

Qianren Wang

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

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.

Manuscript received July 5, 2015; final manuscript received November 2, 2015; published online January 6, 2016. Assoc. Editor: Allen Y. Yi.

J. Manuf. Sci. Eng 138(6), 061008 (Jan 06, 2016) (10 pages) Paper No: MANU-15-1334; doi: 10.1115/1.4032084 History: Received July 05, 2015; Revised November 02, 2015

Fewer-axis ultraprecision grinding has been recognized as an important means for manufacturing large complex optical mirrors. The research on grinding force is critical to obtaining a mirror with a high surface accuracy and a low subsurface damage. In this paper, a unified 3D geometric model of toric wheel–workpiece contact area and its boundaries are established based on the local geometric properties of the wheel and the workpiece at the grinding point (GP). Moreover, the discrete wheel deformation is calculated with linear superposition of force-induced deformations of single grit, resolving the difficulties of applying Hertz contact theory to irregular contact area. The new deformed wheel surface is then obtained by using the least squares method. Based on the force distribution within the contact area and the coupled relationship between grinding force and wheel deformation, the specific grinding energy and the final predicted grinding force are obtained iteratively. Finally, the proposed methods are validated through grinding experiments.

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References

Figures

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Fig. 1

Two major grinding modes for fewer-axis grinding: (a) parallel grinding and (b) cross grinding

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Fig. 2

Toric wheel and its equivalent virtual axes

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Fig. 4

The contact area of toric wheel and workpiece

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Fig. 5

The projection of the wheel–workpiece contact area in the plane P-e1e2

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Fig. 6

The intersection situations of wheel surface and scallop workpiece surface

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Fig. 8

The wheel deformation caused by a single grit

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Fig. 9

The approximate wheel surface and its additional deformation surface

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Fig. 10

The ultraprecision fewer-axis grinder and experiment platform

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Fig. 11

Trajectories of GP and CP in {W}

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Fig. 12

The toric wheel–workpiece contact area at [0, 0, 0] in {W}

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Fig. 13

Grinding force measured by Triax force sensors located inside the force sensing platform: (a) force components along the Y direction in {W} and (b) force components along the Z direction in {W}

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Fig. 14

Actual grinding force (Fza, Fya) and their predicted values (Fzs, Fys)

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Fig. 15

Actual tangential grinding force Fta, actual normal grinding force Fna, and their predicted values Fts, Fns

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Fig. 16

The local deformation of toric wheel in the contact area

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