0
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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Shore, P. , Cunningham, C. , DeBra, D. , Evans, C. , Hough, J. , Gilmozzi, R. , and Tonnellier, X. , 2010, “ Precision Engineering for Astronomy and Gravity Science,” CIRP Ann. Manuf. Technol., 59(2), pp. 694–716. [CrossRef]
Comley, P. , Morantz, P. , Shore, P. , and Tonnellier, X. , 2011, “ Grinding Metre Scale Mirror Segments for the E-ELT Ground Based Telescope,” CIRP Ann. Manuf. Technol., 60(1), pp. 379–382. [CrossRef]
Brinksmeier, E. , Mutlugünes, Y. , Klocke, F. , Aurich, J. C. , Shore, P. , and Ohmori, H. , 2010, “ Ultra-Precision Grinding,” CIRP Ann. Manuf. Technol., 59(2), pp. 652–671. [CrossRef]
Denkena, B. , Turger, A. , Behrens, L. , and Krawczyk, T. , 2012, “ Five-Axis-Grinding With Toric Tools: A Status Review,” ASME J. Manuf. Sci. Eng., 134(5), p. 054001. [CrossRef]
Kuriyagawa, T. , Zahmaty, M. S. S. , and Syoji, K. , 1996, “ A New Grinding Method for Aspheric Ceramic Mirrors,” J. Mater. Process. Technol., 62(4), pp. 387–392. [CrossRef]
Shore, P. , Luo, X. , Jin, T. , Tonnellier, X. , Morantz, P. , Stephenson, D. , and Read, R. , 2005, “ Grinding Mode of the “BoX” Ultra Precision Free-Form Grinder,” 20th Annual ASPE Meeting, Norfolk, VA, pp. 114–117.
Tonnellier, X. , 2009, “ Precision Grinding for Rapid Manufacturing of Large Optics,” Ph.D. thesis, Cranfield University, Cranfield, UK.
Jiang, Z. , and Yin, Y. , 2013, “ Geometrical Principium of Fewer-Axis Grinding for Large Complex Optical Mirrors,” Sci. China Technol. Sci., 56(7), pp. 1667–1677. [CrossRef]
Jiang, Z. , Yin, Y. , and Chen, X. , 2015, “ Geometric Error Modeling, Separation, and Compensation of Tilted Toric Wheel in Fewer-Axis Grinding for Large Complex Optical Mirrors,” ASME J. Manuf. Sci. Eng., 137(3), p. 031003. [CrossRef]
Denkena, B. , de Leon, L. , Turger, A. , and Behrens, L. , 2010, “ Prediction of Contact Conditions and Theoretical Roughness in Manufacturing of Complex Implants by Toric Grinding Tools,” Int. J. Mach. Tools Manuf., 50(7), pp. 630–636. [CrossRef]
Brown, R. H. , Saito, K. , and Shaw, M. C. , 1971, “ Local Elastic Deflections in Grinding,” Ann. CIRP, 19(1), pp. 105–113.
Agarwal, S. , and Rao, P. V. , 2012, “ Predictive Modeling of Undeformed Chip Thickness in Ceramic Grinding,” Int. J. Mach. Tools Manuf., 56, pp. 59–68. [CrossRef]
Agarwal, S. , and Rao, P. V. , 2013, “ Predictive Modeling of Force and Power Based on a New Analytical Undeformed Chip Thickness Model in Ceramic Grinding,” Int. J. Mach. Tools Manuf., 65, pp. 68–78. [CrossRef]
Linke, B. S. , 2015, “ Review on Grinding Tool Wear With Regard to Sustainability,” ASME J. Manuf. Sci. Eng., 137(6), p. 060801. [CrossRef]
Venkatachalam, S. , Fergani, O. , Li, X. , Yang, J. G. , Chiang, K. N. , and Liang, S. Y. , 2015, “ Microstructure Effects on Cutting Forces and Flow Stress in Ultra-Precision Machining of Polycrystalline Brittle Materials,” ASME J. Manuf. Sci. Eng., 137(2), p. 021020. [CrossRef]
Adibi, H. , Rezaei, S. M. , and Sarhan, A. A. , 2014, “ Grinding Wheel Loading Evaluation Using Digital Image Processing,” ASME J. Manuf. Sci. Eng., 136(1), p. 011012. [CrossRef]
Tönshoff, H. K. , Peters, J. , Inasaki, I. , and Paul, T. , 1992, “ Modelling and Simulation of Grinding Processes,” CIRP Ann. Manuf. Technol., 41(2), pp. 677–688. [CrossRef]
Brinksmeier, E. , Aurich, J. C. , Govekar, E. , Heinzel, C. , Hoffmeister, H. W. , Klocke, F. , and Wittmann, M. , 2006, “ Advances in Modeling and Simulation of Grinding Processes,” CIRP Ann. Manuf. Technol., 55(2), pp. 667–696. [CrossRef]
Li, S. , Du, S. , Tang, A. , Landers, R. G. , and Zhang, Y. , 2014, “ Force Modeling and Control of SiC Monocrystal Wafer Processing,” ASME J. Manuf. Sci. Eng., 137(6), p. 061003. [CrossRef]
Ding, S. , Mannan, M. A. , Poo, A. N. , Yang, D. C. H. , and Han, Z. , 2003, “ Adaptive Iso-Planar Tool Path Generation for Machining of Free-Form Surfaces,” Comput. Aided Des., 35(2), pp. 141–153. [CrossRef]
Malkin, S. , and Hwang, T. W. , 1996, “ Grinding Mechanisms for Ceramics,” CIRP Ann. Manuf. Technol., 45(2), pp. 569–580. [CrossRef]
Wang, B. , Liu, Z. , Su, G. , and Ai, X. , 2015, “ Brittle Removal Mechanism of Ductile Materials With Ultrahigh-Speed Machining,” ASME J. Manuf. Sci. Eng., 137(6), p. 061002. [CrossRef]
Cheng, X. , Wei, X. T. , Yang, X. H. , and Guo, Y. B. , 2014, “ Unified Criterion for Brittle–Ductile Transition in Mechanical Microcutting of Brittle Materials,” ASME J. Manuf. Sci. Eng., 136(5), p. 051013. [CrossRef]
Mladenovic, G. , Bojanic, P. , Tanovic, L. , and Klimenko, S. , 2015, “ Experimental Investigation of Microcutting Mechanisms in Oxide Ceramic CM332 Grinding,” ASME J. Manuf. Sci. Eng., 137(3), p. 034502. [CrossRef]
Malkin, S. , and Guo, C. , 2008, Grinding Technology: Theory and Application of Machining With Abrasives, Industrial Press, New York, Chap. 3.
Chang, H. C. , and Wang, J. J. J. , 2008, “ A Stochastic Grinding Force Model Considering Random Grit Distribution,” Int. J. Mach. Tools Manuf., 48(12), pp. 1335–1344. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Toric wheel and its equivalent virtual axes

Grahic Jump Location
Fig. 4

The contact area of toric wheel and workpiece

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

The intersection situations of wheel surface and scallop workpiece surface

Grahic Jump Location
Fig. 8

The wheel deformation caused by a single grit

Grahic Jump Location
Fig. 9

The approximate wheel surface and its additional deformation surface

Grahic Jump Location
Fig. 10

The ultraprecision fewer-axis grinder and experiment platform

Grahic Jump Location
Fig. 11

Trajectories of GP and CP in {W}

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
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}

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 15

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

Grahic Jump Location
Fig. 16

The local deformation of toric wheel in the contact area

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In