薄板工件研磨製程中，隨著工件厚度減少或長度增加，常面臨到難以掌握工件翹曲程度之困難。本文根據ASME Y14.5規範，以平行度描述薄板翹曲程度，並以樑變形理論為基礎，結合一無因次化因子－工件厚長比，建立一套薄板工件平行度預測模式。模式考慮材料楊氏係數與工件慣性矩，以工件兩端端面受到彎矩而翹曲後，工件中心點位置不變為前提，探析工件厚長比與薄板工件平行度之關係。並以氧化鋁砂輪研磨碳鋼薄板工件為例，在不同切深與工件進給速度下，探討工件厚長比對薄板工件平行度之影響，由實驗結果得知，薄板工件平行度與工件厚長比呈現平方反比的關係。透過此模式選擇之研磨條件，亦可有效的將加工道次從30次減少至14次，並使薄板工件平行度提昇76%。

Workpieces after grinding process might bend or deflect due to thermal deformation and induced residual stress after grinding process, especially for slender workpiece with low thickness-to-length ratios. In this paper, the bending extent of thin workpieces is investigated as a parallelism property of thin plate as defined in the ASME Y14.5 Standard. A model for predicting the parallelism prediction of thin workpieces is developed based on the beam deformation theory by using and combined with a dimensionless factor, the thickness-to-length ratio, as a characteric parameter. This model considers Young’s modulus and moment of inertia of area, and assumes the central position of workpieces does not change as bending moments act on the both sides of workpiece. The relationship between thickness-to-length ratio and parallelism of thin workpieces has been analyzed and discussed. Under different cut depths and feed speeds, grinding experiments have been carried out on carbon steel with using an alumina grinding wheel. Experiment results indicate that the relationship between thickness-to-length ratio and parallelism of thin workpieces has an inverse-square relationship. As an application, the use of this model results in giving an indication of grinding conditions with reduced grinding passes from 30 to 14 and improved parallelism of thin workpieces by 76%.

[1] Jaeger, J. C., ‘Moving Sources of Heat and the Temperature at Sliding Contacts’, Proceedings of the Royal Society of New South Wales, 76, p.1177, 1942
[2] S. Malkin, “GRINDING TECHNOLOGY-Theory and Applications of Machining with Abrasives”, ELLIS HORWOOD LIMITED, 1989
[3] Milton C. Shaw, ‘Principles of Abrasive Processing’, OXFORD, 1996
[4] Sato, K., “Grinding Temperature,” Bull. Japan Society of GrindignEngineers, Vol.1,pp. 21-33,1961.
[5] Outwater, J. O., and Shaw, M. C., “Surface Temperature in Grinding”, Transactions of the ASME, Vol.74, pp.73-86,1952.
[6] Kannappan, S. and Malkin, S., “Effects of Size and Operating Parameterson the Mechanics of Grinding”, ASME Journal of Engineering for Industry,Vol.94, pp.833-842,1972.
[7] Malkin, S. and Anderson, R. B., “Thermal Aspects of Grinding: Part 1 Energy Partition”, ASME Journal of Engineering for Industry. Vol.96, pp.1177-1183, 1974.
[8] Kohli, S.,Guo, C. and Malkin, S.."Energy Partition to the Workpiece forGrinding with Aluminum Oxide and CBN Abrasive Wheels", Trans. ASME, Journal of Engineering for Industry . Vol.117,pp.160-168,1995.
[9] Lee, D.G.,Zerkle,R.D. and DesRuisseaux, N.R.,"An Experimental Study of the Thermal Aspects of Cylindrical Plunge Grinding", Trans. ASME, Journal of Engineering for Industry, Vol.94, pp. 1206,1972.
[10] Brinksmeier, E. et al.,‘Residual Stress-Measurement and Causes in Machining
Process’Annals of the CIRP, 31/2: 491-510,1982
[11] T. Matsuo, et al. Curvature in surface grinding of thin workpieces with
superabrasive wheels, Annals of the CIRP Vol.36/1, 1987
[12] S. Okuyama, et al.,Study on the geometrical accuracy in surface grinding- thermal deformation of workpiece in traverse grinding , Annals of the CIRP Vol.37/1/1988
[13] Brinksmeier, E. et al., ‘Prediction of shape deviations in maching’, Annals of the CIRP 58: 507-510, 2009
[14]Okuyama, S., Nishara, T., and Kauamura, S., “Study on the Grinding Condition to prevent the Thermal Displacement of a Work Attracted by Magnetic chuck”, Annals of the CIRP, Vol.37 ,pp.259-298,1988.
[15] W. Lortz, “A model of the cutting mechanism in grinding,” Wear, Vol. 53, pp. 115-128, 1979.
[16]Des Ruisseaux, N. R., and Zerkle, R. D., “Thermal Analysis of the Grinding Process” ,ASME, Journal of Engineering for Industry, Vol.92,pp. 428-434,1970.
[17]Malkin, S., “Thermal Aspects of Grinding: Part 2 Surface Temperatures and Workpiece Burn”, ASME Journal of Engineering for Industry.Vol.96,pp.1184-1191,1974.
[18].Lavine, A. S., “A Simple Model for Convective Cooling during the Grinding Process”, ASME, Journal of Engineering for Industry, Vol.110, pp. 1-6,1988.
[19]Ramanath, S., and Shaw, M. C., “Abrasive Grain Temperature at the Beginning of a cut in Fine Grinding”, ASME Journal of Engineering for Industry, Vol.110 , pp.15-18,1988.
[20]Rowe, W. B., Pettit, J. A., Boyle, A., and Moruzzi, J. L., “Avoidance of Thermal Damage in Grinding and Prediction of the Damage Threshold”,Annals of the CIRP, Vol.37 ,pp. 327-330,1988.
[21]Shaw, M. C., “A Simplified Approach to Workpiece Temperatures in Fine Grinding”, Annals of the CIRP, Vol.39, ,pp.345-347,1990.
[22]Sato, K., “Grinding Temperature,” Bull. Japan Society of Grindign Engineers, Vol.1,pp. 21-33,1961.
[23]Kato, T., and Fujii, H., “Energy Partition in Conventional Surface Grinding”, ASME Journal of Manufacturing Science and Engineering, Vol.121,pp. 393-398,1999.
[24]Ramanath, S., and Shaw, M. C., “Abrasive Grain Temperature at the Beginning of a cut in Fine Grinding”, ASME Journal of Engineering for Industry, Vol.110 , pp.15-18,1988.
[25]Littman, W. E., and Wulff, J., “The Influence of the Grinding Process on the structure of Hardened Steel”, Transaction of ASM, Vol.47,pp. 692-714,1955.
[26]Takazawa, K., “Effects of Grinding Variables on Surface Structure of Hardened Steels”, Bull. Japan Soc. Prec. Engg., Vol.2 ,pp. 14-18,1966. [29].Saver, W.J., “Thermal Aspect of Surface Grinding”, New Developments in Grinding, Proc. International Grinding Conference, Carnegie Press, pp.391-411,1972.
[27]Werner, P.G., Younis, M. A., and Schlingensiepen, R., “Creep Feed-An Effective Method to Reduced Work Surface Temperature in High-Efficiency Grinding Processes”, Proc. 8th North American Metalworking Research Conference, pp.312-319,1980.
[28]Beck, J. V., “Thermocouple Temperature Disturbances in Low Conductivity Materials”, ASME Journal of Heat Transfer, Vol.84 , pp.124-132,1962.
[29]Attia, M. H., and Kops, L., “Distortion in the Thermal Field around Inserted Thermocouples in Experimental Interfacial Studies-Part 3: Experimental and Numerical Verification”, ASME Journal of Engineering for Industry, Vol.115, pp.444-449,1993.
[30].Ueda, T., Hosokawa, A., and Yamamoto, A., “Measurement of Grinding　Temperature Using Infrared Radiation Pyrometer with optical Fiber”, ASME Journal of Engineering for Industry, Vol.108 ,pp.247-251,1986.
[31].Hebbar, Rajadasa, R., Chandrasekhar, S., and Farris, T. N., “Ceramic Grinding Temperatures”, Journal of American Ceramic Society, Vol.75,pp.2742-2748,1992.
[32].Kato, T., and Fujii, H.,”PVD Film Method for Measuring the Temperature Distribution in Cutting Tools”, ASME Journal of Engineering for Industry, Vol.118,pp.117-122,1996.
[33].Kato, T., and Fujii, H., “Temperature Measurement of Workpiece in Surface Grinding by PVD Film Method”, ASME, Journal ofManufacturing Science and Engineering, Vol.119,pp.689-694, 1997.
[34].Hou, Z. B., Komanduri, R., “General Solutions for Stationary/Moving Plane Heat Source Problem in Manufacturing and Tribology”, International J. Heat and Mass Transfer, Vol.43 ,pp.1679-1698,2000.