Abstract
The warm shrink fitting process is generally used to assemble automobile transmission parts (shafts/gears). However, this process causes a deformation in the addendum and dedendum of the gear depending on the fitting interference and gear profile, and this deformation causes additional noise and vibration between the gears. To address these problems, the warm shrink fitting process is analyzed by considering the error in the dimensional deformation of the addendum and dedendum found when comparing the results of a theoretical analysis and finite element analysis (FEA). A correction coefficient that reduces this error is derived through an analysis of the difference in the cross-sectional area between the shapes used for the theoretical analysis and that of the actual gear, and a closed-form equation to predict the dimensional deformation of the addendum and dedendum is proposed. The FEA method is proposed to analyze the thermal-structural-thermal coupled field analysis of the warm shrink fitting process (heating-fitting-cooling process). To verify the closed-form equation using the correction coefficient, measurements are made of actual helical gears used in automobile transmissions. The results are in good agreement with those given by the closed-form equation.
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Abbreviations
- E a , E b :
-
elastic modulus
- K :
-
radial coefficient, r 3/r 2
- P interference :
-
contact pressure
- P i :
-
internal pressure
- P o :
-
external pressure
- r 1 :
-
inner radius of the shaft
- r 2 :
-
outer radius of the shaft or inner radius of the gear
- r 3 :
-
outer radius of the gear
- r 4 :
-
radius of the dedendum circle
- d Fitting :
-
amount of shrink fitting
- n a , n b :
-
Poisson’s ratio
References
Ansel, C. U. and Saul, K. F. (2003a). Advanced Strength and Applied Elasticity. 4th Edn. Prentice Hall. New Jersey. 75–78.
Ansel, C. U. and Saul, K. F. (2003b). Advanced Strength and Applied Elasticity. 4th Edn. Prentice Hall. New Jersey. 315–319.
Choi, S. H. and Kim, Y. S. (2001). Characteristics on the output coupled type cvt combined differential gear unit. J. KSPE 18,3, 205–215.
Kim, H. Y., Choi, C. J., Kim. C. and Bae, W. B. (2006). A study on the prediction of teeth deformation of the automobile transmission part(shaft/gear) in warm shrink fitting process. J. KSPE 23,9, 54–60.
Kim, H. Y., Kim, C. and Bae, W. B. (2006). Development of optimization technique of warm shrink fitting process for automobile transmission part(shaft/gear). J. KSPE 23,5, 37–43.
Kim, T. J., Kang, H. J., Kim, C., Chu, S. J. and Kim, H. Y. (2008). Analysis of the warm shrink fitting process for assembling the part(shaft and output gear). J. KSPE 25,6, 47–54.
Lange, K. (1985). Handbook of Metal Forming. McGraw-Hill. New York. 13.1–16.66.
Laue, K. and Stenger, H. (1981). Extrusion. American Society for Metals. 356–363.
Lee, H. W., Park, S. H., Park, M. W. and Park, N. G. (2009). Vibrational characteristics of automotive transmission. Int. J. Automotive Technology 10,4, 459–467.
Sung, D. H. and Kim, H. S. (2002). A study on 3 shaft hydromechanical transmission design considering power and speed characteristics. J. KSME 26,12, 2615–2623.
Yoh, E. G. and Lee, Y. S. (2001). Integrated analysis for the shrink-fitted die with multi stress-ring of dissimilar materials. J. KSPE 18,3, 40–46.
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Bae, J.H., Kim, J.S., Hwang, B.C. et al. Prediction of the dimensional deformation of the addendum and dedendum after the warm shrink fitting process using a correction coefficient. Int.J Automot. Technol. 13, 285–291 (2012). https://doi.org/10.1007/s12239-012-0026-3
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DOI: https://doi.org/10.1007/s12239-012-0026-3