The Effect of Shaft Diameter and Hole Tolerance on Stress Distribution in Micro Module Gear-Shaft Interference Fitting Connections

Abstract

One of the widely used machine elements in machine design and manufacturing is gears, and in many areas, the use of various sizes of gears is needed. Micro module gears with module 1mm and smaller are used as an important machine element in precision measuring instruments, defense industry and machine manufacturing. Damage to the gear surface, gear teeth, gear body and gear-shaft connection during power transmission affect the normal operation of the entire machine. Any damage that may occur can damage not only the gear or gear connection, but also many machine parts that work with this machine elements. Due to the dimensions of the micro-module gears, the interference-fitting connections come into prominence in the gear-shaft connection. However, there are important shortages in the literature. Designers practicing all interference-fitting connections can lead to both time and economic losses. For this reason, the analytical and numerical calculations are of great importance in the gear hub shaft interference fitting connections.

In this study, the stress distributions are calculated and compared numerically and analytically that occur at different interference fit tolerances and different hub diameters for micro module gear having 20 teeth number, 6mm width and 1mm module. The data obtained from the analytical and numerical studies are in agreement with each other. Axial and radial stress decreases as the nominal diameter increases. At this point, however, the weakened gear surface is vulnerable to damage. For all nominal diameter values used in the study, the axial and radial stress magnitude caused by the gear shaft connection are listed as H7/u6, H7/s6, H7/p6, respectively.

Keywords

• micro module gear
• interference fitting
• gear-shaft connection

Mikro Modüllü Dişli-Mil Sıkı Geçme Bağlantılarında Mil Çapı ve Delik Toleransının Gerilme Dağılımına Etkisi

Abstract

Makine tasarımı ve imalatında yaygın kullanıma sahip makine elemanlarından biri dişliler olup birçok alanda çeşitli boyutlarda dişli kullanımına ihtiyaç duyulmaktadır. Modülü 1mm ve daha küçük olan mikro modüllü dişliler ise, hassas ölçüm aletlerinde, savunma sanayinde ve makine imalatında önemli bir makine elemanı olarak kullanılmaktadır. Güç aktarımı sürecinde dişli yüzeyinde, dişte, dişli gövdesinde ve dişli-mil bağlantısında meydana gelen hasarlar, tüm makinenin normal çalışmasını etkilemektedir. Oluşan herhangi bir hasar yalnızca dişli ya da dişli bağlantısını değil, bu elemanla birlikte çalışan birçok makine parçasını da hasara uğratabilir. Mikro modüllü dişlilerin küçük boyutları nedeniyle dişli-mil bağlantısında sıkı geçme bağlantıları ön plana çıkmaktadır. Ancak bu konuda literatürde önemli eksiklikler bulunmaktadır. Tasarımcıların tüm sıkı geçme toleranslarını uygulamalı olarak denemesi hem vakit hem de ekonomik kayıplara yol açabilir. Bu sebeple analitik ve nümerik hesaplamaların, dişli göbeği mil sıkı geçme bağlantılarında önemi büyüktür.

Bu çalışmada, farklı göbek çaplarına sahip 1mm modül, 6 mm genişlik ve 20 diş sayısına sahip bir mikro modül dişlide; farklı sıkı geçme toleranslarında oluşan gerilme dağılımları sayısal ve analitik olarak hesaplanıp karşılaştırılmıştır. Analitik ve sayısal çalışmadan elde edilen veriler birbiriyle uyum içerisindedir. Nominal çap arttıkça meydana gelen teğetsel ve radyal gerilme azalmaktadır. Ancak bu noktada zayıflayan dişli gövdesi meydana gelebilecek hasarlara açık konumdadır. Çalışmada kullanılan tüm nominal çap değerleri için dişli mil bağlantısından ötürü meydana gelen teğetsel ve radyal gerilme büyüklüğü H7/u6, H7/s6, H7/p6 şeklinde sıralanmaktadır.

Keywords

• mikro modüllü dişli
• sıkı geçme
• dişli mil bağlantısı

References

1. Wittel, H., Muhs D., Jannasch, D., Joachim V. (2013). Roloff/Matek maschinenelemente. Springer, Augsburg, Almanya
2. Kovan, V. (2018). Elasto-Plastic Separation Frequency Analysis of Interference Fitted Joints in Lightweight Materials. International Journal of Computational Methods, 15 (4), 1-15.
3. Kovan V. (2011). Separation frequency analysis of interference fitted hollow shaft-hub connections by finite element method. Advances in Engineering Software, 42, 644-648.
4. Xiang, D., Shen, G., Zhu, K., Shen, Y., Jiang, L. (2017). Interference contact characteristics of planetary gear train for wind turbines. Journal of Vibration and Shock, 36 (5), 17-22.
5. Pedersen, N.L. (2016). On optimization of interference fit assembly. Structural and Multidisciplinary Optimization, 54 (2), 349-359.
6. Zhou, Y., Ding, L., Niu, P.H., Li, D.L. (2018). Study on the Machining Process of Circular Arc Gear with Interference Fit. Transaction of Beijing Institute of Technology, 38 (11), 1120-1125.
7. Zhao, J., Lin, T.J., Zhong, S., Song, J.J. (2016). Fatigue Life and its Influence Factor Analysis of Interference Fit Position of Planetary Gear and Bearing. Journal of Dalian University of Technology, 56 (4), 355-361.
8. Joshi, Y.V. (2018). Gear Interference-Fit Joint Considerations and Design for the Resultant Tooth Distortion. SAE Technical Papers,April.

9. Boutoutaou, H., Fontaine, J.F. (2015). Methodology for a Computer-Aided Design of Shrink Fits that Considers the Roughness and Form Defects of the Manufacturing Process. Journal of Mechanical Science and Technology, 29 (5), 2097-2103.
10. Croccolo, D., De Agostinis, M. and Vincenzi, N. [2011] “How to Improve Static and Fatigue Strength in Press-Fitted Joints Using Anaerobic Adhesive,” P. I. Mech. Eng. C-J. Mec.225, 2792–2803.
11. Kim, S. S. and Lee, D. G. (2006). Design of the Hybrid Composite Journal Bearing Assembled by İnterference Fit. Composite Structures, 75, 222–230.
12. Lewis, R., Marshall, M. B. and Dwyer-Joyce, R. S. (2005). Measurement of Interface Pressure in Interference Fits. Proceedings of The Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science, 219, 127–139.
13. Lame, G. and Clapeyron, B. (1831). Memoire sur l’ equilibre interieur des corps solides homogeenes. Journal für die reine und angewandte Mathematik, 7, 391–423.
14. Eyercioglu, O., Kutuk, M. A. and Yilmaz, N. F. (2009). Shrink Fit Design for Precision Gear Forging Dies. Journal of Materials Processing Technology, 209, 2186–2194.
15. Zhang, Y., McClain, B. and Fang, X. D. (2000). Design of Interference Fits via Finite Element Method. International Journal of Mechanical Sciences, 42, 1835–185.
16. Chakherlou, T. N. and Abazadeh, B. (2012). Experimental and Numerical Investigations about the Combined Effect of Interference Fit and Bolt Clamping on the Fatigue Behavior of Al 2024-T3 Double Shear Lap Joints. Materials & Design, 33, 425–435.
17. Chakherlou, T. N., Mirzajanzadeh, M. and Saeedi, K. H. (2010). Fatigue Crack Growth and Life Prediction of a Single Interference Fitted Holed Plate. Fatigue & Fracture of Engineering Materials & Structures, 33, 633–644.
18. Sniezek, L., Zimmerman, J. and Zimmerman, A. (2010). The Carrying Capacity of Conical Interference-Fit Joints with Laser Reinforcement Zones,” Journal of Materials Processing Technology, 210, 914–925.
19. Lanoue, F., Vadean, A. and Sanschagrin, B. (2009). Finite Element Analysis and Contact Modelling Considerations of Interference Fits for Fretting Fatigue Strength Calculations. Simulation Modelling Practice and Theory, 17, 1587–1602.
20. Sun, M. Y., Lu, S. P., Li, D. Z., Li, Y. Y., Lang, X. G. and Wang, S. Q. (2010). Three-dimensional Finite Element Method Simulation and Optimization of Shrink Fitting Process for a Large Marine Crankshaft,” Materials & Design, 31, 4155–4164.
21. Yang, G. M., Coquille, J. C., Fontaine, J. F. and Lambertin, M. (2001). Influence of roughness on characteristics of tight interference fit of a shaft and a hub. International Journal of Solids and Structures, 38, 7691–7701.
22. Mucha, J. (2009). Finite Element Modeling and Simulating of Thermomechanic Stress in Thermocompression Bondings. Materials & Design, 30, 1174–1182.
23. ASME B4.2-1978, Preferred Metric Limits and Fits. (2009) ASME International, New York.
24. Timoshenko, S. (1947). Strength of materials, part II – Advanced Theory and Problems, D. Lancaster: Van Nostrand Company
25. Budynas, R. G., Nisbett, J. K., Shigley, J. E. (2011). Shigley's mechanical engineering design. New York: McGraw-Hill.