TEMEL DİŞLİ TASARIM PARAMETRELERİNİN TEK DİŞ VE KAVRAMA RİJİTLİĞİNE ETKİSİNİN SONLU ELEMANLAR METODU İLE İNCELENMESİ
Abstract
Dişli
tasarım parametrelerinin en önemlileri arasında tek diş ve kavrama rijitliği
gösterilebilir. Tek diş ve kavrama rijitliği özellikle dişli dinamik yükleri
üzerinde etkin rol oynar. Ayrıca, diş rijitliği temas halindeki dişliler
arasındaki yük paylaşımını belirleyen en önemli parametredir. Bu çalışmada, tek
diş ve kavrama rijitliğinin hesaplanabilmesi için geliştirilen kapsamlı bir
yöntem ele alınmıştır. Çalışmanın ilk bölümünde, tek diş rijitliğinin
hesaplanabilmesi için sonlu elemanlar modeli oluşturulmuştur. Tek diş için elde
edilen rijitlik eğrilerinin kullanılmasıyla dişli mekanizmaları için zamanla
değişen kavrama rijitliği hesaplanmıştır. Hesaplanan rijitlik değerleri
literatürdeki benzer çalışmalarla kıyaslanarak doğrulanmıştır. Çalışmanın
ikinci aşamasında, farklı temel dişli tasarım parametrelerinin tek diş ve
kavrama rijitliğine etkisi incelenmiştir. Beş farklı durum için, diş sayısı,
basınç açısı, profil kaydırma faktörü, diş başı yüksekliği ve kesici takım uç
yarıçapının, etkileri incelenmiştir. Ayrıca elde edilen sonuçların tasarımcılar
tarafından hızlı bir şekilde değerlendirilebilmesi için MATLAB ortamında
kullanıcı arayüzü oluşturulmuştur. Sonuç olarak, diş sayısı, basınç açısı,
kesici takım uç yarıçapının, artması rijitlik değerlerinin artmasına, diş başı
yüksekliğinin artmasının ise rijitliğin azalmasına yol açtığı görülmüştür. Ayrıca
pozitif profil kaydırma işlemi sonucunda kavrama rijitliğinin artıp negatif
profil kaydırma ile de azaldığı görülmüştür.
References
- Aktaş, A. and Orhan, S. (2004) Düşük kavrama oranlı dişlilerde rijitliğin sonlu elemanlar metoduyla belirlenmesi, Teknoloji, 7 (2), 285-288.
- Arıkan, M.A.S. (1987) Computer-aided dynamic modeling of spur gears, Doktora Tezi.O.D.T.Ü.
- Babalık, F.C. and Çavdar, K. (2014) Makine elemanları ve konstrüksiyon örnekleri, Dora, Bursa.
- Chen, Z. and Su, D. (2013) Dynamic simulation of planetary gear set with flexible spur ring gear, Journal of sound and vibration, 332, 7191-7204. doi:10.1115/1.4023300
- Colbourne, J.R. (1987) The geometry of involute gears, Springer-Verlag, New Jersey, USA.
- Cooley, C.G., Liu, C., Dai, X., Parker, R.G. (2016) Gear tooth mesh stiffness: A comparison of calculation approaches, Mechanism and machine theory, 105, 540–553. doi: 10.1016/j.mechmachtheory.2016.07.021
- Coy, J.J. and Chao, C.H.C. (1982) Method Of selecting grid size to account for hertz deformation in finite element analysis of spur gears, Journal of mechanical design, 104 (4) ,759–766. doi: 10.1115/1.3256429
- Filiz, H. and Eyercioğlu, Ö. (1995) Evaluation of gear tooth stresses by using finite element method, Transactions of the ASME, Journal of engineering for industry, 117, 232-239. doi: 10.1115/1.2803299
- Gu, X., Velex, P., Sainsot, P., Bruyere, J. (2015) Analytical investigations on the mesh stiffness function of solid spur and helical gears, Journal of mechanical design, 137, 063301-7. doi: 10.1115/1.4030272
- Karpat, F. Ekwaro-Osire, S., Yılmaz, T.G., Dogan, O., Yuce, C. (2015) Design and analysis of internal gears with different rim thickness and shapes, Proceedings of the ASME international mechanical engineering congress and exposition, Houston, Texas, USA. doi: 10.1115/IMECE2015-52211
- Karpat, F. Engin, B., Dogan, O., Yuce, C., Yılmaz, T.G. (2014) Effect of Rim Thickness on Tooth Root Stress and Mesh Stiffness of Internal Gears, Proceedings of the ASME international mechanical engineering congress and exposition, Montreal, Quebec, Canada. doi: 10.1115/IMECE2014-39181
- Karpat, F., Dogan, O., Ekwaro-Osire, S., Yuce, C. (2014) A novel method for calculation gear tooth stiffness for dynamic analysis of spur gears with asymmetric teeth, Proceedings of the ASME international mechanical engineering congress and exposition, Montreal, Quebec, Canada. doi: 10.1115/IMECE2014-39402
- Karpat, F., Dogan, O., Yuce, C., Ekwaro-Osire, S. (2017) An improved numerical method for the mesh stiffness calculation of spur gears with asymmetric teeth on dynamic load analysis, Advances in Mechanical Engineering, 9 (8), 1-12. doi: 10.1177/1687814017721856
- Kiekbusch, T. and Howard, I. (2007) A common formula for the combined torsional mesh stiffness of spur gears, 5th Australasian congress on applied mechanics, brisbane– Australia, 10-12 December.
- Kiekbusch, T., Sappok, D., Sauer, B., Howard, I. (2011) Calculation of the combined torsional mesh stiffness of spur gears with two- and three-dimensional parametrical fe models, Strojniškivestnik - Journal of Mechanical Engineering , 57 (11), 810-818. doi: 10.5545/sv-jme.2010.248
- Kuang, J.H. and Lin, A. D. (2001) The Effect of tooth wear on the vibration spectrum of a spur gear pair, Journal of vibration and acoustics, 123(3), 311-317. doi: 10.1115/1.1379371
- Kuang, J.H. and Yu, J. A. (1994) Dynamic model for addendum modified gear pair, Proceedings of ASME 1994 design technical conferences, DE- 71, 165–176.
- Lin, H.H. (1985) Computer aided design and analysis of spur gear dynamics, Doktora tezi, University of Cincinnati Ohio.
- Lin, H.H. and Liou, C.H. (1998) A. Parametric study of spur gear dynamics, NASA/CR-1998-206598.
- Litvin, F.L. and Fuentes, A. (2004) Gear geometry and applied theory second edition, Cambridge university press, New York, USA.
- Meagher, J., Wu, X., Kong, D., Lee, C.H. (2010) A comparison of gear mesh stiffness modeling strategies, proceedings of the IMAC-XXVIII, Jacksonville, Florida USA, February 1–4.
- Munro, R.G., Palmer, D., Morrish, L. (2001) An experimental method to measure gear tooth stiffness throughout and beyond the path of contact, Proceedings of the institution of mechanical engineers part c journal of mechanical engineering science, 215 (7), 793-803. doi: 10.1243/0954406011524153
- Pedersen, N.L. and Jorgensen, M.F. (2014) On gear tooth stiffness evaluation, Computer and structures, 135, 109 – 117. doi: 10.1016/j.compstruc.2014.01.023
- Wang, Q. and Zhang, Y. (2015) A Model for analyzing stiffness and stress in a helical gear pair with tooth profile errors, Journal of vibration and control, 1-18. doi: 10.1177/1077546315576828
Investigation of Basic Design Parameters Effect on the Single Tooth and Mesh Stiffness by Finite Element Method
Abstract
Single tooth stiffness and mesh stiffness are
the one of the most important parameters of the gear design. They play an
active role especially on dynamic loads of gears. Furthermore, gear stiffness
is the most important parameter that determines the load sharing in the teeth
in contact. In this study, a comprehensive method was developed to calculate
single tooth stiffness and mesh stiffness. In the first part, a finite element
model was created to calculate the single tooth stiffness. By using the
stiffness curves obtained for one tooth, the time-varying mesh stiffness is
calculated for the gear mechanisms. The calculated stiffness values were
verified by comparing with similar studies in the literature. In the second
phase, the effect of different basic gear design parameters on single tooth
stiffness and mesh stiffness is investigated. The effects of number of teeth,
pressure angle, profile shift factor, tooth addendum height and cutting tool
tip radius were investigated. In addition, a user interface created in the
MATLAB environment so that designers can quickly evaluate the results obtained.
As a result when the number of teeth, the pressure angle, cutting tool tip
radius are increase the stiffness values increase too. Increment in the tooth
addendum height is led to a decreasement in tooth stiffness. Positive profile
shifting operation is increased the stiffness and the negative profile shifting
operation is decreased the stiffness of the gear.
References
- Aktaş, A. and Orhan, S. (2004) Düşük kavrama oranlı dişlilerde rijitliğin sonlu elemanlar metoduyla belirlenmesi, Teknoloji, 7 (2), 285-288.
- Arıkan, M.A.S. (1987) Computer-aided dynamic modeling of spur gears, Doktora Tezi.O.D.T.Ü.
- Babalık, F.C. and Çavdar, K. (2014) Makine elemanları ve konstrüksiyon örnekleri, Dora, Bursa.
- Chen, Z. and Su, D. (2013) Dynamic simulation of planetary gear set with flexible spur ring gear, Journal of sound and vibration, 332, 7191-7204. doi:10.1115/1.4023300
- Colbourne, J.R. (1987) The geometry of involute gears, Springer-Verlag, New Jersey, USA.
- Cooley, C.G., Liu, C., Dai, X., Parker, R.G. (2016) Gear tooth mesh stiffness: A comparison of calculation approaches, Mechanism and machine theory, 105, 540–553. doi: 10.1016/j.mechmachtheory.2016.07.021
- Coy, J.J. and Chao, C.H.C. (1982) Method Of selecting grid size to account for hertz deformation in finite element analysis of spur gears, Journal of mechanical design, 104 (4) ,759–766. doi: 10.1115/1.3256429
- Filiz, H. and Eyercioğlu, Ö. (1995) Evaluation of gear tooth stresses by using finite element method, Transactions of the ASME, Journal of engineering for industry, 117, 232-239. doi: 10.1115/1.2803299
- Gu, X., Velex, P., Sainsot, P., Bruyere, J. (2015) Analytical investigations on the mesh stiffness function of solid spur and helical gears, Journal of mechanical design, 137, 063301-7. doi: 10.1115/1.4030272
- Karpat, F. Ekwaro-Osire, S., Yılmaz, T.G., Dogan, O., Yuce, C. (2015) Design and analysis of internal gears with different rim thickness and shapes, Proceedings of the ASME international mechanical engineering congress and exposition, Houston, Texas, USA. doi: 10.1115/IMECE2015-52211
- Karpat, F. Engin, B., Dogan, O., Yuce, C., Yılmaz, T.G. (2014) Effect of Rim Thickness on Tooth Root Stress and Mesh Stiffness of Internal Gears, Proceedings of the ASME international mechanical engineering congress and exposition, Montreal, Quebec, Canada. doi: 10.1115/IMECE2014-39181
- Karpat, F., Dogan, O., Ekwaro-Osire, S., Yuce, C. (2014) A novel method for calculation gear tooth stiffness for dynamic analysis of spur gears with asymmetric teeth, Proceedings of the ASME international mechanical engineering congress and exposition, Montreal, Quebec, Canada. doi: 10.1115/IMECE2014-39402
- Karpat, F., Dogan, O., Yuce, C., Ekwaro-Osire, S. (2017) An improved numerical method for the mesh stiffness calculation of spur gears with asymmetric teeth on dynamic load analysis, Advances in Mechanical Engineering, 9 (8), 1-12. doi: 10.1177/1687814017721856
- Kiekbusch, T. and Howard, I. (2007) A common formula for the combined torsional mesh stiffness of spur gears, 5th Australasian congress on applied mechanics, brisbane– Australia, 10-12 December.
- Kiekbusch, T., Sappok, D., Sauer, B., Howard, I. (2011) Calculation of the combined torsional mesh stiffness of spur gears with two- and three-dimensional parametrical fe models, Strojniškivestnik - Journal of Mechanical Engineering , 57 (11), 810-818. doi: 10.5545/sv-jme.2010.248
- Kuang, J.H. and Lin, A. D. (2001) The Effect of tooth wear on the vibration spectrum of a spur gear pair, Journal of vibration and acoustics, 123(3), 311-317. doi: 10.1115/1.1379371
- Kuang, J.H. and Yu, J. A. (1994) Dynamic model for addendum modified gear pair, Proceedings of ASME 1994 design technical conferences, DE- 71, 165–176.
- Lin, H.H. (1985) Computer aided design and analysis of spur gear dynamics, Doktora tezi, University of Cincinnati Ohio.
- Lin, H.H. and Liou, C.H. (1998) A. Parametric study of spur gear dynamics, NASA/CR-1998-206598.
- Litvin, F.L. and Fuentes, A. (2004) Gear geometry and applied theory second edition, Cambridge university press, New York, USA.
- Meagher, J., Wu, X., Kong, D., Lee, C.H. (2010) A comparison of gear mesh stiffness modeling strategies, proceedings of the IMAC-XXVIII, Jacksonville, Florida USA, February 1–4.
- Munro, R.G., Palmer, D., Morrish, L. (2001) An experimental method to measure gear tooth stiffness throughout and beyond the path of contact, Proceedings of the institution of mechanical engineers part c journal of mechanical engineering science, 215 (7), 793-803. doi: 10.1243/0954406011524153
- Pedersen, N.L. and Jorgensen, M.F. (2014) On gear tooth stiffness evaluation, Computer and structures, 135, 109 – 117. doi: 10.1016/j.compstruc.2014.01.023
- Wang, Q. and Zhang, Y. (2015) A Model for analyzing stiffness and stress in a helical gear pair with tooth profile errors, Journal of vibration and control, 1-18. doi: 10.1177/1077546315576828
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 31, 2018 |
| Submission Date | November 1, 2018 |
| Acceptance Date | December 20, 2018 |
| Published in Issue | Year 2018 Volume: 23 Issue: 3 |
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