Oğuzhan DOĞAN, Onur KALAY, FATİH KARPAT

Doğrusal Profil Modifikasyonlarının Bir Düz Dişli Çarkın Dinamik Yüklenmesi Üzerine Etkisi

Dişli dinamiği, titreşim seviyeleri, yük taşıma kapasitesi ve gürültü üzerindeki dikkat çekici etkisi sebebi ile dişli tasarımındaki en kritik konulardan birisidir. Uç modifikasyonu, endüstride dinamik yükleri azaltmak için basit bir yöntem olarak bilinmektedir. Bu çalışmanın ana amacı da doğrusal profil modifikasyonlarının düz dişli çarkların dinamik davranışına etkisinin anlaşılmasıdır. Bu kapsamda, kavrama süreci ve dişli kavrama rijitliği hesaplama yöntemi tanımlanmıştır. Düz dişli çark çiftinin dinamik cevabını bulmak için iki serbestlik dereceli bir dinamik model oluşturulmuştur. Simülasyonlar, standart ve farklı miktarlarda uç modifikasyonuna tabi tutulmuş düz dişli çark çiftleri ile gerçekleştirilmiştir. Uç modifikasyonunun dişli çark dinamik cevabı üzerinde mükemmel bir etkiye sahip olduğu görülmüştür. Ancak, bu etki belirli bir miktar ile sınırlıdır. Optimum uç modifikasyonu miktarından sonra, dinamik yükler önemli ölçüde artmaktadır. Bu çalışmada, dişli çark tasarımcıları için MATLAB® programında optimum uç modifikasyonu miktarını bulmak için bir bilgisayar programı geliştirilmiştir. Program çıktıları iki farklı vaka için verilmiştir.

Anahtar Kelimeler:

Dişli Dinamiği, Uç Modifikasyonu, Düz Dişli, Kavrama Rijitliği

INFLUENCE OF LINEAR PROFILE MODIFICATIONS ON THE DYNAMIC LOADING OF A SPUR GEAR

Gear dynamics is one of the most critical subjects in gear design because of its remarkable effect on vibration levels, load-carrying capacity, and noise. The tip relief modification is known as a simple method to decrease dynamic loads in the industry. The primary goal of this study is to understand the influence of tip relief modification on the dynamic performance of the spurs gears. In this paper, the meshing process and gear mesh stiffness calculation method are defined. A dynamic model with two-degree-of-freedom is created to find the dynamic response of the spur gear pair. The simulations are carried out with standard and different tip modified spur gear pairs. It is observed that the tip relief modification has an excellent effect on the gear dynamic response. However, this effect is restricted until a certain amount of tip relief modification. After the optimum amount of tip relief modification, the dynamic loads are increased considerably. Thus, a computer program is developed to find the optimum amount of tip relief modification in MATLAB® for the gear designers. The program outputs are given for two different case studies. As a result of the study, the dynamic factor behaves like a “V form” according to the tip relief modification, and the dynamic force decreased approximately 25% for optimum profile modification.

Keywords:

Gear Dynamics, Tip Relief, Spur Gear, Mesh Stiffness,

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Alemayehu, F.M. and Ekwaro-Osire, S. (2014) Loading and design parameter uncertainty in the dynamics and performance of high-speed-parallel-helical stage of a wind turbine gearbox, Journal of Mechanical Design, 136(9). https://doi.org/10.1115/1.4027496.
Baud, S. and Velex, P. (2002) Static and dynamic tooth load in spur and helical geared systems – experiments and model validation, Journal of Mechanical Design, 124(2), 334 –346. https://doi.org/10.1115/1.1462044.
Ding, F., Tian, Z., Zhao, F. and Xu, H. (2018) An integrated approach for wind turbine gearbox fatigue life prediction considering instantaneously varying load conditions, Renewable Energy, 129, 260 – 270. https://doi.org/10.1016/j.renene.2018.05.074.
Frazer, R.C., Shaw, B.A., Palmer, D. and Fish, M. (2010) Application examples from optimizing gear geometry for minimum transmission error, mesh friction losses and scuffing risk through computer-aided engineering, Gear Technology, August.
Guerine, A., El-Hami, A., Walha, L., Fakhfakh, T. and Haddar, M. (2017) Dynamic response of wind turbine gear system with uncertain-but-bounded parameters using interval analysis method, Renewable Energy, 113, 679 – 687. https://doi.org/10.1016/j.renene.2017.06.028.
Hu, Z., Tang, J., Zhong, J., Chen, S. and Yan, H. (2016) Effects of tooth profile modification on dynamic responses of a high speed gear-rotor-bearing system, Mechanical Systems and Signal Processing, 76(77), 294 – 318. https://doi.org/10.1016/j.ymssp.2016.01.020.
Kahraman, A. and Blankenship, G.W. (1999) Effect of involute tip relief on dynamic response of spur gear pairs, Journal of Mechanical Design, 121(2), 313 – 315. https://doi.org/10.1115/1.2829460.
Karpat, F., Ekwaro-Osire, S., Cavdar, K. and Babalik, F.C. (2008) Dynamic analysis of involute spur gears with asymmetric teeth, International Journal of Mechanical Sciences, 50(12), 1598 – 1610. https://doi.org/10.1016/j.ijmecsci.2008.10.004.
Karpat, F. and Ekwaro-Osire, S. (2008) Influence of tip relief modification on the wear of spur gears with asymmetric teeth, Tribology Transactions, 51(5), 581 – 588. https://doi.org/10.1080/10402000802011703.
Karpat, F. and Ekwaro-Osire, S. (2008) Dynamic analysis of high-contact-ratio spur gears with asymmetric teeth, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Boston, Massachusetts, 285 – 291. https://doi.org/10.1115/IMECE2008-67838.
Karpat, F., Dogan, O., Yuce, C. and 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. https://doi.org/10.1177/1687814017721856.
Karpat, F., Yuce, C., and Dogan, O. (2020) Experimental measurement and numerical validation of single tooth stiffness for involute spur gears, Measurement, 150. https://doi.org/10.1016/j.measurement.2019.107043.
Lin, H.H., Huston, R.L. and Coy, J.J. (1990) Dynamic loads in parallel shaft transmissions part 1, Gear Technology, March/April, 25 – 34.
Lin, H.H., Huston, R.L. and Coy, J.J. (1990) Dynamic loads in parallel shaft transmissions part 2, Gear Technology, May/June, 8 – 27.
Lin, H.H., Oswald, F.B. and Townsend, D.P. (1994) Dynamic loading of spur gears with linear or parabolic tooth profile modifications, Mechanism and Machine Theory, 29(8), 1115 – 1129. https://doi.org/10.1016/0094-114X(94)90003-5.
Liou, C.H., Lin, H.H., Oswald, F.B. and Townsend, D.P. (1996) Effect of contact ratio on spur gear dynamic load with no tooth profile modifications. Journal of Mechanical Design, 118(3), 439 – 443. https://doi.org/10.1115/1.2826905.
Liu, H., Zhang, C., Xiang, C.L. and Wang, C. (2016) Tooth profile modification based on lateral-torsional-rocking coupled nonlinear dynamic model of gear system, Mechanism and Machine Theory, 105, 606 – 619. https://doi.org/10.1016/j.mechmachtheory.2016.07.013.
Marković, K. and Franulović, M. (2011) Contact stresses in gear teeth due to tip relief profile modification, Engineering Review, 31(1), 19 – 26.
Marković, K. and Vrcan, Z. (2016) Influence of tip relief modification an involute spur gear stress, Transactions of Famena, 40(2), 59 – 70. https://doi.org/10.21278/TOF.40205.
Marques, M.T., Martins, R.C. and Seabra, J.H.O. (2016) Gear dynamics and power loss. Tribology International, 97, 400 – 411. https://doi.org/10.1016/j.triboint.2016.02.002.
Ozguven, H.N. (1991) A non-linear mathematical model for dynamic analysis of spur gears including shafts and bearing dynamics, Journal of Sound and Vibration, 145(2), 239 – 260. https://doi.org/10.1016/0022-460X(91)90590-G.
Palmer, D. and Fish, M. (2012) Evaluation of methods for calculating effects of tip relief on transmission error, noise and stress in loaded spur gears, Gear Technology, January/February, 56 – 67.
Shanmugasundaram, S., Kumaresan, M. and Muthusamy, N. (2014) Effects of pressure angle and tip relief on the life of speed increasing gearbox: A case study, SpringerPlus, 3(1), 1 – 10.
Tharmakulasingam, R., Alfano, G. and Atherton, M. (2008) Reduction of gear pair transmission error with tooth profile modification. Proceedings of the ISMA 2008 International Conference on Noise and Vibration Engineering, Leuven, Belgium.
Tharmakulasingam, R. (2009) Transmission error in spur gears: Static and dynamic finite-element modeling and design optimization, Ph.D. Thesis, Brunel University.
Wei, S., Zhao, J., Han, Q. and Chu, F. (2015) Dynamic response analysis on torsional vibrations of wind turbine geared transmission system with uncertainty, Renewable Energy, 78, 60 – 67. https://doi.org/10.1016/j.renene.2014.12.062.
Yildirim, N. and Munro, R.G. (1999) A systematic approach to profile relief design of low and high contact ratio spur gears, Proceedings of the Institution of Mechanical Engineers Part C, 213(6), 551 – 562. https://doi.org/10.1243/0954406991522482.
Yoon, K.Y. and Rao, S.S. (1996) Dynamic load analysis of spur gears using a new tooth profile, Journal of Mechanical Design, 118(1), 1 – 6. https://doi.org/10.1115/1.2826851.