İbrahim PAZARKAYA, Mehmet YAZAR, Ahmet ÖZDEMİR

Eliptik Dişli Tasarımı, İmalatı, Analizi ve Eliptik Dişli Esaslı Endüstriyel Uygulamalar

Eliptik dişliler, bir elips üzerine eşit adımlarla diş profillerinin dizildiği ve tahrik edilen mil hızının aynı dönüş içerisinde değiştirilmesi istenen durumlarda kullanılan özel bir dişli türdür. Eliptik dişliler üzerine yapılan çalışmaların diş profillerinin tasarımı üzerine yoğunlaştığı ve prototip imalatlarına yönelik araştırmaların arttığı görülmektedir. Eliptik dişlilerin diş profillerinin silindirik dişliler gibi özdeş olmayacağından hareketle geliştirilen eliptik dişlinin diş profili; kramayer veya silindirik düz dişli formlu kesicinin bölüm elipsi üzerinde yuvarlanma yöntemine uygun olarak evolvent eğriye sahip diş yanaklarının şekillendirilmesiyle elde edilmektedir. Eliptik dişlilerin imalatında CNC tel erozyon tezgahlarından faydalanmanın yaygınlaştığı, bununla birlikte azdırma tezgâhları için elektronik dişli kutuları geliştirilerek eliptik dişlilerin standart modülde imalatının da mümkün olduğu tespit edilmiştir. Eliptik dişli çiftleri farklı makine ve teçhizatta kullanılmakta, özellikle eliptik dişli çiftine sahip debimetre ve pompaların yaygınlaştığı görülmektedir. Enerji verimliliğinin son derece önem kazandığı günümüzde, yüksek miktardaki akışkanların debilerinin doğru ve hassas ölçülmesi, aynı zamanda akışkan transferindeki kayıpların da giderilmesi de gerekmektedir. Bu derleme çalışmasında eliptik dişlilerin tasarımı, geleneksel ve geleneksel olmayan imal usulleri ile imalatı, dayanım ve titreşim analizleri ve literatürde yer alan muhtelif endüstriyel uygulamaları gözen geçirilmiş ve çalışmanın ortak bulguları elde edilmiştir. Eliptik dişlilerin yakın gelecekte bünyesinde mekanik kısım barındıran birçok akıllı ürünün vazgeçilmez bir organı olacağı öngörülmektedir.

Elliptical Gear Design, Manufacturing, Analysis and Elliptical Gear Based Industrial Applications

Elliptical gears are a specific type of gear used in situations where tooth profiles are arranged with equal steps on an ellipse and the driven shaft speed is desired to be changed within the same turn. The studies that covered elliptical gears focused on the design of tooth profiles, and the research increased on prototype manufacturing of elliptical gears. The elliptical gear tooth profile is developed based on the fact that the tooth profiles of elliptical gears are not identical to cylindrical gears and are obtained by shaping tooth flanks with involute curves by the rolling method on the section ellipse with a rack or cylindrical spur gear cutter. It has been determined that the use of CNC electrical discharge machining (EDM) in the manufacture of elliptical gears has preferably become the manufacturability of elliptical gears in standard modules by developing electronic gearboxes for hobbing machines. Elliptical gear pairs are used in different machines, mechanisms and equipment, especially flow meters, and pumps with elliptical gear pairs are widespread.In today's world, where energy efficiency is of utmost importance, it is necessary to measure the flow rates of high volumes of fluids accurately and precisely, as well as to eliminate the losses in fluid transfer. In this compilation study, the design of elliptical gears, traditional and non-traditional manufacturing methods, strength and vibration analyzes, and various industrial applications in the literature were evaluated, and the common result of the literary works was obtained. It is predicted that elliptical gears will be an indispensable part of many smart products that contain mechanical parts soon.

PDF

___

[1] M. Addomine, G. Figliolini, and E. Pennestrì, “A landmark in the history of non-circular gears design: The mechanical masterpiece of Dondi’s astrarium,” Mech. Mach. Theory, vol. 122, pp. 219–232, Apr. 2018, doi: 10.1016/j.mechmachtheory.2017.12.027.
[2] M. J. LAI, “An Investigation of The Dynamic Behaviour of Systems With, Noncircular Gears,” Cnkijournal, Beijing, pp. 377–388, 1996.
[3] D. Mundo, “Geometric design of planetary gear train with non-circular gears,” Mech. Mach. Theory Elsevier Ltd, pp. 456–472, 2006.
[4] Y. A. Yao and H. S. Yan, “A new method for torque balancing of planar linkages using non- circular gears,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 217(5), pp. 495–503, 2003.
[5] S. L. Chang, C. B. Tsay, and L. I. Wu, “Mathematical model and undercutting analysis of elliptical gears generated by rack cutters,” Mech. Mach. Theory, vol. 31, no. 7, pp. 879–890, 1996, doi: 10.1016/0094-114X(95)00121-E.
[6] F. L. Litvin, “Gear Geometry and Applied Theory,” PTR Prentice-Hall, New Jersy, pp. 300–400, 1994.
[7] L. Gang and Z. Weidong, “Design and power loss evaluation of a noncircular gear pair for an infinitely variable transmission,” Mech. Mach. Theory, vol. 156, 2021.
[8] W. Junfeng, L. Xiaobo, L. Chuan, L. Bo, and Z. Fangyan, “Three-dimensional design and motion analysis of non-circular gear [J].,” J. hubei Univ. Technol., vol. 29(04), pp. 69–72, 2014.
[9] S. MEDVECKÁ-BEŇOVÁ, “DESIGNING PITCH CURVES OF NON-CIRCULAR GEARS,” Sci. J. Silesian Univ. Technol. Ser. Transp., vol. 99, pp. 105–114, Jun. 2018, doi: 10.20858/sjsutst.2018.99.10.
[10] S. H. Tong and C. H. Yang, “Generation of Identical Noncircular Pitch Curves,” ASME J. Mech. Des., vol. 120(2), pp. 337–341, 1998.
[11] F. L. Litvin and A. Fuentes, “Gear Geometry and Applied Theory,” Cambridge Univ. Press. New York, 2004.
[12] D. D. Chung and R. Wolfgramm, “Maxillary arch perimeter prediction using Ramanujan’s equation for the ellipse,” Am. J. Orthod. Dentofac. Orthop., vol. 147, no. 2, pp. 235–241, 2015, doi: 10.1016/j.ajodo.2014.10.022.
[13] İ. PAZARKAYA and A. ÖZDEMİR, “Eliptik Dişli Çarklarda Bölüm Elipsinin Analitik Olarak Hesaplanması,” 1. ULUSLARARASI MÜHENDİSLİK BİLİMLERİ VE MULTİDİSİPLİNER YAKLAŞIMLAR KONGRESİ, pp. 490–498, 2021.
[14] J. Han, D. Z. Li, T. Gao, and L. Xia, “Research on Obtaining of Tooth Profile of Non-circular Gear Based on Virtual Slotting,” 14th IFToMM World Congr. (Taipei Taiwan), no. URL:http://www.iftomm2015.tw/IFToMM2015CD/PDF/PS6-001.pdf, pp. 25–30, 2015.
[15] X. Wang, “A numerical algorithm of tooth profile of non-circular cylindrical gear,” in AIP Conference Proceedings, Jul. 2017, vol. 1864, doi: 10.1063/1.4992991.
[16] A. A. Lyashkov, K. L. Panchuk, and I. A. Khasanova, “Automated Geometric and Computer- aided Non-Circular Gear Formation Modeling,” in Journal of Physics: Conference Series, Jul. 2018, vol. 1050, no. 1, doi: 10.1088/1742-6596/1050/1/012049.
[17] B. W. Bair, “Computer aided design of elliptical gears with circular-arc teeth,” Mech. Mach. Theory, vol. 39, no. 2, pp. 153–168, Feb. 2004, doi: 10.1016/S0094-114X(03)00111-3.
[18] J. BETTEN, “involute of an ellipse,” Math. Model. Mater. Sci. Contin. Mech. Augustinerbach, pp. 4–20, 2009.
[19] J. HAN, D. LI, L. XIA, and B. JIANG, “Research on Design Method of Non-Circular Gear Pair with Double Generating Angles, , Computer Aided Drafting,” Des. Manuf. Vol., vol. 25, p. 52, 2015.
[20] M. YAZAR and Ö. Ahmet, “COMPUTER-AIDED DESIGN, MANUFACTURE AND EXPERIMENTAL ANALYSIS OF A PAIR OF ELLIPTICAL SPUR GEARS,” ANADOLU Univ. J. Sci. Technol. A - Appl. Sci. Eng., vol. 17, no. 5, pp. 869–869, Dec. 2016, doi: 10.18038/aubtda.279855.
[21] Y. Hou and C. Lin, “Kinematic analysis and experimental verification of an oval noncircular bevel gears with rotational and axial translational motions,” . J. Braz. Soc. Mech. Sci. Eng., p. 60, 2019.
[22] A. Prikhodko, “Experimental kinematic analysis of an intermittent motion planetary mechanism with elliptical gears,” J. Meas. Eng., vol. 8, pp. 122–131, 2020.
[23] S. Maláková, M. Urbanský, G. Fedorko, V. Molnár, and S. Sivak, “Design of geometrical parameters and kinematical characteristics of a non circular gear transmission for given parameters,” Appl. Sci., vol. 11, no. 3, pp. 1–24, Feb. 2021, doi: 10.3390/app11031000.
[24] K. Zhou, Y. Guo, and X. Li, “Modeling and Dynamics Analysis of Non-Circular Gears,” in PervasiveHealth: Pervasive Computing Technologies for Healthcare, Apr. 2020, pp. 442–447, doi: 10.1145/3436286.3436434.
[25] F. Zheng, L. Hua, D. Chen, and X. Han, “Generation of Noncircular Spiral Bevel Gears by Face- Milling Method,” ASME J. Manuf. Sci. Eng., vol. 138(8), p. 081013, 2016.
[26] F. L. Litvin, I. Gonzalez-Perez, K. Yukishima, A. Fuentes, and K. Hayasaka, “Generation of planar and helical elliptical gears by application of rack-cutter, hob, and shaper,” Comput. Methods Appl. Mech. Eng., vol. 196, no. 41–44, pp. 4321–4336, 2007, doi: 10.1016/j.cma.2007.05.003.
[27] A. Katz, K. Erkorkmaz, and F. Ismail, “Virtual Model of Gear Shaping— Part I: Kinematics, Cutter–Workpiece Engagement, and Cutting Forces,” ASME J. Manuf. Sci. Eng., vol. 140(7), p. 071007, 2018.
[28] B. W. Bair, “Computerized tooth profile generation of elliptical gears manufactured by shaper cutters,” J. Mater. Process. Technol., vol. 122, no. 2–3, pp. 139–147, 2002, doi: 10.1016/S0924- 0136(01)01242-0.
[29] J. Li, X. Wu, and S. Mao, “Numerical computing method of noncircular gear tooth profiles generated by shaper cutters,” Int. J. Adv. Manuf. Technol., vol. 33, no. 11–12, pp. 1098–1105, 2007, doi: 10.1007/s00170-006-0560-0.
[30] F. Zheng, L. Hua, X. Han, B. Li, and D. Chen, “Linkage model and manufacturing process of shaping non-circular gears,” Mech. Mach. Theory, vol. 96, pp. 192–212, 2016, doi: 10.1016/j.mechmachtheory.2015.09.010.
[31] F. Zheng, L. Hua, X. Han, B. Li, and D. Chen, “Synthesis of Shaped Noncircular Gear Using a Three-Linkage Computer Numerical Control Shaping Machine,” J. Manuf. Sci. Eng. Trans. ASME, vol. 139, no. 7, 2017, doi: 10.1115/1.4035794.
[32] F. Zheng, X. Guo, and M. Zhang, “Non-uniform flank rolling measurement for shaped noncircular gears,” Meas. J. Int. Meas. Confed., vol. 116, pp. 207–215, Feb. 2018, doi: 10.1016/j.measurement.2017.07.048.
[33] F. Zheng, H. Lin, X. Han, M. Zhang, W. Zhang, and X. Guo, “Avoidance of Cutter Retracting Interference in Noncircular Gear Shaping Through 4-Linkage Model,” J. Manuf. Sci. Eng. Trans. ASME, vol. 141, no. 5, 2019, doi: 10.1115/1.4043193.
[34] F. Zheng, H. Xinghui, L. Hua, M. Zhang, and W. zhang, “Design and manufacture of new type of non-circular cylindrical gear generated by face-milling method,” Mech. Mach. Theory, vol. 122, pp. 326–346, 2018, doi: 10.1016/j.mechmachtheory.2018.01.007.
[35] X. Tian, J. Han, L. Xia, and L. Wu, “A fexible electronic helical guide controller,” Procedia CIRP, vol. 56, pp. 173–177, 2016.
[36] J. Han, L. Wu, B. Yuan, X. Tian, and L. Xia, “A novel gear machining CNC design and experimental research,” Int J Adv Manuf Tech, vol. 88, pp. 1711–1722, 2016.
[37] L. Wu, J. Han, Y. Zhu, X. Tian, and L. Xia, “Non-circular gear continuous generating machining interpolation method and experimental research,” J. Brazilian Soc. Mech. Sci. Eng., vol. 39, no. 12, pp. 5171–5180, 2017, doi: 10.1007/s40430-017-0873-y.
[38] J. Han, D. Li, X. Tian, and L. Xia, “Linkage model and interpolation analysis of helical non- circular gear hobbing,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 42, no. 11. 2020, doi: 10.1007/s40430-020-02663-1.
[39] W. Dan, C. Ken, and W. Xiankui, “An investigation of practical application of variable spindle speed machining to noncircular turning process,” Int J Adv Manuf Technol, vol. 44, pp. 1094– 1105, 2009.
[40] W. Dan, Z. Tong, and W. ChenXiankui, “Application of active disturbance rejection control to variable spindle speednoncircular turning process,” Int. J. Mach. Tools Manuf., vol. 49, pp. 419– 423, 2009.
[41] Q. Li, W. Ai, and B. Chen, “Variable angle compensation control of noncircular turning,” Int J Adv ManufTechnol, vol. 70(1):735, p. 46, 2014.
[42] J. Yang, P. Rao, B. Chen, H. Ding, and W. Ai, “Form error on-line estimation and compensation for non-circular turning process,” Int. J. Mech. Sci., vol. 184, no. May, 2020, doi: 10.1016/j.ijmecsci.2020.105847.
[43] H. Jiang, L. Dazhu, T. Xiaoqing, and X. Lian, “Meshing principle and transmission analysis of a beveloid non-circular gear,” Adv. Mech. Eng., vol. 12(11), pp. 1–11, 2020.
[44] Y. Liu, J. Gong, and X. Wu, “Investigation on the grinding of elliptical gears with CNC conical wheel gear grinder,” Int. J. Adv. Manuf. Technol., vol. 64, no. 1–4, pp. 349–356, 2013, doi: 10.1007/s00170-012-4028-0.
[45] T. Sałaciński, A. Przesmycki, and T. Chmielewski, “Technological aspects in manufacturing of non-circular gears,” Appl. Sci., vol. 10, no. 10, 2020, doi: 10.3390/app10103420.
[46] M. Yazar, “Design, Manufacturing and Operational Analysis of Elliptical Gears,” Int. J. Precis. Eng. Manuf., vol. 22, no. 8, pp. 1441–1451, 2021, doi: 10.1007/s12541-021-00549-3.
[47] C. García-Hernández, R. M. Gella-Marín, J. L. Huertas-Talón, N. Efkolidis, and P. Kyratsis, “WEDM manufacturing method for noncircular gears, using CAD/CAM software,” Stroj. Vestnik/Journal Mech. Eng., vol. 62, no. 2, pp. 137–144, 2016, doi: 10.5545/sv-jme.2015.2994.
[48] M. Lai, “An investigation of the dynamic behavior of systems with noncircular gears,” hD Thesis, Univ. Wisconsin-Madison, USA., 1997.
[49] A. Kahraman and R. Singh, “Non-linear dynamics of a spur gear pair,” J. Sound Vib., vol. 142, pp. 49–75, 1990.
[50] N. Gao, C. Meesap, S. Wang, and D. Zhang, “Parametric vibrations and instabilities of an elliptical gear pair,” JVC/Journal Vib. Control, vol. 26, no. 19–20, pp. 1721–1734, 2020, doi: 10.1177/1077546320902543.
[51] J. Lin and R. G. Parker, “Mesh stiffness variation instabilities in two-stage gear systems,” J. Vib. Acoust., vol. 124(1), pp. 68–76, 2002.
[52] O. Karpov, P. Nosko, and P. Fil, “Prevention of resonance oscillations in gear mechanisms using non-circular gears,” Mech. Mach. Theory, vol. 114, pp. 1–10, 2017.
[53] X. Liu, K. Nagamura, and K. Ikejo, “Simulation on the vibration characteristics of elliptical gears,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 227, no. 4, pp. 819–830, 2013, doi: 10.1177/0954406212454372.
[54] X. LIU, K. NAGAMURA, and K. IKEJO, “Analysis of the Dynamic Characteristics of Elliptical Gears,” J. Adv. Mech. Des., vol. 6, p. 4, 2012.
[55] S. MALÁKOVÁ, “TEETH DEFORMATION OF NON-CIRCULAR GEARS,” Sci. J. Silesian Univ. Technol. Ser. Transp., vol. 110, 2021.
[56] D. W. Liu, R. . . Zhi, and J. Xin, “Dynamic model and its application of transmission system in noncircular gears,” J. Mach. Des., vol. 33(1), pp. 35–39, 2016.
[57] K. Zhou, Y. Li, C. Wang, and C. Li, “Non-circular Gear Modal Analysis Based on ABAQUS,” in Proceedings - 8th International Conference on Intelligent Computation Technology and Automation, ICICTA 2015, May 2016, pp. 576–579, doi: 10.1109/ICICTA.2015.147.
[58] L. V. Vanegas-Useche, M. M. Abdel-Wahab, and G. A. Parker, “Nuevo par de engranajes no circulares para reducir las aceleraciones del eje: Comparación con engranajes sinusoidales y elípticos,” DYNA, vol. 83, no. 198, pp. 220–228, Sep. 2016, doi: 10.15446/dyna.v83n198.49170.
[59] K. Zhou, Y. Li, C. Li, and C. Wang, “Non-circular Gear Kinematics Simulation Based on ADAMS,” Proc. - 8th Int. Conf. Intell. Comput. Technol. Autom. ICICTA 2015, pp. 572–575, 2016, doi: 10.1109/ICICTA.2015.146.
[60] K. J. Waldron, G. L. Kinzel, and S. K. Agrawal, “Kinematics, Dynamics, and Design of Machinery, 3th Edition,” Wiley, New York, 2004.
[61] Z. X. Sun and K. Hebbale, “Challenges and opportunities in automotive transmission control,” Proc. 2005 Am. Control Conf. Portl., pp. 3284–3289, 2005.
[62] X. F. Wang and W. D. Zhu, “Design, modeling, and simulation of a geared infinitely variable transmission,” ASME J. Mech. Des, vol. 136(7), p. 071011, 2014.
[63] F. Litvin and A. Fuentes-Aznar, “Noncircular Gears: Design and Generation,” Cambridge Univ. Press. New York, 2009.
[64] P. A.A. and S. A.I., “Kinematic analysis of mechanism for converting rotational motion into reciprocating rotational motion,” Procedia Eng., vol. 129, pp. 87–92, 2015.
[65] G. S. Lee and M. Y. Park, “FLOW FIELD CHARACTERISTICS IN THE HOUSING OF NONCIRCULAR GEAR FLOWMETER,” no. July, 2008.
[66] D. Liu, Y. Ba, and T. Ren, “Flow fluctuation abatement of high-order elliptical gear pump by external noncircular gear drive,” Mech. Mach. Theory, vol. 134, pp. 338–348, 2019, doi: 10.1016/j.mechmachtheory.2019.01.011.
[67] A. M. Moinfar, G. Shahgholi, Y. A. Gilandeh, and T. M. Gundoshmian, “The effect of the tractor driving system on its performance and fuel consumption,” Energy, vol. 202, p. 117803, 2020, doi: 10.1016/j.energy.2020.117803.
[68] K. Rongping, “Port Ship Energy Consumption Management Based On Beidou Satellite Communication[J],” Jimei Univ., 2017.
[69] J. Firth, F. Ladouceur, Z. Brodzeli, M. Wyres, and L. Silvestri, “A novel optical telemetry system applied to flowmeter networks,” Flow Meas. Instrum., vol. 48, pp. 15–19, 2016, doi: 10.1016/j.flowmeasinst.2016.01.006.
[70] A. Zaza, E. G. Bennouna, N. E. Laadel, and Y. El Hammami, “Experimental Study of Fouling in Hybrid Cooling Tower Used in CSP Plants: Effects of the Polymer and galvanized steel tubes,” Therm. Sci. Eng. Prog., vol. 25, no. June, p. 101005, 2021, doi: 10.1016/j.tsep.2021.101005.
[71] L. Xiao, M. Yang, S. Zhao, W. Z. Yuan, and S. M. Huang, “Entropy generation analysis of heat and water recovery from flue gas by transport membrane condenser,” Energy, vol. 174, pp. 835– 847, 2019.
[72] S. Soleimanikutanaei, C. X. Lin, and D. Wang, “Numerical modeling and analysis of Transport Membrane Condensers for waste heat and water recovery from flue gas,” Int J Therm Sci, vol. 136, pp. 96–106, 2019.
[73] Y. Yang, N. F. Li, S. M. Huang, C. H. Liang, and L. Xiao, “State-space model for transient behavior of transport membrane condenser,” Int. J. Heat Mass Transf., vol. 165, 2021, doi: 10.1016/j.ijheatmasstransfer.2020.120667.
[74] M. Meribout, A. Azzi, N. Ghendour, N. Kharoua, L. Khezzar, and E. AlHosani, “Multiphase Flow Meters Targeting Oil & Gas Industries,” Meas. J. Int. Meas. Confed., vol. 165, p. 108111, 2020, doi: 10.1016/j.measurement.2020.108111.
[75] X. Li, Z. Huang, Z. Meng, B. Wang, and H. Li, “Oil-water two-phase flow measurement using a venturi meter and an oval gear flow meter,” Chem. Eng. Commun., vol. 197, no. 2, pp. 223–231, 2010, doi: 10.1080/00986440902938469.
[76] J. Yan, S. Li, and R. Li, “Numerical study on the auxiliary entrainment performance of an ejector with different area ratio,” Appl. Therm. Eng., vol. 185, no. August 2020, p. 116369, 2021, doi: 10.1016/j.applthermaleng.2020.116369.
[77] J. J. Park and E. S. Lee, “A study on the elliptical gear design for oval flowmeter,” Trans. Korean Soc. Mech. Eng. A, vol. 37, no. 8, pp. 1029–1033, 2013, doi: 10.3795/KSME-A.2013.37.8.1029.