Tooth Tip Interference and Stress Analysis of High Contact Ratio Spur Gear Pairs Using an Optimized Design Tool

Year 2024, Volume: 12 Issue: 2, 157 - 162, 27.12.2024

Samet Turan , Hüseyin Enes Salman

https://doi.org/10.51354/mjen.1220364

Abstract

Gears are structural elements that function to transmit power in mechanical systems. The power transmission is carried out by the rolling motion of the teeth pair. The average number of teeth that come into contact while the gears are running is called the contact ratio and this value is generally between 1 and 2 for gears with standard profile. As the number of teeth of the gear increases, the contact ratio may exceed 2, and the gears with a contact ratio greater than 2 are called high contact ratio (HCR) gears. For HCR gears, there is a higher risk of tooth tip interference when compared to the standard gears and they require contact point calculation to avoid interference. In this study, a mathematical tool is developed using MATLAB to analyze and avoid tool tip interference in HCR spur gears. The addendum diameter, dedendum diameter, pressure angle and modulus values are optimized using the developed mathematical tool in order to obtain an HCR geometry with minimal volume and no tip interference. In addition, the spur gear stresses are calculated using the AGMA standards. According to the results, it has been analytically proven that the load carrying capacity of the HCR spur gear is higher than that of the standard gear with the same diameter and volume. The developed optimization tool provided accurate and optimized geometries for the analyzed HCR spur gears.

Keywords

high contact ratio gear, optimization, tip interference

References

• [1] Turan S., “Yüksek Kavrama Oranına Sahip Düz Dişli Çiftlerinin Uç-Kök Girişim Analizi ve Yük Taşıma Kapasitesinin Belirlenmesi”, Master’s Thesis, (2023), TOBB University of Economics and Technology.
• [2] Özgüven H.N., “A non-linear mathematical model for dynamic analysis of spur gears including shaft and bearing dynamics”, Journal of Sound and Vibration, 145, (1991), 239-260.
• [3] Rackov M., Vers M., Kuzmanovic Z.K., “HCR gearing and optimization of its geometry”, Advanced Materials Research, 633, (2013), 117-132.
• [4] Rameshkumar M., Sivakumar P., Sundaresh S., Gopinath K., “Load Sharing Analysis of High-Contact- Ratio Spur Gears in Military Tracked Vehicle Applications”, Gear Technology, 1, (2010), 115-126.
• [5] Mohanty S.C., “Tooth load sharing and contact stress analysis of high contact ratio spur gear in mesh”, Journal of the Institution of Engineers (India), Part MC, Mechanical Engineering Division, 84, (2003), 66-70.
• [6] Marimuthu P., Muthuveerappan, G., “Investigation of load carrying capacity of asymmetric high contact ratio spur gear based on load sharing using direct gear design approach”, Mechanism and Machine Theory, 96, (2016), 52-74.
• [7] Podzharov E., Mozuras A., “Design of high contact ratio spur gears cut with standard tools”, Gear Technology, 20, (2003), 34-37.
• [8] Anderson N.E., Loewenthal S.H., “Efficiency of nonstandard and high contact ration involute spur gears”, Journal of Mechanisms, Transmissions, and Automation in Design, 108, (1986), 119-126.
• [9] Aydeniz A.İ., “Yüksek kavrama oranının düz alın dişli mekanizmalarında statik ve dinamik davranışa etkileri”, Doctoral Dissertation, (2007), Istanbul Technical University.
• [10] Thirumurugan, R., Muthuveerappan, G., “Critical loading points for maximum fillet and contact stresses in normal and high contact ratio spur gears based on load sharing ratio”, Mechanics Based Design of Structures and Machines, 39, (2011), 118-141.
• [11] Huang K., Yi Y., Xiong Y., Cheng Z., Chen H., “Nonlinear dynamics analysis of high contact ratio gears system with multiple clearances”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42, (2020), 98.
• [12] Yildirim N., Gasparini G., Sartori S., “An improvement on helicopter transmission performance through use of high contact ratio spur gears with suitable profile modification design”, Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 222, (2008), 1193-1210.
• [13] AGMA 913 A-98, “Method for specifying the geometry of spur and helical gears”, American Gear Manufacturers Association, 1998.
• [14] AGMA 908 B-98, “Geometry factors for determining the pitting resistance and bending strength of spur, helical and herringbone gear teeth”, American Gear Manufacturers Association, 1989.
• [15] AGMA 2101-C95, “Fundamental rating factors and calculation methods for involute spur and helical gear (Metric version)”, American Gear Manufacturers Association, 1995.