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<p>The American Gear Manufacturers Association (AGMA) and the International Organization for Standardization (ISO) have developed widely used analytical methods for the bending stress of internal symmetric spur gears. However, there are no provisions in the AGMA 908-B89, ISO 6336:1996 and ISO 6336:2006 procedures to assess the critical fillet parameters for internal asymmetric spur gears. According to ISO 6336:1996 and ISO 6336:2006, the crucial position in the fillet region of internal symmetric gears is defined by a straight tangent line that forms the 30° and 60° angle with the tooth axis. The angle of the tangent in internal asymmetric gears is not the same on either side of the fillet profiles; the drive side tangent angle is greater than the coast side tangent angle. The equations have been developed to evaluate the coast side tangent angle for the standard drive side tangle angle of 45° and 60° in the modified ISO methods. The present research work provides a detailed analytical procedure for determining the critical parameters at the root fillet region of internal asymmetric gears using the modified ISO methods. A precise multi-pair finite element-based contact analysis is also executed for the internal asymmetric gears to estimate the critical parameters and the corresponding non-dimensional factors which are compared with the modified ISO methods. The influence of drive and coast-side pressure angles on fillet parameters, bending strength, contact strength, and the efficiency of the internal symmetric and asymmetric spur gears is investigated. The bending stress is less in the asymmetric internal spur gear with <i>α</i><sub><i>od</i></sub> / <i>α</i><sub><i>od</i></sub> 25°/20° than symmetric gear with <i>α</i><sub><i>od</i></sub> / <i>α</i><sub><i>od</i></sub> 20°/20°. The maximum Hertzian contact stress is higher in the internal symmetric gear than in the internal asymmetric spur gear. The enhancement of the contact strength is almost 73% in the internal asymmetric spur gear with <i>α</i><sub><i>od</i></sub> / <i>α</i><sub><i>od</i></sub> 30°/20° (<i>σ</i><sub><i>Hmax</i></sub> 476.47) compared with the symmetric gear with <i>α</i><sub><i>od</i></sub> / <i>α</i><sub><i>od</i></sub> 20°/20° (<i>σ</i><sub><i>Hmax</i></sub> 1824.7 MPa).</p>

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Evaluation of Bending Strength and Stress Factor of Internal Asymmetric Spur Gears

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • R. Prabhu Sekar

摘要

The American Gear Manufacturers Association (AGMA) and the International Organization for Standardization (ISO) have developed widely used analytical methods for the bending stress of internal symmetric spur gears. However, there are no provisions in the AGMA 908-B89, ISO 6336:1996 and ISO 6336:2006 procedures to assess the critical fillet parameters for internal asymmetric spur gears. According to ISO 6336:1996 and ISO 6336:2006, the crucial position in the fillet region of internal symmetric gears is defined by a straight tangent line that forms the 30° and 60° angle with the tooth axis. The angle of the tangent in internal asymmetric gears is not the same on either side of the fillet profiles; the drive side tangent angle is greater than the coast side tangent angle. The equations have been developed to evaluate the coast side tangent angle for the standard drive side tangle angle of 45° and 60° in the modified ISO methods. The present research work provides a detailed analytical procedure for determining the critical parameters at the root fillet region of internal asymmetric gears using the modified ISO methods. A precise multi-pair finite element-based contact analysis is also executed for the internal asymmetric gears to estimate the critical parameters and the corresponding non-dimensional factors which are compared with the modified ISO methods. The influence of drive and coast-side pressure angles on fillet parameters, bending strength, contact strength, and the efficiency of the internal symmetric and asymmetric spur gears is investigated. The bending stress is less in the asymmetric internal spur gear with αod / αod 25°/20° than symmetric gear with αod / αod 20°/20°. The maximum Hertzian contact stress is higher in the internal symmetric gear than in the internal asymmetric spur gear. The enhancement of the contact strength is almost 73% in the internal asymmetric spur gear with αod / αod 30°/20° (σHmax 476.47) compared with the symmetric gear with αod / αod 20°/20° (σHmax 1824.7 MPa).