Comparative analysis of root bending strength calculation for spiral bevel gears based on HB, ISO standard and AGMA standard

WANG Qiuju; WEI Jing; CHEN Siyu; XING Bin; SONG Zhenhai; TAN Yuxin

doi:10.16578/j.issn.1004.2539.2026.03.002

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Comparative analysis of root bending strength calculation for spiral bevel gears based on HB, ISO standard and AGMA standard

Structural Design and Parameter Optimization | 更新时间：2026-05-27

- Comparative analysis of root bending strength calculation for spiral bevel gears based on HB, ISO standard and AGMA standard
- Journal of Mechanical Transmission Vol. 50, Issue 3, Pages: 11-22(2026)
- 作者机构：
  
  1.中国航空发动机集团有限公司沈阳发动机研究所，沈阳 110015
  2.中国航空发动机集团有限公司航空发动机动力传输航空科技重点实验室，沈阳 110015
  3.重庆大学高端装备机械传动全国重点实验室，重庆 400044
- 作者简介：
- 基金信息：
- DOI：10.16578/j.issn.1004.2539.2026.03.002
  CLC： TH113
- Received：14 November 2024，
  
  Revised：2025-01-06，
  
  Published：15 March 2026
- 稿件说明：
移动端阅览
王秋菊，魏静，陈思宇，等. 基于HB、ISO标准与AGMA标准的弧齿锥齿轮齿根弯曲强度计算对比分析［J］. 机械传动，2026，50（3）：11-22.

WANG Qiuju，WEI Jing，CHEN Siyu，et al. Comparative analysis of root bending strength calculation for spiral bevel gears based on HB, ISO standard and AGMA standard［J］. Journal of Mechanical Transmission，2026，50（3）：11-22.
王秋菊，魏静，陈思宇，等. 基于HB、ISO标准与AGMA标准的弧齿锥齿轮齿根弯曲强度计算对比分析［J］. 机械传动，2026，50（3）：11-22. DOI： 10.16578/j.issn.1004.2539.2026.03.002.

WANG Qiuju，WEI Jing，CHEN Siyu，et al. Comparative analysis of root bending strength calculation for spiral bevel gears based on HB, ISO standard and AGMA standard［J］. Journal of Mechanical Transmission，2026，50（3）：11-22. DOI： 10.16578/j.issn.1004.2539.2026.03.002.

摘要

目的

针对我国航空行业标准（简称HB）、国际标准化组织（International Organization for Standardization

ISO）标准和美国齿轮制造商协会（American Gear Manufacturers Association

AGMA）标准中，强度校核基准对弧齿锥齿轮齿根弯曲强度评价的差异性问题，通过对比分析得出弧齿锥齿轮设计的最佳策略。

方法

首先，基于各自标准的基础数学模型，分析了3种标准的本质差别；然后，从原理性上探究了3种标准的弯曲应力和强度安全系数的影响参数及其对应的影响机制；最后，通过实例分析进一步探究了由3种标准得到的应力结果的影响规律和强度计算结果的差异。

结果

研究结果表明，ISO标准、HB利用30°切线法确定危险截面，并将载荷作用点选在齿顶进行计算；而AGMA标准利用抛物线法确定危险截面，并将载荷作用点选在危险点进行计算；由这2种方法求得的齿形系数及应力修正系数稍有不同。依据修正系数及其对应的计算公式，AGMA标准中的几何系数

代替了HB、ISO标准中的多个修正系数，所以，AGMA标准的计算过程最简便，引入修正系数的个数最少。依据修正系数及应力计算结果，ISO标准的应力结果大于HB的结果，且远大于AGMA标准的结果；ISO标准中的齿形系数、载荷分担系数、重合度系数的取值与HB中的相应系数相近；动载系数、应力修正系数及螺旋线载荷分布系数的取值与HB、AGMA标准中的相应系数的差异较大。依据这3种标准得到的弯曲应力的变化规律，齿数、模数、螺旋角、压力角、齿宽及设计转速等参数对弯曲应力的影响较大。

Abstract

Objective

Addressing the issue of difference in the evaluation of tooth root bending strength for spiral bevel gears based on the strength verification benchmarks in Aviation Industry Standard of China (HB for short)

International Organization for Standardization (ISO) standard

and American Gear Manufacturers Association (AGMA) standard

a comparative analysis was conducted to derive the optimal strategy for the design of spiral bevel gear.

Methods

Firstly

based on the foundational mathematical models of each standard

the essential differences among the three standards were analyzed. Secondly

the influence parameters and their corresponding influence mechanisms of bending stress and strength safety factors obtained from the three standards were investigated from a theoretical perspective. Finally

through case analysis

the influence law of stress results and differences in strength calculation results obtained from the three standards were further explored.

Results

The results show that ISO standard and HB use the 30° tangent method to determine the dangerous section and select the load point at the top of the tooth for calculation

while AGMA standard uses the parabolic method to determine the dangerous section and select the load point at the dangerous points for calculation. Compared with the 30° tangent method

the chord tooth thickness and bending moment arm obtained by the parabola method are more accurate

so the tooth form coefficient and stress correction coefficient obtained by the two methods are slightly different. According to the correction coefficients and their corresponding calculation formula

because the geometric coefficient

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2.62466669

3.21733332

in AGMA standard replaces multiple correction coefficients in HB and ISO standard

the AGMA standard has the most concise calculation process and introduces the least number of correction coefficients. According to the correction coefficients and stress calculation results

the stress results of ISO standard are larger than those of HB and much larger than those of AGMA standard. The values of the tooth form coefficient

load sharing coefficient and coincidence coefficient in ISO standard are similar to those of HB

while the values of dynamic load coefficient

stress correction coefficient and helix load distribution coefficient are significantly different from those of HB and AGMA standard. According to the vari

ation law of bending stresses obtained from the three standards

the parameters such as tooth number

modulus

spiral angle

pressure angle

tooth width and design speed have great influence on the bending stress.

关键词

Keywords

references

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