多误差作用下花键载荷分配和可靠性分析

赵庆岩; 赵志豪; 鲁婷婷; 庄新臣; 喻天翔

doi:10.13224/j.cnki.jasp.20240771

多误差作用下花键载荷分配和可靠性分析

doi: 10.13224/j.cnki.jasp.20240771

赵庆岩^{1, 2,},
赵志豪³,
鲁婷婷³,
庄新臣^{1, 2},
喻天翔^{1, 2,*, ,}

1.
西北工业大学航空学院，西安 710072
2.
飞行器基础布局全国重点实验室，西安 710072
3.
中国航发湖南动力机械研究所，湖南株洲 412002

基金项目: 国家自然科学基金（52075443）

详细信息

作者简介:
赵庆岩（1993-），男，博士生，主要从事飞机结构、机构可靠性设计。E-mail：iqyzhao@163.com

通讯作者:
喻天翔（1977-），男，教授，博士，主要从事飞行器可靠性工程、飞行器创新机构设计等。E-mail：tianxiangyu@nwpu.edu.cn

中图分类号: V215.7
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- 被引次数: 0
出版历程
- 收稿日期: 2024-11-15
- 网络出版日期: 2026-03-23

Load distribution and reliability analysis of splines under multiple errors

ZHAO Qingyan^{1, 2
,},
ZHAO Zhihao³,
LU Tingting³,
ZHUANG Xinchen^{1, 2},
YU Tianxiang^{1, 2,*
, ,}

1.
School of Aeronautics，Northwestern Polytechnical University，Xi’an 710072，China
2.
National Key Laboratory of Aircraft Configuration Design，Xi’an 710072，China
3.
Hunan Aviation Powerplant Research Institute，Aero Engine Corporation of China，Zhuzhou Hunan 412002，China

摘要

摘要:
加工误差、平行不对中和角向不对中导致花键各齿受载不均，严重影响其使用寿命和可靠性。针对以上问题，提出了一种考虑多误差作用的花键载荷分配模型和可靠性分析方法。首先，考虑不同误差对花键齿形位的影响，推导了一定误差和不对中量下的花键不均匀齿间隙。在此基础上，根据扭矩对花键轴扭转变形和齿弹性变形的影响，建立了花键沿轴向的不均匀扭矩分配计算模型，获得了各齿上的不均匀载荷，并通过仿真验证了所提模型的准确性。最后，根据经典疲劳损伤准则，建立了花键疲劳可靠性模型。案例分析表明：在经历10⁶次循环载荷作用后，公差等级由4下降至6时，花键的可靠度降低了0.011；平行不对中由0.01 mm增至0.03 mm时，可靠度下降了0.054；而角向不对中由0.01°增至0.03°时，可靠度则降低了0.935。不对中对花键可靠性的影响显著，特别角向不对中的增大导致花键可靠度大幅降低。
- 花键 /
- 加工误差 /
- 平行不对中 /
- 角向不对中 /
- 载荷分配 /
- 可靠性
Abstract:
Machining errors, parallel misalignment, and angular misalignment lead to uneven load distribution on spline teeth, significantly impacting their life and reliability. To address these issues, a spline load distribution model and reliability analysis method accounting for multiple errors were proposed. First, the effects of different errors on the shape and position of spline teeth were analyzed, and the uneven tooth clearance was derived. Based on this, a model for uneven torque distribution along the axial direction was developed, which incorporated the effects of torque on the torsional deformation of the spline shaft and the elastic deformation of the teeth. The accuracy of the proposed model was validated through finite element analysis. Finally, a spline fatigue reliability model was developed using classical fatigue damage criteria. Case analysis showed that after 10⁶ cycles of load, when the tolerance class decreased from 4 to 6, the spline reliability decreased by 0.011; when the parallel misalignment increased from 0.01 mm to 0.03 mm, the spline reliability decreased by 0.054; and when the angular misalignment increased from 0.01° to 0.03°, the spline reliability decreased by 0.935. The influence of misalignment on spline reliability was significant, especially the increase of angular misalignment led to a significant decrease in spline reliability.
- spline /
- machining errors /
- parallel misalignment /
- angular misalignment /
- load distribution /
- reliability

HTML

图 1 加工误差对间隙的影响

Figure 1. Influence of machining error on clearance

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图 2 平行不对中花键及间隙

Figure 2. Spline with parallel misalignment and its clearance

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图 3 角向不对中花键

Figure 3. Spline with angular misalignment

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图 4 花键承载示意图

Figure 4. Schematic diagram of spline bearing

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图 5 无误差花键配合模型

Figure 5. Error-free spline fit model

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图 6 花键等效载荷分配模型

Figure 6. Equivalent load distribution model of spline

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图 7 花键有限元仿真及接触力云图

Figure 7. Finite element simulation and contact force cloud map of spline

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图 8 有限元仿真与模型计算的轴向扭矩分布

Figure 8. Distribution of axial torque calculated by the finite element simulation and the proposed model

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图 9 花键疲劳载荷谱

Figure 9. Spline fatigue load spectrum

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图 10 最小齿间隙概率密度

Figure 10. Probability density of minimum tooth clearance

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图 11 花键齿根等效弯曲应力幅值分布

Figure 11. Equivalent bending stress amplitude distribution at tooth root

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图 12 考虑加工误差时花键的可靠度

Figure 12. Reliability of spline with machining errors

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图 13 花键3种不对中组合情况

Figure 13. Three misalignment combinations of spline

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图 14 不同情况下花键最小齿间隙概率密度

Figure 14. Probability density of minimum tooth clearance under different conditions

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图 15 高周循环下齿根等效弯曲应力幅值分布

Figure 15. Equivalent bending stress amplitude distribution at tooth root under high cycle

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图 16 低周循环下齿根等效弯曲应力幅值分布

Figure 16. Equivalent bending stress amplitude distribution at tooth root under low cycle

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图 17 情况1时花键的可靠度

Figure 17. Reliability of spline with condition 1

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图 18 情况2时花键的可靠度

Figure 18. Reliability of spline with condition 2

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图 19 情况3时花键的可靠度

Figure 19. Reliability of spline with condition 3

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表 1 花键基本参数

Table 1. Basic parameters of the spline

参数	数值
齿数z	24
模数m/mm	2.5
标准压力角α_D/（°）	30
花键轴向接触长度L/mm	30
配合类别	H/f

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表 2 花键材料参数

Table 2. Spline material parameters

名称	材料	弹性模量/ GPa	泊松比	抗拉强度极限σ_b/MPa
内花键	38CrMoAl	210	0.28	1100
外花键	40Cr钢	205	0.3	835

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表 3 内、外花键加工误差中各随机变量的分布参数

Table 3. Distribution parameters of variables in the machining errors of internal and external splines

误差类型	分布类型	公差等级	均值/ mm	标准差/ 10⁻³ mm
分度误差	正态分布	4	0	3.00
		5	0	3.42
		6	0	4.08
齿槽宽误差	正态分布	4	3.96	4.33
		5	3.98	7.50
		6	4.01	12.17
齿厚误差	正态分布	4	3.86	4.33
		5	3.84	7.50
		6	3.82	12.17
齿向误差	正态分布	4	0	2.79
		5	0	3.49
		6	0	4.38

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表 4 考虑加工误差的齿间隙分布参数

Table 4. Distribution parameters of clearances considering machining errors

公差等级	分布类型	均值/mm	标准差/10⁻³ mm
4	正态分布	0.049	5.58
5	正态分布	0.0675	7.57
6	正态分布	0.0955	10.85

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表 5 花键齿根的S-N曲线数值点（R=−1）

Table 5. Points of S-N curve for spline root （R=−1）

寿命N	等效应力$ {\sigma }_{\text{F,e}} $/MPa
10⁵	250
5×10⁵	214
10⁶	204
5×10⁶	200
10⁷	197

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