Prediction of fretting fatigue life with consideration of stress gradient and relative slip amplitude
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摘要:
以TC11钛合金为研究对象，基于临界平面法以及应力场强法的思想建立了考虑应力梯度的微动疲劳寿命预测模型。该模型以疲劳影响区域内的SWT（Smith-Watson-Topper）临界平面损伤参量的场强预测微动疲劳寿命；以普通单轴疲劳试验机和横向液压加载装置为试验平台，设计了可调切向刚度夹持装置，开展了考虑相对滑移幅值影响的微动疲劳试验，试验表明在相同力载荷下随着相对滑移幅值的增加微动疲劳寿命先减小后增加。结合文献中已有的微动疲劳试验数据，对寿命预测模型参数进行拟合并在寿命模型中引入相对滑移幅值参量，形成了考虑应力梯度以及相对滑移幅值影响的微动疲劳寿命预测方法。利用文献中燕尾榫结构模拟件的微动疲劳试验结果对本文形成的寿命预测方法进行验证，预测寿命和试验平均寿命相比误差在3倍分散带以内。
Abstract:Focusing on TC11 titanium alloy, a fretting fatigue life prediction method considering stress gradients was established by employing the critical plane method and stress field intensity approach. This life prediction model could predict fretting fatigue life by forecasting the stress field intensity of the SWT （Smith-Watson-Topper） critical plane damage parameter within the fatigue-affected region. Using a conventional uniaxial fatigue testing machine and a transverse hydraulic loading device, a tunable tangential stiffness clamping device was designed, and fretting fatigue tests considering the influence of relative slip amplitude were conducted. The tests indicated that under the same force load, the fretting fatigue life initially decreased and then increased with the increase of relative slip amplitude. The model parameters were fitted by combining fretting fatigue test data, and the relative slip amplitude parameter was introduced into the life model, which resulted in a fretting fatigue life prediction method considering the effects of stress gradients and relative slip amplitude. The validity of the proposed method was verified using fretting fatigue test results of dovetail joint structure, with a prediction error within a 3 times dispersion band compared with testing average life.
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图 3 微动疲劳简化有限元模型示意图
Figure 3. Schematic diagram of the simplified fretting fatigue finite element model
图 5 赫兹接触解和有限元解对比
Figure 5. Comparison between Hertzian contact solutions and finite element solutions
图 6 工况A3滑移幅值随接触面x坐标分布情况
Figure 6. Distribution of slip amplitude along the contact interface （x-coordinate） for case A3
图 7 SWT参量计算所选区域示意图
Figure 7. Schematic of the selected region for SWT parameter calculation
图 8 工况A6 SWT参量随接触面x坐标分布情况
Figure 8. Distribution of SWT parameters along the contact interface （x-coordinate） for case A6
图 11 可调刚度夹具结构示意图
Figure 11. Schematic diagram of a tunable tangential stiffness clamping device
图 13 试验件微动垫尺寸图（单位：mm）
Figure 13. Dimension of fretting fatigue main specimen and pad (unit：mm)
图 14 峰谷值下相对滑移距离分布
Figure 14. Distribution if relative slip distance under peak-valley conditions
图 15 接触表面相对滑移幅值随x坐标分布
Figure 15. Distribution of relative slip amplitude on the contact surface along the x-coordinate
图 16 微动疲劳试验寿命随相对滑移幅值变化
Figure 16. Variation of fretting fatigue life with relative slip amplitude
图 17 微动疲劳预测寿命与试验寿命对比图
Figure 17. Comparison of the predicted life with the testing observed lives
图 18 微动疲劳预测寿命和试验寿命随相对滑移幅值变化曲线图
Figure 18. Variation of the predicted and testing fretting fatigue life with relative slip amplitude
图 21 燕尾榫结构微动疲劳预测寿命与试验寿命对比
Figure 21. Comparison of the dovetail joint structure’s fretting fatigue lives between prediction and test
疲劳常数 $\sigma _{{\mathrm{f}}}' $/MPa $\varepsilon _{{\mathrm{f}}}' $ b c 数值 1568 0.469 −0.1 −0.88 
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表 2 有限元接触算法验证载荷表
Table 2. Load table for verification of finite element contact algorithm
工况 1 2 压力载荷/MPa 40 60
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表 3 引用文献的微动疲劳寿命试验及分析结果[22, 26]
Table 3. Fretting fatigue life testing and analysis results from the literature[22, 26]
工况 应力/MPa 平均寿命/
循环数危险点相对
滑移幅值/µm法向 轴向 A1 65.45 200 172997 1.5 A2 65.45 300 26002 6 A3 65.45 400 25065 28 A4 98.17 400 15322 7.5 A5 130.90 200 109307 0.2 A6 130.90 300 24989 6 A7 130.9 400 12856 3 A8 229.07 300 26410 0.2 A9 229.07 400 8375 0.4 B1 65.45 400 88863 59
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表 4 试验工况fSWT,max计算结果
Table 4. fSWT,max calculation results for the test conditions
MPa 工况 fSWT,max 工况 fSWT,max A1 2.81 A6 8.67 A2 3.05 A7 10.83 A3 4.04 A8 9.18 A4 5.43 A9 14.23 A5 3.72 B1 4.01
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表 5 各工况下最佳预测寿命结果的H参量值
Table 5. The best results of H parameter for all cases
工况 H/μm 工况 H/μm A1 15 A6 60 A2 8 A7 75 A3 25 A8 60 A4 40 A9 120 A5 30 B1 40
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表 6 式（14）拟合参数结果
Table 6. Fitting results of equation (14)
参数 数值 参数 数值 a1 703500 k1 0.0357 a2 −0.585 k2 28 a3 1.39 b1 −29.093
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表 7 钛合金TC11微动疲劳试验件分配
Table 7. The series of TC11 titanium alloy fretting fatigue specimen
工况 应力/MPa 轴向
载荷比相对滑移
幅值/µm试验件
件数法向 轴向 TC_1 65.45 400 0.1 11 3 TC_2 65.45 400 0.5 10 3 TC_3 65.45 400 0.1 0 3
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表 8 微动疲劳寿命试验结果
Table 8. Testing results of fretting fatigue lives
工况 试验寿命/
循环数试验平均寿命/
循环数TC_1 47300 51373 54803 52018 TC_2 422000 332981 252613 324332 TC_3 82205 83617 93843 74804
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表 9 相对滑移幅值计算结果
Table 9. Calculated results of relative slip amplitude
工况 TC_1 TC_2 TC_3 相对滑移幅值/µm 11 10 0
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表 10 微动疲劳寿命预测表
Table 10. Predicted fretting fatigue lives
工况 fSWT,fi/MPa 预测寿命/
循环数平均寿命/
循环数A1 1.730 117846 172997 A2 2.049 51102 26002 A3 2.457 21070 25065 A4 2.549 17647 15322 A5 1.757 109143 109307 A6 2.574 17713 24989 A7 2.460 20946 12856 A8 2.279 30355 26410 A9 3.144 6544 8375 B1 1.671 139969 88863 TC_1 2.031 53497 51373 TC_2 1.437 303561 332981 TC_3 1.671 140385 83617
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工况 轴向
载荷/kN相对滑移
幅值/µm圆弧
半径/mm试验寿命/
循环数Dove_1 11 14 平面 91903 Dove_2 13 16 平面 45285 Dove_3 17 20 平面 20081 Dove_4 11 14 30 200439 Dove_5 13 16 30 74819 Dove_6 17 22 30 24654 Dove_7 11 14 50 172621 Dove_8 13 16 50 65544 Dove_9 17 20 50 26610 Dove_10 11 13 100 129756 Dove_11 13 15 100 45030 Dove_12 17 20 100 19906
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表 12 榫连接模拟试验件寿命预测结果
Table 12. Fretting fatigue predicted lives of dovetail joint structure
工况 H/µm fSWT,fi/
MPa预测寿命/
循环数试验寿命/
循环数Dove_1 45 1.870 80376 91903 Dove_2 87 1.837 87560 45285 Dove_3 172 2.23 33670 20081 Dove_4 35 1.741 114528 200439 Dove_5 58 1.871 79973 74819 Dove_6 94 2.332 27135 24654 Dove_7 17 1.725 119720 172621 Dove_8 46 1.792 98975 65544 Dove_9 90 2.320 27769 26610 Dove_10 16 1.475 260179 129756 Dove_11 13 2.385 24137 45030 Dove_12 62 3.060 7406 19906
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