Research on the parameterized proxy model of surface wear of sliding bearings in aviation fuel gear pumps
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摘要:
滑动轴承磨损退化是影响航空燃齿泵寿命和可靠性的重要因素之一，以此为对象的数值仿真模型在不断提高与试验结果的拟合程度的同时也牺牲了计算效率，不利于其应用于工程实践。对此，针对轴承磨损过程提出了一种将磨损量参数化后建立高斯过程模型的方法，通过将不同转速、偏心率和磨损时间下的磨损量周向分布进行参数化，简化了输入输出参数，构建了计算效率远高于传统仿真方法的数据驱动模型。在此基础上，研究了模型预测结果在不同训练集、不同工况和磨损时间下的误差和置信程度，并通过对比试验结果与模型预测验证了模型的准确性。研究发现：选取合适训练集的可以部分改善模型预测效果，表现为95%置信区间的收窄；以轴颈转速、偏心率和磨损时间分别为自变量时，预测模型给出的结果与仿真模型均有较高的一致性，最大相对误差为5.26%，进一步的，通过将模型预测与相同工况下的试验结果对比发现其相对误差低于5%，符合精度需求，预测模型的合理性得以验证；以磨损时间为自变量时平均绝对误差最低，仅0.001 µm，以偏心率为自变量时最高，为1.33 µm；进一步对比研究发现，模型预测的误差来自参数化过程的系统误差和高斯过程回归模型的系统误差两个方面，并分析了不同工况、磨损时间下预测误差的主导因素。
Abstract:The wear and degradation of sliding bearings is one of the important factors affecting the life and reliability of aviation fuel pumps. The numerical simulation model based on this object sacrifices computational efficiency while continuously improving the fitting degree with test results, which is not conducive to its application in engineering practice. This article proposes a method of parameterizing the wear amount and establishing a Gaussian process model. By parameterizing the circumferential distribution of wear amount at different speeds, eccentricities, and wear times, the input-output parameters are simplified, and a Gaussian process regression model with much higher computational efficiency than traditional simulation methods is constructed. On this basis, the error and confidence level of the model prediction results were studied under different training sets, operating conditions, and wear times, and the accuracy of the model was verified by comparing the test results with the model prediction. Research has found that selecting an appropriate training set can partially improve the predictive performance of the model, manifested as a narrowing of the 95% confidence interval; When the journal speed, eccentricity, and wear time are used as independent variables, the results provided by the prediction model are highly consistent with the simulation model, with a maximum relative error of 5.26%. Furthermore, by comparing the model predictions with test results under the same operating conditions, it was found that the relative error was less than 5%, which meets the accuracy requirements and validates the rationality of the prediction model. The rationality of the prediction model is verified; When using wear time as the independent variable, the average absolute error is the lowest, only 0.001 µm, and when using eccentricity as the independent variable, it is the highest, at 1.33 µm; Further comparative studies have found that the prediction errors of the model come from two aspects: systematic errors in the parameterization process and systematic errors in the Gaussian process regression model. The dominant factors of prediction errors under different operating conditions and wear times have been analyzed.
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图 1 燃油齿轮泵滑动轴承结构示意图
Figure 1. Schematic diagram of sliding bearing structure for fuel gear pump
图 2 粗糙表面间隙下润滑油膜示意图
Figure 2. Schematic diagram of lubricating oil film under rough surface gaps
图 4 仿真计算结果与Ferron轴承试验结果的对比
Figure 4. Comparison between simulation results and Ferron bearing test results
图 5 发生磨损时的Ferron轴承仿真计算结果
Figure 5. Simulation results of Ferron bearings when wear occurs
图 6 轴承磨损训练数据及GPR模型磨损预测结果
Figure 6. Bearing wear training data and GPR model wear prediction results
图 7 同一工况下轴瓦磨损量在4个时刻的仿真计算结果与GPR模型预测结果的对比及1 000 h内相对误差
Figure 7. Comparison of simulation calculation results and GPR model prediction results of bearing wear at 4 time points under the same operating conditions, and relative error within
1000 hours
图 8 同一工况下轴瓦磨损量随时间变化的仿真与预测结果的对比
Figure 8. Comparison of simulation and prediction results of the variation of bearing wear over time under the same operating conditions
图 9 同一时刻不同转速下轴瓦磨损量的仿真计算结果与GPR模型预测的对比及80%～120%相对转速的相对误差
Figure 9. Comparison between simulation calculation results of bearing wear at different speeds at the same time and GPR model prediction, and relative error of 80% to 120% relative speed
图 10 同一时刻不同转速下轴瓦磨损量的仿真计算结果与GPR模型预测的对比
Figure 10. Comparison between simulation results of bearing wear at different speeds at the same time and GPR model prediction
图 11 同一时刻不同偏心率下轴瓦磨损量的仿真计算结果与GPR模型预测的对比及偏心率0.7～0.9之间的相对误差
Figure 11. Comparison between simulation results of bearing wear under different eccentricities at the same time and GPR model prediction, and relative error between eccentricities of 0.7 to 0.9
图 12 同一时刻不同偏心率下轴瓦磨损量的仿真计算结果与GPR模型预测的对比
Figure 12. Comparison between simulation results of bearing wear under different eccentricities at the same time and GPR model prediction
表 1 Ferron轴承参数
Table 1. Parameters of Ferron bearings
参数 数值 参数 数值 轴承宽度/mm 80 额定转速/（r/min） 4000 轴孔直径/mm 100 环境温度/K 313.15 轴颈直径/mm 99.71 供油温度/ K 313.15 轴瓦导热系数/（W/（m·K）） 100 介质密度/（kg/m3） 860 轴颈导热系数/（W/（m·K）） 50 介质黏度/Pa·s 0.0277 轴瓦密度/（kg/m3） 7850 介质比热容/（J/（kg·K）） 2 000 进口压力/MPa 0.07 介质体积模量/108 Pa 5 出口压力/MPa 0.07 介质导热系数/（W/（m·K）） 0.13 
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表 2 仿真对象参数
Table 2. Parameters of simulation objects
参数 数值 参数 数值 轴承宽度/mm 24 额定转速/（r/min） 7733 轴孔直径/mm 20.01 环境温度/K 313.15 轴颈直径/mm 19.94 供油温度/K 313.15 轴瓦导热系数/（W/（m·K）） 100 介质密度/（kg/m3） 860 轴颈导热系数/（W/（m·K）） 50 介质黏度/10−3 （Pa·s） 0.842 3 轴瓦密度/（kg/m3） 7850 介质比热/（J/（kg·K）） 2 000 进口压力/MPa 8.5 介质体积模量/108 Pa 5 出口压力/MPa 0.5 介质热传导/（W/（m·K）） 0.13
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表 3 试验载荷谱
Table 3. Test load spectrum set
参数 数值 转速/（r/min） 6000 ±10进口油压/MPa 0.872± 0.0025 出口油压/MPa 7.55±0.1 额定压差/MPa 6.678 进口温度/K 327.15±10 试验时间/s 540000
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