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摘要: 为了提高疲劳强度评定和疲劳寿命预测的可靠性与精度, 基于结构可测位置应力提出了全域应力推演方法进行任意位置的应力预测。引入了基于无网格计算的径向基函数插值理论, 建立了新的插值域选择规则, 改进了传统Multi-Quadric(M-Q)径向基函数。为了验证改进的M-Q径向基函数的插值性能, 在对转向架构架施加横向载荷为58 kN, 牵引载荷为55 kN, 垂向载荷为85 kN, 选取了应力不可直接测量的8个位置, 分别采用改进的M-Q径向基函数与薄板样条(TPS)径向基函数进行插值精度比较。分析结果表明: 采用改进的M-Q径向基函数预测的应力最大相对误差为0.090 6%, 平均相对误差为0.028 4%, 采用TPS径向基函数预测的应力最大相对误差为1.611 3%, 平均相对误差为0.604 2%, 因此, 采用改进的M-Q径向基函数推演转向架构架应变片不可测位置应力的计算精度远优于采用TPS径向基函数的精度; 结合改进的M-Q径向基函数插值算法, 开发了一套车辆转向架全域应力推演和实时监控系统(TPL Monitoring), 具有良好的交互性、实时性和可扩展性。Abstract: In order to improve the reliability and accuracy of fatigue strength evaluation and fatigue life prediction, on the basis of the stresses at the predictable positions on the structure, a whole-field stress prediction method was proposed to predict the stresses at the arbitrary positions, a meshless computation-based radial basis function interpolation theory was introduced, a novel selection rule of interpolation domain was built, and the traditional multiquadric (M-Q) radial basis function was refined.In order to verify the interpolation performance of modified M-Q radial basis function, under the condition of exerting 58 kN lateral force, 55 kN longitudinal force and 85 kN vertical force loading on the frame of vehicle bogie, 8 stress unmeasurable positions on the frame were selected, and the interpolation accuracies were compared between the modified M-Q radial basis function and the thin plate spline (TPS) radial basis function.Analysis result shows that the maximal and average relative errors of stress by using the modified M-Q radial basis function are 0.090 6% and 0.028 5% respectively, while the values by using the TPS radial basis function are 1.611 3% and 0.604 2% respectively, so the calculation accuracy of modified M-Q radial basis function is much more better than the value ofTPS radial basis function in predicting the stresses at the unmeasurable positions on the frame of vehicle bogie.Combining with the interpolation algorithm based on the modified M-Q radial basis function, a fatigue strength monitoring system named TPL monitoring for vehicle bogie is developed, and has better interactivity, real-time property and scalability.
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图 4 不同c值的M-Q径向基函数曲线
Figure 4. Curves of M-Q radial basis function with different c values
图 6 改进的M-Q和TPS径向基函数相对误差比较
Figure 6. Comparison of relative errors between modified M-Q and TPS radial basis functions
表 1 改进的M-Q和TPS径向基函数推演结果
Table 1. Prediction results of modified M-Q and TPS radial basis functions
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