Issue 48

B. Chen et alii, Frattura ed Integrità Strutturale, 48 (2019) 385-399; DOI: 10.3221/IGF-ESIS.48.37 394 where v denotes basic input variables, ( ) g v is the performance function, ( ) X f v is the joint probability density function of a random variables, ( ) V p v is the assumed importance sampling density(ISD). Obviously, the success of importance sampling relies on the proper choice of ISD. The optimal ISD can be drawn through theoretical analysis [19]. [ ( )] ( ) ( ) X X opt f I g v f v p v P = (6) In order to illustrate the influence of uncertainties in design parameters on control points, 46 experimental design control points are given based on Tab. 7. Comparing Fig. 3 and Fig. 10 it is seen that due to the uncertainty of design parameters, the control points show a large degree of discreteness, which greatly exceeds the evaluation range of fatigue limit of bogie frame. Fig. 11 plots the distribution of control points based on importance sampling method. It can be clearly seen from the figure that the fluctuation of design parameters leads to a greater dispersion of control points. Comparing Fig. 10 and Fig. 11 shows that the distribution of the control points in the dense area is reasonable, which can reflect the influence of the fluctuation of the over-standard points near the fatigue limit diagram on the fatigue strength analysis results well. Compared with the deterministic model, the results of uncertainty analysis are more in line with engineering practice. Figure 10 : The fluctuation of control points under uncertain factors Figure 11 : Importance sampling results of control points Functional expression of Goodman-Smith fatigue limit diagram GSFLD is widely used in fatigue strength checking of materials in the world. At present, most railway rolling stock adopt modified GSFLD to design fatigue strength of its parts. The modified Goodman curves are generally divided into two forms: Haigh graphics and Smith graphics. In this paper, the modified GSFLD is used to evaluate the fatigue strength of the frame [20]. The determination of the modified GSFLD requires three limit values, i.e. strength limit  b and yield limit yt  of materials and fatigue limit  − 1 N of frame. According to Tab. 3, the yield strength of the material is 345 MPa. The ultimate strength of S355J2(H) material is 520 MPa. In the traditional GSFLD, when calculating the fatigue limit  − 1 N of frame, factors such as size, shape and surface machining quality are involved in the calculation in the form of safety factor. -1 -1 1 1 = =38+0.43 N f b k       − − (7) where -1  is the surface machining factor,  is the size factor, f k is the stress concentration factor. As can be seen from Eqn. (7), the calculation of fatigue limit -1 N  based on safety factor is too conservative, resulting in high redundancy of fatigue strength, which is not conducive to the lightweight design of the frame. Therefore, GSFLD