Issue 48

B. Chen et alii, Frattura ed Integrità Strutturale, 48 (2019) 385-399; DOI: 10.3221/IGF-ESIS.48.37 391 F ATIGUE STRENGTH ANALYSIS OF BOGIE FRAME IN CONSIDERATION OF PARAMETERS UNCERTAINTY Establishment of polynomial response surface function raditional fatigue strength analysis based on deterministic model can't reflect the influence of uncertainty factors such as size and shape on fatigue strength. Therefore, taking the maximum fatigue strength as the control point and analyzing its fluctuation under the influence of uncertainty factors can effectively characterize the fatigue strength reliability of the frame and provide a basis for lightweight design. In view of this, this study chooses the parameters which have a large impact on fatigue strength of control point as uncertainty variables, and uses APDL language to establish a parametric finite element model. In order to improve the computational efficiency, the D-optimal experimental design is used to select sample points, and the polynomial response surface surrogate model is adopted to characterize the functional relationship between variables and responses [15-17]. According to the fatigue strength analysis results of Fig. 3 and Fig. 4, the node number 287745 is taken as the control point, and the influence of uncertainties on it is calculated. Tab. 6 and Tab. 7 show the range of variables and the D-optimal experimental design process, respectively. Design parameters Sign Unit Lower limit Mean value Upper limit Cross beam t 1 mm 15 16 17 Vertical inertia F 1 kN -21.84 -20.8 -19.76 Transverse inertia F 2 kN -21.84 -20.8 -19.76 Longitudinal inertia F 3 kN -21.84 -20.8 -19.76 Vertical inertia F 4 kN 29.64 31.2 32.76 Transverse inertia F 5 kN 19.76 20.8 21.84 Longitudinal inertia F 6 kN 19.76 20.8 21.84 Table 6 : Uncertainty design parameters. Run number Factors Response t 1 (mm) F 1 (kN) F 2 (kN) F 3 (kN) F 4 (kN) F 5 (kN) F 6 (kN) X Y 1 15 -19.76 -19.76 -19.76 31.1844 21.84 19.76 12.4326 118.454 2 15 -19.76 -21.7568 -21.84 30.108 20.9917 21.84 14.3174 121.604 3 15 -21.84 -21.84 -19.76 29.64 19.76 19.76 11.2513 117.517 … … … … … … … … … … 44 17 -19.76 -21.84 -19.76 29.64 19.76 19.76 7.86325 112.135 45 17 -21.84 -19.76 -21.84 29.64 19.76 21.84 8.02718 113.298 46 17 -21.84 -21.84 -19.76 29.64 19.76 21.84 6.61196 113.293 Table 7 : D-optimal experimental design and response value. The polynomial response function with cross-terms is obtained by fitting the sample points obtained by experiment design with the least square method and the basic equation is given by 2 0 1 1 n n n ii i ij i j i i i i j i y c x c x x c x c =  = = + + +    (2) where n is the number of uncertain variables, 0 c is the constant, and i c , ii c , and ij c are the polynomial coefficients, respectively. According to Eqn. (2), the experimental data in Tab. 7 are fitted to obtain the response surface function of the control point coordinates, in which X represents the mean stress and Y represents the stress amplitude. T