PSI - Issue 54

V.M.G. Gomes et al. / Procedia Structural Integrity 54 (2024) 561–567 Author name / Structural Integrity Procedia 00 (2023) 000–000

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B

Fig. 2. Installation of the running gear system instrumented with strain gauges and vertical potentiometer.

2.3. Numerical Model

A computational model of the parabolic leaf spring in a freight wagon is developed in ANSYS FEM code to evaluate the structural behaviour when operating under a real loading spectrum (see Fig. 3). Being and numerical problem with physical and geometrical symmetries, only a quarter of full model is considered (with XY and YZ as symmetry planes).

Fig. 3. Representation of the 1 / 4 of geometric model for structural analysis due to the vertical vehicular dynamics,

For the investigation of the structural behaviour of the leaf spring under the real operating conditions, only vertical loading with very sti ff er springs representing the double link is considered. The solution of the equations system (1) is obtained by LDLT factorization using the Sparse direct method and a Newton-Raphson procedure in a static analysis solver, with convergence criterion, the L 2-Norm, such that: K ( n )( i ) t + K ( n )( i ) c ∆ u ( n )( i ) = F ( n )( i ) ext + F ( n )( i ) c − F ( n )( i ) int , (1) with i , denoting the iteration and n denoting the time step increment. K t denotes the tangent sti ff ness matrix, ∆ u the increment displacement vector, F ext the nodal external force vector, and F int , the restoring nodal force vector. The tangent sti ff ness matrix, K t , encompasses the shape sti ff ness matrix, stress sti ff ness matrix. and the com putation of shape sti ff ness matrix and restoring nodal force vector is made accordingly the corotational approach (Rankin and Brogan (1986); Argyris (1982)). Solid elements are three-dimensional brick, tetrahedral, or pyramidal