Traditional rolling stock dynamics studies often rely on simplified 2D models, limiting stability predictions for innovative designs at high speeds. This work proposes a refined spatial multi-mass mathematical model that accounts for nonlinear interrelationships and the superposition of deterministic and random disturbances. This approach enables a detailed reproduction of components with variable stiffness and diagonal connections, identifying critical dependencies inaccessible to standard analytical methods. The model describes spatial vibrations using linear differential equations, considering vertical and horizontal perturbations to simulate real-world operational conditions. To ensure accuracy, the simulation results were validated against field test data, showing high correspondence in force levels and displacements. The study optimizes spring suspension parameters for speeds of 40–140 km/h. Key findings include: Relative friction coefficients (φ0) should be adjusted: reduced to 6% for new bogie designs, but increased to 12% for model 18-9996 equipped with diagonal braces. Dynamic stability improves significantly with increased horizontal coupling stiffness. This is achieved through the integration of diagonal braces with side frames and the use of elastic-roller side bearers. This methodology provides a robust framework for evaluating the stability and performance of innovative railway vehicle designs.
Malik et al. (Sat,) studied this question.