PSI - Issue 77

Francisco Castro et al. / Procedia Structural Integrity 77 (2026) 611–630 Francisco Castro/ Structural Integrity Procedia 00 (2026) 000 – 000

615

5

Figure 1 – Longitudinal vehicle dynamic model (x-z cross section). According to Newton’s Law of rigid body dynamics, the resulting force acting on a body in motion (applied on the centre of mass) equals the product of body mass by the resulting acceleration, equation (1) . The horizontal forces are due to tire adhesion against track surface. + = ℎ × (1) When brakes are applied, they exert a forward pitch torque, inducing the vehicle to “dive”. The Moments are taken on point G (centre of mass of the vehicle). Thus, the equilibrium of forces, • On x-direction, ( + )× = ×( − )+ × (2) • On z-direction, − ℎ × + ( + ) =0 (3) The increment of force reactions at wheel hubs are transmitted to the vehicle body by spring deformations. Once, springs deform due to the applied force, = × (4) Considering only as relevant the spring displacement variations due to vehicle forward pitch, then, once they are generated by torque coming by a horizontal inertia force, both forces cancel each other, i.e., since at front the spring force the increases while at rear axle that force is relieved. + =0 (5) By kinematic relation, , = × ( − ) (6) , = × (7) And by constitutive relation, = × , = × × ( − ) (8)