Wheeled Vehicle Brake Drum Computation by Fracture Toughness Criteria

Abstract

To ensure vehicle safety at the design stage, of primary importance is the development of a mathematical model, within whose framework it is possible to effectively predict crack initiation in the break drum of a braking wheeled vehicle. Considered is the contact fracture mechanics problem of the initiation of a cohesive crack in the brake drum of a wheeled vehicle. It is believed that during the multiple braking of a wheeled vehicle, the vehicle material is destroyed during friction due to contact interaction. It is considered that the real surface of the brake drum is never absolutely smooth, but it has technological micro- or macroscopic irregularities that make the surface rough. A mathematical model is proposed, within whose framework crack initiation in the brake drum of a braking wheeled vehicle is described. The crack initiation zone is modeled as a region of weakened interparticle bonds of the material (pre-fracture zone). The location and size of the pre-fracture zone are not known in advance and must be determined in the process of solving the problem. Both the perturbation method and the apparatus of the theory of singular integral equations are used. The equilibrium problem of the wheeled vehicle brake drum with an embryonic crack reduces to the solution, in each approximation, of a nonlinear integro-differential equation of Cauchy type. When a collocation solution scheme is used in each approximation, the singular integral equation reduces to a system of nonlinear algebraic equations. To solve them, both the method of successive approximations and an iterative algorithm of elastic solutions are used. From the solution of the obtained system of equations, normal and tangential stresses in the pre-fracture zone are found. The condition for the initiation of a cohesive crack in the brake drum is formulated taking into account the criterion of the ultimate stretching of material bonds.

Keywords

• brake drum
• pre-fracture zone
• crack initiation
• rough surface