The development of contact theories and numerical formula for various applications is a field which expands rapidly. This publication focuses on the rolling contact problem both for tire-road and wheel-rail contact. For the tire-road application a central problem is the modeling of the composite structure of the tire under internal pressure and axle load. One actual contact problem is the rolling on soft soil, which is discussed as the main application. In the wheel-rail case the contact area is much smaller and much more emphasis has been laid on the treatment of material changes, wear and creep phenomena. These approaches are discussed in detail as well as a more recent finite element formulation following the arbitrary Lagrange-Eulerian concept. Ideas about damage mechanisms finish the article.

Advanced Contact Mechanics–Road and Rail

Lateral stiffness, cornering stiffness and relaxation length of the pneumatic tire

By using a comprehensive rotating laminated shell model of the tire, the effects of viscoelastic damping on the standing wave phenomenon are investigated in more detail than was previously possible. The shell theory employed is a nonlinear version of Novoshilov's work and the onset of the standing wave is characterized as a small dynamic deformation superposed on a finite deformation. To expand the scope of the model, the viscoelastic constitutive law is treated as either of the differential or hereditary integral type. The solution for the stated model is obtained by the finite element procedure, and the results of several numerical experiments are presented. The substantial role of viscoelastic effects in the development of the standing wave phenomenon of tires is emphasized by the results.

On Standing Waves in Tires

Performance evaluation of cord material models applied to structural analysis of tires

Analysis of initially stressed multilayered shells

The pneumatic tire is treated as a laminated, anisotropic, toroidal shell of revolution possessing bending rigidity. The plies, which are constructed of elastic textile cords embedded in an elastic rubber matrix, are considered homogeneous and orthotropic on a macroscopic scale. The tire shell is considered to deform according to the classical Love hypothesis. The equilibrium, strain‐displacement, and laminate constitutive equations governing the tire shell are reduced to a system of six first order, nonlinear, ordinary differential equations with variable coefficients which are solved numerically by a multi‐segment forward integration technique. The geometrical nonlinearities due to finite displacements are accounted for by an incrementing process using transient coordinates. The theory is illustrated by a numerical calculation which shows good agreement with actual measurements.

Tire Stress and Deformation from Composite Theory

Studies of aircraft directional control during takeoff and landing are best carried out with programmed simulators in which the pilot interacts directly with the aircraft systems. A vital input to such simulations is accurate tire force data, which at the present time are difficult to obtain because of lack of experimental facilities. This paper describes new test equipment for measuring aircraft tire forces which is now available at the Air Force Flight Dynamics Laboratory, Wright‐Patterson Air Force Base. Sample data are presented and discussed which pertain to conventional and experimental radial ply aircraft tires.

H. K. Brewer

Papers

Tire Stress and Deformation from Composite Theory

Measurement of Steady State and Transient Aircraft Tire Forces