Numerical analysis for dynamic contact between high‐speed wheel and elastic beam with Coulomb friction

Abstract

SUMMARYFor numerical analysis of the dynamic contact between a high-speed wheel and an elastic beam, the equation of motion of each body is time integrated by a simple ODE solution technique and frictional contact conditions are imposed by the augmented Lagrange multiplier method using the contact errors defined in this work. For the stability of the numerical solution, the velocity and acceleration contact conditions as well as the displacement contact condition are imposed with special consideration for the high-velocity contact point moving on the deformed beam. Especially, it is shown that the Coriolis and centripetal accelerations of the contact point moving rapidly on the deformed beam play crucial roles for the stability of the solution. It is also shown that, for a wheel rolling on a beam with friction, the acceleration constraint in the tangential direction is important for the stability of the solution.

A stabilized numerical solution for the dynamic contact of the bodies having very stiff constraint on the contact point

“…The author showed that the similar stabilizing technique using the differentiated constraints can be applied for the solution of the dynamic contact problems of rigid or elastic bodies [10][11][12][13]. For the contact problem of this work where a stiff spring is installed on the contact point, the same stabilizing technique may also be applied because the equation of motion is again a differential equation and the contact constraint is again an algebraic constraint.…”

“…Even though the solution strategy of this work may be applied to the more complex multibody models by the author's previous work [11][12][13], for the sake of simplicity, only the two-body contact having a single contact point is considered here. Each body may be a rigid body or an elastic body, and the equation of motion of each body can be easily formulated by rigid body dynamics or finite element techniques by treating the contact force as an unknown force.…”

“…4, and the iteration continues until the contact condition is satisfied. As the solution procedure is essentially the same as those shown in the references [11][12][13], only the additional procedure associated with the stiff contact constraint by a spring on the contact point is explained here.…”

“…From a physical point of view it may be expected that the contact with a spring between the bodies would be almost equivalent to the direct contact between the surfaces if the spring becomes very stiff. In the author's previous works on the dynamic contact where the contact occurs directly between the surfaces of the elastic or rigid bodies [11][12][13], it has been shown that the time integration technique of ordinary differential equations (ODE) can be efficiently applied to solve the resulting differential algebraic equations (DAE) of the contact problems by imposing the acceleration and velocity constraints as well as the displacement constraint on the equation of motion. Especially the author demonstrated that the precise computation of the acceleration contact constraint is crucial for the accurate and stable solution [13].…”

“…In the author's previous works on the dynamic contact where the contact occurs directly between the surfaces of the elastic or rigid bodies [11][12][13], it has been shown that the time integration technique of ordinary differential equations (ODE) can be efficiently applied to solve the resulting differential algebraic equations (DAE) of the contact problems by imposing the acceleration and velocity constraints as well as the displacement constraint on the equation of motion. Especially the author demonstrated that the precise computation of the acceleration contact constraint is crucial for the accurate and stable solution [13]. In this work it is shown that the dynamic contact problem formulated with a stiff massless spring between the contact points can also be solved by a similar technique imposing the velocity and acceleration constraints as well as the displacement constraint.…”