Influence of the contact—impact force model on the dynamic response of multi-body systems

Abstract

This work deals with contact -impact force models for both spherical and cylindrical contact surfaces. The incorporation of the friction phenomenon, based on the Coulomb friction law, is also discussed together with an effective computational strategy, which includes the automatic step size selection procedure. Impacts within a revolute clearance joint in a basic slider -crank mechanism are used as an example to compare the different contact force models. The collision is a prominent phenomenon in many multi-body systems such as mechanisms with intermittent motion, kinematic discontinuities, and clearance joints. As a result of an impact, the values of the system state variables change very fast, eventually looking like discontinuities in the system velocities and accelerations. The impact is characterized by large forces that are applied and removed in a short time period. The knowledge of the peak forces developed in the impact process is very important for the dynamic analysis of multibody systems and it has consequences in the design process. The model for the contactimpact force must consider the material and geometric properties of the colliding surfaces, consider information on the impact velocity, contribute to an efficient integration, and account for some level of energy dissipation. These characteristics are ensured with a continuous contact force model, in which the deformation and contact forces are considered as continuous functions.

On the continuous contact force models for soft materials in multibody dynamics

“…This fact is not surprising because, for instance, Lankarani and Nikravesh [33] derived their model for high values of restitution coefficient, being, therefore, valid for hard contacts, such as those between metals [49][50][51][52]. The values of the coefficient of restitution for soft materials are low or medium [40,43,48,53], which clearly indicate that the hysteresis damping factor given by (6) and (8) cannot be used.…”

Cable-Pulley Interaction with Dynamic Wrap Angle Using the Absolute Nodal Coordinate Formulation

“…The Rayleigh-damping approach [13], wherein the damping matrix is defined as a linear combination of the mass and stiffness matrices, is used in the current model. Thus, (14) where K l and K t are respectively the longitudinal and transverse components of the stiffness matrix defined in Equation 13, and α, β 1 , and β 2 are scalar damping coefficients.…”

“…The normal force vector F n acting at a single point on the element is defined using the Hunt-Crossley model [8], which represents the surface as a non-linear spring-damper (21) where ȓ is the unit vector normal to the pulley surface at the point of contact, K n is the contact stiffness, δ is the relative "penetration" of the node into the surface, D is a damping coefficient and b is a positive constant with a value between 1 and 1.5 from the Hertz contact theory [14]. Selecting the origin at the center of the pulley with radius R and noting that a negative value of the penetration has no physical meaning, the penetration and penetration velocity are defined [7]:…”

Development of a planar multibody model of the human knee joint

“…The generalized stiffness depends on the material properties and on the geometry of the contacting bodies. For two spheres in contact the generalized stiffness coefficient is function of the radii of the spheres i and j and the material properties as [45],…”