On the contact detection for contact-impact analysis in multibody systems

Abstract

One of the most important and complex parts of the simulation of multibody systems with contactimpact involves the detection of the precise instant of impact. In general, the periods of contact are very small and, therefore, the selection of the time step for the integration of the time derivatives of the state variables plays a crucial role in the dynamics of multibody systems. The conservative approach is to use very small time steps throughout the analysis. However, this solution is not efficient from the computational view point. When variable time step integration algorithms are used and the pre-impact dynamics does not involve high-frequencies the integration algorithms may use larger time steps and the contact between two surfaces may start with initial penetrations that are artificially high. This fact leads either to a stall of the integration algorithm or to contact forces that are physically impossible which, in turn, lead to post-impact dynamics that is unrelated to the physical problem. The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step, in variable time step integration algorithms, in the vicinity of contact of multibody systems.The proposed methodology ensures that for any impact in a multibody system the time step of the integration is such that any initial penetration is below any prescribed threshold. In the case of the start of contact, and after a time step is complete, the numerical error control of the selected integration algorithm is forced to handle the physical criteria to accept/reject time steps in equal terms with the numerical error control that it normally uses. The main features of this approach are the simplicity of its computational implementation, its good computational efficiency and its ability to deal with the transitions between non contact and contact situations in multibody dynamics. A demonstration case provides the results that support the discussion and show the validity of the proposed methodology.

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

“…Positive values of δ mean that there is no contact between the ball and ground. Therefore, the detection of the instant of contact occurs when the sign of deformation changes between two discrete instants in time [61]. This problem was analyzed by using a FORTRAN code named MUBODYNA (acronym for Multibody Dynamics) [62].…”

A parametric study on the dynamic response of planar multibody systems with multiple clearance joints

“…One of the disadvantages associated with this formulation is that it can introduce highly-frequency dynamics into the system, due to the presence of stiff springs in compliant surfaces. If these dynamics require the integration algorithm to take smaller steps, then the speed of simulation will be strongly penalized [32]. Another drawback of the regularized approach is that the difficulty to chosen the contact parameters such as the equivalent stiffness or the degree of nonlinearity of the deformation, especially for complex contact scenarios [33].…”

Implementation of Multi-Body Dynamics Simulation for the Conveyor Chain Drive System

“…The constraint equation relates with bodies is given to assemble bodies by: (3) where is the number of constraints. The dynamic equation of system is expressed in the matrix form by: (4) where is the rigidity matrix.…”

“…The constraints which relate with bodies are used to limit motions of the system. The contact-impact constraint is a major condition to detect the precise of impact and to achieve the contact-impact force by MBD simulation [3]. The dynamic characteristics of movable components in systems can be investigated.…”