# Multi-body simulation

The multi-body simulation (FMD) is a method of numerical simulation , wherein the real multi-body systems are imaged by a plurality of non-deformable body. In addition, the ability of the bodies to move relative to one another is restricted by idealized kinematic joints.

## variants

In a dynamic model, an operating point can only be determined by solving a differential equation . This can only be done analytically for extremely simple systems, which are normally characterized by linear equations of motion or a single degree of freedom . Therefore, multi-body simulation programs always have one or more solution methods for numerical integration, e.g. B. Runge-Kutta method .

The multi-body simulation is a very rough simplification of the real world. In order to map a system in more detail and more precisely, the method is therefore often combined with other simulation methods. The methods of the finite element method (FE), numerical flow simulation , thermodynamics , control technology , as well as special programs for tires , rubber elements, hydraulic bearings and other construction simulations are integrated into the multi-body model.

A special method in connection with the multi-body simulation is the modal reduction . Here, a body whose flexibility cannot be neglected is mapped using its external properties. To do this, however, it must be determined before the actual simulation where the connection points to the rest of the system are. The movement of the flexible body is then reduced to the rigid body movement and a defined number of degrees of freedom (e.g. eigenmodes from a modal analysis in the Craig-Bampton method) using a reduction process. Thanks to fast processors and modern formulations of the system of equations, however, the direct integration of flexible bodies is becoming increasingly popular. The networks, as they are known from FE, and the multi-body systems are combined directly in a system of equations .

## function

Kinematic systems are part of our daily life. They range from simple commuting to complete vehicles. With the multi-body simulation, the movement sequence of such systems can be calculated and analyzed. The simulation provides results on the forces, speeds, accelerations and contacts of the bodies.

MKS systems have been used intensively in the automotive sector for several years, e. B. for the analysis of chassis. There are special extensions to the MKS programs for this purpose. Another example of the use of the MKS is the analysis of loading games in backhoe excavators . There are z. B. calculated the dynamic loads in the bearing points.

The MBS model can also be expanded by integrating the hydraulic system. Forces for the movement of the boom are then provided from the hydraulic simulation. The integration of an FE analysis in the MBS model enables the component loads to be calculated during movement.

## application areas

• Motion analysis of complex kinematic systems
• Determination of dynamic component loads
• Provision of dynamic load assumptions for the FEM
• Localization of design deficits in existing machines
• Realization of the virtual prototyping