How do you model contact forces in multibody systems?

1 Contact models

The first step to model contact forces in multibody systems is to choose a suitable contact model. A contact model is a mathematical representation of the contact geometry, kinematics, and mechanics between two or more bodies. There are two main types of contact models: continuous and discrete. Continuous contact models assume that the bodies are infinitely smooth and deformable, and use differential equations to describe the contact forces as functions of the relative displacement and velocity of the bodies. Discrete contact models assume that the bodies are composed of discrete elements, such as points, lines, or polygons, and use algebraic equations to describe the contact forces as functions of the relative gap and slip of the elements. Each type of contact model has its advantages and disadvantages, depending on the complexity, accuracy, and efficiency required for the analysis.

2 Contact detection

The second step to model contact forces in multibody systems is to perform contact detection. Contact detection is the process of identifying and locating the potential contact points or regions between two or more bodies. Contact detection can be done either analytically or numerically. Analytical contact detection involves solving the equations of the contact geometry to find the exact contact points or regions. Numerical contact detection involves using algorithms or data structures to approximate the contact points or regions. Some common methods for numerical contact detection are bounding volume hierarchies, spatial partitioning, and distance fields. Contact detection can be done either before or during the simulation, depending on the type of contact model and the dynamics of the system.

3 Contact resolution

The third step to model contact forces in multibody systems is to resolve the contact forces. Contact resolution is the process of computing the magnitude and direction of the contact forces based on the contact model and the contact detection. Contact resolution can be done either explicitly or implicitly. Explicit contact resolution involves solving the equations of the contact mechanics separately from the equations of motion of the system, and applying the contact forces as external forces to the bodies. Implicit contact resolution involves solving the equations of the contact mechanics together with the equations of motion of the system, and enforcing the contact constraints as internal forces to the bodies. Each method has its trade-offs between speed, accuracy, and stability.

4 Contact simulation

The fourth step to model contact forces in multibody systems is to simulate the contact dynamics. Contact simulation is the process of integrating the equations of motion of the system with the contact forces over time. Contact simulation can be done using different numerical methods, such as explicit or implicit Euler, Runge-Kutta, or Newmark methods. The choice of the numerical method depends on the properties of the system, such as stiffness, damping, nonlinearity, and discontinuity. The numerical method also affects the stability, accuracy, and efficiency of the simulation.

5 Contact analysis

The fifth step to model contact forces in multibody systems is to analyze the contact results. Contact analysis is the process of evaluating and interpreting the contact forces and the resulting motion and deformation of the bodies. Contact analysis can be done using different tools, such as graphs, tables, animations, or visualizations. Contact analysis can help to understand the behavior and performance of the system, such as energy dissipation, friction losses, wear and tear, impact forces, or stress and strain distributions.

6 Contact optimization

The sixth step to model contact forces in multibody systems is to optimize the contact parameters. Contact optimization is the process of finding the optimal values of the contact parameters, such as stiffness, damping, friction, restitution, or geometry, that maximize or minimize a certain objective function, such as efficiency, durability, safety, or comfort. Contact optimization can be done using different techniques, such as gradient-based, evolutionary, or stochastic methods. Contact optimization can help to improve the design and control of the system, such as reducing vibration, noise, or wear, or increasing stability, agility, or robustness.