MBSLIM: Multibody Systems at Laboratorio de Ingeniería Mecánica

MBSLIM is a library for the dynamic simulation of generic multibody systems, developed since 2007 by the Laboratorio de Ingeniería Mecánica at University of A Coruña. In addition to the dynamic simulation, its main purpose, MBSLIM incorporates some extra features like the static equilibrium position, the kinematic simulation or the inverse dynamics and some singular advanced features like the EKF (Extended Kalman Filter) state estimation, the kinematic and dynamic sensitivity analysis, the dynamic optimization and the optimal control of multibody systems.

In recent years, its capabilities were extended by adding flexible bodies through FFR (Floating Frame of Reference) and it currently allows solving both dynamics and sensitivity analysis of multibody systems with rigid and flexible bodies.

In order to carry out the simulation tasks, the library writes and solves the equations of motion of the mechanisms or machines defined by the user, with the help of functions included as a part of it.

MBSLIM implements cutting-edge state-of-the-art dynamic formulations, not available in other codes, allowing the user to tackle specific problems in which other codes fail. Moreover, the analytical gradient based optimization and optimal control advanced features give it an important advantage compared to other simulation softwares.

The software was developed in Fortran 2008 as a colection of modules and it was verified in several different platforms, compilers and operating systems. The library includes a module to interact with Matlab and Octave, sending data, running calclulations and recovering results if needed.

For the most complex simulations the library can make use of MBSmodel, a separate C++ library also developed at LIM for the 3D rendering and collision detection between bodies with complex geometries given by 3D CAD files.

MBSLIM implements two families of formulations: a family of global formulations in natural coordinates and a family of toplological formulations in joint (relative) coordinates. The mechanisms definition is unique, independent of the formulation selected and both families are perfectly fit in the software.

The dynamic formulations currently supported in MBSLIM are the following:

• Kinematic formulation.
• Inverse dynamics formulation.
• Global ALI3-P formulation (index-3 Augmented Lagrangian with proyections of velocities and accelerations).
• Global Matrix R formulation.
• Global penalty/augmented Lagrangian formulation.
• Global augmented Hamiltonian formulation.
• Topological semi-recursive ALI3-P RtDyn0 and ALI3-P RtDyn1 formulations.
• Topological semi-recursive Matrix R RtDyn0 and Matrix R RtDyn1 formulations.
• Topological semi-recursive penalty/augmented Lagrangian RtDyn0 and penalty/augmented Lagrangian RtDyn1 formulations.
• Topological fully-recursive Lagrange RtDyn0 and Lagrange RtDyn1 formulations.

The following direct and adjoint sensitivity formulations are also available:

• Direct sensitivity of the kinematic formulation.
• Direct and adjoint sensitivity of the global ALI3-P formulation.
• Direct and adjoint sensitivity of the global Matrix R formulation.
• Direct and adjoint sensitivity of the topological semi-recursive ALI3-P RtDyn0 and ALI3-P RtDyn1 formulations.
• Direct and adjoint sensitivity of the topological semi-recursive Matrix R RtDyn0 and Matrix R RtDyn1 formulations.
• Direct and adjoint sensitivity of the topological fully-recursive Lagrange RtDyn0 and Lagrange RtDyn1 formulations.

Flexible bodies are simulated by means of FFR (Floating Frame of Reference) and for the representation of deformations any type of modes are allowed, without any restriction (static, dynamic, constraint, etc.). The method makes use of a finite element preprocessing that can be done in the commercial software Siemens NX with Nastran solver, by means of the PDE toolbox of Matlab, or by means of the DINA3D code, a proprietary finite element code developed specifically for MBSLIM.

For the sake of robutsness and due to the usual stiff character of the equations of motion, most of the time-stepping integration schemes are implicit. For the resolution of the nonlinear systems, Newton schemes with approximate and exact tangent matrices are used. Fixed-point iteration is optional for the formulations compatible with the scheme. The numerical integration schemes currently implemented are:

• Implicit single-step trapezoidal rule.
• Newmark with dissipation.
• HHT (Hilber, Hughes and Taylor).
• Generalized-alpha.
• 4th order explicit Runge-Kutta.

The library includes a complete module of constraints and the user has the option of customizing the existing constraints or defining new ones and add them to the MBSLIM models. The following categories of constraints are available in the library:

• Geometric (scleronomic) constraints: they allow to model the usual kinematic joints in machines or the typical primitive constraints between geometric entities.
• Rehonomic constraints: needed to model time dependent constraints, e.g. driving constraints for actuators.
• Non-holonomic constraints: 3D rolling constraints.

The software includes a module of forces as well. The user has the option of customizing the existing forces or defining new ones from scratch to use them in the existing MBSLIM models. The following forces are available:

• Translational and rotational linear and nonlinear spring-damper forces.
• Normal contact forces: they allow to simulate impact forces or permanent contacts between bodies by means of Kelvin-Voigt or dissipative Hertzian normal models.
• Friction forces: several models available with dry and viscous fiction, Stribeck effect and stiction.
• Tire forces: the code implements several tire models like Pacejka, TMeasy, Dugoff or a basic linearized model with saturation ellipsis.
• Brake force model with blocking.