10 | SIMPACK News | September 2010

CUSTOMER APPLICATION | Alexandra Lehnart, Florian Fleißner, Peter Eberhard, Institute of Engineering and Computational Mechanics, University of Stuttgart

INTRODUCTIONSIMPACK is a very powerful tool in its application to coupled multi-body system (MBS) simulations of various vehicles. But when considering tank vehicles, the motion of the cargo and the tank design (including the number of compartments or the general shape) need to be accounted for, too. One way to approach this challenge is to use simple non-physical pendulum models for the cargo. However, this is just a crude approximation with little regard to the reality of the tank’s shape and cargo dynamics. Much better results can be obtained by coupling the MBS simulation with another simulation method specifically designed to simulate the liquid cargo material interacting with the tank. In our approach, we couple SIMPACK with PASIMODO (PArticle SImulation and MOlecular Dynamics in an Object oriented fashion), a Lagrangian simulation framework for the 3D simulation of granular materials and fluids, developed at the Institute of Engineering and Computational Mechanics at the University of Stuttgart.

Simulating Tank Vehicles with Sloshing Liquid Load

The cargo, particularly a liquid cargo, of a transport vehicle can have a significant influence on the driving characteristics of a vehicle. The design of the tank is of upmost importance as it greatly affects the dynamics of the cargo and, therefore, the dynamics and stability of the vehicle. These issues have to be taken into account when performing a simulation. A co-

simulation approach is proposed coupling a multi-body system simulation using SIMPACK for the vehicle with a particle-based fluid simulation using the software PASIMODO for the cargo.

Fig. 2: Simulink® model of a PASIMODO-SIMPACK co-simulation loop with fixed synchronization time interval

Fig. 1: Tank vehicles with sloshing liquid load

kernel function

SIMPACK News | September 2010 | 11

Alexandra Lehnart, Florian Fleißner, Peter Eberhard, | CUSTOMER APPLICATION Institute of Engineering and Computational Mechanics, University of Stuttgart

Fig. 4: Exemplary particles with their corresponding moving kernel functions

Fig. 3: Model of the truck with 17 degrees of freedom

DYNAMIC CO-SIMULATIONThe co-simulation delegates the simulation of the tank and silo vehicles to the two specialized programs. PASIMODO calculates the forces on the tank geometry resulting from the sloshing liquid or moving solid cargo, while SIMPACK calculates the behavior of the vehicle. For this purpose, SIMPACK needs to know the particle forces and torques on the tank to account for their influence on the vehicle’s dynamics. On the other hand, PASIMODO needs the recent tank states to be able to calculate the resulting particle forces. This exchange is established via MATLAB® and Simulink® as SIMPACK already provides a co-simulation interface that allows for data exchange. To couple PASIMODO with MATLAB and Simulink, we took advantage of PASIMODO’s plug-in interface, which enables users to implement their own custom subroutines in C++. These can be used to reposition geometries during a simulation, e.g. the tank’s internal surface geometry according to the recent tank states received from SIMPACK. Then, the plug-in sends the calculated particle forces and torques with respect to the tank’s center of gravity back to SIMPACK. The data exchange is carried out via a TCP/IP interface both between PASIMODO and Simulink as well as between Simulink and SIMPACK. The exchange always takes place after a fixed time interval, but in between, each simulation program can use its own variable time stepping. This is especially relevant for the particle simulation as the particle dynamics solver usually has a much smaller time step than the dynamics solver of the truck. For these time steps, the position of the tank geometry is updated via extrapolation from the already received tank states. Fig. 2 depicts the co-simulation procedure as implemented in the Simulink model.

VEHICLE MODELFor the simulation of the vehicle, a classical MBS approach is used. The model of the truck has 17 degrees of freedom, schematically shown in Fig. 3. The computation of the tire forces follows the Tire Similarity Model from Pacejka. To account for a driver, two additional degrees of freedom are added which are influenced by a feedback controlled driver model. The truck has a total dead weight of 10310 kg, a wheelbase of 3.1 m and a track of 1.66 m.

PARTICLE MODELConsidering the MBS model and the particle model, different aspects of the vehicle are of interest. In SIMPACK, the forces and torques on the tank resulting from the moving cargo are supplied by the particle simulation. They can be treated as applied forces on the tank’s center of gravity and no further information on the tank’s geometry is needed. The particle simulation, on the other hand, needs a detailed internal tank geometry and the states of the tank to place it appropriately, but doesn’t need any information about the remaining MBS.The program PASIMODO follows the Discrete Element Method approach for the simulation of granular systems and the Smoothed Particle Hydrodynamics (SPH) method for fluids. SPH is a discretization method in space for partial differential equations, where the discretization points, called particles, carry the important information like velocity, density and pressure as mean values over the volume surrounding them and move along the velocity field of the material they represent. The discrete values at the particle positions are then smoothed by means of a differentiable kernel function, often similar to a Gaussian function, and summed up to yield an approximation of the corresponding function that is also differentiable. Using these approximations in the partial differential equations gives ordinary differential equations in time that can be

solved with a given time stepping scheme. Fig. 4 shows some moving particles with their corresponding kernel functions.Boundaries and non-spherical objects are defined by triangular surface meshes. To prevent particles from passing through the mesh, a penalty force is evaluated and

applied for each pair of particle and triangle. If the mesh is not fixed,

“PASIMODO calculates the forces on the tank geometry, while SIMPACK calculates the

behavior of the vehicle.”

12 | SIMPACK News | September 2010

CUSTOMER APPLICATION | Alexandra Lehnart, Florian Fleißner, Peter Eberhard, Institute of Engineering and Computational Mechanics, University of Stuttgart

it is defined relative to a moving coordinate system that lies in the center of gravity and accumulates all the forces and torques on the triangles. The position and orientation of the coordinate system and with it the mesh geometry can then be either integrated in time or, as in our case, taken from the tank states supplied by SIMPACK. The accumulated forces and torques are sent to the MBS simulation.

RESULTSTo investigate the influence of moving cargo on driving dynamics, classical benchmark driving maneuvers are performed, among Fig. 7: Relative angular velocity at the rear tire

Fig. 6: Normalized displacement of the cargo’s center of gravity in longitudinal direction

Fig. 5: Snapshots during a full braking maneuver with a tank with an elliptical cross section and one and three compartments, respectively

“Regarding the evaluation of the simulation results, the

co-simulation approach offers all the possibilities that SIMPACK

offers, together with those from PASIMODO.”

them a full braking with different tank designs. As cargo, water is used with a total mass of 4700 kg.Regarding the evaluation of the simulation results, the co-simulation approach offers all the possibilities that SIMPACK offers, together with those from PASIMODO. The exchanged data can be stored by MATLAB and loaded later to compare results from different simulations. This includes the states and forces for every body in the simulation. PASIMODO offers the additional ability to track the cargo’s center of gravity.Fig. 5 depicts some snapshots taken from a full braking with an undivided and tripartite tank, respectively. Please note that in the visualization particles moving within the liquid are displayed. The corresponding displacement of the cargo’s center of gravity is shown in Fig. 6. In Fig. 7 the tire locking that occurs during full braking with the undivided tank can be seen, while the compartments in the other tank prevent it.

CONCLUSIONThe results obtained show that the SIMPACK-PASIMODO co-simulation is suitable for predicting the stability of driving maneuvers of transport vehicles. It can be used to investigate the impact of different

tank designs on the behavior of the vehicle system, easily taking into account compartments or curved walls. Comparisons between different tank designs show

the significant influence that the movement of the cargo and the tank design have on the driving characteristics of the vehicle. A positive effect of subdivisions in the tank in longitudinal directions in terms of braking stability can be seen, as they reduce the sloshing motion in that direction.For details about PASIMODO please see www.itm.uni-stuttgart.de/research/pasimodo/pasimodo_en.php. More information about the methods and simulations is provided in the authors’ publications.