Using the example of an automatic parking system, it will be shown how multi or rigid body simulations (MBS) can be used to solve specific kinetic or kinematic tasks. Automatic parking systems carry transport vehicles from the entrance level to the different parking levels. The case under consideration here, the parking garage is cylindrical, the vehicles must also be rotated on a platform so that the pallet can be pushed into the corresponding parking space.
A so-called belt-lifting table was used as a solution concept to overcome the differences in height. The lift table consists of two pairs of scissors which can be moved by means of roller-cam pulley pairs. The belt pulls the rollers, which can be moved along the scissors, against the cam disks like a cable pull and thus pushes the scissors apart. The belt has a supporting function. On the one hand, it must be ensured that the permissible belt forces are not exceeded, and on the other hand, the holding torque of the electric motor must not be exceeded, otherwise the entire device will collapse.
The calculations were performed with PRO/MECHANICA MOTION. The geometry of the cams were taken from existing CAD data and the model with the position of the hinge points in the extended state was created as a 2D model. This assumption is admissible, since it can be assumed that all four belts distributed over the table width carry equally. The resulting forces must be converted accordingly.
Figure 1 shows the MKS model with the names of the individual components. The names of the individual bearings can be taken from Figure 2.
The FMD model and the assumptions are described in more detail below.
Since the forces in the joints of the lift table and in the belt increase strongly in certain positions of the table, considerations were made to relieve the joints and the belt by means of pneumatic pull cylinders.
With the aid of multi-body simulation, the kinematics and the force progression in the belt and at the articulation points were analyzed and the position and optimum characteristic values of the tension cylinders were determined.
The calculations were performed with PRO/MECHANICA MOTION.
For this purpose, the geometry of the cams was taken from existing CAD data and the model was created as a 2D model with the position of the hinge points in the extended state.
This assumption is admissible, since it can be assumed that all four belts distributed over the table width bear equally. The resulting forces must be converted accordingly.
Figure 1 shows the MKS model with the names of the individual components.
The names of the individual bearings can be taken from Figure 2.
The FMD model and assumptions are described in more detail below.
1. All bodies  are considered rigid.
2. The masses are idealized as point masses in the center of gravity of the bodies.
3. The belt force is considered constant in the whole system (no friction).
4. The belt wrap around the trolleys is assumed to be constant at 180° (the reaction force is twice the belt force).
5. The reaction forces of the belt deflections are taken into account by external forces
6. All joints are considered to be friction-less and ideal
7. 4 cam discs and rollers are included in the model. The cams are firmly connected to the scissors running from bottom left to top right. The rollers can be moved along the scissors running from bottom right to top left. Friction-less, rigid couplings have been designed between the cam plate and rollers, which do not allow the roller to be lifted off the cam plate.
8. A drive (driver) was placed between the base and the upper frame at a predetermined, constant speed. An empirically determined value is used as belt force. The resulting residual force in the drive is measured, averaged over existing values and offset against the belt force so that the auxiliary force converges towards the value 0.
9. The total travel distance of the drive is 5160 mm.
10. The speed curve during start-up has been smoothed to facilitate the convergence behavior of the model
11. The total stroke is reached after 13 seconds (see figure 4).
12. Starting position for the model is the upper position.
13. The belt loads outside the pulleys were applied as external loads at the deflection points.
14. The load arrows with springs are directionally locked, the loads without springs are body locked.
15. The amount of force corresponds to the time-dependent belt force determined in the drive.
The calculations were carried out dynamically, taking into account the inertial forces by an implicit time integration method.
Figure 3 shows the two extreme positions of the lift table. The predetermined progression of height over time is shown in Figure 4.
Figure 5 shows the course of the roller forces over height. The curve of the forces, which should ideally be constant, shows that the cam plates are not exactly matched to the kinematics. This is due to the fact that, for manufacturing reasons, a shape was chosen that is composed of two circular arcs. At the transition between the two arcs a kink in the course of the forces can be observed (Fig. 5).
When starting up, the model must be accelerated from 0 to the constant travel speed in one time step. This explains the transient processes (at height 0), which are not to be expected in reality, since the acceleration of the drive motor is also finite.
Bearing MR and the two middle bearings UM and OM show the highest forces that occur in the retracted position (see Figure 6). The belt force increases to about 58 kN in the retracted position. Since the permissible belt force is 60 kN, there is no longer sufficient safety here to ensure that the system can be operated with fatigue strength. Furthermore, the joint forces in the bearings are also too high at 175 to 180 kN, which would result in a reconstruction of the shears.
The idea was to provide additional pneumatic traction cylinders, which act between the trolleys, to relieve the strain on the joints and belts. A problem in this context is the danger that the dead weight of the lift table without the weight of the vehicle is no longer sufficient to move the system to the lowest position.
Mathematically, this means that the belt forces become negative. Since a belt cannot transmit compressive forces, the system would no longer function.
On the basis of several studies in which the articulation points of the pull cylinders and the spring characteristics were varied, an optimized constellation could be found with the help of multi-body simulation. The belt forces could be reduced to 38 kN when loaded and the minimum belt force of 9 kN is still sufficiently high without loading.
The maximum joint forces were reduced from 180 kN to 45 kN. This meant that the safety of the system could be guaranteed at a reasonable cost without restricting its function.
In the simulation of the lift table, the multi-body simulation proved to be a suitable instrument for better understanding the kinematics, finding critical zones and deriving suitable measures for optimization.
Bodies: In this context, each unit that can be considered rigid on its own and is kinematically connected to other bodies via so-called joints.
 Directional lock: The orientation of the load vector in the global coordinate system remains the same.
 Body lock: The orientation of the load vector in the local coordinate system of the body remains the same. Here: The load direction always acts in the direction of the shear.
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