PELAB has participated in the development of BEAST (BEAring Simulation Toolbox). The program BEAST is developed by SKF and PELAB to perform simulations of bearing dynamics on any major bearing types. This enables studies of internal motions and forces in a bearing under given loading. The model is fully three-dimensional, solving the general differential equations of motion for all components; all components have six degrees of freedom. External forces and moments can be applied to all bearing components except the rolling elements. Most bearing types can be modelled.

### Approach

The simulation of the dynamics of rolling bearing requires the solution of ordinary differential equations (ODEs) and partial differential equations (PDEs). The ODEs arises from the dynamics of the rigid bodies in the bearing. The PDEs comes from the Tribology (the theory about interacting surfaces) in the contacts between the bodies. In the parallel version of the code a master/slave approach has been taken. The master solves the ODEs and instructs the slaves which contact calculation the slave should take care of.

The mathematical model of bearings has been partially developed using the ObjectMath environment , an object-oriented extension of Mathematica designed at PELAB.

### Challenges

Some tricky parts of doing rolling bearing simulation are:
• How to solve stiff ordinary differential equations on parallel computers? This is a tough task and is done in cooperation with DNA at Lund University.
• Load balancing problems for the computations, how to use semi-stable historical data for the load balancing problem? How should the load balancing take into account the fact the code runs on any machine ranging from a Cray T3E to a workstation cluster connected via Ethernet.
• Since the code is object oriented, how should class/objects be designed so that they are flexible, reusable, and fast?
• Simulation results in huge amounts of data. Hence we need some compression algorithms. Visualization of large data set is another research topic.

### Hardware

The BEAST code have been ported to a number of platforms, such as

• Cray T3E at the National Supercomputer Centre in Linköping, Sweden.
• Various SUN Sparc servers, e.g. Sun Enterprise 10000 at UNICC, Chalmers Göteborg, Sweden.
• Parsytec GC/PP-128 at National Supercomputer Centre in Linköping, Sweden.
• Clusters of DIGITAL Alpha Workstations, SUN Sparc Workstations.
• The IBM SP-2 at PDC Stockholm, Sweden.
• Clusters of PC's running Linux (Beowulf). Check out the NSC pages about Banan and Alice.
• A Windows PC can also be used.

### User Interaction

The post-processing is illustrated here:

The production simulations is mainly done on remote parallel computers at the Linköping University in Sweden. Currently we use the Linux clusters mentioned above, an 8 processor Alpha cluster and the Sun Enterprise 4000.

### Can the Results be Trusted?

To ensure that the data calculated with BEAST is correct, SKF has also performed verification tests, where they have recorded cage movements and the forces between balls and cage.These values have then been compared to values calculated with BEAST, and the agreement is between reasonable and good, varying with conditions and the accuracy of both measurements and calculations.

### Benefits of BEAST

Dynamic simulations can be regarded as having a test rig in the computer. This tool makes possible detailed studies of internal phenomena in the bearing. The tool will lead to accelerated product development speed, by replacing long and costly experiments on a test rig with faster and more detailed simulations on a computer.