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
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
environment , an object-oriented extension of Mathematica designed at
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
- 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
The BEAST code have been ported to a number of platforms, such as
- Cray T3E at the National Supercomputer Centre in Linköping,
- Various SUN Sparc servers, e.g. Sun Enterprise 10000 at UNICC,
Chalmers Göteborg, Sweden.
- Parsytec GC/PP-128 at National Supercomputer Centre in
- 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
- A Windows PC can also be used.
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.