Dag Fritzson

Lossless compression of high-volume numerical data from simulations

Summary form only given. We propose a lossless algorithm of delta compression (a variant of predictive coding) that attempts to predict the next point from previous points using higher-order polynomial extrapolation. In contrast to traditional predictive coding our method takes into account varying (non-equidistant) domain (typically, time) steps. To save space and guarantee lossless compression, the actual and predicted values are converted to 64-bit integers. The residual (difference between actual and predicted values) is computed as difference of integers. The unnecessary bits of the residual are truncated, e.g., 1111110101 is replaced by 10101. The length of the bit sequence (5/sub 10/=(000101)/sub 2/) is prepended.

BEAST—a rolling bearing simulation tool:

Abstract Rolling bearings are high-precision, low-cost machine elements used in all kinds of rotating machinery. Dynamic simulations of rolling bearings bring increased understanding of their dynamic behaviour and shorten product development time. Owing to the high demands on contact geometry description and contact force calculations (including traction), simulations are computationally intensive and cannot generally be done with traditional multibody dynamic programs. A rolling bearing simulation model called BEAST (BEAring Simulation Tool) has been developed by SKF. It is used daily by SKF engineers to improve their understanding of bearings and, as a consequence, improve the bearings themselves. A few typical examples of BEAST usage are presented.

Dynamic behaviour of rolling bearings: Simulations and experiments

Abstract Rolling bearings have been very common machine elements for more than 100 years. During this time, vast experiences about their steady state behaviour, e.g. their load-carrying capacity has been accumulated. Fatigue life predictions have been refined to handle clean and contaminated bearings. The understanding of the dynamic behaviour of rolling bearings has not reached the same level of maturity. Still most phenomena that occur in rolling bearings, under both normal and unacceptable operation, are dynamic in nature. These dynamic phenomena have to be studied with dynamic tools. One such tool is the bearing simulation tool, called BEAST. BEAST is based on multi-body techniques, with special focus on contact problems. It allows for studies of the dynamic behaviour of all bearing components under general loading conditions, e.g. the forces on and motions of the cage, skew and tilt behaviours of rollers and skidding of balls. A description of the most important aspects of the BEAST model and some examples of comparisons with experiments, are given in this paper.

High-level mathematical modeling and programming

Scientific computing and advanced mechanical analysis demand high-level support for modeling and solving complex equations. To meet this need, the authors designed ObjectMath and applied it to real problems in machine-element analysis. >

The need for high-level programming support in scientific computing applied to mechanical analysis

We describe the current state of the art in computerized support of mathematical and numerical modelling for mechanical analysis. An overview of relevant high-level languages, computer algebra systems, and hybrid symbolic-numerical systems is also given. Several problems with current tools are identified, and a high-level programming environment is proposed as a solution. Such an environment should include object oriented model description, symbolic formula manipulation, generation of numeric code, automatic use of equation solvers and optimization techniques, in addition to graphical presentation of model and simulation data.

Automatic Generation of User Interfaces From Data Structure Specifications and Object-Oriented Application Models

Applications in scientific computing operate with data of complex structure and graphical tools for data editing, browsing and visualization are necessary.

General meta-model based co-simulations applied to mechanical systems

Abstract A fully functional meta-model co-simulation environment that supports integration of many different simulation tool specific models into a co-simulation is described in this paper. The continuously increasing performance of modern computer systems has a large influence on simulation technologies. It results in more and more detailed simulation models. Different simulation models typically focus on different parts (sub-systems) of the complete system, e.g., the gearbox of a car, the driveline, or even a single bearing inside the gearbox. To fully understand the complete system it is necessary to investigate several or all parts simultaneously. This is especially true for transient (dynamic) simulation models with several interconnected parts. One solution for a more complete and accurate system analysis is to couple different simulation models into one coherent simulation, also called a co-simulation. This also allows existing simulation models to be reused and preserves the investment in these models. Existing co-simulation applications are often capable of interconnecting two specific simulators where a unique interface between these tools is defined. However, a more general solution is needed to make co-simulation modelling applicable for a wider range of tools. Any such solution must also be numerically stable and easy to use in order to be functional for a larger group of people. The presented approach for mechanical system co-simulations is based upon a general framework for co-simulation and meta-modelling [9] . Several tool specific simulation models can be integrated and connected by means of a meta-model. A platform independent, centralised, meta-model simulator is presented that executes and monitors the co-simulation. All simulation tools that participate in the co-simulation implement a single, well defined, external interface that is based on a numerically stable method for force/moment interaction.

Rolling Bearing Simulation On Mimd Computers

Rolling bearing simulations are very computationally in tensive. Serial simulations may take weeks to execute, and there is a need to use the potential of parallel comput ing. The specific structure of the rolling bearing problem is used to develop suitable scheduling strategies. The authors discuss the system of stiff ordinary differential equations arising from a bearing model and show how to numerically solve these ordinary differential equations on parallel computers. Benchmarking results are presented for two test cases on three platforms.

Object-oriented mathematical modelling—Applied to machine elements

Machine element analysis has a goal of describing function and other aspects of machine elements in a theoretical form. This paper shows how ideas from object-oriented modelling can be applied to machine element analysis. The models thus obtained are both easier to understand, better structured, and allow a higher degree of re-use than conventional models. An object-oriented model description is natural and suitable for machine element analysis. As a realistic example an equational model of rolling bearings is presented. The structure of the model is general, and applies to many types of rolling bearings. The model and one solution require approximately 200 + 200 equations. The model is extensible, e.g. simple submodels of detailed properties can be made more complex without altering the overall structure. The example model has been implemented in a language of our own design, ObjectMath (Object-oriented Mathematical language for scientific computing). Using ObjectMath, it is possible to model classes of equation objects, to support multiple and single inheritance of equations, to support composition of equations, and to solve systems of equations. Algebraic transformations can conveniently be done since ObjectMath models are translated into the Mathematica computer algebra language. When necessary, equations can be transformed to C++ code for efficient numerical solution. The re-use of equations through inheritance reduced the size of the model by a factor of two, compared to a direct representation of the model in the Mathematica computer algebra language.

Adaptive scheduling strategy optimizer for parallel rolling bearing simulation

Rolling bearing simulations are very computationally intensive and need to utilize the potential of parallel computing. The load distribution over the processors in a rolling bearing simulation is very dynamic. In this paper we present the Adaptive Scheduling Strategy Optimizer (ASSO) for scheduling parallel simulations. The result of this is that the application can automatically select a near optimal scheduling strategy (with respect to the available scheduling strategies). The ASSO is used daily in real bearing simulations.