AN ALGORITHM FOR SYSTEMATIC GENERATION OF SUBSCALES WITH APPLICATION TO A TWO-DISK FRICTION SYSTEM

摘要

In this paper we propound an algorithm for development ofscale models of complex physical systems. The algorithmsystematically treats the three sub-tasks of scaling, whichincludes creation of dimensionless parameters, application ofscaling law and similitude requirements, and determination ofscale factors. Optimum set of dimensionless parameters areobtained in which the pertinent variables with only integerpowers appear. This is achieved by seeking integer solutions toappropriate set of linear algebraic equations in the powers,using a simple iterative technique.Application of the scaling law and similitude requirementsalong with a logarithmic transformation leads to a set of linearalgebraic equations in the scale factors. In many applications,over-constrained systems are resulted for which true scaling cannot be achieved. Two techniques are introduced in the proposedalgorithm which circumvent the difficulty in treating overconstrainedsystems. The first method is based on a relaxationtechnique, whereas the second method introduces the concept ofauxiliary variables to obtain the least squares solutions to thenew set of linear equations. The effectiveness of the algorithmis demonstrated through its application in finding scale modelsof a two disk friction system.