In this work, characteristics of various ball bearing parameters are studied under different loads and rotational speeds. By using Dimensional Analysis (DA), dimensionless parameters are computed which provides solution for a group of parameters. This analysis can be accomplished by using the Buckingham π-theorem. DA leads to reduction of the number of independent parameters involved in a probl...

The dimensions in the previous examples are analysed using Rayleigh's Method. Alternatively, the relationship between the variables can be obtained through a method called Buckingham's π. Buckingham ' s Pi theorem states that: If there are n variables in a problem and these variables contain m primary dimensions (for example M, L, T) the equation relating all the variables will have (n-m) dimen...

The use of similarity transforms in the design and the interpretation of feed-forward neural networks is proposed. The method is based on the so-called Buckingham-Theorem or Pi-Theorem and is valid for all neural network function approximation problems which belong to the class of dimensionally homogeneous equations. The new design method allows the a priori determination of a minimal topology ...

A mathematical model for predicting the peeling efficiency of a cassava peeler was developed using dimensional analysis based on Buckingham' s pi theorem. The validated data from experimental studies which revealed maximum coefficient determination R2 = 0.8366 between measured and predicted values. proved appropriate in estimating peel removal by up to 83.66%. There no significance difference v...

On the verge of the centenary of dimensional analysis (DA), we present a new matrix generalisation of the Buckingham Theorem on which it is based. The proof is based on a solution we have found for inverting non-square block matrices and gives rise naturally to a new pair of transforms the similarity transform (S) that converts physical dimensional data into dimensionless space and its inverse ...

A generalized dimensional analysis performed by using Buckingham’s Pi-theorem for the generalized Burgers’ equation is presented. The application of the Buckingham Pi-theorem is used to reduce the governing partial differential equation with the boundary and initial conditions to an ordinary differential equation with appropriate corresponding conditions. By using a scaling invariant we simplif...