The Use Of Numerical Regression Analysis In Modeling Various Types Of Experimental Friction

Modeling is vital to engineering, yet students have difficulty understanding and appreciating the concept. This paper describes a series of dynamic experiments that utilizes a rotating disk to reinforce concepts involved in creating an empirical model. These experiments have many positive pedagogical attributes. The apparatus is simple, plus the required mass, length and time measurements are not difficult to make with simple instruments. The equipment is inexpensive and portable for both classroom and laboratory use. The experiments range from simple moment of inertia concepts to the testing of more complex friction models and may be easily modified to vary the results. The disk is an appropriate system for sophomore level students to analyze, since the solution of its angular momentum differential equation results in a simple angular displacement versus time relationship, q(t), even though the frictional model is non-linear, varying with the angular velocity w raised to some unknown power. This permits superior results since the q vs. t data set can be accurately determined over the range of angular velocities using an ordinary stopwatch. The drag devices generate kinetic friction ( Fm μ constant), eddy current friction (Fm μ w) and aerodynamic friction (Fm μ w). Trend lines that undergraduates typically use to correlate data are inappropriate here because none have the proper functional form. Excel is utilized because a) it is a natural platform to record and manipulate experimental data, b) its Solver package permits an iterative nonlinear regression analysis to determine the unknown empirical coefficients by minimizing the error between experimental and model predictions, and c) Visual Basic function modules may be utilized to calculate the empirical model values. The discovery-based experiments, run as coupled or independent experiments, may also be utilized as demonstrations since the empirical results are in excellent agreement with accepted physical models. Further, the exceptional agreement obtained between the general empirical model results and the various friction laws allows students to deduce specific relationships from more general relationships.