# Error Reduction and Effect of Step Size in Adjustment Calculus for Cam Applications

## Date of this Version

4-2012

A THESIS Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Master of Science, Major: Mechanical Engineering, Under the Supervision of Professor Wieslaw M. Szydlowski. Lincoln, Nebraska: April, 2012

Copyright (c) 2012 Sai Siddhartha Nudurupati

## Abstract

Any measurement, however carefully done, will never be free from errors. Similarly, machining of cams for automobiles is prone to contain errors. These errors are naturally a part and parcel of cam manufacturing. The nature of deviations of the manufactured cam profile from the theoretical cam determines its usability. Sometimes, allowable deviations in high speed cams may be in the order of 2540 µm. Larger deviations will disqualify the cams for applications.

Velocity and acceleration of the cam are estimated from the measured displacement of the cam follower during quality control implementation. This data helps in eliminating the unfit cams. Existing methods deal with a notorious challenge from propagation of measurement errors in the displacement data to predicted velocity and acceleration values.

J. Oderfeld developed a little known method called ‘Adjustment Calculus’ which is an alternative method for this purpose. This method combines the ‘marching point’ method that fits a polynomial to discrete data and a symmetric Stirling interpolation method. Until now, adjustment calculus has been applied to reduce errors in acceleration data. In this work, adjustment calculus is implemented to velocity predictions. ‘Weights’ for calculation of adjusted velocity are derived using a cubic polynomial fit and symmetric Stirling interpolation formula. The effect of step size on application of adjustment calculus to different cam profiles is probed using the Monte Carlo method.

Effective step size for practical applications in automotive cam quality control is suggested for each cam profile. Practical pointers for application to cam inspection for velocity and acceleration analysis are formulated.