Dependence of Measuring Instrument Eccentricity and Tilt Error on the Four Mathematical Methods of Circularity Form Errors

Abstract

In precision machining of cylindrical parts, the measurement and evaluation of circularity is an indispensable component to quantify form tolerance. Of all the methods of measuring these form errors, the most precise is the one with accurate spindle/turntable type measuring instrument. On the instrument, the component is rotated on a highly accurate spindle which provides an imaginary circular datum. The workpiece axis is aligned with the axis of the spindle by means of a centering and tilt adjustment leveling table. Based on reference circles, this paper focuses on the four modeling methods of roundness, namely, (1) Least Squares Circle (LSC), (2) Maximum Inscribed Circle (MIC), (3) Minimum Circumscribed Circle (MCC) and (4) Minimum Zone or Minimum Radial Separation (MRS) Circles. These methods have been explained in author’s previous article in the context of their implications on design applications, advantages and disadvantages. In this article, the authors have investigated the dependence of these mathematical methods based circularity form error on instrument’s centering error (also known as eccentricity) and tilt error. Some intriguing results were observed for the highly nonlinear relationship of machine’s centering/tilt error with circularity results outside its useful linear region (50–600 μin for this specific machine used in this investigation). Further, the linear and nonlinear relationship was mapped within the effective boundaries of eccentricity settings to investigate the best and worst methods of circularity measurements that are susceptible to instrument errors. Very high and low machine eccentricity settings in its nonlinear regions were not accurately compensated by the machine in circularity results processing. In this study, a master part with different circular and cylindrical features was studied with varying levels of preset instrument eccentricity and tilt errors. Off the four methods, MRS reported the least circularity results. The other three methods didn’t provide any predictable trend. Circularity results were observed to differ up to 35% within these four methods. However, in this preliminary investigation, this maximum difference doesn’t appear to follow any predictable trend with varying machine eccentricities. This article also reinforces the significance of these parameters, and the way they should be understood and be incorporated into undergraduate and graduate engineering curriculum, and be taught as an improved toolkit to the aspiring engineers.