Probability characteristic of perturbing moments in contactless suspension systems for mass unbalance measurement of sphere

Abstract

Purpose -It is well known that precision of mass unbalance measurement of sphere is determined by perturbing moments in contactless suspension systems. Therefore, estimating perturbing moment level in those systems is important and necessary to meet the requirements of a specified precision of mass unbalance measurement. Design/methodology/approach -In this paper, probability-theoretic method is employed to determine probability characteristics of the perturbing moments in both electrostatic suspension system and gas suspension system by statistically estimating of the quality of sphere surface. As a result, the relationship between probability characteristics of the perturbing moment and statistical estimates of the quality of sphere surface is established. It is expressed as a simple formula by specifying the correlation function of random field of sphere surface. Findings -Numerical experiments of the perturbing moment calculation in the two suspension systems show that for sphere with small correlation coefficient a, it is better to use gas suspension system for mass unbalance measurement. While for sphere with large correlation coefficient a, electrostatic suspension system is more suitable for its perturbing moment are less than gas suspension system. Originality/value -Knowledge of this relationship is of great theoretic and practical importance, since the probabilistic depiction of the perturbing moments, and hence the accuracy of the mass unbalance measurement systems can be estimated without a detailed roundness measurement of the sphere surface.