A Study on the Contidence Limit for Two Independent Probability Variables in Engineering Problems : Applications to Limit of Transmitted Torque in Disk Clutch and Bolt Axial Tension Control

Abstract

The problem of the product of two independent probability variables which are normally distributed was theoretically analyzed using the confidence limit ellipse. By applying 𝓏 = x/y type problems to a disk clutch, the limit of transmitted torque was rationally calculated. On the axial tension control in bolted joints for the 𝓏 = x/y type problem, experimental analysis concerning bolt tightening by the calibrated wrench method was carried out under dry, oil and anaerobic adhesive conditions. For this type of problem, the proposed method is applicable in the case in which the hyperbolic relation can be treated linearly. For the distribution of product 𝓏, the method for the calculation of probability P_f, when 𝓏 did not exceed a limit, was shown. From the result of the analysis by the proposed method, it was found that the maximum and minimum values in the scatter of the product 𝓏 by the conventional method resulted in the use of a higher confidence limit level that corresponded to √(2) times greater in the percentile value in the standafd normal distribution table.