Studying the influence of selected controlled factors on the coefficient of sliding friction through experimental planning methods

Abstract

The article presents the use of mathematical statistics to determine controllable factors that influence the coefficient of friction in a dual-flow three-stage spur gear transmission of a newly designed sucker rod pumping unit. The load acting on the bearing units, the rotational speed of the main and auxiliary shafts, and the diametrical gap between the shaft and the bushing were assessed through tests. The tests were carried out in random order. The multivariate testing was used to determine the number of tests to be performed as well as the test conditions in order to achieve the required accuracy bushing. In the statistical analysis of the results, the Cochrane criterion was applied to verify the homogeneity of the variance values. Student's t-test was used to verify the significance of the coefficients included in the regression equation, Fisher’s F-test was used to determine the suitability of the adopted output function for describing the real object of study, i.e., the adequacy of the model, and sensitivity coefficients were used to assess the influence of the corresponding parameters on the optimization parameter. The analysis also considered the dispersion of optimization parameters, measurement repeatability, and errors in the model coefficients. Experimental values of the criteria, along with the dispersion of the adequacy and repeatability of the mathematical model, were evaluated to determine whether the model is fully suitable for the object of study. The impact of significant factors and their combinations, as well as their critical values, were assessed by comparing calculated values of the criteria. The significance or insignificance of the corresponding coefficients of the regression equation was determined. To investigate the impact of these controlled factors — load, rotational speed of the main and auxiliary shafts, and the diametrical gap between the auxiliary shaft and the bushing — on the sliding friction coefficient, a modernized device was developed. This device simulates the operating conditions of a double friction sliding bearing in a dual-flow, three-stage spur gearbox bushing. The experiments were conducted using I-40A industrial oil at room temperature. It has been determined that these factors significantly impact the coefficient of friction in a double friction bearing. Consequently, it is necessary to calculate their limit values to ensure the bearing assembly operates without failure during the required service life. Compared to other examined parameters, the optimization parameter, i.e., the coefficient of friction, is most significantly influenced by the diametrical gap between the auxiliary shaft and the bushing, and least affected by the magnitude of the load acting on the bearing assembly. The overall impact of controlled factors on the coefficient of friction is minimal. Employing the test planning method, a mathematical formula was derived, enabling the determination of the coefficient of friction in a double sliding friction bearing without additional tests within the range of limit bushing values of contact parameters.