Mathematical Modelling of Ring Spinning Machine Productivity under Electric Drive Failure and Motor Speed Reduction

The operational performance of modern ring spinning machines is closely related to the technical condition and operating stability of their electric drive systems. Temporary drive failures and reductions in motor rotational speed can affect production continuity, machine productivity, and the efficient use of electrical energy. This study develops a second-order mathematical model for evaluating the performance of an electrically driven ring spinning machine by considering the combined effects of electric drive failure duration and motor rotational speed reduction. The experimental investigation was conducted using a second-order orthogonal design based on the Kono experimental planning method. Two independent variables were considered: electric drive failure duration and reduction in motor rotational speed. The experimental programme included nine design points, with twelve randomized replications at each point. The experimental data were processed using regression analysis to determine the linear, quadratic, and interaction effects of the investigated factors on machine productivity. The adequacy and statistical reliability of the developed model were evaluated using Cochran’s criterion, Student’s t-test, and Fisher’s F-test at a 95% confidence level. The obtained results demonstrate that both investigated factors have a measurable effect on machine productivity, while their combined variation produces a nonlinear response. The developed response surface provides a means of identifying operating conditions associated with reduced productivity losses and more efficient use of the machine’s operating resources. The proposed mathematical approach can be used to predict productivity under different electric drive conditions and can support the selection of more energy-efficient operating regimes. In this way, the model provides a basis for reducing unnecessary operational losses and improving the sustainability of energy-intensive textile production processes.