Determination of the main performance indicators of a forced-action concrete mixer using similarity criteria

Abstrac. The article presents a theoretical approach to determining the main performance parameters of a forced-action three-shaft concrete mixer based on the application of similarity theory. A system of dimensionless similarity criteria has been developed, which enables the transfer from a basic laboratory model to a full-scale industrial machine. This method is proposed as a means of optimizing the design and operating parameters of concrete mixers for the preparation of stiff and low-mobility concrete mixes without costly full-scale experimentation. Problem. The intensification of technological processes in modern construction requires highly efficient and reliable mixing equipment. Determining the performance characteristics of a real-scale concrete mixer through experimentation can be resource-intensive and time-consuming. Therefore, the need arises for a universal method that allows predicting the operational parameters of the equipment at the design stage. Goal The goal of the study is to justify the applicability of similarity criteria for calculating the productivity and drive power of a three-shaft forced concrete mixer. The method aims to provide a mathematically grounded alternative to experimental determination by using a scaling approach based on geometric and dynamic similarity. Methodology. The study uses the principles of dimensional analysis and the theory of similarity, particularly Buckingham’s π-theorem, to derive a set of key similarity criteria. These criteria describe the interactions between the working elements of the mixer and the concrete mixture, taking into account density, elasticity, surface activity, gravitational and inertial forces. Using these dimensionless numbers, transition coefficients between the basic model and the full-scale machine were calculated. Based on them, formulas for determining productivity and required drive power were derived. Results. The research resulted in a set of validated equations for calculating the main performance indicators of a full-scale mixer based on known parameters of a prototype or laboratory model. The system of similarity criteria allows taking into account the influence of design and operating factors without direct testing. It was shown that the three-shaft design enables three-circuit material flow and increased mixing intensity across the entire volume. The proposed approach is recommended for use in the design of energy-efficient and productive mixers for construction applications.