Dynamic processes modeling in a peristaltic pump with a hydraulic drive for a Bingham fluid

Abstract

Problem. At present, peristaltic pumps are widely used in construction, chemical production, mining industry, processing plants, food processing industry, etc. The creation of such devices and methods for the rational choice of their parameters is a vital task. One of the effective directions of its solution is the adequate dynamic process modeling in indicated mechanisms. Goal. The work is devoted to the creation of a universal mathematical model of dynamic processes in a peristaltic pump with a hydraulic drive for determining the technological qualities of the device, and the choice of its rational parameters. The model contains the primary geometric of the rotor, mass characteristics, the hydraulic motor dynamic characteristics, the parameters of the hose, and the mixture that is moving. Methodology. The procedure for the generation of Lagrange equations of the second kind was used for building a mathematical model of dynamic processes in the device. The model has been created in the form of a differential equation concerning the rotor angle of rotation. A method has been developed for forming the resistance moment to the pump rotor spinning from the rollers that deform the hose. A non-linear model of drag forces to the mixture movement, which is the Bingham fluid, is obtained by using the Buckingham equation. An expression is found for the drag forces due to the gravity forces of the mixture particles in the hose discharge part. An approach has been suggested to the usage of the catalog data for representing a hydraulic motor torque as an angular velocity function of its rotor . Results. Important technological features of the device operation have been established: the presence of a significant variable component in the mixture motion speed; the influence of the lift height hose length, coefficients of rolling friction for rollers, plastic viscosity, and yield strength in mixture motion speed and pump capacity. Originality. Important technological regularities of the device functioning were established: the speed of the mixture motion can have a significant variable component; the speed of the mixture motion and pump’s performance increase with a decrease in the length of the discharge hose and a decrease in its height, a decrease in the rolling friction coefficients for the rollers and a rejection of side rollers. Practical value. The results of using the developed method for studying dynamic processes were presented when a real construction of a peristaltic pump was being created. The suggested approach is high-potential for the modernization of existing and the development of new models of peristaltic pumps.