Mathematical Model of Dynamics of Centrifuge for Formation of Concrete Tubular Products

Abstract

The paper presents an advanced complex mathematical model of centrifuge dynamics for the formation of tubular products made of concrete or any other plastic and viscous confining mixtures. In the two-dimensional (plane) formulation of the problem, the studied mechanical system consists of a framework form (hollow rotor) with a partial confining filling, its elastic-damping suspension and power drive. It is assumed that the rotor is rigid, of correct design, has a certain static imbalance and can be both horizontal and vertical. The used filling is a concrete or some other mixture as a quasi-homogeneous plastic and viscous rheological body, which spreads slowly and in a shear flow over the inner surface of the rotor under the action of gravity forces and transfer forces of inertia. The rotor suspension is a roller lever type, but can be of any design, with certain inertial, rigid and damping characteristics. The variable power drive provides application of a variable torque to the rotor. The general theorems and dynamics equations, including the theorem on the motion of the mass center and the differential equation of rotation at the plane motion of a body with a pole other than the mass center, are used to construct differential equations of rotor dynamics. This eliminates the shortcomings of the known mathematical models with the similar problem statement. The proposed mathematical model can be implemented according to the well-known algorithms for numerical integration and used to develop or adjust the appropriate software. This enables the centrifuge dynamics to be studied more fully, to take into account and optimize its important parameters and characteristics.