Maintaining the required temperature deformations of the viscoelastic disc

Abstract

In the process of creating various equipment, machines, mechanisms, devices and other
constructions, the technological process of thermal shrink fit is often used. It is reasonable to heat ring discs for fitting them on round axes or in cylindrical holes in order to achieve energy savings by using time-varying power of heat sources. The mathematical model of seating is described using the thermo-viscoselasticity equations, which take into account the heating modes, thermal, elastic and viscous characteristics of the material. The physical relations for a viscoelastic body are presented according to the Maxwell's model. The problem is to heat the disc using heat sources with time-varying heat output so that the displacement on the inner contour becomes equal to the required displacement during heat treatment. The problem of thermal viscoelasticity is solved using the method of small parameter, and the integral equation for finding the law of time-varying specific power of heat sources, which ensures the creation of the required displacement on the inner contour of the disc for a given time, is obtained. The materials presented in this research are aimed at further development of the method of thermo-viscoselasticity in accordance with the solution of two-dimensional problems of optimal control and placement of axisymmetric thermal sources in order to create a certain radial displacement for a certain time with minimal energy consumption.