Mathematical model of temperature field distribution in thin plates during polishing with a free abrasive

Alex Avilov,Vladimir Syrovatka,Olga Baryshnikova,Rustam Hubiev

doi:10.1051/matecconf/201710201004

Alex Avilov, Vladimir Syrovatka + Show 2 more

Open Access

https://doi.org/10.1051/matecconf/201710201004

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Abstract

The purpose of this paper is to estimate the dynamic characteristics of the heating process of thin plates during polishing with a free abrasive. A mathematical model of the temperature field distribution in space and time according to the plate thickness is based on Lagrange equation of the second kind in the thermodynamics of irreversible processes (variation principle Bio). The research results of thermo elasticity of thin plates (membranes) will allow to correct the modes of polishing with a free abrasive to receive the exact reflecting surfaces of satellites reflector, to increase temperature stability and the ability of radio signal reflection, satellite precision guidance. Calculations of temperature fields in thin plates of different thicknesses (membranes) is held in the Excel, a graphical characteristics of temperature fields in thin plates (membranes) show non-linearity of temperature distribution according to the thickness of thin plates (membranes).

Highlights

In the aerospace industry circular membranes are used as reflectors of optic-electronic devices for orientation and celestial navigation of spacecraft and satellites
Modern technology and equipment used in polishing of thin plates allow to receive precision of surface machining, commensurate with the fractions of light wavelength
The process of thin steel plates polishing is accompanied by a considerable friction, the uneven distribution of heat flow in the plate material, the fluctuations of the technological system elements, the occurrence of thermo elasticity effects, the substantial depth of the broken layer and other phenomena that affect the quality of thin plates surface [2]

Summary

Introduction

In the aerospace industry circular membranes are used as reflectors of optic-electronic devices for orientation and celestial navigation of spacecraft and satellites. The process of thin steel plates (membranes) polishing is accompanied by a considerable friction, the uneven distribution of heat flow in the plate material, the fluctuations of the technological system elements, the occurrence of thermo elasticity effects, the substantial depth of the broken layer and other phenomena that affect the quality of thin plates (membranes) surface [2]. The goal of theoretical studies is the analysis of thermal processes occurring in polishing of thin plates (membranes) with a free abrasive. Where: U - heat capacity (the temperature elastic potential Bio), an analogue of the potential function in mechanics; ) -the potential of scattering, analogue of the dissipative function in mechanics; Fk - thermal mechanical strength, the analogue of the external force in mechanics; Dk - the generalized coordinate. The expression (5) after the differentiation and integrating has the form:

H 2dz c2 U 2T12

Findings

Conclusions