# Determination of the stress-deformed state of the grinding circle adjustment pencil

## Authors

• Ivan Belmas Dnipro State Technical University, Ukraine
• Olena Bilous Dnipro State Technical University, Ukraine
• Anna Tantsura Dnipro State Technical University, Ukraine
• Illia Puzyretskyi Dnipro State Technical University, Ukraine
• Oleksandr Shablia Dnipro State Technical University, Ukraine

## Keywords:

pencil for straightening an abrasive wheel, two-layer composite, mechanical properties of the material, displacement, stress, load, Erie stress function

## Abstract

Using the Ery stress function in a linear formulation, using the methods of the classical theory of elasticity, an algorithm for analytically determining the stress-strain state of the working part of the abrasive wheel straightening tool as a two-layer composite material was developed. The algorithm allows considering arbitrarily distributed normal and tangential loads of the working surface of the abrasive grain of the tool. It considers the mandrel's limitation of deformations of the grain and the material that attaches it to it, the compatibility of the deformation of the grain and the material of its attachment to the mandrel, and their mechanical properties.

Calculations performed according to the obtained algorithm allowed the following to be established. The maximum standard stresses on the working face of the grain exceed the corresponding stresses on the opposite face due to their more uniform distribution. The tangential stresses are almost uniformly distributed along the specified face. The material connecting the grain to the tool mandrel deforms almost uniformly due to its lower modulus of elasticity and smaller thickness than the abrasive grain's modulus of elasticity and thickness. Determining the stress-deformed state of the executive part of the pencil for correcting the working surfaces of grinding wheels for abrasive processing of materials makes it possible to specify the known mechanism of their interaction and increase the efficiency of the technological process of restoring the working surfaces of the tool for abrasive processing of metals.

Taking into account the simultaneous deformation of the abrasive grain and the material that attaches it to the pencil mandrel, determining their stress-strain states using the methods of the classical theory of elasticity allows us to consider the results obtained by the given algorithm as sufficiently reliable within the limits of linear deformation. It is advisable to direct further research to determine the durability of the "abrasive grain-bond" system under variable cyclic loads.

## Author Biographies

### Ivan Belmas, Dnipro State Technical University

Doctor of Technical Sciences, Professor, Head of the Department of Mechanical Engineering and Welding Technology

### Olena Bilous, Dnipro State Technical University

Candidate of Technical Sciences, Secretary of the Faculty of Mechanical Engineering, Associate Professor of the Department of Mechanical Engineering

### Anna Tantsura, Dnipro State Technical University

candidate of technical sciences, associate professor, associate professor of the Department of Mechanical Engineering

### Illia Puzyretskyi, Dnipro State Technical University

graduate student of the Department of Mechanical Engineering

### Oleksandr Shablia, Dnipro State Technical University

seeker of the second (master's) level of higher education

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