## Abstract

Introduction. Grinding remains the most efficient and effective method of final finishing that is indispensable in the production of high-precision parts. The characteristic features of grinding materials are that the removal of the material roughness of the workpiece surface occurs due to the stochastic interaction of the grains of the abrasive material with the surface of the workpiece, in the presence of mutual oscillatory movements of the abrasive tool and the workpiece being processed. During processing workpieces with abrasive tools, the material is removed by a large number of grains that do not have a regular geometry and are randomly located on the working surface. This makes it necessary to apply probability theory and the theory of random processes in mathematical simulation of operations. In real conditions, during grinding, the contact of the wheel with the workpiece is carried out with a periodically changing depth due to machine vibrations, tool shape deviations from roundness, unbalance of the wheel or insufficient rigidity of the workpiece. To eliminate the influence of vibrations in production, tools with soft ligaments are used, the value of longitudinal and transverse feeds is reduced, but all these measures lead to a decrease in the operation efficiency, which is extremely undesirable. To avoid cost losses, mathematical models are needed that adequately describe the process, taking into account the influence of vibrations on the output indicators of the grinding process. The purpose of the work is to create a theoretical and probabilistic model of material removing during finishing and fine grinding, which allows, taking into account the relative vibrations of the abrasive tool and the workpiece, to trace the patterns of its removal in the contact zone. The research methods are mathematical and physical simulation using the basic provisions of probability theory, the laws of distribution of random variables, as well as the theory of cutting and the theory of deformable solids. Results and discussion. The developed mathematical models allow tracing the effect on the removal of the material of the superimposition of single sections on each other during the final grinding of materials. The proposed dependencies show the regularity of the stock removal within the arc of contact of the grinding wheel with the workpiece. The considered features of the change in the probability of material removal when the treated surface comes into contact with an abrasive tool in the presence of vibrations, the proposed analytical dependences are valid for a wide range of grinding modes, wheel characteristics and a number of other technological factors. The expressions obtained allow finding the amount of material removal also for the schemes of end, profile, flat and round external and internal grinding, for which it is necessary to know the magnitude of relative vibrations. However, the parameters of the technological system do not remain constant, but change over time, for example, as a result of wear of the grinding wheel. To assess the state of the technological system, experimental studies are carried out taking into account the above changes over the period of durability of the grinding wheel.

Original language | English |
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Pages (from-to) | 33-47 |

Number of pages | 15 |

Journal | Obrabotka Metallov |

Volume | 24 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2022 |

## Keywords

- Abrasive grain
- Grinding of titanium
- Microcutting
- Probability of material not removing
- Probability of material removing
- The contact area of the workpiece with the tool

## ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials
- Metals and Alloys