Mathematical Model of the YaMZ-239 Gear Box as an Object of Diagnosis

Abstract

Features of the operation of road transport provide for frequent stops and further acceleration, braking, gear changes, and the like. This leads to an increase in the dynamic load of vehicle units, and, as a consequence, to an intensification of the processes of wear of the friction surfaces of clutch discs, gear and cardan gears, and the like. Defects of the components of the gear box also arise due to improper use. Timely and high-quality diagnostics of the car’s gear box will increase the uptime of the car and improve its technical and economic indicators.

A significant increase in the number of vehicles, an increase in brands and models require the development of modern diagnostic tools and methods. The value of the general principles of operation of gear boxes allows you to localize the area of malfunctions, minimize the process of trial and error.

Now, in most cases, malfunctions of the YaMZ-239 type gear box are detected by external signs. It is possible to improve the quality of the process of diagnosing gear boxes, among other things, by creating new mathematical models of their functioning.

That the existing methods and means of diagnosing gear boxes of motor vehicles do not fully allow determining their current technical condition, which requires the development of mathematical models of their units and parts as an object of diagnostics it was found when analyzing the literary sources.

The YMZ-239 type gear box, which is part of the power unit of trucks, was selected as the object of diagnostics.

An overview of the designs of the model range of gear boxes of the YaMZ-239 type, as objects of diagnostics are presents in the article.

Replacing real technical devices with their idealized models makes it possible to widely apply various mathematical methods. In this case, the gear box, as an object of diagnostics, is presented in the form of a "black box", the input and output parameters of which have a finite set of values. To represent this diagnostic object in the form of a "black box", the following are set: the number of all incoming actions Y; the number of all output signs of malfunction S; the number of all faults of the diagnostic object X; operator A, which converts the quantities X and Y into the number S.

In general, the mathematical model is a system of functional dependencies between each diagnostic signal and structural parameters.

For the YaMZ-239 gear box, a diagnosis matrix has been compiled, which includes a list of faults and symptoms of faults.

That the process of making a diagnosis based on the model of the object being diagnosed is possible if the reverse transformation of the number of signs of malfunctions into the number of structural parameters (malfunctions) of the object was unambiguous it has been determined.

The proposed mathematical model for diagnosing a gear box of the YaMZ-239 type will make it possible to identify malfunctions of its assemblies and parts, depending on their signs, which will significantly increase the uptime of both the gear box itself and the entire vehicle.