Influence of geometrical deviation of shape

on functionality and reliability of conical joints

M.Dudziak

University of Technology; Poznań, Poland

A.Kołodziej

Higher Vocational State School in Kalisz; Kalisz, Poland

G.Domek

Kazimierz Wielki University in Bydgoszcz; Bydgoszcz, Poland

Features such as reliability and safety of conical joints in machine and tools design highly depend on variation of designed geometrical shape and stereometry of surfaces of the elements. The work shows results of research of deviations of rectilinearity, roundness and angle of the cone. Problems connected with evaluation of real geometry and condition of surface structure as well as functionality of axisymmetric cone joints are discussed. Identification of essential deviations: rectilinearity, roundness and the angle of the cone together with their description allows development of new methodology in designing of safety and reliability characteristics of joints. Experimental research was carried out on the basis of joints used in car and aircraft industry.

For introduction we note.

Geometrical tolerances are limited only by geometrical deviations of an actual object from its nominal counterpart. That is why they are included in the group of simple geometrical tolerances. In machine industry, actual objects, like rollers or balls of bearings, rarely have elementary shape, e.g. of a cylinder or a sphere. Geometrical shape of machine parts is usually more complex, e.g. a stepped shaft consists of several cylindrical surfaces, a wheel-case is a solid with several holes, etc. In such cases, apart from necessity to meet dimensional and geometrical requirements, it is also necessary to ensure proper orientation and location of individual components. For example, surfaces of a double-step shaft should be coaxial cylinders, whereas axes of holes in a wheel-case should be parallel. It is not easy to achieve that for technological reasons.

Geometric shape of an actual surface of an object in only approximately consistent with nominal shape of that surface. For example, the surface of a shaft can be tapered or barrel-shaped, whereas its cross-section made by a plane perpendicular to the shaft axis can be elliptic. Deviations from the nominal shape are called geometrical deviations. In order to define acceptable limits for relative deviations of direction and position of those components, ISO standards define tolerances of orientation, location and run-out. Tolerances of orientation, location and run-out are limited both by actual object shape deviations and orientation or/and location deviations. In most cases, tolerances of orientation, location and run-out require specification of the base, that is why in the ISO 1101 standard they are classified as geometrical tolerances with a reference element. The ISO 1101:1985 standard defines a geometrical tolerance as an area (tolerance range) in which a surface or line of an actual object should be included. This area has a form of a cylinder or a circle, space between two parallel planes or straight lines, space between two coaxial cylinders or circles etc. Value of the form tolerance specifies respectively: the diameter of a cylinder or a circle, the distance between planes or straight lines or the difference of radii of cylinders or circles that limit the range of tolerance. There are no limitations for (simple) form tolerances as regards the location of the range of tolerance in space. Whereas for the orientation, location and run-out tolerances the range of tolerance is specified in space by bases.

As rule it is accepted the assumption about ideal geometrical properties and physical parameters for connection components.

Besides obtained conditions do not take into account changes of the friction factor values in main directions (the equilibrium or movement) within coordinate planes caused by form deviations of mating elements. Here we propose a model that takes into account non-ideality of joints and variability of the friction factor.

In conclusion we note.

The most popular way of the analysis of functionality and reliability of axisymmetric joints is determining the minimum and maximum value of the analysed parameter. However due to performance deviations of the axisymmetric joints, it is necessary to apply more complex methods. Actual functioning of those joints is associated with: reduction of the contour contact area, change of function (negative allowance, play), assembly stresses, stress concentration, friction factor scatter, which reduces ability of load transfer. Assessment of actual functionality of axisymmetric joints depends on appropriate selection of the fit, shape, and geometric structure of the joint components. It is the aim of this project.

 

The work reported in this paper was funded in part by the Ministry of Science and Higher Education, Poland.