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Warianty tytułu
The method of analysis of pressure and friction in roler bearings from the aspect of the contact correction
Języki publikacji
Abstrakty
W artykule jest opisany model zastosowany przy obliczaniu nacisków kontaktowych i momentu tarcia w łożysku wałeczkowym dowolnego rodzaju. W modelu tym uwzględnia się zmienność ciśnienia i poślizgu w obszarze styku wałeczków z bieżniami oraz zmienność współczynnika tarcia w zależności od poślizgu i ciśnienia, a także odchylenie wałeczków od nominalnego kierunku toczenia. Obciążenia wałeczka są obliczane przez całkowanie jednostkowych sił normalnych i stycznych. W wyniku rozwiązania równań równowagi wałeczka wyznacz się moment tarcia łożyska .Program komputerowy umożliwia obliczanie maksymalnych nacisków kontaktowych i momentu tarcia w zależności od dowolnie przyjętej korekcji.
In the previous article (Purposes and Possibilities of the Use of Correction in Roller Bearings) the author has demonstrated that the use of correction can serve the purpose of reducing friction work, and as a result can lead to an increase in the mechanical efficiency of a bearing. To theoretically develop appropriate correction, one needs a calculation method allowing the moment of friction of a bearing to be determined depending on the correction. A mathematical-physical model is always the basis of a calculation method. The model assumed for the present analysis is as follows. The bearing rollers are subjected to the action of normal and tangent forces. Normal forces manifest themselves in the form of certain pressure fields in the contact with the roller races, while tangent forces - in the form of fields of unit forces. The pressure distribution I is calculated according to Boussinesq problem, by the finite element I method, taking into consideration the differences between the nomi- I nal and the actual position of the roller. (In reality, forces acting on the rollers cause their skew and tilt). Unit tangent forces are calcu- I lated on the basis of local unit pressures (related to pressure) and a ! local coefficient of friction. The local coefficient of friction depends on the pressure and slide, ace. to the literature data. Characteristics I of the coefficient of friction appropriate for the races (where small I slide occurs) and for the flanges (characterised by great slide). It is I slightly more difficult to calculate the coefficient of friction on the I flange when the area of contact starts on the edge of the roller end, since mixed friction occurs of a different proportion of fluid friction at different points of the contact area. The author has presented his own proposal of a solution to this problem, relating the contribution of fluid friction to the distance from the edge of the roller end. Lost motion at the contact of the roller with the ring is calculated basing on the differences in their tangential velocities. This difference results from the curved profile of these elements, from the skew of the roll- ' ers, and from the fact that the geometrical vertex of the cone of the roller does not lie on the bearing axis (which is a deliberate geometrical discrepancy). After the discussion of the mathematical model, a model of action of the rings on the roller of the cone bearing is presented in the article. This is the most complicated case (asymmetrical structure of the bearing, loads acting on the roller from three sides, greatly diversified lost motion on the races and on the flange, and considerable tendency of the roller to skew). First, the interaction of the race of the inner ring (FIG. 7) has been illustrated. Unit normal and tangent forces are integrated and then represented by concentrated normal and tangent forces and the moment of tangent forces. Next, the interaction of the flange has been illustrated, where the determination of concentrated resultant forces has also been presented. FIG. 8a shows a complete juxtaposition of normal forces and moments acting on the roller of the cone bearing. This juxtaposition is the basis of formulation of equations of balance of the roller (expressions 29-34). Moreover, equations of balance of the outer ring are used (expressions 35-40, FIG. 8b). In these equations there are certain geometrical and kinetic parameters which are functions of the following groups of quantities: a) the dimensions of the bearing imposed by the constructor, b) the normal loads on three races, Qi,Q0, Qf, c) the roller shift parameters: the skew angle Q and the tilt angle r\, as well as the angles of the roller cones j3<(, fito- The parameters enumerated under points b and c are unknowns of the system of equations of equilibrium. The system of equations cannot be solved analytically, since the unknowns are involved in most variables occurring in the equations. Thus, a numerical solution using approximate methods must be used. After solving the equations of equilibrium, the moment of friction from the lost motion on the surfaces of contact of the rollers and rings and the contact pressures occurring in the bearing in the state of equilibrium are calculated. In this manner information is obtained about the parameters of operation of the bearing under consideration, having a given set of dimensions and correction and the load imposed. By repeating such calculations for successive variants of correction, an image of the effect of correction upon the parameters of operation is obtained, which allows one to choose the most advantageous correction.
Czasopismo
Rocznik
Tom
Strony
151--169
Opis fizyczny
bibliogr. 14 poz., tab., wykr.
Twórcy
autor
- Katedra Techniki Ogrzewczej i Wentylacyjnej Politechniki Łódzkiej
Bibliografia
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPS1-0003-0021
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