Wyniki wyszukiwania - Biblioteka Nauki

1

Modeling and experimental validation of walking processes

100%

Nigmatullin R. R. , Morozov A. L. , Awrejcewicz J. , Ludwicki M.

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tom Vol. 40, no. 1

200--210

EN

The so-called intermediate model (IM) was applied in the paper to quantitatively describe complex trajectories. Using this model it was possible to find the proper fitting function for describing random trajectories that were recorded during the walking process performed by a volunteer. Experimental data were acquired using a three-dimensional Motion Capture system during normal gait of a healthy person on an automatic treadmill. The major aim of this research was to find if the IM is applicable to fit typical biomechanical measurement data. Motion Capture data collection is very time-consuming and requires a lot of memory, so storing movement trajectories in a parametric form helps to increase the data processing efficiency and mathematical analysis. As a result of the original treatment procedure described in this paper, we obtained a very accurate fit of the measured data. The results of this research can be used to model the movement of mechanical devices and for diagnostic purposes.

2

Cele i mozliwości stosowania korekcji w łożyskach wałeczkowatych

70%

Raczyński A.

Tribologia

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1999

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tom nr 1

55-70

PL

Korekcja wałeczków i bieżni pierścieni łożysk wałeczkowych jest od dawna stosowana w celu wyrównania nacisków kontaktowych. Mniej są znane inne możliwości, jakie może dać korekcja. Poprzez korekcję bieżni głównych i wałeczków można wpływać na rozkład prędkości ślizgania. w efekcie można wywołać taki moment sil stycznych. że wspomaga on właściwe toczenie wałeczków po bieżniach. W kontakcie wałeczków z bieżnia pomocniczą dzięki korekcji czoła wałeczka i tej bieżni można osiągnąć hydrodynamiczny film olejowy i w rezultacie tarcie płynne. Tak więc dzięki korekcji można zmniejszyć prace tarcia w łożysku.

EN

It is well-known that the distribution of contact pressures is improved by the correction of working surfaces of roller bearings, since edge concentrations of these pressures are reduced. However, there are various kinds of correction of different degrees of manufacturing difficulties and different effects. Arc correction, chord correction and logarithmic correction with modification are most frequently used. In the paper, comparisons of the three correction types taken from the literature are quoted. In the comparisons different loads of contact and the tilt of the roller with respect to the raceway axis that can occur in practice have been taken into consideration. The diagram of the ,,contact load capacity" proves that logarithmic correction with modification generally gives the best effects. The second purpose of using correction is to reduce the friction work at the contact of the rollers with the side flange. Correction of this contact can consist in: - deflecting the generatrix of the side flange from the roller end plane, - replacing the flat roller end with the convex end, - introducing a convex generatrix of the side flange. In the article different forms of corrected contact have been analysed (basing on the figures given) and their advantages in the aspect of the formation of fluid friction on the roller end have been shown. The best conditions for the formation of an hydrodynamic oil film occur when the convex roller end and the side flange of the slightly tilted generatrix are combined. This is the case of a small sensitivity to the manufacturing errors and load changes. The possibility of the easy formation of an oil film has been assessed on the grounds of the shape of the bearing interspace and the rate of the lubricant inflow to the contact area. The third aim of using correction is the possibility to modify the moments of tangent forces acting upon the roller from the side of raceway of the inner and outer ring. This refers to bearings of the tilted axis of the rollers in relation to the bearing axis, since the correction of these raceways and the correction of the lateral surface of the roller affects the contact length, the distribution of the rubbing speed and the distribution of unitary tangent forces. By modifying moments of tangent forces one can control the tendency of the roller to skew and there by affect friction work in the bearing. In barrel bearings a reduction in the tendency to skew results in the so called self-stabilisation of the roller, i.e. the loss of the pressure force between the roller and the side flange. The preservation of such a state during operation of the bearing greatly decreases friction work. In cone bearings there is a tendency of the roller to skew, caused by the friction force on the side flange. The moments of friction deliberately generated and determined by the correction on the main raceways can compensate this tendency. This also results in a decrease in the total friction work. However, in order to achieve this goal a certain perturbation of the kinematic conformity in the cone bearing is necessary. In view of the purposes being so different, it is not easy to select the proper magnitude of correction. A certain compromise is necessary and it is for the designer of the bearing to decide about it.

3

Metodyka analizy nacisków i tarcia w łożyskach wałeczkowych w aspekcie korekcji styku

60%

Raczyński A.

Tribologia

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1999

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tom nr 2

151-169

PL

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.

EN

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.