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1

Automatyzacja kontroli jakości wyrobów w linii technologicznej wytwarzania wałeczków łożysk tocznych

Zbrowski A.

Technologia i Automatyzacja Montażu

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2008

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nr 2

36-40

EN

Quality inspection is one of the crucial problems in modern manufacturing processes. The implementation of the in-line quality control with ensuring continuity and efficiency of manufacturing process needs an automation of inspection process. The solution of the automation of quality inspection in the manufacturing line of bearing rollers is presented in the article. For inspecting rollers and defects detecting the optical inspection method was applied. The developed AOI system contains computer based image analysing software, process control system and mechatronics modules for transporting and selecting rollers. The AOI system was successfully implemented in the manufacturing line of bearings. The system enables the inspection of 30 defects of rollers with the high resolution and the efficiency of about 10.000 parts per hour.

2

Wpływ mikrogeometrii na parametry pracy łożysk stożkowych

Raczyński A.

Tribologia

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2000

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nr 1

90-110

PL

W artykule przedstawiono badanie wpływu korekcji i geometrii styku na biezni pomocniczej łożyska stożkowego na tarcie i naciski kontaktowe przy różnej makrogeometrii i różnych obciążeniach. Metoda obliczeń jest opisana w poprzednim artykule autora. Charakterystyki momentu tarcia i nacisków kontaktowych służą określeniu optymalnych wartości parametrów mikrogeometrycznych. Są przedstawione zależności tych optymalnych parametrów od makrogeometrii łożyska. Podane zalecenia mogą być bezpośrednio wykorzystane do projektowania kształtu powierzchni roboczych łożyska stożkowego, charakteryzującego się zmniejszonymi oporami ruchu i większą prędkością graniczną.

EN

The following work represents the continuation of the former articles written by the same author: "Purposes and Possibilities of the Use of Correction in Roller Bearings" and "The Method of Analysis of Pressures and Friction in Roller Bearings from the Aspect of the Contact Correction". .In order to do research work on the influence of microgeometrical dimensions (beta,hi, ho, hw, delta, Rk) on friction lisses and contact pressure the author worked out the computer programme based on method shown in (L.6). In the programme, equations of equilibrium are solved first, then running parameters are calculated (primarily the moment of friction of a bearing and contact pressures) for given bearing dimensions and axial load Fa. The choice of correction of main bearing races and main surface of roller. Research was carried out for ten bearing sizes. For each size, 306 correction combinations were determined. For each combination calculations in the range of angle beta from (βn - 4') to (βn + 4') ware made to obtain the smallest moment M(T) value. Relative load was assumed at P/C =0,35 level. In all series with a contact angle α less then 17° the smallest values of M(T) are achieved at the correction system that is hi=hw>0 ho=0. Only in the 313 series (α=28°48'39") the smallest values of M(T) are achieved at the correction system: hi=hw>0, ho(…)2hi.The proper correction value depends and its dimensional proportions. Therefore, the choice of correction value was solved by means of non-dimensional method for fictitious bearings with different macrogeometry. The results of these calculations are illustrated in DRAWING 4. The characteristics of the most favourable correction values depending on bearing macrogeometry is shown in DRAWING 5. The choice of angle β. Drawing 6 present an example of characteristics of a moment of friction for a certain macrogeometrical case. The most favourable value β is about 1°59'55". Taking working tolerance into consideration, it was assumed that the tolerance range of angle β should lie between -4" and +26". As result of the calculations of the friction moment for other variants of macrogeometry, depedence of recommended angle β deviations on quotient Lw/Dw was determined, which is shown in DRAWING 7. The choice of angle δ an radius Rk. The studies of the influence of these parameters on pressure in a roller 's contact with a side flange and on the friction moment of a bearing were jointly conducted by means of a non-dimensional method. One of the resultant diagrams is demonstrated in DRAWING 8. On exceeding a certain value of Rk the moment of friction rapidly rises as a result of extension of the contact area, which starts on the edge of the roller end. This causes an increase in friction force and makes the formation of an oil film difficult. The successive curves attributed to the increasing values of an angle δ are displaced downwards and to the left. The value of the angle is compromising due to the friction and contact pressures and it is enclosed in the range of 89°40'÷89°45'. The minimum moment of friction occurs at Rk=0,95÷0,96 value. Owing to the analogus calculations made for others macrogeometrical variants, the dependence of the most favoruable values δ and Rk on macrogeometry parameters was obtained. It is shown in DRAWING 10 in a form of diagrams. At the end an example of the correction choice is presented. On comparing the results with the recommendation stated in work (L.2), it was assumed that there was a little difference between them. On the other hand, using the above described method one can divide the recommended in (L.2) sum of correction between a bearing roller and bearing rings.

3

Korekcja styku wałeczków i bieżni łożysk baryłkowych poprzecznych

Raczyński A.

Tribologia

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2000

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nr 6

1009-1125

PL

W artykule jest przedstawione badanie wpływu korekcji styku na bieżniach głównych łożyska baryłkowego na tarcie i naciski kontaktowe przy różnych obciążeniach i dwóch różnych rodzajach korekcji. Metoda obliczeń jest opisana w jednym z poprzednich artykułów autora. Uzyskane charakterystyki momentu tarcia i nacisków kontaktowych służą do określenia optymalnych wartości parametrów mikrogeometrycznych. Zaprezentowana na jednym przykładzie metoda postępowania może być zastosowana do konstruowania dowolnego łożyska baryłkowego dwurzędowego. Analiaza wyników obliczeń wykazała, że przy obciążeniach małych i średnich (P/C<0,2) wystarcza zastosowanie jednołukowej korekcji wałeczków. Przy większych obciążeniach pożądana jest korekcja dwułukowa ze względu na spiętrzenia nacisków kontaktowych.

EN

The present article is the fourth of a series by this author concerning the microgeometry of roller bearings.published in "Tribology". The previous had the following titles "Purpose and possibilities of the use of correction in roller bearings" ,"The Method of analysis of pressures and friction in roller bearings in aspect of contact correction" and "The effect of microgeometry on running parameters of taper roller bearings". In order to investigate the effect of the microgeometrical dimensions of the spherical roller bearings on power losses and contact pressures, the author has written a special computer program. It is base on the methodology presented in paper(L11). In the program, equations of balance are solved first. Then, contact pressures the skew of the roller and the moment of frictionof the bearing for the pre-set dimensions and load are computed. One significant checking parameter is the roller skew self-stabilisation angle.Its absolute value shows whether the roller presses against the side flange during the rolling(L8). The operation of a bearing is considered correct if the rollers are in the state of self-stabilisation without any contact with the side flange (L.3). In such a case, the microgeometry of the spherical roller bearing resolves itself to the form of adhesion of the roller profile to the inner and outer ring profile. This form results from the correction of an appropriate contact. In practice, two kinds of correction of spherical roller bearings are possible (FIG.1a) and two-arc correction (FIG. 1b). In the analyses made so far, the attention was paid only to the importance of correction for the uniform distribution of pressures in the contact, and not to the resistance to motion of the bearing. The aim of the calculations presented herein is to investigate the effect of the spherical roller bearing microgeometry on the contact capacity and the resistance to motion. These properties of the bearings are practically defined by two parameters: the maximum contact pressures and the moment of friction. The sample calculations refer to one type bearing only, namely 22316. Two levels of the relative load of the bearing was assumed P/C=0.1 (average load) and P/C = 0.35 (large load).The calculation results are presented in the form of graphs which show the characteristics of the greatest unit pressures at the contact of the roller and the rings p(max.w) and p (max.z) as a function of the radius R(BW), the characteristics of the self-stabilisation angle Θ 0 for the loaded rollers and the characteristics of the moment of friction of the bearing. Owing to these graphs the most favourable values of R(BW) can be selected; the minimum of the moment of friction and the smallest values of pressures should be aimed at; at the same time, the self-stabilisation angles Θ 0 of the loaded rollers should be kept within -0.006rad - +0.006rad. An analysis of the results of the computer computations has shown that spherical roller bearings with the rollers made without two-arc correction can be satisfactority used under small and medium loads (P/C<0.2). By using the selected dimensions R(B) and R(BW),the concentraction of stresses can be avoided and a satisfactory compromise beteween the minimisation of the resistance to motion and the minimisation of contact stresses achieved. If the relative load of the bearing is geater than 0.2, the concentration of stresses is formed, first of all at the contact of the roller and the outer ring (due to the greater adhesion coefficient). In this situation, the correction of the rollers is necessary. Analyses have proved that the two-arc correction of the parameters conformant with the results of the work is effective (L.7). The same radii, R(B) and R(BW), which turned out to be the most favourable in the case of the roller made without two-arc correction can be used here as the main radii of the lateral generatrix of the roller and the race of the outer ring. The method of finding the most favourable dimensions of the bearing of reference number 22316 can be used for any type and size of a spherical roller bearing. Thus, it is a practical method for the engineering shaping of the working surfaces of double -row spherical roller bearings.

4

Obciążenie wałeczków łożyska stożkowego w zależności od napięcia wstępnego

Raczyński A.

Problemy Eksploatacji

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2000

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nr 3

211-219

PL

W artykule jest przedstawiona metoda obliczeniowa i wyniki obliczeń. Metoda ta została oparta na równaniach Hertza i Lundberga, dotyczących współzależności obciążenia i odkształceń w styku liniowym. Ponieważ odkształcenia w obydwóch łożyskach są ze sobą powiązane [poprzez wał], więc w procedurze obliczeniowej jest zastosowana metoda iteracyjna. Zakładane są odkształcenia promieniowe i osiowe tak długo, aż wartości sił, które im odpowiadają, okażą się zgodne z obciążeniem zewnętrznym. W odkształceniach uwzględnia się napięcie wstępne łożysk. Wyniki obliczeń wykonanych dla pewnego przypadku są zilustrowane w tabeli. Zostało wykazane, że średnie obciążenie wałeczków może zostać zmniejszone wskutek dobrania odpowiedniego napięcia wstępnego.

EN

In this paper the calculation method and calculation results are presented. The method is based on the model introduced by Lundberg [L. 4], with taking into account Hertz equations suitable for line contact. The iteration method was used to the calculation procedure: The radial loads of both of bearings and the axial load of shaft are known [given]. The displacement of one bearing ring with respect to the other one is assumed and for this the internal forces are calculated time after time, until the equilibrium Equations of forces are satisfied. When the right displacement is obtained, one can determine the distribution of roller loads. An adequate computer programmed was built which affords possibilities of calculation of load distribution in dependence on: 1) radial and axial load acting on bearing arrangement, and 2) bearing preload, expressed by bearing outer rings one to other close up. Except this, the average load of roller for each of bearings is point out, which determines the durability of bearing. It was proved on the way of calculations, than thanks suitable values of preload, the average load of roller can be decreased. On the diagrams [FIG. 4] the values of rollers load for various values of preload (e) are shown.

5

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

Raczyński A.

Tribologia

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1999

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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.

6

Cele i mozliwości stosowania korekcji w łożyskach wałeczkowatych

Raczyński A.

Tribologia

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1999

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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.