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1

A method of preload selection for a system of angular contact ball bearings due to the moment of friction

Kaczor Jarosław

Tribologia

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2019

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nr 1

5--12

EN

Angular contact ball bearings are usually used in the situation when high stiffness of a bearing is demanded. However, a significant stiffness improvement can be achieved only after introducing a preload (“assembly clamp”) into a system of angular bearings. The aim of the research was to develop a method of preload selection for a system of angular contact ball bearings. As a result, a higher stiffness of the bearing without significant loss in its durability will be obtained.

PL

Łożyska kulkowe skośne są zwykle stosowane w sytuacjach, kiedy potrzebne jest uzyskanie dużej sztywności łożyskowania. Jednakże znaczące zwiększenie sztywności można uzyskać dopiero dzięki wprowadzeniu napięcia wstępnego (tzw. zacisku montażowego) do układu łożysk skośnych. Celem przedstawionej pracy było opracowanie takiej metody doboru napięcia wstępnego układu łożysk kulkowych skośnych, wskutek której byłoby osiągnięte zwiększenie sztywności łożyskowania bez znaczącego uszczerbku dla jego trwałości.

2

The selection of preload in angular contact ball bearings according to the criterion of moment of friction

Kaczor J., Raczyński A.

Tribologia

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2018

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nr 1

35--44

EN

The article [L. 3]presents a method of preload selection in angular contact ball bearings based on their durability. The preload can be expressed as a force or as a dislocation (distance). Depending on the regulation method, the preload is also indirectly connected with the moment of friction in a bearing. The objective of the paper is to determine a maximum preload in angular contact ball bearings, based on the moment of friction in a system of bearings.

PL

W artykule [L. 3]przedstawiono metodę doboru napięcia wstępnego w łożyskach kulkowych skośnych, kierując się ich trwałością. Napięcie wstępne może być wyrażone jako siła lub jako przemieszczenie (odległość). Zależnie od metody regulacji, napięcie wstępne jest pośrednio związane także z momentem tarcia w łożysku. Celem tej pracy jest określenie maksymalnego napięcia wstępnego w łożyskach kulkowych skośnych, kierując się momentem tarcia występującym w układzie łożysk.

3

Uszczelnienia wałów korbowych o zmniejszonych oporach tarcia

Romanik G., Rogula J.

Autobusy : technika, eksploatacja, systemy transportowe

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2018

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R. 19, nr 6

686--690, CD

PL

W artykule omówiona została współpraca elastomerowego pierścienia uszczelniającego z wałem pod kątem zużycia i strat na pokonanie sił tarcia, konstrukcja klasycznego uszczelnienia oraz uszczelnienia o obniżonym oporze ruchu. Ponieważ układ warga uszczelnienia-wał to specyficzna para cierna, skoncentrowano się na lokalnych warunkach styku w skali mikro jako parametrze decydującym o globalnych oporach ruchu w skali makro. Ponieważ wystąpienie przedwczesnej awarii uszczelnienia mimo niedużych kosztów samego elementu generuje poważne koszty naprawy oraz przestój taboru transportowego problem trwałości i niezawodności pracy opisywanego typu uszczelnień pozostaje wciąż aktualny.

EN

The article discusses the cooperation of the elastomeric sealing ring with the shaft in terms of wear and losses to over-come friction forces, the construction of a classic seal and a seal with reduced resistance to movement. Because the lip-shaft system is a specific friction pair, the focus has been on local micro contact conditions as a parameter that determines global motion resistances on a macro scale. Since the occurrence of premature sealing failure in spite of small costs of the element itself generates serious costs of repair and downtime of the transport fleet, the problem of durability and reliability of the described type of seals remains valid.

4

The Influence of the Form Deviations of Sleeve-Shaft Couple on the Variation of Frictional Resistance in a Connection

Dudziak M., Kołodziej A.

Machine Dynamics Research

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2014

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Vol. 38, No. 4

15-22

EN

The frictional capacity of service load transmission is defined for the nominal mating surfaces in machine units which are constructed of elements with form deviations. Variable profile of elements obtained during production is the reason of variable values of frictional resistance which are caused by the limited (actual) contact in a connection. The paper presents the test stand for the measurement of the force and moment of friction of sleeve-shaft couple. The sleeve was connected with special shafts which were manufactured intentionally with radial deviations, cross-section deviations and their compilations. The experimental investigations were performed in order to determine the influence of the form deviations and angular positions of the shaft on the value of axial friction force (during shaft translation) and moment of friction (during shaft rotation).

5

Stanowiskowe badania procesu wkręcania łączników gwintowych

Nieoczym A.

TTS Technika Transportu Szynowego

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2012

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R. 19, nr 9

393--400, CD

PL

W artykule przedstawiono wyniki badań procesu wkręcania śrub oraz dokonano analizy statystycznej zarejestrowanych wartości momentu skręcającego, momentu tarcia oraz siły osiowej. Dodatkowo zaprezentowano wyniki zmian tych wartości pod wpływem różnych powłok ochronnych śrub oraz obecności czynnika smarnego. Scharakteryzowano stanowisko badawcze oraz zaprezentowano algorytmy sterujące jego pracą.

EN

In the article findings of the process of driving screws were presented as well as they caused a statistical analysis of registered values of the turning moment, the moment of the friction and axial force. Additionally results of changes of these values were presented under the influence of different protective coatings of screws and the presence of the spreadable factor. A research position was characterized as well as algorithms controlling his work were expressed.

6

Analiza zmian momentu i współczynnika tarcia poprzez wykorzystanie pomiaru wielkości elektrycznych

Paszeczko M., Lenik K., Skalski P.

Tribologia

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2004

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nr 5

205-212

PL

Znajomość przebiegu procesów tribologicznych jest niezwykle ważna w prognozowaniu trwałości elementów maszyn i urządzeń, co bez wątpienia wpływa na wydłużenie czasu pracy danej maszyny. Dlatego też autorzy niniejszego artykułu przeprowadzili szereg badań określających zmiany natężenia prądu zabezpieczającego pracę układu napędowego głowicy roboczej. Badania te miały na celu przedstawienie korelacji zmian natężenia prądu z wielkością zmian momentu tarcia oraz ukazanie możliwości określania podstawowych wielkości tribologicznych (moment tarcia, współczynnik tarcia, siła tarcia) przy pomocy odczytu i analizy wielkości elektrycznych.

EN

The analysis of frictional drags is a basic trouble in the job opinion of the tribological arrangement. Having in view were explored indication possibility the taken by driving arrangement of working knuckle to qualification of correlation with sizes of frictional drags utilization of measurement of changes of current electric intensity, and in peculiarity of moment the friction as well as coefficient of friction. They experimental tests were conducted on modified Amsler's tribotester. The modification in main measure depended on passage with registration of changes of size frictional drag with mechanical measures on measurements these the size the electronic units, as well as in relays the investigative method with arrangement of type the shield - the shield (the disk he disk) on arrangement of type the pin -the shield (the pin the he disk). All the measured sizes can be sended for mediation of converters and record-keeper of universal type Vectron to computer store, which permits on it the follow-up action the changes in real-time as well as the easy and quick analysis of got results. In conducted investigations measurement depended on inrolment the changes of size of current electric intensity taken by arrangement with the help of amperometer APPA engaged in exciting circuit. However the use of arrangement tensometer gave the possibility of registration of moment friction. It in of assurance of linear dependence taken by arrangement of electric current with weight of measuring knuckle aim belonged to alter the kind of excitement with daisy chain the engine on parallel arrangement. They in track of investigation be recorded simultaneously: the size of current electric intensity, temperature of race, moment of friction. Execution on three samples these investigations simultaneously as well as the conducted to the end analysis of mass losses permitted to establish, it with exactitude of measurements be closes in borders 10-11%. How to be visible from calculations both these values Pt-elektr and Pt - mech are to me the moss approximate what the received direction of investigations confirms relating the utilization of measurements of electric sizes to carrying out the analysis of changes of moment friction together with with coefficient of friction, as well as to controlment of course of process of friction. The measurement of electric sizes (the intensity and voltage) is a lot of easier from direct measurement of frictional drags, which joins with precise realization of bridges the tensometrycznych fault-tolerant little mechanical and temperature. This permits in future to explore the post of frictional tests chosen rubbing in this steams also and materials from modified top layer.

7

Możliwości zmniejszenia oporów tarcia w ślizgowym łożysku wzdłużnym

Kuśmierz L., Gajewska Z.

Tribologia

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2002

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nr 4

1211-1220

PL

W pracy rozważono model ślizgowego łożyska wzdłużnego z płytkami wahliwymi, pracującego w warunkach smarowania hydrodynamicznego. Założono, że przepływ czynnika smarnego przez szczelinę olejową jest adiabatyczny, a wymiana ciepła w filmie olejowym odbywa się na drodze konwekcji. Uwzględniono zmiany lepkości oleju w funkcji temperatury oraz deformacje sprężyste i termosprężyste segmentów wahliwych łożyska. Zbadano wpływ dwóch postaci konstrukcyjnych płytek wahliwych, ich sztywności oraz szerokości względnej na opory tarcia w łożysku. Przeprowadzono badania symulacyjne dotyczące wpływu lepkości oleju, prędkości kątowej wału oraz liczby płytek wahliwych na wartości momentu tarcia. Obliczenia numeryczne zostały przeprowadzone w oparciu o opracowany własny program komputerowy BEARING, umożliwiający wyznaczenie rozkładu ciśnienia oraz temperatury w filmie olejowym zintegrowany z systemem metody elementów skończonych ALGOR. Wyniki badań numerycznych wykazały widoczny wpływ wybranych czynników na wartości momentu tarcia w ślizgowym łożysku wzdłużnym.

EN

In the paper the model of the tilting pad thrust bearing operating in conditions of hydrodynamic lubrication has been considered. The adiabatic flow of the lubricating medium in the oil clearance has been assumed. The assumption that the heat exchange in the oil film is performing by the way of convection was adopted. Changes of the oil viscosity with temperature, elastic and thermoelastic deflections of tilting pads were taken into account. The influence of the two variants of pads, their stiffness, and the relative width parameter on the frictional resistance of the bearing has been studied. The simulation examinations concerning the influence of the oil viscosity, shaft rotational velocity and the number of tilting pads on the values of friction moment were carried on. The computations were executed basing on the own computer programme BEARING making possible the determination of the oil film pressure and temperature distributions. This programme is integrated with the finite element method system ALGOR. The results of computations show the essential influence of chosen factors on the thrust bearing frictional resistance.

8

Wpływ mikrogeometrii na parametry pracy łożysk stożkowych

Raczyński A.

Tribologia

|

2000

|

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.

9

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.