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1

Comparison of the stiffness of 3D-printed wire raceway slewing bearing based on simplified FEA model and experiment

Gunia Dominik, Smolnicki Tadeusz, Stańco Mariusz

Engineering Transactions

|

2023

|

Vol. 71, iss. 3

383--397

EN

The wire-raceway bearings are a subcategory of slewing bearings. Their popularity has recently increased due to their advantages, including weight that is lower than that of other similar slewing bearings, and the ability of transferring various loads, such as axial load, radial load and tilting moment. Currently, metal rings (steel or aluminum) are the most popular choice for all kinds of slewing bearings; however, with advent of additive manufacturing a new ‘chapter’ opens for the development of wire raceway slewing bearings, where the interface between the rolling elements and the raceway is the same as in other bearings (i.e., contact between steel-steel). At the same time, rings can be made from other lightweight materials, such as composites or plastics, with high-level shape customization due to 3D printing. Stress between wire raceways and rings is much lower. Hence, rings’ lower material properties do not significantly affect bearing capacity. Proper calculation methodology should be created to analyze lightweight wire raceway bearings, as materials can differ significantly from typical materials covered by current theories. The paper presents a prototyped 3D-printed bearing with rings made from polylactic acid (PLA). The bearing stiffness is measured and compared with the simplified finite element analysis (FEA) model using the equivalent bearing model with nonlinear springs and beam elements.

2

Digital twin of slewing roller bearings operating in wind turbine structures

Krynke Marek

Zeszyty Naukowe Akademii Morskiej w Szczecinie

|

2022

|

nr 71 (143)

64--71

EN

A digital twin is a digital replica, a mathematical model of a given object, product, process, system, or service. A digital twin enables the attainment of a significant amount of data and it can be used to gain comprehensive knowledge about a given object, its behaviors, and reactions. The constant ability to monitor the product and its reactions contribute to its improvement and the exclusion of errors, as well as its optimization, which in turn allows for a more perfect product. This article presents a model of a digital twin for the analysis of the operation of a slewing bearing in the structure of a wind turbine. The quality of the bearing is directly related to the quality of the materials from which they were made, the process of thermo-chemical treatment, and the accuracy of all its elements, as well as its proper assembly. The bearings are characterized by very narrow tolerances. Errors in the shape of cylindricity cause distortion of the bearing raceway, stress accumulation, and jamming of rolling parts. This leads to rapid bearing wear as a result. The condition for the approval of bearings for sale is the successful passing of all tests, both geometric and strength. This is to develop quality standards that bearing suppliers must meet. The article presents an analysis of the load distribution that prevail in rotor blade bearings at the limit loads of a wind turbine. The basic types of the most commonly used coronary bearings for wind turbine applications were considered. A methodology for constructing computational models of slewing bearings, using the finite element method, was developed. An original way of simulating rolling parts with rod elements – for rollers and superelements – for the support balls was proposed. A numerical FEM model of a slewing bearing with a wind turbine rotor hub is presented. The calculations accounted for the susceptibility of the bearing rings and hub, as well as the stiffness of the mounting screws. Areas of bearing raceways, where rolling parts achieve the greatest loads, have been identified. Demonstrated by diagrams are the deformations of the rotor hub seats and bearing rings.

3

Management the safety of exploitation of the rotation mechanism in a self-propelled crane

Krynke Marek, Vaško Alan

System Safety : Human - Technical Facility - Environment

|

2019

|

Vol. 1, nr 1

624--631

EN

The article analyzes of the load capacity of the rotation mechanism of the boom arm sub-assembly for a self-propelled crane. The uneven flexibility of systems supporting structures of the machine was taken into account in the identification of the load. The consideration are illustrated by the example slewing bearing from self-propelled crane. FEM method was used for calculations. The basic problems of construction of numerical model were discussed. Sample calculations of bearing carrying capacity has been done taking into account flexibility of bearings supporting structures, which also allowed to define the internal load distribution in the bearing. On example of the supporting structure of the mobile crane DST 5050 the internal load distribution in the crane bearing at different positions of the crane machine body were defined. During the rotation of the crane body priority angels were indicated. It has been shown that the deformations of the supporting frames are so large that they significantly change the distribution of forces transmitted by the individual bearing rollers.

4

Wpływ kierunku działania sił promieniowych na przebieg charakterystyk nośności statycznej łożyska wieńcowego jednorzędowego

Śpiewak S.

Przegląd Mechaniczny

|

2016

|

nr 3

26--33

PL

Artykuł dotyczy problematyki katalogowego doboru łożysk tocznych wieńcowych obciążonych siłami promieniowymi o dużych wartościach. W pracy zaprezentowano metodykę modelowania łożysk wieńcowych. Obiektem analizy było łożysko wieńcowe jednorzędowe, produkcji krajowej, które jest zastosowane w koparce jednoczerpakowej F250H. W artykule przedstawiono charakterystyki nośności statycznej badanego łożyska zależne od kierunku działania obciążeń promieniowych względem wektora momentu wywrotnego, co w dotychczasowych pracach nie było rozważane. Dodatkowo do oceny własności użytkowych bieżni łożyska zaproponowano wykorzystanie metod statystycznych. Parametry rozpatrywanego łożyska oraz wartości uzyskanych wielkości statystycznych zestawiono w tabelach. Całość badań prezentowana w publikacji obejmuje wykorzystanie metody elementów skończonych, równań opisujących mechanikę kontaktu układu kulka-bieżnia oraz elementy statystyki do rozwiązywania problematyki łożyskowań.

EN

Article concerns the problems related to catalog selection of rolling bearings which are loaded large radial forces. A methodology for modeling of slewing bearing was presented. The object of the analysis was the one row ball slewing bearing, domestic production, which is used in excavator type F250H. The static carrying load curvatures of the slewing bearing which are depend on direction acting the radial loads relative to the vector of tilting moment were shown, what in previous works wasn't considered, Additionally to evaluation of functional properties of the bearing raceway the statistics methods were used, The parameters of the considering bearing and the values obtained of statistic quantity have been contained in the tables. The whole study that are presented in the publication involves the use of finite element method, the equations of contact mechanics for ball-race way and statistic method to solving the bearing problems.

5

The modification of the raceway profile in the double row slewing bearing

Kania L., Śpiewak S., Pytlarz R.

Journal of KONES

|

2016

|

Vol. 23, No. 1

139--146

EN

The slewing bearings are applied in heavy working machines and operated in extreme conditions. A characteristic feature of these bearings are a high load which determining a large deflection of a contact zone rolling element - raceway. This phenomenon combined with the effects of a bearing clearance causes a significant increase in a contact angle of the bearing. This in turn causes displacement of the contact zone to an undesirable position. In the construction of slewing bearing is applied of a large value of the osculation ratio. This leads to occur of large sizes of the contact zone identified in a radial cross-section. The sizes are comparable to values of the radius of the ball. The contact zone is type of quasi-linear. Effects of changes the position of the contact zone in the double-row ball slewing bearing has been presented in the paper. The raceway profile for such bearing consists of the arc section changing in the radial section. When the contact zone includes a change point of curvature of the raceway profile it comes to a concentration of a contact stress, and this is unfavourable for operation of the bearing. In order to eliminate this phenomenon to the profile introduced a transition curve. For this purpose was selected a clothoid. The curve ensures a gradual change of curvature from the arc section of the profile to the zero curvature of the straight profile section. The raceway profile becomes the smooth curve of the second rank. In the article are presented a numerical model of the contact zone for the double-row ball slewing bearing and the distributions of a pressure in the contact zone for the ordinary and modified raceway profiles. The calculation results have been presented as graphs of the distributions of the pressure along the contact zone. It has been shown that the introduction modification of the raceway profile eliminates the concentration of the pressure along the contact zone profile. The results obtained can be used during design of the raceway profiles of the double-row ball slewing bearing.

6

Numerical analysis of bolts loading in slewing bearing

Krynke M.

Czasopismo Techniczne. Mechanika

|

2016

|

Y. 113, iss. 4-M

89--94

EN

This article analyzes screw connection of slewing bearings to various structures of support elements. The susceptibility of support elements to the load distribution in particular bearing screws was examined by means of the Finite Element Method. The load values of screws and their distribution around the perimeter of the combined bearing rings were also specified.

PL

W niniejszym artykule dokonano analizy połączenia śrubowego mocującego łożysko wieńcowe do różnych struktur jego zabudowy. Korzystając z metody elementów skończonych, zbadano wpływ podatności podzespołów wsporczych na rozkład sił przypadających na poszczególne śruby mocujące łożysko. Określono wartości obciążenia śrub i ich rozkład po obwodzie łączonych pierścieni łożyska.

7

Influence of Radial Forces Positively, Negatively and Perpendiculary Directed on the Static Carrying Capacity of the one Row Ball Slewing Bearing

Jaskot A., Śpiewak B., Śpiewak S.

Machine Dynamics Research

|

2015

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Vol. 39, No. 3

33-47

EN

Problems of determining the static limiting load curves of slewing bearings where were taken into account all possible directions of radial forces have been presented in the paper. The object of the analysis was the one row ball slewing bearing, domestic production, which is used in excavator type F250H. In order to carry out the evaluation of functional properties of the bearing raceway the statistics methods were used. The parameters of the considering bearing and the values obtained of statistic quantity have been contained in the tables. Calculations were performed by using the finite elements method (FEM), ADINA program, analytical Eschmann's formulas and classical mechanics equations.

8

Modeling of selected load-bearing structures using the truss and beam elements

Jaskot A., Śpiewak S.

Journal of Applied Mathematics and Computational Mechanics

|

2015

|

Vol. 14, nr 3

37--47

EN

The article presents the methodology of adjusting the usable properties of rodlike and beam elements for modeling the complex load-bearing structures. The basic object of consideration was the single-row slewing ball bearing. In this paper the mapping issues of usable qualities of the slewing bearings are summarized in relation to use of the finite element method. The emphasis is primarily on using the rod-like and beam elements for modeling the contact phenomena in the ball-raceway contact zone. In addition, ideas for use of the beam elements to modeling bearing bolts were presented.

9

Influence of Radial Forces on Change of Friction Torque in Twin Slewing Bearing

Kania L., Śpiewak S.

Machine Dynamics Research

|

2014

|

Vol. 38, No. 2

121-131

EN

A method of numerical conduct research of phenomena which occur in slewing bearing has been presented in the paper. The basic problems concerning technical peculiarity of slewing bearing were defined. The object of the analysis was twin slewing bearing for which a model of contact zone ball-raceway was developed. Results of calculations which are presented in the paper were obtained by using a model of twin slewing bearing described in a separate publication. Nascent conditions of rolling resistance in slewing bearing were specified. The paper presents importance of radial forces as a component of the external load of slewing bearing. The results of numerical analysis of changing friction torque of twin slewing bearing caused by external load were submitted. In especially action of radial forces on the slewing bearing has been taken into account. The values of fraction torque were shown on the background of static limiting load curve for the slewing bearing which was considered. The original numeric method was used to determine the fraction torque for slewing bearing. Calculations were performed by using the finite element method, ADINA program, analytical Eschmann formulas and classical mechanics equations.

10

Wyznaczanie oporów ruchu łożyska tocznego wieńcowego w oparciu o rozkład obciążenia wewnętrznego

Kania L., Śpiewak S.

Tribologia

|

2013

|

nr 1

59--68

PL

W artykule zaprezentowano oryginalną metodę wyznaczania momentu tarcia w łożyskach wieńcowych. Do analizy przedstawionych problemów wykorzystano metodę elementów skończonych i analityczny model tarcia tocznego. Obliczenia potrzebne do wyznaczenia rozkładu obciążenia wewnętrznego w łożysku i maksymalnej wartości siły obciążającej elementy toczne łożyska były przeprowadzone za pomocą procedur wykorzystujących system ADINA L. 8, 9]. Zamieszczono autorski model pozwalający na wyznaczanie współczynnika tarcia tocznego dla układu kulka–bieżnia łożyska. Przyjęte modele uwzględniają uwarunkowania techniczne przekazywania obciążenia zewnętrznego na elementy składowe łożysk wieńcowych podwójnych. Wyznaczono charakterystyki momentu tarcia, które zaprezentowano na tle charakterystyk nośności statycznej, odpowiadających zadanej wartości luzu łożyskowego.

EN

The original method to determine the friction torque for twin slewing bearings is presented in the article. The finite element method and analytic model of rolling friction has been used for the analysis of presented problems. The calculation to determine the maximum contact force on the rolling element was done using a ADINA program 8, 9]. The copyrighted model that made it possible to determine the various friction coefficients for contact zone ball–bearing race in slewing bearings is attached. Accepted models allow the estimation of the technical conditions of acting external load on component parts of twin slewing bearings. The profile of the carrying capacity and friction torque of twin slewing bearing for a constant value of bearing clearance is presented.

11

Porównanie wybranych parametrów łożysk wieńcowych podwójnych i łożysk wieńcowych jednorzędowych

Kania L., Śpiewak S.

Przegląd Mechaniczny

|

2013

|

nr 1

27--33

PL

W artykule porównano wybrane parametry łożysk wieńcowych podwójnych i jednorzędowych. W analizie uwzględniono wpływ luzu osiowego na zmianę charakterystyk nośności statycznej obu typów analizowanych łożysk. Przedstawiono wykresy momentu tarcia łożysk w odniesieniu do ich nośności statycznej. Do analizy przedstawionych problemów wykorzystano metodę elementów skończonych i analityczny model tarcia tocznego. Zamieszczono wykresy rozkładów obciążenia wewnętrznego w analizowanych łożyskach.

EN

The chosen selected parameters of twin slewing bearings and slewing bearing single-row ball have been presented in the article. The effect of bearing clearance on change of static carrying capacity of both analyzed types has been considered. Diagrams of carrying capacity and friction torque have been created. The finite element method and analytic model of rolling friction has been used to the analysis of presented problems. The diagrams of distribution the internal load in analyzed beadings has been presented.

12

Analiza numeryczna wpływu przylegania kulki do bieżni łożysk wieńcowych na wartość współczynnika twardości

Kania L., Pytlarz R., Reszka P.

Biuletyn Wojskowej Akademii Technicznej

|

2013

|

Vol. 62, nr 1

89-99

PL

W artykule przedstawiono tok postępowania oraz rezultaty analizy numerycznej zagadnienia kontaktowego występującego w łożyskach tocznych wieńcowych. Analiza dotyczyła wpływu stosunku promieni krzywizn stykających się ze sobą elementów pary tocznej łożyska, czyli kulki i bieżni, na współczynnik wpływu twardości. Współczynnik wpływu twardości jest szczególnie ważny w łożyskach wieńcowych, gdyż pozwala uwzględnić rożne twardości pary tocznej. Łożyska wieńcowe, m.in. ze względu na swoje znaczne rozmiary, są elementami maszyn, które sprawiają wiele trudności technologicznych związanych z ich wykonaniem. Jednym z kluczowych problemów jest hartowanie bieżni łożyskowych. Z tego też względu przy projektowaniu węzłów obrotu maszyny należy uwzględniać twardość współpracujących ze sobą elementów tocznych i bieżni, do czego służy współczynnik wpływu twardości. W pracy przeprowadzono obliczenia numeryczne z uwzględnieniem odkształceń plastycznych w strefie styku. W tym celu posłużono się metodą elementów skończonych, wykorzystując program ADINA.

EN

The paper presents the procedure and the results of numerical analysis of contact problems occurring in the slewing bearing. The analysis concerned the effect of osculation in contact pair of rolling bearings, the ball and raceway, on hardness factor. Hardness factor is particularly important in the large bearings, because it allows us to consider the different hardness of a contact pair. Slewing bearings, among other things for their substantial dimensions, are machine elements which cause a lot of technical difficulties associated with their workmanship. One of the key problems is the hardening of the bearing raceway. Therefore, designing the machine revolution nodes, the hardness of cooperating rolling elements and raceway should be considered, what for the correctional hardness factor is used. In this work, a numerical calculation considering the plastic deformation in the contact zone has been carried out. For this purpose, a finite element method using the ADINA program has been used.

13

Wpływ luzu łożyskowego na nośność statyczną łożysk tocznych wieńcowych podwójnych w odniesieniu do oporów toczenia

Kania L., Śpiewak S.

Pomiary Automatyka Kontrola

|

2012

|

R. 58, nr 1

119-122

PL

W artykule przedstawiono analizę wpływu luzu łożyskowego na przebieg charakterystyki nośności statycznej łożyska wieńcowego podwójnego. Wyznaczono w oryginalny sposób charakterystyki momentu tarcia, które zaprezentowano na tle charakterystyk nośności statycznej, odpowiadających wybranym wartościom luzu łożyskowego. Uzyskane wyniki przedstawiono w formie graficznej. Przeprowadzone analizy wykonano z użyciem metody elementów skończonych.

EN

The effect of selected bearing clearances in twin slewing bearing on their static carrying capacity is presented in the paper. Basic parameters of analyzed bearing are presented in the Tab. 1. The finite element method and analytic model of rolling friction has been used to the analysis of presented problems. Obtained results of profile static carrying for selected values of bearing clearance are presented as graph (Fig. 5). It is claimed to be a possibility to single out the range of bearing clearance which optimal profile of static limiting load curves is obtained. The way of determining (modeling) the effect of bearing clearance on the static carrying capacity of twin slewing is based on works [1, 5] and it is introduced in chapter 2. The original method to determining the friction torque for twin slewing bearings is presented (chapter 3) in the article. The calculation which is needed to calculate the maximum contact force on the rolling element has been done using the ADINA program [2, 7]. Profile of carrying capacity and friction torque of twin slewing bearing for selected values of bearing clearances have been presented (Fig. 6). It was thought that the permissible tension force for the fixing bolts should be predicted to the selection of construc-tional bearing clearances. The proposed method of determining of friction torque can be used to the selection of engine power which drive has been transmitted with using slewing bearing. The method presented in the article can be used to the analysis of twin- and other kinds of slewing bearings.

14

Numerical analysis of the screw connection with preload tension used in the mounting of slewing bearings

Reszka P., Kania L., Pytlarz R.

Journal of KONES

|

2012

|

Vol. 19, No. 2

465-472

EN

Slewing bearings are used as devices that connect two part working machine, usually with a rotating chassis body must meet safety criteria, manage to cope with extreme loads and environmental factors operation life. In this paper the distribution of pressure on surfaces of the screw's connections with preload tension is considered. A joining model which is used in rolling bearing is the subject of the analysis. The aim of the work is to introduce an auxiliary criterion of 'connection tightness' to the calculating methodology of bearings' fastening connections with building structure. Considered part of the three-row roller bearing, rings bearings and mounting elements are modelled solid type, and the bolts are modelled with beam-type element introduced preload tension value equivalent catalogue. Connected elements of the screw head rigid elements. The screws used in such a combined coronary bearings are not close fit, and established contact between the surfaces of the rings and the building is not homogeneous. Work is not only dedicated to the stress of contact between the contact surfaces A and B, but also considered is the effect of pitch spacing of the screws on the pitch rolling element bearing in the numerical solution ADINA system was used to prepare numerical models of junction. The results of the calculations of pressure distributions for changeable screw's span are shown graphically and the table of percentages of the load loss of contact between the surfaces A and B of slewing bearing screw connection.

15

Wpływ wybranych parametrów konstrukcyjnych na nośność statyczną łożysk tocznych wieńcowych podwójnych

Kania L., Śpiewak S.

Pomiary Automatyka Kontrola

|

2010

|

R. 56, nr 8

930-933

PL

W artykule przedstawiono analizę wpływu luzu między-pierścieniowego i kształtu zakończenia bieżni łożyska wieńcowego podwójnego na jego nośność statyczną. Wykorzystano modelowanie numeryczne za pomocą metody elementów skończonych. Uzyskano oryginalne wyniki, które zaprezentowano w formie graficznej. Określono pewne wytyczne odnośnie luzu między pierścieniowego i kształtu zakończenia bieżni łożyska wieńcowego podwójnego, które mogą być wykorzystane w projektowanych strukturach łożysk wieńcowych podwójnych a także innych typów łożysk wieńcowych.

EN

The effect of selected constructional parameters of twin slewing bearings on their static carrying capacity is presented in the paper. The radial gap between internal and external bearing rings and shape of bearing race profile is analyzed. To the analysis of the problem, the finite element method has been used. The bearing balls are modeled with superelements [7]. Computation was realized in two stages. In the first computation stage the models of contact zone ball - bearing race in elastic-plastic state of material have been developed. The meshing zones of balls and segments of bearing rings are presented in Fig. 1. The method presented in work [8] has been used. In particular models, values of radial gap between bearing rings and shape of edge of bearing race have been changed as in the Tab. 2. To obtain equivalent characteristics of ball - bearing race system, the iteration computations have been used. These characteristics have been used to specify characteristics of elastic truss elements which are being used in superelements. In the second computation stage, the characteristics of the carrying capacity of slewing bearing have been computed. The numerical model of twin slewing bearing presented in Fig. 3 has been used. Exemplary computations have been made for the twin slewing bearing SL023.50.2000 produced by Wuxi Lida Gear Manufacturing Co. (China). Parameters of analyzed bearing are presented in Tab. 1. The results of computation are presented in graphical form in Fig. 4 and Fig. 7. The effect of radial gap between bearing rings on equivalent characteristic of contact zone and on characteristic of bearing carrying capacity has been proved, recommended values of radial gap have been given. The method presented in the article can be used to the analysis of twin- and other kinds of slewing bearings.

16

Wyznaczanie charakterystyk zastępczych kulek w numerycznym modelowaniu łożysk tocznych wieńcowych

Kania L., Śpiewak S.

Pomiary Automatyka Kontrola

|

2009

|

R. 55, nr 6

334-337

PL

Charakterystyki zastępcze części tocznych umożliwiają ich modelowanie za pomocą elementów prętowych w modelach numerycznych łożysk wieńcowych wykonanych przy użyciu metody elementów skończonych. W pracy omówiono sposób wyznaczania charakterystyki zastępczej kulek w łożysku wieńcowym kulkowym jednorzędowym. Wykorzystano w tym celu model strefy styku kulki z bieżnią łożyska oraz segment modelu numerycznego pierścienia łożyska z tzw. superelementem. Przedstawiono założenia budowy modelu i przykładowe wyniki obliczeń numerycznych. Obliczenia wykonano przy założeniu sprężysto-plastycznego stanu materiału z uwzględnieniem tarcia na powierzchniach styku.

EN

Equivalent characteristics of rolling elements enable their modelling with help of truss elements in finite element method based numerical models of slewing bearings [2, 3, 4]. A new method for determination of equivalent characteristics of balls in a single-row ball slewing bearing (Fig. 1) is presented in the paper. At the first stage of calculations the numerical model of the ball contact zone with the bearing raceway was developed (Fig. 2). The model is divided into sections. In the 2 and 3 contact sections There was used a material in elastic-plastic state with bilinear characteristic (Fig. 3) in 2 and 3 contact sections, while in 1 and 4 sections - an elastic one. At the second stage the numerical model of a bearing ring segment (Fig 4.) with a super-element (Fig. 5) was developed. The super-element consists of two pairs of rigid beam elements (2) and an elastic truss element (1) with nonlinear characteristic ??-?. The model was loaded with a force calculated by formula (2) with the material hardness coefficient according to [9]. Numerical calculations were carried out with ADINA software [7]. Table 1 and Fig. 6. present the equivalent characteristic of the ball. The calculations results were approximated by power function (4). The new method for calculation of the bearing ball equivalent characteristic allows for accurate simulation of the bearing contact zone. It can be applied to all types of ball slewing bearings. Accurate estimation of the ball equivalent characteristic will have positive influence on accuracy of calculating the bearing capacity.

17

Modelowanie korekcji cięciwowo-łukowej w wałeczkach łożysk tocznych wieńcowych

Kania L.

Pomiary Automatyka Kontrola

|

2008

|

R. 54, nr 7

417-420

PL

W pracy przedstawiono analizę korekcji cięciwowo-łukowej stosowanej w wałeczkach łożysk tocznych wieńcowych. Analizę przeprowadzono wykorzystując metodę elementów skończonych. Przedstawiono model obliczeniowy strefy styku. Wykonano obliczenia rozkładu nacisków wzdłuż tworzącej wałeczka dla różnych wartości parametrów analizowanej korekcji w sprężystym i sprężysto-plastycznym stanie materiałów bieżni i wałeczka. Przedstawiona metoda pozwala na dobór poprawnych parametrów korekcji dla specyfiki łożysk wieńcowych.

EN

In the paper the analysis of cylindrical crowned correction applied for rollers in slewing bearings has been presented. The analysis has been executed with the help a finite element method. Numerical model of contact zone has been presented. Computations of the normal traction across the contact line of the roller with bearing race for different correction parameters at elastic and elastic-plastic state of materials of rollers and bearing rings has been performed. Analysis method presented in paper allows for selection of correct parameters of rollers correction for specific to slewing bearings.