Four-Point Contact Ball Bearing Model With Deformable Rings

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Samy Lacroix ◽  
Daniel Nélias ◽  
Alexandre Leblanc
Keyword(s):  
Contact Pressure ◽  
Ball Bearing ◽  
Point Contact ◽  
Contact Angles ◽  
Structural Deformation ◽  
Geometrical Parameters ◽  
Fe Model ◽  
The Impact ◽  
Maximum Contact ◽  
Contact Ellipse

In many applications, such as four-point contact slewing bearings or main shaft angular contact ball bearings, the rings and housings are so thin that the assumption of rigid rings does not hold anymore. In this paper, several methods are proposed to account for the flexibility of rings in a quasi-static ball bearing numerical model. The modeling approach consists of coupling a semianalytical approach and a finite element (FE) model to describe the deformation of the rings and housings. The manner in which this weak coupling is made differs depending on how the structural deformation of the ring and housing assemblies is injected into the set of nonlinear geometrical and equilibrium equations in order to solve them. These methods enable us to account for ring ovalization, ring twist, and raceway opening (including change of conformity) since a tulip deformation mode of the ring groove is observed for high contact angles. Either the torus fitting technique or mean displacement computation are used to determine these geometrical parameters. A comparison between the different approaches allows us to study, in particular, the impact of raceway conformity change. The loads used in this investigation are chosen in order that the maximum contact pressure (the Hertz pressure) at the ball-raceway interface remains below 2000 MPa, without any contact ellipse truncation. For the ball bearing example considered here, relative differences of up to 30% on the axial displacement, 10% on the maximum contact pressure, and 10% on the contact angle are observed by comparing rigid and deformable rings for a typical loading representative of the one encountered in operation. Despite the local change of conformity, which becomes significant at high contact angles and for thin ball bearing flanges, it is shown that this hardly affects the internal load distribution. The paper ends with a discussion on how the ring and housing flexibility may affect the loading envelope when the truncation of the contact ellipse is an issue.

scholarly journals The Influence of the Geometrical Parameters for Stress Distribution in Wire Raceway Slewing Bearing

2017 ◽  
Vol 64 (3) ◽  
pp. 315-326 ◽  
Author(s):  
Dominik Gunia ◽  
Tadeusz Smolnicki
Keyword(s):  
Stress Distribution ◽  
Internal Pressure ◽  
Ball Bearing ◽  
Point Contact ◽  
Geometrical Parameters ◽  
Contact Wire ◽  
Slewing Bearing ◽  
Distribution Of Stresses

Abstract This paper presents the current study of the distribution of stresses for four-point contact wire race ball bearing. The main aim of this article is to define the most important geometrical rules in a wire-race bearing. The results for bearings of different geometrical parameters are presented. In the study, one also estimates the distribution of internal pressure in particular bearing elements.

Analysis of contact mechanics in McKee-Farrar metal-on-metal hip implants

2003 ◽  
Vol 217 (5) ◽  
pp. 333-340 ◽  
Author(s):  
A Yew ◽  
M Jagatia ◽  
H Ensaff ◽  
Z M Jin
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Region ◽  
Radial Clearance ◽  
Geometrical Parameters ◽  
Contact Pressure Distribution ◽  
Acetabular Cup ◽  
Metal On Metal ◽  
Half Angle ◽  
Maximum Contact

Contact mechanics analysis for a typical McKee-Farrar metal-on-metal hip implant was carried out in this study. The finite element method was used to predict the contact area and the contact pressure distribution at the bearing surfaces. The study investigated the effects of the cement and underlying bone, the geometrical parameters such as the radial clearance between the acetabular cup and the femoral head, and the acetabular cup thickness, as well as other geometrical features on the acetabular cup such as lip and studs. For all the cases considered, the predicted contact pressure distribution was found to be significantly different from that based upon the classical Hertz contact theory, with the maximum value being away from the centre of the contact region. The lip on the cup was found to have a negligible effect on the predicted contact pressure distribution. The presence of the studs on the outside of the cup caused a significant increase in the local contact pressure distribution, and a slight decrease in the contact region. Reasonably good agreement of the predicted contact pressure distribution was found between a three-dimensional anatomical model and a simple two-dimensional axisymmetric model. The interfacial boundary condition between the acetabular cup and the underlying cement, modelled as perfectly fixed or perfectly unbonded, had a negligible effect on the predicted contact parameters. For a given radial clearance of 0.079 mm, the decrease in the thickness of the acetabular cup from 4.5 to 1.5 mm resulted in an increase in the contact half angle from 15° to 26°, and a decrease in the maximum contact pressure from 55 to 20 MPa. For a given acetabular cup thickness of 1.5 mm, a decrease in the radial clearance from 0.158 to 0.0395mm led to an increase in the contact half-angle from 20° to 30°, and a decrease in the maximum contact pressure from 30 to 10 MPa. For zero clearance, although the contact pressure was significantly reduced over most of the contact area, the whole acetabular cup came into contact with the femoral head, leading to stress concentration at the edge of the cup. Design optimization of the geometrical parameters, in terms of the acetabular cup thickness and the radial clearance, is important, not only to minimize the contact stress at the bearing surfaces, but also to avoid equatorial and edge contact.

scholarly journals Study of Contact Pressures in Total Hip Replacement

2020 ◽  
Author(s):  
Myron Czerniec ◽  
Jarosław Zubrzycki
Keyword(s):  
Contact Pressure ◽  
Hip Joint ◽  
Correct Selection ◽  
Radial Clearance ◽  
Total Hip ◽  
Metal Head ◽  
Hip Joint Endoprosthesis ◽  
Joint Load ◽  
The Impact ◽  
Maximum Contact

Total hip arthroplasty is a complex procedure. The achievements of implantology enabled the development of a faithful representation of hip joint physiology as well as the production of materials that can successfully replace damaged natural tissues. A very important issue is the correct selection of the geometry of the endoprosthesis adequate to the load of the joint. Materials used for endoprosthesis are a metal head and a polymer cup (e.g. PE-UHMW). The main interactions in the endoprosthesis are friction and surface pressure, which must be limited, exceeding them causes the destruction of the biomechanical system - plastic deformation of the polymer and the formation of too large and unacceptable radial clearances. Based on the author's developed calculation method of hip joint endoprosthesis contact parameters, the impact on maximum contact pressure and the angle of contact of the joint load was estimated depending on the diameter of the endoprosthesis and radial clearance. The correctness of changing the values of maximum contact pressure from the mentioned parameters was determined. Correspondingly: an increase in joint load causes a linear increase in the maximum contact pressure; increasing the diameter of the endoprosthesis head - their non-linear decrease, and increasing radial clearance - their increase

An Analytical Model of Four-Point Contact Rolling Element Ball Bearings

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
Jacob D. Halpin ◽  
Anh N. Tran
Keyword(s):  
Analytical Model ◽  
Ball Bearing ◽  
Minimum Energy ◽  
Point Contact ◽  
Contact Angles ◽  
State Theory ◽  
Operating Conditions ◽  
Rolling Element Bearing ◽  
Design Guideline ◽  
Rolling Element

The purpose of this work is to establish an analytical model and standard way to predict the performance characteristics of a four-point contact, or gothic arch type, rolling element ball bearing. Classical rolling element bearing theory, as developed by Jones, has been extended to include the complex kinematics of the four-point contact bearing; thereby providing complete elementwise attitude and internal load distribution of the bearing under operating conditions. Standard performance parameters, such as element contact stresses, contact angles, inner ring deflections, nonlinear stiffness's, torque, and L10 life, are solved explicitly via standard Newton–Raphson techniques. Race control theory is replaced with a minimum energy state theory to allow both spin and slip to occur at the ball-to-raceway contact. The developed four-point model was programed within the orbis software program. Various test cases are analyzed and key analytical results are compared with the Jones four-point contact ball bearing analysis program, the Wind Turbine Design Guideline, DG03, and traditional two-point (angular contact) analysis codes. Model results for the internal distribution of ball loads and contact angles match the Jones program extremely well for all cases considered. Some differences are found with the DG03 analysis methods, and it is found that modeling a four-point contact bearing by overlaying two opposed angular contact bearings can result in gross errors.

scholarly journals Elastic and Elasto-Plastic Contact Behavior on Ball Bearing

2020 ◽  
Vol 8 (6) ◽  
pp. 3622-3628
Keyword(s):  
Silicon Nitride ◽  
Contact Pressure ◽  
Ball Bearing ◽  
Great Influence ◽  
Aluminium Oxide ◽  
Elastic Model ◽  
Plastic Model ◽  
Elliptical Shape ◽  
Contact Behaviour ◽  
Maximum Contact

Contact pressure has a great influence on the realiability and the life of ball bearings. However, most of the previous contact and wear model mainly focussed on the elastic model. In this paper, considering the contact between ball bearing and inner ring, both elastic and elasto-plastic contact model are established to investigate the contact behaviour on ball bearing. Three types of materials have been used to compare the contact behaviour which are bearing steel, silicon nitride and aluminium oxide. Aluminium oxide experienced highest maximum contact pressure for elastic model while silicon nitride experienced highest maximum contact pressure for elasto-plastic model. The stress contour of elastic model was elliptical shape while elasto-plastic model was elliptical shape before the material yields.

scholarly journals EFFECTS OF DESIGN PARAMETERS ON STATIC EQUIVALENT STRESS OF RADIAL ROLLING BEARINGS

2021 ◽  
Vol 61 (1) ◽  
pp. 163-173
Author(s):  
Mehmet Bozca
Keyword(s):  
Contact Pressure ◽  
Contact Area ◽  
Elasticity Modulus ◽  
Equivalent Stress ◽  
Point Contact ◽  
Design Parameters ◽  
Line Contact ◽  
Rolling Bearings ◽  
Von Mises ◽  
Maximum Contact

The aim of this study is to theoretically investigate the effects of design parameters on the static equivalent stress of radial rolling bearings, such as the point contact case for ball bearings and line contact case for roller bearings. The contact pressure, contact area and von Misses stress of bearings are calculated based on geometrical parameters, material parameters and loading parameters by using the developed MATLAB program. To achieve this aim, both the maximum contact pressure pmax and Von Mises effective stress σVM are simulated with respect to design parameters such as varying ball and roller element diameters and varying ball and roller element elasticity modulus. For the point contact case and line contact case, it was concluded that increasing the diameter of ball and roller elements results in reducing the maximum contact pressure pmax Furthermore, increasing the elasticity modulus of the ball and roller elements results in increasing the maximum contact pressure σVM. Furthermore, increasing the elasticity modulus of the ball and roller element results in increasing the maximum contact pressure pmax and Von Mises effective stress σVM because of the decrease of contact area A. The determination of the diameter of the ball and roller elements and the selection of material are crucial and play an effective role during the design process. Therefore, bearing designers and manufacturers should make the bearing geometrical dimensions as large as possible and bearing material as elastic as possible. Furthermore, the stress-based static failure theory can also be used instead of the standard static load carrying capacity calculation. Moreover, Von Mises stress theory is also compatible with the finite element method.

scholarly journals Damage Risk of the Raceway Edge Arise in Four-Point Slewing Bearing

2019 ◽  
Vol 1 (1) ◽  
pp. 632-638
Author(s):  
Marek Krynke ◽  
Krzysztof Mielczarek
Keyword(s):  
Contact Angle ◽  
Ball Bearing ◽  
Point Contact ◽  
Contact Angles ◽  
Bearing Ring ◽  
Rolling Elements ◽  
Damage Risk ◽  
Slewing Bearings ◽  
Early Damage ◽  
Selection Of

AbstractIn the article some forms of damage to raceway of slewing bearings for single-row ball bearing slewing ring with four-point contact and their causes were shown. Changes of the contact angle and its influence on the geometry for contact zone of the rolling elements raceway were analyzed. An identification of changes for contact angle of individual balls for different parameters of the contact was received. It was showed that contact angles of some rolling elements were increasing. It can cause damage to the raceway by spalling or rolling out of edge of the bearing ring. Ways of avoiding too early damage to the raceway at the stage of the design and the selection of coronary bearings were suggested.

THEORETICAL STUDY OF THE EFFECT OF GEOMETRICAL PARAMETERS AND LOCATION OF ROTOR IMPACT ELEMENTS OF AN IMPACT-CENTRIFUGAL GRINDER ON SPEED AND ANGLES OF CRUSHED PARTICLES FLIGHT

2020 ◽  
Keyword(s):  
Granulometric Composition ◽  
Theoretical Study ◽  
Process Efficiency ◽  
Geometrical Parameters ◽  
Grinding Process ◽  
Main Work ◽  
Impact Element ◽  
The Impact ◽  
Positive Effect ◽  
Efficiency Indicators

One of efficiency indicators of grain grinders is grain granulometric composition. The basis of mixed fodder is crushed grain, the particles of which must have a leveled granulometric composition for subsequent mixing and obtaining a high-quality feed mixture. In agricultural production, hammer crushers are widely used, in which the destruction of grain occurs due to the impact of a hinged hammer. The main disadvantage of these crushers is that not the entire surface of the hammers is involved in grinding, thus reduces grinding process efficiency. A slightly different principle of material destruction is laid down in the basis of the proposed design of the shock-centrifugal grinder. Main work is performed by flat impact elements located on the rotor, which serve to accelerate crushed particles with subsequent impact of them on the bump elements. An important step in the design of new constructions of shock-centrifugal grinders is to determine size and location of the impact elements on the rotor, without which the grinding process is not possible. In the calculation method presented, the dependencies for determining the velocities and angles of a single particle flight from the surface of a flat impact element for its specified dimensions are proposed. Two variants of an impact element location on the rotor are considered and analyzed: radial and at an angle in the direction of rotor rotation. As a result of research carried out, it is noted that in the case of inclined position of an impact element on the rotor an increase in flight speed and flight angles change in crushed particles, which gives the opportunity to have a positive effect on grinding process.

scholarly journals Influence of finite element mesh size on the carrying capacity analysis of single-row ball slewing bearing

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110090
Author(s):  
Peiyu He ◽  
Qinrong Qian ◽  
Yun Wang ◽  
Hong Liu ◽  
Erkuo Guo ◽  
...  
Keyword(s):  
Finite Element ◽  
Carrying Capacity ◽  
Mesh Size ◽  
Finite Element Mesh ◽  
Fe Model ◽  
Element Mesh ◽  
Heavy Load ◽  
Slewing Bearing ◽  
Maximum Contact ◽  
Slewing Bearings

Slewing bearings are widely used in industry to provide rotary support and carry heavy load. The load-carrying capacity is one of the most important features of a slewing bearing, and needs to be calculated cautiously. This paper investigates the effect of mesh size on the finite element (FE) analysis of the carrying capacity of slewing bearings. A local finite element contact model of the slewing bearing is firstly established, and verified using Hertz contact theory. The optimal mesh size of finite element model under specified loads is determined by analyzing the maximum contact stress and the contact area. The overall FE model of the slewing bearing is established and strain tests were performed to verify the FE results. The effect of mesh size on the carrying capacity of the slewing bearing is investigated by analyzing the maximum contact load, deformation, and load distribution. This study of finite element mesh size verification provides an important guidance for the accuracy and efficiency of carrying capacity of slewing bearings.

scholarly journals Treatment of wood with atmospheric plasma discharge: study of the treatment process, dynamic wettability and interactions with a waterborne coating

Holzforschung ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jure Žigon ◽  
Matjaž Pavlič ◽  
Pierre Kibleur ◽  
Jan Van den Bulcke ◽  
Marko Petrič ◽  
...  
Keyword(s):  
Plasma Treatment ◽  
Treatment Process ◽  
Beech Wood ◽  
Treated Wood ◽  
Plasma Discharge ◽  
Contact Angles ◽  
Atmospheric Plasma ◽  
Waterborne Coating ◽  
Spruce Wood ◽  
The Impact

AbstractPlasma treatment is becoming a mature technique for modification of surfaces of various materials, including wood. A better insight in the treatment process and the impact of the plasma on properties of wood bulk are still needed. The study was performed on Norway spruce and common beech wood, as well as their thermally modified variations. The formations of the airborne discharge, as well as mass changes of the treated wood, were monitored. The impact of such treatment on wood-coating interaction was investigated by evaluating the dynamic wettability and penetration into wood. At the wood surface, plasma streamers were observed more intense on denser latewood regions. Wood mass loss was higher with increasing number of passes through the plasma discharge and was lower for thermally modified wood than for unmodified wood. Plasma treatment increased the surface free energy of all wood species and lowered the contact angles of a waterborne coating, these together indicating enhanced wettability after treatment. Finally, the distribution and penetration depth of the coating were studied with X-ray microtomography. It was found that the coating penetrated deeper into beech than into spruce wood. However, the treatment with plasma increased the penetration of the coating only into spruce wood.

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