Formulas for Moderately Elliptical Hertzian Contacts

1985 ◽  
Vol 107 (4) ◽  
pp. 501-504 ◽  
Author(s):  
J. A. Greenwood
Keyword(s):  
Contact Pressure ◽  
Contact Area ◽  
Hertzian Contact ◽  
Radius Of Curvature ◽  
Asymptotic Equation ◽  
Equivalent Radius ◽  
Circular Contact

For small ellipticities the Hertzian contact pressure and approach can be obtained to a good approximation by using the formulae for circular contact with an equivalent radius of curvature (AB) −1/2, where A and B are the principal relative curvatures. For higher ellipticities (AB(A + B)/2)−1/3 should be used to find the contact area and pressure; an equivalent radius for finding the approach is also given. The ellipticity of the contact can be estimated from the asymptotic equation (a/b) ≈ (B/A)2/3.

Prediction of the Leakage Threshold for Hertzian Contact Seals: An Experimental Approach

2018 ◽  
Author(s):  
Jeroen Van Wittenberghe ◽  
John Vande Voorde
Keyword(s):  
High Pressure ◽  
Contact Pressure ◽  
Contact Area ◽  
Oil And Gas ◽  
Empirical Evaluation ◽  
Evaluation Criteria ◽  
Hertzian Contact ◽  
Surface Topology ◽  
Current Form ◽  
Leak Tightness

The prediction and evaluation of leakage and leak tightness is an important issue in a multitude of high-pressure applications, such as valves, flanges and threaded pipe connections that are used under extreme service conditions that occur in oil and gas exploration and production. Using Hertzian contact theory or finite element techniques it is possible to determine the local contact conditions at the seal on a macroscopic level (to wit the extent of the contact area and the contact pressure in this area). However, the leak tightness of such a contact depends also on the surface topology, which is a microscopic characteristic. Therefore, the assessment of leak tightness requires an evaluation criterion relating both scales. Empirical evaluation criteria have been postulated in the past, each with their own application domain. More recently the Persson method has been developed that models the contact area microscopically using contact models developed in the field of tribology. However, in its current form this model is limited to flat surfaces while in many applications, such as valves, O-ring seals or metal-to-metal seals of threaded pipe connections, the contact is Hertzian and the contact pressure distribution is not uniform but parabolic. This paper provides the experimental results that will be used to validate an extension of the Persson model to Hertzian contact seals. A set of samples for leakage experiments was produced with varying surface topology. The surface roughness of these samples is measured and the leakage behaviour under high pressure is evaluated. This paper focusses on the experimental evaluation of the influence of surface topology on leakage.

An Elliptical Microcontact Model Considering Elastic, Elastoplastic, and Plastic Deformation

2003 ◽  
Vol 125 (2) ◽  
pp. 232-240 ◽  
Author(s):  
Yeau-Ren Jeng ◽  
Pei-Ying Wang
Keyword(s):  
Plastic Deformation ◽  
Contact Pressure ◽  
Contact Area ◽  
Contact Model ◽  
Real Area Of Contact ◽  
Elliptical Contact ◽  
The Mean ◽  
Elliptic Contact ◽  
Circular Contact ◽  
Real Area

This study developed an elastic-plastic microcontact model that considers the elliptical contact of surface asperities. In the elastoplastic regime, the relations of the mean contact pressure and contact area of asperity to its contact interference are modeled considering the continuity and smoothness of variables across different modes of deformation. Results obtained from this model are compared with other existing models such as that calculated by the GW, CEB, Zhao and Horng models. The elliptic contact model and circular contact model can deviate considerably in regard to the separation and real area of contact.

Prediction of the Leakage Threshold for Hertzian Contact Seals: A Cellular Automata Model

2018 ◽  
Author(s):  
John Vande Voorde ◽  
Jeroen Van Wittenberghe
Keyword(s):  
Finite Element ◽  
High Pressure ◽  
Cellular Automata ◽  
Contact Pressure ◽  
Contact Area ◽  
Empirical Evaluation ◽  
Hertzian Contact ◽  
Surface Topology ◽  
Cellular Automata Model ◽  
Leak Tightness

The prediction and evaluation of leakage and leak tightness is an important issue in a multitude of high-pressure applications, such as valves, flanges or threaded connections. Through the use of finite element techniques it is in general possible to determine the local contact conditions at the seal on a macroscopic level (to wit the extent of the contact area and the contact pressure in this area). However, the leak tightness of a contact area depends also on the surface topology, which is a microscopic characteristic. Therefore the assessment of leak tightness requires an evaluation criterion relating both scales. Over the years a lot of empirical evaluation criteria have been developed, each with their own application domain. However, in terms of modelling the leakage a big step forwards was made only in the last decades. The Persson method models the contact area microscopically using contact models developed in the field of tribology. This contact evaluation is then combined with results from percolation theory, which state that for a sufficiently large contact area and a uniform contact pressure leakage will occur beyond a well-specified threshold. This has yielded a potent way of evaluating leakage, but the application is limited by the requirement that the contact pressure be uniform. In many applications, such as valves or O-ring seals, the contact is Hertzian and the contact pressure distribution is not uniform but parabolic. This paper will report the first results of an effort to extent such models to Hertzian contact seals. A set of samples for leakage experiments was produced with varying surface topology. The surface of these samples is measured and the leakage behaviour under high pressure is evaluated. At the same time a cellular automata model was built and used to model percolation under non-uniform contact pressures in an effort to adapt the Persson model. Finally the experiments and the modelling results are brought together via a finite element model and compared to each other. This paper will focus on the development of the cellular automata model and the obtained simulation results.

Measurement and Visualization of the Contact Pressure Distribution of Rubber Disks and Tires

1995 ◽  
Vol 23 (4) ◽  
pp. 238-255 ◽  
Author(s):  
E. H. Sakai
Keyword(s):  
Pressure Distribution ◽  
Contact Pressure ◽  
Contact Area ◽  
Light Absorption ◽  
Lateral Force ◽  
Contact Pressure Distribution ◽  
High Definition ◽  
The Road ◽  
Close Relationship ◽  
Processing Techniques

Abstract The contact conditions of a tire with the road surface have a close relationship to various properties of the tire and are among the most important characteristics in evaluating the performance of the tire. In this research, a new measurement device was developed that allows the contact stress distribution to be quantified and visualized. The measuring principle of this device is that the light absorption at the interface between an optical prism and an evenly ground or worn rubber surface is a function of contact pressure. The light absorption can be measured at a number of points on the surface to obtain the pressure distribution. Using this device, the contact pressure distribution of a rubber disk loaded against a plate was measured. It was found that the pressure distribution was not flat but varied greatly depending upon the height and diameter of the rubber disk. The variation can be explained by a “spring” effect, a “liquid” effect, and an “edge” effect of the rubber disk. Next, the measurement and image processing techniques were applied to a loaded tire. A very high definition image was obtained that displayed the true contact area, the shape of the area, and the pressure distribution from which irregular wear was easily detected. Finally, the deformation of the contact area and changes in the pressure distribution in the tread rubber block were measured when a lateral force was applied to the loaded tire.

scholarly journals Improved design criterion for frictionally engaged contacts in overrunning clutches

2021 ◽  
Author(s):  
Nadine Nagler ◽  
Armin Lohrengel
Keyword(s):  
Design Process ◽  
Contact Area ◽  
Axial Load ◽  
State Of The Art ◽  
Tangential Force ◽  
Design Criterion ◽  
Hertzian Contact ◽  
Loss Of Function ◽  
Axial Loads ◽  
Improved Design

AbstractOverrunning clutches, also known as freewheel clutches, are frictionally engaged, directional clutches; they transmit torque depending on the Freewheel clutch rings’ rotation directions. The torque causes a tangential force in the Hertzian contact area. The hitherto “state-of-the-art design criterion” bases on this load situation. In practice, axial loads additionally act on the frictionally engaged Hertzian contact area. This additional axial load can cause the loss of the friction connection and so the freewheel clutch slips. This publication presents an improved design criterion for frictionally engaged contacts in freewheel clutches. It allows to consider tangential as well as axial loads during the design process. Additionally, it offers the possibility to estimate the probability of frictional engagement loss and gross slip based on the freewheel clutch’s application scenario. This publication points out how to use the improved design criterion to design freewheel clutches that are more robust against a loss of function.

scholarly journals Effect of Distal Tibial Varus and Valgus Deformity on Tibiotalar Joint Contact

2020 ◽  
Vol 5 (4) ◽  
pp. 2473011420S0025
Author(s):  
Zhao Hong-Mou
Keyword(s):  
Contact Pressure ◽  
Ankle Joint ◽  
Contact Area ◽  
Peak Pressure ◽  
Tibiotalar Joint ◽  
Force Center ◽  
Fibular Osteotomy ◽  
Group I ◽  
Joint Contact ◽  
Group A

Category: Ankle; Basic Sciences/Biologics Introduction/Purpose: To study the effect of different degrees of distal tibial varus and valgus deformities on the tibiotalar joint contact, and to understand the role of fibular osteotomy. Methods: Eight cadaveric lower legs were used for biomechanical study. Nine conditions were included: normal ankle joint (group A), 10° varus (group B), 5° varus (group C), 5° valgus (group D), 10° valgus (group E) with fibular preserved, and 10° varus (group F), 5° varus (group G), 5° valgus (group H), and 10° valgus (group I) after fibular osteotomy. The joint contact area, contact pressure, and peak pressure were tested; and the translation of contact force center was observed. Results: The joint contact area, contact pressure, and peak pressure had no significant difference between group A and groups B to E (P>0.05). After fibular osteotomy, the contact area decreased significantly in groups F and I when compared with group A (P<0.05); the contact pressure increased significantly in groups F, H, and I when compared with group A (P<0.05); the peak pressure increased significantly in groups F and I when compared with group A (P<0.05). There were two main anterior-lateral and anterior-medial contact centers in normal tibiotalar joint, respectively; and the force center was in anterior-lateral part, just near the center of tibiotalar joint. While the fibula was preserved, the force center transferred laterally with increased varus angles; and the force center transferred medially with increased valgus angles. However, the force center transferred oppositely to the medial part with increased varus angles, and laterally with increased valgus angles after fibular osteotomy. Conclusion: Fibular osteotomy facilitates the tibiotalar contact pressure translation, and is helpful for ankle joint realignment in suitable cases.

Experimental and Theoretical Study of the Contact Mechanics of Five Total Knee Joint Replacements

1995 ◽  
Vol 209 (4) ◽  
pp. 225-231 ◽  
Author(s):  
T Stewart ◽  
Z M Jin ◽  
D Shaw ◽  
D D Auger ◽  
M Stone ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Knee Joint ◽  
Contact Pressure ◽  
Contact Stress ◽  
Linear Elasticity ◽  
Contact Area ◽  
Elasticity Analysis ◽  
Joint Replacements ◽  
Total Knee ◽  
Maximum Contact

The tibio-femoral contact area in five current popular total knee joint replacements has been measured using pressure-sensitive film under a normal load of 2.5 kN and at several angles of flexion The corresponding maximum contact pressure has been estimated from the measured contact areas and found to exceed the point at which plastic deformation is expected in the ultra-high molecular weight polyethylene (UHMWPE) component particularly at flexion angles near 90°. The measured contact area and the estimated maximum contact stress have been found to be similar in magnitude for all of the five knee joint replacements tested. A significant difference, however, has been found in maximum contact pressure predicted from linear elasticity analysis for the different knee joints. This indicates that varying amounts of plastic deformation occurred in the polyethylene component in the different knee designs. It is important to know the extent of damage as knees with large amounts of plastic deformation are more likely to suffer low cycle fatigue failure. It is therefore concluded that the measurement of contact areas alone can be misleading in the design of and deformation in total knee joint replacements. It is important to modify geometries to reduce the maximum contact stress as predicted from the linear elasticity analysis, to below the linear elastic limit of the plastic component.

Experimental and numerical study on cavitation under elastohydrodynamic lubrication point contact

2021 ◽  
pp. 135065012110527
Author(s):  
Mingfei Ma ◽  
Wen Wang ◽  
Wenxun Jiang
Keyword(s):  
Contact Area ◽  
Numerical Study ◽  
Ambient Pressure ◽  
Point Contact ◽  
Elastohydrodynamic Lubrication ◽  
Hertzian Contact ◽  
Pressure Area ◽  
Cavitation Pressure ◽  
Experimental Researches ◽  
State 1

As a common phenomenon in elastohydrodynamic lubrication, cavitation has an effect on the completeness of the oil film in the contact area. Many studies have therefore been conducted on cavitation. Experimental researches on cavitation usually rely on optical interference observation, which offers a limited resolution and observation range. In this paper, an infrared thermal camera is used to observe the cavity bubbles on a ball-on-disc setup under sliding/rolling conditions. The results show that the cavity length increases with an increases of the entrainment speed and the viscosity of the lubricants. These observations are explained by a numerical model based on Elrod's algorithm. Effects of entrainment speed and lubricant viscosity on the breakup of cavitation bubbles and the cavitation states are investigated. Both the simulation and experimental results show that a negative pressure area is present behind the Hertzian contact area. The ambient pressure plays a role in maintaining cavitation state 1. The cavitation pressure is close to the vacuum pressure when the entrainment speed is low and to the ambient pressure instead when the entrainment speed is high.

Approximate Analytical Model for Hertzian Elliptical Wheel/Rail or Wheel/Crossing Contact Problems

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
F. D. Fischer ◽  
M. Wiest
Keyword(s):  
Contact Pressure ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Theory ◽  
Technical Accuracy ◽  
Elliptical Contact ◽  
Current Approximation ◽  
Analytical Expressions ◽  
Maximum Contact ◽  
Hertzian Contact Theory

The Hertzian contact theory is approximated according to a concept by Tanaka (2001, “A New Calculation Method of Hertz Elliptical Contact Pressure,” ASME J. Tribol., 123, pp. 887–889) yielding simple analytical expressions for the elliptical semi-axes, the maximum contact pressure, the mutual approach and the contact spring constant. Several configurations are compared using the exact Hertz theory and the current approximation. The results agree within technical accuracy.

scholarly journals Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat

2005 ◽  
Vol 128 (2) ◽  
pp. 230-235 ◽  
Author(s):  
J. Jamari ◽  
D. J. Schipper
Keyword(s):  
Experimental Investigation ◽  
Contact Pressure ◽  
Contact Area ◽  
Measurement Method ◽  
Contact Load ◽  
Model Predictions ◽  
The Mean

In this paper we report the experimental investigation to evaluate the published models for the contact of a deformable sphere against a hard flat in the fully plastic contact regime. A new measurement method has been used to measure the contact area. The behavior of the mean contact pressure and the contact area as a function of the contact load are presented. Substantial differences are found between the measurements and the model predictions. A constant value of the mean contact pressure as the load increases is observed, however, the value is lower than the hardness, as often reported. The contact area is found to be a simple truncation of the sphere by a hard flat.

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