Hertzian Contact and Adhesion of Elastomers

1969 ◽  
Vol 91 (4) ◽  
pp. 732-737 ◽  
Author(s):  
Richard C. Drutowski
Keyword(s):  
Stress Distribution ◽  
Tensile Stress ◽  
Contact Area ◽  
Hard Sphere ◽  
Continuous Measurement ◽  
Hertzian Contact ◽  
Initial Contact ◽  
Circular Zone ◽  
Outer Annulus ◽  
Contact Size

The contact of a hard sphere with a flat elastomer is examined both analytically and experimentally when adhesive stresses are present. Use of a transparent spherical indenter enables continuous measurement of contact size while the samples are pulled apart. For any combination of load and contact area, the superposition of a Hertz and a Boussinesq stress distribution separates the contact into a circular zone under compression and an outer annulus under tension. During separation, while the contact size decreases and the tensile annulus becomes a larger percentage of the total contact, the average tensile stress remains constant. This average adhesive is a material property which is easily measured and is shown to be invariant with respect to indenter radius and initial contact pressure. An application of this analysis to opaque indenters is described.

scholarly journals A Vibration Model of Ball Bearings with a Localized Defect Based on the Hertzian Contact Stress Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Fanzhao Kong ◽  
Wentao Huang ◽  
Yunchuan Jiang ◽  
Weijie Wang ◽  
Xuezeng Zhao
Keyword(s):  
Stress Distribution ◽  
Contact Force ◽  
Contact Stress ◽  
Contact Area ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Proposed Model ◽  
Vibration Model ◽  
Hertzian Contact Stress ◽  
Contact Stress Distribution

To study the vibration mechanism of ball bearings with localized defects, a vibration model of a ball bearing based on the Hertzian contact stress distribution is proposed to predict the contact force and vibration response caused by a localized defect. The calculation of the ball-raceway contact force when the ball passes over the defect is key to establishing a defect vibration model. Hertzian contact theory indicates that the contact area between the ball and the raceway is an elliptical contact surface; therefore, a new approach is used to calculate the ball-raceway contact force in the defect area based on the stress distribution and the contact area. The relative motion between the inner ring, the outer ring, and the balls is considered in the proposed model, and the Runge-Kutta algorithm is used to solve the vibration equations. In addition, vibration experiments of a bearing with an outer ring defect under different loads are performed. The numerical signals and experimental signals are compared in the time and frequency domains, and good correspondence between the numerical and experimental results is observed. Comparisons between the traditional model and the proposed model reveal that the proposed model provides more reasonable results.

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.

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.

Research on Vibration Control of Thin Plate Based on Pre-Stressing

2018 ◽  
Author(s):  
Cheng Zhang ◽  
Jian-run Zhang ◽  
Xi Lu
Keyword(s):  
Differential Equation ◽  
Stress Distribution ◽  
Tensile Stress ◽  
Vibration Control ◽  
Thin Plate ◽  
Natural Frequencies ◽  
Control Method ◽  
Dynamic Stiffness ◽  
Thin Plates ◽  
Shape Functions

The weak dynamic stiffness of thin plate is one of the important factors that limit the use of thin plate. Improving the dynamic stiffness of thin plate is one of the effective methods for the vibration control of thin plate. In this paper, the influence of pre-stress on the vibration characteristics of thin plate is studied. A vibration control method of thin plate based on pre-stress is proposed. The vibration differential equation of quadrate thin plate under pre-stressing is established. Using the Galerkin principle, the natural frequencies corresponding to the shape functions of the quadrate thin plates under pre-stressing in different distribution forms are obtained. By comparison, it is found that pre-stressing on the thin plate can change the dynamic stiffness of thin plate. In particular, tensile stress can increase the dynamic stiffness of thin plate while compressive stress can reduce the dynamic stiffness of the thin plate. The greater the pre-stress, the more obvious the effect. In the end, the requirements of the pre-stress distribution which can improve the dynamic stiffness of thin plate effectively are derived.

FEM Simulation of the Effects of Residual Stress on Deformation of Gyroscope Frame

2010 ◽  
Vol 439-440 ◽  
pp. 838-841
Author(s):  
Jun Zhan ◽  
Gui Min Chen ◽  
Xiao Fang Liu ◽  
Qing Jie Liu ◽  
Qian Zhang
Keyword(s):  
Finite Element Method ◽  
Residual Stress ◽  
Finite Element ◽  
Stress Distribution ◽  
Tensile Stress ◽  
Large Deformation ◽  
Deformation Process ◽  
Fem Simulation ◽  
Machining Process ◽  
The Core

Gyroscope is the core of an inertia system and made by machining process. Machining process imports large residual stress. The residual stress will be released and induces large deformation of gyroscope frame. In this paper, the effects of residual stress on deformation of gyroscope frame were simulated by finite element method. Different stress distribution leads different deformation. Compressive stress can make sample long and tensile stress make sample short. The stress released in deformation process which reduced about 90%.

scholarly journals The Elastic Contact of Rough Spheres Investigated Using a Deterministic Multi-Asperity Model

2019 ◽  
Vol 10 (01) ◽  
pp. 1841002 ◽  
Author(s):  
Vladislav A. Yastrebov
Keyword(s):  
Contact Area ◽  
Rough Surfaces ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Geometrical Shape ◽  
Elastic Contact ◽  
Deterministic Analysis ◽  
Asperity Model ◽  
Deformation Modes

In this paper, we use a deterministic multi-asperity model to investigate the elastic contact of rough spheres. Synthetic rough surfaces with controllable spectra were used to identify individual asperities, their locations and curvatures. The deterministic analysis enables to capture both particular deformation modes of individual rough surfaces and also statistical deformation regimes, which involve averaging over a big number of roughness realizations. Two regimes of contact area growth were identified: the Hertzian regime at light loads at the scale of a single asperity, and the linear regime at higher loads involving multiple contacting asperities. The transition between the regimes occurs at the load which depends on the second and the fourth spectral moments. It is shown that at light indentation the radius of circumference delimiting the contact area is always considerably larger than Hertzian contact radius. Therefore, it suggests that there is no scale separation in contact problems at light loads. In particular, the geometrical shape cannot be considered separately from the surface roughness at least for approaching greater than one standard roughness deviation.

Research on Hole Making Mechanism of High Pressure Hydraulic Perforation

2014 ◽  
Vol 590 ◽  
pp. 96-100 ◽  
Author(s):  
Hai Cheng Li ◽  
Xu Jing Zhang ◽  
Fu Min Liang
Keyword(s):  
Finite Element ◽  
High Pressure ◽  
Stress Distribution ◽  
Tensile Stress ◽  
Water Jet ◽  
Rock Fragmentation ◽  
Rock Stress ◽  
Element Simulation ◽  
Pressure Water ◽  
High Pressure Water Jet

In this paper, we integrated use hydraulics, seepage flow mechanics, rock mechanics, and finite element simulation analysis and other methods to study the rock fragmentation mechanism of high pressure water jet. We make tensile stress - crack expansion comprehensive rock fragmentation model for the screw drilling of high pressure water jet. We make finite element simulation according to the mechanism of integrated model of high pressure water jet process, to analysis the internal rock stress distribution and external rock stress distribution of the fluid, and come to the reasonable number of high-pressure water jet nozzle hole. It is verified by the high pressure water jet breaking rock inside experiments of tensile stress - comprehensive rock fragmentation fracture expansion model, summarizes the law of high pressure water jet breaking rock, and we get to know reasonable drilling mode of the high pressure water jet is screw drilling with pitch of 120mm. At present there are two main types of the micro mechanism of the high pressure water jet. One is stress and tensile damage, because of the action produced by stress wave of the high pressure water jet impacting on rock, which mainly makes the tensile failure of rock; another one is crack expansion damage, under the effect of quasi static pressure radiation of water jet, the coupling effect between water shooting jet and rock pore skeleton, which make the rock pore, throat, and micro cracks expanding gradually, eventually the macro damage.

Nano-Meter Film Rheology and Asperity Lubrication

2002 ◽  
Vol 124 (3) ◽  
pp. 595-599 ◽  
Author(s):  
Bo Jacobson
Keyword(s):  
Contact Area ◽  
Pressure Fluctuations ◽  
Slip Rate ◽  
Hertzian Contact ◽  
Metal Contact ◽  
Rolling Motion ◽  
Oil Film ◽  
Pure Rolling ◽  
Total Separation ◽  
Molecular Dimensions

It is today possible to manufacture so smooth surfaces that they can elastically conform totally to each other over the whole Hertzian contact area. For pure rolling lubrication such surfaces only need an oil film of molecular dimensions to get total separation. When the rolling motion is combined with sliding, the pressure fluctuations inside the Hertzian contact redistribute the oil and make metal-to-metal contact possible. The redistribution velocity is a function of the slip rate S and the number of asperities N from the inlet to the outlet of the Hertzian contact area. The asperity top oil film thickness decreases with a factor of the order 2NS going from the inlet to the outlet of the Hertzian contact.

Stress Distribution Characteristics of Runway Pavement under New Generation Large Aircrafts

2013 ◽  
Vol 811 ◽  
pp. 218-222
Author(s):  
Li’an Zhang ◽  
Lei Zhang ◽  
Cao Shi ◽  
Shun Xin Yang
Keyword(s):  
Sensitivity Analysis ◽  
Stress Distribution ◽  
Tensile Stress ◽  
Critical Load ◽  
Contact Pressure ◽  
Pavement Design ◽  
Distribution Characteristics ◽  
Parameter Sensitivity Analysis ◽  
New Generation ◽  
High Contact Pressure

New Generation Large Aircrafts became a new member of China large airports. However, its heavy weight and high contact pressure would have great impact on the flexible runway pavement. in this paper, based on the multilayered elastic theory, the tensile stress distribution under different airplane was studied to obtain the critical load positions. Furthermore, parameter sensitivity analysis was conducted, including thickness and modulus of Asphalt Stabilized Base (ATB) layer. Results indicated that increasing ATB thickness can only decrease the tensile stress a little, and increasing the modulus of the ATB layer will be more efficient than increasing its thickness. Finally pavement design suggestions composing of both the structural and material considerations were proposed.

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