Singularity Consideration in Numerical Solution of Contact Stress Problems

1982 ◽  
Vol 104 (3) ◽  
pp. 352-356 ◽  
Author(s):  
L. Nayak
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Contact Stress ◽  
Contact Area ◽  
Fundamental Equation ◽  
Elliptic Functions ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Elastic Displacement ◽  
Proper Analysis

The paper gives an account of different approaches to deal with the weak singularity in numerical methods of contact stress problems when the methods are based on the fundamental equation relating the elastic displacement with pressure. Singularity consideration in a new method to simultaneously determine the shape of the contact area and the pressure distribution, particularly in non-Hertzian contact problems, has been dealt with using elliptic functions. Necessity of proper analysis of singularity is discussed and the final results when compared with Hertz solution have been shown to be satisfactory.

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.

A Simplified Approach to Predict Elastic Pressure Distribution in Non-Hertzian Contact Stress Problems

1991 ◽  
Vol 113 (2) ◽  
pp. 218-223 ◽  
Author(s):  
L. Nayak
Keyword(s):  
Numerical Methods ◽  
Pressure Distribution ◽  
Contact Stress ◽  
Normal Load ◽  
Hertzian Contact ◽  
Two Dimensional ◽  
Simple Method ◽  
Simplified Approach ◽  
Design Engineers ◽  
Hertzian Contact Stress

An approximate but simple method to predict elastic pressure distribution in non-Hertzian contact stress problems has been developed using the two-dimensional Hertz relations and experimentally observed footprint shapes. Predicted pressures have been compared with results available from other numerical methods and are found to be quite satisfactory. The method has been applied to determine pressure distribution in wheel-rail contact under the normal load only. Because of its simplicity and reasonably accuracy in predicting pressure it can be readily used by industrial design engineers for many practical problems of contact mechanics.

Numerical Solution of Non-Hertzian Elastic Contact Problems

1974 ◽  
Vol 41 (2) ◽  
pp. 484-490 ◽  
Author(s):  
Krishna P. Singh ◽  
Burton Paul
Keyword(s):  
Integral Equation ◽  
Numerical Analysis ◽  
Numerical Solution ◽  
Arbitrary Shape ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Elastic Contact ◽  
New Techniques ◽  
General Method

A general method for the numerical analysis of frictionless nonconformable non-Hertzian contact of bodies of arbitrary shape is developed. Numerical difficulties arise because the solution is extremely sensitive to the manner in which one discretizes the governing integral equation. The difficulties were overcome by utilizing new techniques, referred to as the method of redundant field points (RFP) and the method of functional regularization (FR). The accuracy and efficiency of the methods developed were tested thoroughly against known solutions of Hertzian problems. To illustrate the power of the methods, a heretofore unsolved non-Hertzian problem (corresponding to the case of rounded indentors with local flat spots) has been solved.

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.

Thermomechanical Coupling of a Hyper-viscoelastic Truck Tire and a Pavement Layer and its Impact on Three-dimensional Contact Stresses

2021 ◽  
pp. 036119812110171
Author(s):  
Angeli Jayme ◽  
Imad L. Al-Qadi
Keyword(s):  
Contact Stress ◽  
Contact Area ◽  
Three Dimensional ◽  
Interaction Model ◽  
Rolling Resistance ◽  
Contact Stresses ◽  
Thermomechanical Coupling ◽  
Temperature Profiles ◽  
Near Surface ◽  
Truck Tire

A thermomechanical coupling between a hyper-viscoelastic tire and a representative pavement layer was conducted to assess the effect of various temperature profiles on the mechanical behavior of a rolling truck tire. The two deformable bodies, namely the tire and pavement layer, were subjected to steady-state-uniform and non-uniform temperature profiles to identify the significance of considering temperature as a variable in contact-stress prediction. A myriad of ambient, internal air, and pavement-surface conditions were simulated, along with combinations of applied tire load, tire-inflation pressure, and traveling speed. Analogous to winter, the low temperature profiles induced a smaller tire-pavement contact area that resulted in stress localization. On the other hand, under high temperature conditions during the summer, higher tire deformation resulted in lower contact-stress magnitudes owing to an increase in the tire-pavement contact area. In both conditions, vertical and longitudinal contact stresses are impacted, while transverse contact stresses are relatively less affected. This behavior, however, may change under a non-free-rolling condition, such as braking, accelerating, and cornering. By incorporating temperature into the tire-pavement interaction model, changes in the magnitude and distribution of the three-dimensional contact stresses were manifested. This would have a direct implication on the rolling resistance and near-surface behavior of flexible pavements.

Elastoplastic Frictional Contact Study on Interference Fits of Compressor

2011 ◽  
Vol 211-212 ◽  
pp. 535-539
Author(s):  
Ai Hua Liao
Keyword(s):  
Stress Distribution ◽  
Contact Stress ◽  
Frictional Contact ◽  
Contact Problems ◽  
Boundary Problems ◽  
Interference Fit ◽  
Parametric Variational Principle ◽  
Design And Manufacturing ◽  
Contact Stress Distribution ◽  
Fit Tolerance

The impeller mounted onto the compressor shaft assembly via interference fit is one of the key components of a centrifugal compressor stage. A suitable fit tolerance needs to be considered in the structural design. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading was considered in the numerical analysis. The FE parametric quadratic programming (PQP) method which was developed based on the parametric variational principle (PVP) was used for the analysis of stress distribution of 3D elastoplastic frictional contact of impeller-shaft sleeve-shaft. The solution of elastoplastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. The effect of fit tolerance, rotational speed and the contact stress distribution on the contact stress was discussed in detail in the numerical computation. The study play a referenced role in deciding the proper fit tolerance and improving design and manufacturing technology of compressor impellers.

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.

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