• Tribology and Lubricants
• /
• v.31 no.5
• /
• pp.189-194
• /
• 2015

This paper focuses on the conformal contact problem. A typical example of conformal contact is the contact between a pin and hole. In particular, this paper focuses on the condition for assuming a contact stress field to be a Hertzian pressure profile by using well-known classical solutions associated with Hertzian contact. Persson first developed the conformal contact analysis method around half a century ago, but there have been no significant improvements since then. The present research also adopted this method, but developed new solutions from the viewpoint of application to structural design. The analysis began with a comparison between Persson°Øs conformal contact stress and the Hertzian stress fields. The next step was to check the differences in the normalized stress values of both. This study used the tolerance for the difference in the peak stresses of Persson°Øs solution and the Hertz solution to validate the Hertzian assumption. This gave the range for the difference in radii of the pin and hole when the contact force and mechanical properties of the material are specified. The results showed that, at a tolerance of 5%, the Hertzian assumption is valid if half of the contact angle is less than 35°ý. In addition, the Hertzian assumption holds even for a relatively long contact length, in contrast to the general incomplete contact problem. This paper discusses these results along with other aspects of the application to the design.

• KSTLE International Journal
• /
• v.1 no.1
• /
• pp.8-11
• /
• 2000

A surface crack in a semi-infinite body under Hertzian contact was considered. The simplified method used to estimate stress intensity factor K for specimen was extended to the model which is chosen in this paper. Very satisfactory results are obtained comparing with those known and it is proved that the method is more convenient than other methods. The results of the analysis show that due to the presence of $K_I$ for unlubricated condition, mode I fracture is active in the field below the surface and the maximum $K_{I}$ is obtained when the trailing edge of Hertzian contact reaches a position over the crack. The magnitudes of stress intensity factors $K_I$ and $K_Il$ increase with increasing friction forces. For a surface crack perpendicular to the contact surface, the stress intensity factor $K_I$ reaches its maximum value at a depth very close to the surface. Driving forve fer crack initiation and propagation is $K_I$ for unlubricated condition and $K_Il$ for both fluid and boundary lubricated condition.n.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.14 no.3
• /
• pp.624-635
• /
• 1990

Analytical study based on linear fracture mechanics was conducted on propagation behavior of inclined surface crack in semi-infinite elastic body. The analytical model was assumed to be inclined surface crack under plane strain condition upon which Hertzian stress was superimposed. Supposing continuous distribution of dislocation and applying Erdogan-Gupta's method to this crack problem, the stress intensity factors $K_{I}$ and $K_{II}$) at the crack-tip were obtained for various Hertzian contact positions. Analytic results have shown that driving force for crack growth is $K_{I}$ for non-lubricated condition and $K_{II}$ for fluid and boundary lubricated condition. The coefficient of friction at the hertzian contact and crack surfaces plays an important role in predicting the direction of crack propagation. It is also found that the maximum effective stress intensity factor exists at cracks of a certain specific length depending on lubricated condition.ion.n.

• Tribology and Lubricants
• /
• v.30 no.4
• /
• pp.205-211
• /
• 2014

Recent studies emphasize the importance of pivot stiffness in the analysis of tilting pad bearings (TPBs). The present paper develops a finite element model of the pad pivot and compares the predicted pivot stiffness to the results of Hertzian contact model calculations. Specifically, a finite element analysis generates tetrahedral mesh models with ~40,000 nodes for a ball-socket pivot and ~50,000 nodes for a rocker-back pivot. These models assume a frictionless boundary condition in the contact area. Increasing the applied loads on the pad in conjunction with increasing time steps ensures rapid convergence during the nonlinear numerical analysis. Predictions are performed using the developed finite element model for increasing the differential diameters between the pad pivot (or ball) and the bearing housing (or socket). The predictions show that the pivot contact area increases with decreasing differential diameters and increasing applied loads. Further, the maximum deformation occurring at the pivot center increases with increasing differential diameters and increasing applied loads. The pivot stiffness increases nonlinearly with decreasing differential diameters and increasing applied loads. Comparisons of results of the developed finite element model to those of Hertzian contact model calculations assuming a small contact area show that the latter model underestimates the pivot stiffnesses predicted by the finite element models of the ball-socket and rocker-back pivots, particularly for small differential diameters. This result implies the need for cautionduring the design of pivot stiffness by the Hertzian contact model.

• Journal of the Society of Naval Architects of Korea
• /
• v.41 no.3
• /
• pp.35-40
• /
• 2004

Since the scale of vessels is growing up recently, some troubles between the shaft and after bush bearing are frequently reported. Generally, mean pressure on bush bearing is used as a design criterion. However, in some case of the long bearing such as after bush bearing of the propulsion shaft, it might be liable to be locally under high pressure. As for the main engine bearings and the intermediate shaft bearing, it is reasonable to take the mean pressure as a design criterion. But, in case of after bush bearing, it is not sufficient because of the possibility of high pressure caused by local contact. In this study, Hertzian contact condition was applied to evaluation of the local pressure for after bush bearing. To reduce the local maximum pressure, the height of the after bush bearing was controlled. It was found that local maximum pressure could be reduced effectively by taking a partial slope on the white metal of the aft bush bearing.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.22 no.3
• /
• pp.253-263
• /
• 2012

With the local Hertz deformation on the contact point, the dynamic contact between a high-speed wheel and an elastic beam having a gap is numerically analyzed by solving the whole equations of motion of the wheel and the beam subjected to the contact condition. For the stability of the time integration the velocity and acceleration constraints as well as the displacement constraint are imposed on the contact point. Especially the acceleration contact condition on the gap is formulated, and it is demonstrated that the contact force variation computed by the velocity contact constraint or by the acceleration contact constraint agrees well with that computed by the displacement contact constraint. The numerical examples show that, when the wheel passes on the gap, the solution is governed by the stiffness of the local Hertzian deformation.

• Proceedings of the Korean Vacuum Society Conference
• /
• 2014.02a
• /
• pp.460-460
• /
• 2014

Organic photovoltaic cells (OPV) have been extensively studied due to their unique properties such as flexibility, light-weight, easy processability, cost-effectiveness, and being environmental friendly. These advantages make them an attractive candidate for application in various novel fields and promising development with new features. Photovoltaic cell-integrated textiles have greatly attractive features as a power source for the smart textile solutions, and OPV is most ideal form factor due to advantage of flexibility. In this study, we develop a textile-based OPV through various experimental methods and we suggest the direction for the design of the photovoltaic textile. We used a textile electrode and tried to various layouts for textile-based OPV. Finally, we determined the contact area by using Hertzian theory for the calculation of power conversion efficiency (PCE). Based on the results of calculation, the short circuit current density, Isc, was $13.11mA/cm^2$ under AM 1.5condition and the PCE was around 2.5%.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
• /
• 2002.10b
• /
• pp.291-292
• /
• 2002

Using a low viscosity synthetic traction oil and a low viscosity mineral oil with nearly equal viscosity grade of ISO VG 32, the effect of kind of oil on the fatigue life of bearing steel rollers was examined. A pair of rollers finished the contact surfaces to a mirror-like condition were driven under rolling with sliding conditions of s = -3.2% and a maximum Hertzian stress in the range of $P_H=2.8GPa{\sim}4.0GPa$ was applied in point contact condition. As a result of experiments, the fatigue life with a mineral oil was longer than that with a traction oil under higher stress conditions above $P_H=3.4GPa$. Based on the numerical calculation results of the thermal EHL which simulates the present experiment, the authors discuss the reason why such a difference in the fatigue life comes out.

• Journal of the Korean Ceramic Society
• /
• v.51 no.5
• /
• pp.399-405
• /
• 2014

Porous alumina with different porosities, 5.2 - 47.5%, were coated with cover-glass having a thickness of $160{\mu}m$, using epoxy adhesive. We investigated the effect of the porosity of the substrate layer on the crack initiation load, and the size of cracks propagated in the coating layer. Hertzian indentations were used to evaluate the damage behavior under a constrained loading condition. Typically, two types of cracks, ring cracks and radial cracks, were observed on the surface of the glass/porous alumina structure. Indentation stress-strain curves, crack initiation loads, crack propagation sizes, and flexural strengths were investigated as a function of porosities. The results indicated that a porosity of less than 30% and a higher substrate elastic modulus were beneficial at suppressing cracks occurrence and propagation. We expect lightweight mechanical components with high strength can be successfully fabricated by coating and controlling porosities in the substrate layer.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.18 no.12
• /
• pp.135-139
• /
• 2017

The main reason for heat accidents occurring at the after stern tube bearing (STB) is excessive local pressure caused by the deflection of the propulsion shaft due to propeller loads. The probability of a heat accident is increased by the low flexibility of the shaft system in very large crude oil carriers (VLCCs) as the engine power and shaft diameter increase and the distance decreases between the forward and after STBs. This study proposed shaft system with only an after STB and no forward STB for a flexibility acquisition method for a VLCC shaft system under hull deformation. A Hertzian contact condition was applied, which assumes a half-elliptical pressure distribution along the contact width for the calculation of the local squeeze pressure. The propeller loads, heat effect, and hull deflection under engine operating conditions are also considered. The results show that the required design criteria were satisfied by building a partial slope at the white metal, which is the material at the axial contact side in the after STB. This system could reduce building cost by simplification of the shaft system.