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

• Korean Journal of Optics and Photonics
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• v.15 no.4
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• pp.337-342
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• 2004

Laser optical power stabilization of a radio frequency excited $CO_2$ slab laser using the opto-Hertzian effect generated from the laser itself is achieved on the peak of the Doppler broadened gain curve. The opto-Hertzian signal was generated by a modulation of the optical flux circulating inside the laser cavity from a variation in the cavity length caused by the vibrations of the PZT. The opto-Hertzian signal is directly coupled from a RE discharge chamber via a loop antenna into a detector and applied to a lock-in stabilizer as an reference signal. The power stability of an RF excited slab laser is estimated to be better then 0.2%.

• The Korean Journal of Ceramics
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• v.4 no.4
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• pp.356-362
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• 1998

Hertzian crack suppression phenomena and relatively high damage tolerance were investigated in hard/soft silicon nitride ($Si_3N_4$) bilayers. Coarse $\alpha}-Si_3N_4$ powder was wsed for the hard coating layer and fine $\alpha}-Si_3N_4$ powder was used for the soft substrate layer. The two layers were designed with a strong interface. Hertzian indentation was used to investigate contact fracture and damage tolerance property. Hertzian crack suppression has occurred with increasing applied load and decreasing coating thickness. The crack suppression contributed strength improvement, especially in the bilayers with thinner coatings. Ultimately, the combination of hard coating with soft but tough underlayer improved the damage tolerance of brittle $Si_3N_4$ ceramics.

• Tribology and Lubricants
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• v.14 no.4
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• pp.121-127
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• 1998

In this study, a numerical procedure to solve a contact problem has been developed. The procedure takes advantage of signal processing technique in frequency domain to achieve shorter computing time. Boussinesq's equation was adopted as the response function. This procedure is applicable to a non-periodic surface profile as well as a periodic one. The validity of this procedure has been established by comparing the numerical results with the exact solutions. The fastness of this procedure was shown in comparison with other algorithm.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.383-388
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• 2008

A modeling method for the impact analysis of plate structures employing Hertzian contact theory is presented in this paper. Since local deformation as well as bending deflection of the plate occurs due to the collision, it has to be considered for the impact analysis. When the coefficient of restitution is employed for the impact analysis, the local deformation is not considered. For more accurate and reliable impact analysis, however, the local deformation should be considered. The effects of the location of collision and the collision mass on the impact duration time and the contact force magnitude are investigated through numerical studies employing Hertzian contact theory.

• Proceedings of the KSR Conference
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• 2010.06a
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• pp.1478-1485
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• 2010

In this paper, the nonlinear dynamic response of Vehicle-Bridge interaction with the coupled equations of motion including nonlinear Hertzian contact is presented. The moving train model is chosen to have 10 degrees of freedom (DOF). The bridge is modeled as 2D Euler-Bernoulli beam element with 4 DOF for each element, two for rotations and another two for translations. The nonlinear Hertzian contact is used to simulate the interaction between vehicle and bridge. Base on the relationship of wheel displacement of the vehicle and the vertical displacement of the bridge in Hertzian contact, the coupled equations of motion of the whole system is derived. The convenient formulation was encoded into a computer program. The contact forces, contact area and stress of the rail surface were also computed. The accuracy and efficiency of the proposed program are verified and compared with exact analytical solution and other previous studies. Various numerical examples and parametric studies have demonstrated the versatility and applicability of the proposed program.

• Tribology and Lubricants
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• v.11 no.5
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• pp.114-121
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• 1995

An ultrasonic technique using normal-incident compressional waves was used to evaluate the surface and subsurface damage in ceramics produced by Hertzian indentation. Damage was produced by a blunt indenter (tungsten carbide ball) in glass-ceramic, green glass and silicon nitride. The damage was classified into two types; (1) Hertzian cone crack, in green glass and fine grain silicon nitride, and (2) distributed subsurface micro fractures, without surface damage, produced in glass ceramic. The ultrasonic technique was successful in detecting cone craks. The measurement results with the Hertzian cone cracks indicated that cracks perpendicular to the surface could be detected by the normal-incident compressional waws. Also shown is the capability of normal-incident compressional waves in detection distributed micro-sized cracks size of subsurface microfractures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.10a
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• pp.993-993
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• 2014

Increasing the density magnetic recording of a hard disk drive needs to improve position control of a slider. We have troubles analyzing position of a slider by nonlinear property of pivot ball bearing. Many researches analyze a hard disk drive to change pivot ball bearing part from balls to springs. Pivot ball bearing operates by rotation and movement of balls. This study considers Hertzian contact force when balls contact with outer race to analyze nonlinear movement of a ball bearing. Experiment of this study measures movement of a circular center of a pivot ball bearing. We also verify the simulation results and the experiment results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.8
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• pp.1163-1172
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• 2001

The two dimensional problem of a layered tribological system(TiN/Steel) containing a vertical surface breaking crack and subject to rolling contact is considered in this study. Using finite elements and stress extrapolation method, a series of preliminary models are developed. Preliminary results indicate that the extrapolation technique is valid to determine Modes I and II stress intensity factors for cracks. In the case of TiN/Steel medium, KI and KII were determined for variations in crack length, layer thickness, and load location. The results show that KII reaches maximum values when the contact is adjacent to the crack where Mode I stresses are compressive. KII values decrease with decreased crack length and significantly decrease for reduced layer thickness.

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