• Title/Summary/Keyword: Hertzian

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A Stress Analysis on the Involute-Circular Arc Composite Tooth Profile Gear (인벌류우트-圓弧 合成齒形기어의 應力解析)

  • 탁계래;최상훈;윤갑영
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.11 no.2
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    • pp.198-204
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    • 1987
  • In a new involute-circular arc tooth profile which is composed of an involute curve in the vicinity of pitch point, a circular arc in the addendum part, and a curve in the dedendum part which is generated by the circular arc profile of mating gear tooth profile, the tooth contact stress is calculated analytically and the root fillet stress is calculated by the finite element analysis. The root fillet stress and the Hertzian contact stress of composite tooth profile gear are decreased with increasing the pressure angle and with decreasing the radius of circular arc and unwound angle. Compared with the standard involute gear, the root fillet stress is decreased by 2-15% and the Hertizian contact stress is decreased by 6-24%.

Bearing Vibration and Fatigue Life Analysis According to Fitting between Ball Bearing and Housing with Geometrical Errors (형상오차를 갖는 보올 베어링과 하우징의 끼워 맞춤에 따른 베어링 진동 및 수명의 영향)

  • Lee, Young-Keun;Lee, Seok-Hoon;Jung, Il-Kwon;Cha, Cheol-Hwan;Han, Hyo-Seup
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11a
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    • pp.112-118
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    • 2005
  • Ball bearings which were fitted between housing and shaft play an important role in rotating shaft system smoothly, Therefore bearing's running accuracy has significant influence on that of rotating machinery. Manufacturing accuracy of bearings as well as that of shaft and housing is main factor to affect bearing running accuracy In this paper, bearing's vibration and fatigue life considering raceway roundness of ball bearing before and after being fitted into housing are theoretically estimated. To perform analysis, a simple three degrees of freedom model was proposed and then these analysis was conducted utilizing the Newton-Raphson iterative method. The results show that vibration magnitude of ball bearing fitted into housing is considerably larger than before assembly, and bearing's theoretical L$_{10}$ fatigue life that ninety percent of the bearing population will endure decreased in about fifty percent.

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Low-velocity impact response of laminated FG-CNT reinforced composite plates in thermal environment

  • Ebrahimi, Farzad;Habibi, Sajjad
    • Advances in nano research
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    • v.5 no.2
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    • pp.69-97
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    • 2017
  • In this study, nonlinear response of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate under low-velocity impact based on the Eshelby-Mori-Tanaka approach in thermal conditions is studied. The governing equations are derived based on higher-order shear deformation plate theory (HSDT) under von $K\acute{a}rm\acute{a}n$ geometrical nonlinearity assumptions. The finite element method with 15 DOF at each node and Newmark's numerical integration method is applied to solve the governing equations. Four types of distributions of the uniaxially aligned reinforcement material through the thickness of the plates are considered. Material properties of the CNT and matrix are assumed to be temperature dependent. Contact force between the impactor and the laminated plate is obtained with the aid of the modified nonlinear Hertzian contact law models. In the numerical example, the effect of layup (stacking sequence) and lamination angle as well as the effect of temperature variations, distribution of CNTs, volume fraction of the CNTs, the mass and the velocity of the impactor in a constant energy level and boundary conditions on the impact response of the CNTRC laminated plates are investigated in details.

Diamond-like Carbon Tribological Endurance using an Energetic Approach

  • Alkelae, Fathia;Jun, Tea-Sung
    • Tribology and Lubricants
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    • v.37 no.5
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    • pp.179-188
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    • 2021
  • Reputed for their low friction coefficient and wear protection effect, diamond-like carbon (DLC) materials are considered amongst the most important lubricant coatings for tribological applications. In this framework, this investigation aims to elucidate the effect of a few operating parameters, such as applied stress and sliding amplitude on the friction lifetime of DLC coatings. Fretting wear tests are conducted using a 12.7 mm radius counterpart of 52100 steel balls slid against a substrate of the same material coated with a 2 ㎛ thickness DLC. Approximately, 5 to 57 N force is applied, generating a maximum Hertzian contact pressure of 430 to 662 MPa, corresponding to the applied force. The coefficient of friction (CoF) generates three regimes, first a running-in period regime, followed by a steady-state evolution regime, and finally a progressive increase of the CoF reaching the steel CoF value, as an indicator of reaching the substrate. To track the wear scenario, interrupted tests are performed with analysis combining scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDX), 3D profilometer and micro-Raman spectroscopy. The results show two endurance values: one characterizing the coating failure (Nc1), and the other (Nc2) indicating the friction failure which is situated where the CoF reaches a threshold value of μth = 0.3 in the third regime. The Archard energy density factor is used to determine the two endurance values (Nc1, Nc2). Based on this approach, a master curve is established delimitating both the coating and the friction endurances.

Elastic Deformation Induced Preload Change in Tilting Pad Journal Bearing (탄성변형으로 인한 틸팅패드 저널베어링의 예압 변화)

  • Donghyun Lee;Junho Suh
    • Tribology and Lubricants
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    • v.39 no.3
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    • pp.102-110
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    • 2023
  • This study aims to quantify the variation in the performance of a tilting pad journal bearing (TPJB) owing to the elastic deformation of its pad. To this end, we first defined a parameter, "elastic preload", and predicted the changes in the performance of the TPJB, as a function of the preload amount. We used the iso-viscosity Reynolds equation, which ignores the temperature rise due to viscous shear in thin films, and the resultant thermal deformation of the bearing structure. We employed a three-dimensional finite element model to predict the elastic deformation of the bearing pad, and a transient analysis, to converge to a static equilibrium condition of the flexible pads and journal. Conducting a modal coordinate transformation helped us avoid heavy computational issues arising from a mesh refinement in the three-dimensional finite element pad model. Moreover, we adopted the Hertzian contact model to predict the elastic deformation at the pivot location. With the aforementioned overall strategy, we predicted the performance changes owing to the elastic deformation of the pad under varying load conditions. From the results, we observed an increase in the preload due to the pad elastic deformation.

Development of a Quasi-Three Dimensional Train/Track/Bridge Interaction Analysis Program for Evaluating Dynamic Characteristics of High Speed Railway Bridges (고속철도 교량의 동특성 해석을 위한 준3차원 차량/궤도/교량 상호작용 해석기법의 개발)

  • 김만철
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.2
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    • pp.141-151
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    • 2003
  • Railway bridges are subject to dynamic loads generated by the interaction between moving vehicles and the bridge structures. These dynamic loads result in response fluctuations in bridge members. To investigate the real dynamic behavior of the bridge, therefore, a number of analytical and experimental Investigations should be carried out. In this paper, a train/track/bridge interaction analysis program for evaluating the dynamic characteristics of bridges due to KTX operation in terms of structural safety, operational safety and passenger comfort is developed. To build a practical model of train/track/bridge, Hertzian spring for wheel/rail contact modeling and Winkler element for ballast are applied. This program also used torsional degree of freedom and constraint equation based on geometrical relationship in order to take into consideration three-dimensional eccentricity effect due to the operation on double track through quasi-three dimensional analysis. To verify the developed Program, comparison has been made between the measured results and those of simulation of the typical PSC box bridge(2@40m=80m) of the KHSR bridges.

Influence of Subsurface Layer on the Indentation Damage Behavior of YSZ Thermal Barrier Coating Layers Deposited by Electron Beam Physical Vapor Deposition (전자 빔 물리적 증착(EB-PVD)법으로 코팅된 YSZ 열차폐층의 압흔손상 거동에 대한 하부층의 영향)

  • Heo, Yong-Suk;Park, Sang-Hyun;Han, In-Sub;Woo, Sang-Kuk;Jung, Yeon-Gil;Paik, Un-Gyu;Lee, Kee-Sung
    • Journal of the Korean Ceramic Society
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    • v.45 no.9
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    • pp.549-555
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    • 2008
  • The thermal barrier coating must withstand erosion when subjected to flowing gas and should also maintain good stability and mechanical properties while it must also protect the turbine component from high temperature, hot corrosion, creep, and oxidation during operation. In this study we investigated the influence of subsurface layer, $Al_2O_3$ or NiCrCoAIY bond coat layer, on the indentation damage behavior of YSZ thermal barrier coating layers deposited by electron beam physical vapor deposition (EB-PVD). The bond coat is deposited using different process such as air plasma spray (APS) or spray of high velocity oxygen fuel (HVOF) and the thickness is varied. Hertzian indentation technique is used to induce micro damages on the coated layer. The stress-strain behaviors are characterized by results of the indentation tests.

Experimental and Finite Element Study of Tribological Characteristics of SU-8 Thin Film (실험 및 유한요소해석에 의한 SU-8 박막의 Tribological 특성 연구)

  • Yang, Woo Yul;Shin, Myounggeun;Kim, Hyung Man;Han, Sangchul;Sung, In-Ha
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.37 no.4
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    • pp.467-473
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    • 2013
  • In this study, two-dimensional finite element models were developed and experiments were conducted using an atomic force microscope to investigate the tribological characteristics of an SU-8 layer coated on a patterned wafer for microsystem applications. The results revealed that both the adhesion and the friction forces measured by the atomic force microscope were lower for the SU-8 coated surface than for the bare silicon surface. This is attributed to the hydrophobicity of SU-8. Another important result derived from the finite element analysis was the critical load required to fracture the SU-8 film with respect to the thickness. The critical loads for thicknesses of 200, 400, and 800 nm were approximately 13, 22, and 28 mN, respectively, which corresponded to a Hertzian contact pressure of 1.2-1.8 GPa. These results will aid in the design of a suitable SU-8 thickness for microsystem components that are in contact with one another.

Frictional and Fatigue Characteristics of Journal Bearings by Ultrasonic Nanocrystal Surface Modification (UNSM) (초음파나노표면개질기술을 이용한 저널베어링 마찰 및 피로특성 연구)

  • Choi, Gab-Su;Darisuren, Shirmendagva;Lee, Seung-Chul;Kim, Jun-Hyong;Amanov, Auezhan;Pyun, Young-Sik
    • Tribology and Lubricants
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    • v.31 no.1
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    • pp.1-5
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    • 2015
  • In this study, we apply an ultrasonic nanocrystal surface modification (UNSM) technique to radial journal bearings (JBs) and disks made of SUJ2 and SCM440, respectively. We investigate frictional properties of untreated and UNSM-treated specimens using a ball-on-disk tester. We construct the Stribeck curve at the boundary, under mixed and full hydrodynamic lubrication conditions for the specimens using friction data obtained from JB tests. The friction at the boundary lubrication condition and the transition period to mixed lubrication condition on the UNSM-treated specimens is reduced, which improves the service life of JBs. The major effects of this reduction in the three lubrication regimes can be explained in the terms of improved mechanical properties and the presence of micro dimples. Moreover, we estimate the friction and fatigue properties of SCM440 specimens using a ball-on-disk specimen under dry and oil-lubricated conditions. Friction test results reveal that the UNSM-treated specimens show lower friction coefficient than the untreated specimens under both dry and oil-lubricated conditions. We evaluate the fatigue properties of SCM440 specimens by calculating the Hertzian stress with respect to the failure cycles. Fatigue tests results also reveal that the UNSM-treated specimens possess a longer fatigue life than the untreated specimens. The improved properties are effective in increasing the energy efficiency of bearings.

Behavior of the Crack Initiation, Transition and Fatigue Crack Growth of Rail Steel (레일강의 균열발생·천이 및 피로균열진전거동)

  • Lee, Jong Sun;Kang, Ki Weon;Choi, Rin;Kim, Jung Kyu
    • Journal of Korean Society of Steel Construction
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    • v.11 no.1 s.38
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    • pp.33-42
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    • 1999
  • In the present study, crack initiation criteria, static failure and tensile mode fatigue behavior for a rail steel are evaluated to assure the railway vehicle's safety. The transverse fissure, which is the most critical damage in the rail, is initiated by the maximum shear stress and its location is subsurface. In addition, the possibility of transition from the shear mode to the mixed mode increases with increasing the length of subsurface crack. Because of the brittleness by the welding, the fracture toughness of the welded part is lower than of the base metal. For low ${\Delta}K$, the stage II fatigue crack growth rates of the welded part is slower than of the base metal but, for high ${\Delta}K$, this different behavior for fatigue crack growth rate is nearly diminished. These trends are more remarkable for low stress ratio, R=0.1. It is believed that this behavior is caused by the change of the microstructure which that of the welded part is coarser than of base metal.

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