• Title/Summary/Keyword: Hertz model

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Stress based Fatigue Life Prediction for Ball Bearing (볼 베어링의 응력 기반 접촉피로수명 예측)

  • Kim, Tae-Wan;Cho, Yong-Joo
    • Journal of the Korean Society for Precision Engineering
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    • v.24 no.5
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    • pp.44-55
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    • 2007
  • The method for fatigue life prediction of ball bearing is proposed applying the algorithm of contact fatigue prediction based on stress analysis. In order to do this, a series of simulation such as initial surface stress analysis, EHL analysis, subsurface stress analysis and fatigue analysis are conducted from the loading at each ball location calculated for a bearing subjected to external bearing load and contact shape function. And uniaxial fatigue tests are performed to obtain fatigue parameter of AISI 52100 steel. It was found that since stress is usually higher at the inner raceway contact than at the outer raceway contact, fatigue failure occurs on the inner raceway first. When the fatigue life calculated in the stress-based method are compared with L50 life of L-P model, Crossland criterion for the radial load increment is similar to L50 life and Dang Van criterion for the axial load increment is similar. In the case of EHL contact, there is no difference of fatigue life between dry contact and EHL contact, when maximum Hertz pressure exceeds 2.5GPa.

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

  • Lee, Young-Keun;Lee, Seok-Hoon;Jung, Il-Kwon;Cha, Cheol-Hwan;Han, Hyo-Seup
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.16 no.5 s.110
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    • pp.441-451
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    • 2006
  • It is known that ball bearings mounted in housing or on shaft are playing a key role to keep it running smoothly. The roundness of a housing bore on which bearing outer ring is mounted with interference has directly affected the running accuracy of bearing. The running accuracy of bearing, therefore, can extend the significant influence to the rotating machinery as well. In this paper, bearing's vibration and fatigue life considering raceway roundness of ball bearing before and after mounted in housing bore are theoretically estimated. To perform analysis, a simple three degrees of freedom model was proposed and then Newton-Raphson iterative method was introduced to be utilized in the analysis. The results show that the vibration magnitude of ball bearing fitted into housing unit is appeared considerably larger than the one of its pre-assembling. And theoretical $L_{10}$ life which ninety percent of the bearing population will endure decreased in about fifty percent.

Fracture characterization with high frequency single-hole EM survey

  • Seo, Soon-Jee;Song, Yoon-Ho;Kim, Hee-Joon;Lee, Ki-Ha;Suh, Jung-Hee
    • Proceedings of the KSEEG Conference
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    • 1999.04a
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    • pp.90-93
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    • 1999
  • We present a high frequency electromagnetic (EM) inversion scheme for detecting and characterizing a fracture using single-hole data. At high frequencies, say above tens of mega-hertz, since displacement currents cannot be ignored, electrical permittivity as well as electrical conductivity is to be considered together for analyzing the EM scattering data. In this paper, we have developed a three-step inversion scheme to map the fracture and to evaluate its electrical conductivity and permittivity. We performed EM profiling along the z-axis using three-component receivers for each source. The model was excited by a vertical magnetic dipole and the resistant magnetic fields were inverted using the non-linear least-squares method. Background resistivity and permittivity were easily obtained using vertical magnetic fields below 1 MHz and above 10 MHz, respectively. Both the vertical and dipping sheets were successfully mapped using the phase difference between 40 and 41 MHz. The electrical property of the sheet was well resolved using the information obtained in the previous two steps and secondary magnetic fields. Our study shows the potential of imaging the fracture in single-hole survey environment using the high frequency EM method.

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Sustainable Vibration Energy Harvesting Based on Zr-Doped PMN-PT Piezoelectric Single Crystal Cantilevers

  • Moon, Seung-Eon;Lee, Sung-Q;Lee, Sang-Kyun;Lee, Young-Gi;Yang, Yil-Suk;Park, Kang-Ho;Kim, Jong-Dae
    • ETRI Journal
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    • v.31 no.6
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    • pp.688-694
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    • 2009
  • In this paper, we present the results of a preliminary study on the piezoelectric energy harvesting performance of a Zr-doped $PbMg_{1/3}Nb_{2/3}O_3-PbTiO_3$ (PMN-PZT) single crystal beam. A novel piezoelectric beam cantilever structure is used to demonstrate the feasibility of generating AC voltage during a state of vibration. The energy-harvesting capability of a PMN-PZT beam is calculated and tested. The frequency response of the cantilever device shows that the first mode resonance frequency of the excitation model exists in the neighborhood of several hundreds of hertz, which is similar to the calculated value. These tests show that several significantly open AC voltages and sub-mW power are achieved. To test the possibility of a small scale power source for a ubiquitous sensor network service, energy conversion and the testing of storage experiment are also carried out.

Giga-Hertz-Level Electromagnetic Field Analysis for Equivalent Inductance Modeling of High-Performance SoC and SiP Designs

  • Yao Jason J.;Chang Keh-Jeng;Chuang Wei-Che;Wang, Jimmy S.
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.5 no.4
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    • pp.255-261
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    • 2005
  • With the advent of sub-90nm technologies, the system-on-chip (SoC) and system-in-package (SiP) are becoming the trend in delivering low-cost, low-power, and small-form-factor consumer electronic systems running at multiple GHz. The shortened transistor channel length reduces the transistor switching cycles to the range of several picoseconds, yet the time-of-flights of the critical on-chip and off-chip interconnects are in the range of 10 picoseconds for 1.5mm-long wires and 100 picoseconds for 15mm-long wires. Designers realize the bottleneck today often lies at chip-to-chip interconnects and the industry needs a good model to compute the inductance in these parts of circuits. In this paper we propose a new method for extracting accurate equivalent inductance circuit models for SPICE-level circuit simulations of system-on-chip (SoC) and system-in-package (SiP) designs. In our method, geometrical meshes are created and numerical methods are used to find the solutions for the electromagnetic fields over the fine meshes. In this way, multiple-GHz SoC and SiP designers can use accurate inductance modeling and interconnect optimization to achieve high yields.

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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A Study on the Change in the Film Thickness of Ball Bearing in Starved EHL (윤활유 부족 상태에서의 볼 베어링 유막 두께 변화에 대한 연구)

  • Jung, SoonBi;Lee, Bora;Yu, YongHun;Cho, YongJoo
    • Tribology and Lubricants
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    • v.33 no.3
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    • pp.119-125
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    • 2017
  • In this study, we perform a numerical analysis to predict the film thickness and lubrication regions for a thrust ball bearing under different operating conditions. Film thinning and replenishment affect the film thickness in starved lubrication. As the inlet meniscus position is brought to the edge of the Hertz contact, the thin film thickness is calculated as starved equation. We use a film replenishment model to determine the recovery film thickness between rolling elements. We use a hydrodynamic model to describe film recovery, that results from the effects of surface tension. In this model, we consider the surface tension gradient in fluid depression as the driving force for fluid recovery. We use Fourier transform method to determine the time-dependent depth of depressed oil. We calculate the change in the central film thickness graphically by using the recovery equation in starved elastohydrodynamic lubrication(EHL) under operating conditions that include numbers of balls, sliding velocity, applied force, and ambient film thickness. We evaluate the degree of starvation by using the distance from the center of the contact area to the meniscus position. Parched lubrication, a phenomenon where the film thickness decreases consistently, occurs at the severe condition. We determine optimal values with respect to the numbers of balls, and sliding velocity. The investigation can contribute to the design operating conditions for proper lubrication.

Formulation of Friction Forces in LM Ball Guides (LM 볼가이드의 마찰력 정식화)

  • Oh, Kwang-Je;Khim, Gyungho;Park, Chun-Hong;Chung, Sung-Chong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.40 no.2
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    • pp.199-206
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    • 2016
  • Linear motion (LM) ball guides with rolling contact are core units of feed-drive systems. They are widely applied for precision machinery such as machine tools, semiconductor fabrication machines and robots. However, the friction force induced from LM ball guides generates heat, which deteriorates positioning accuracy and incurs changes of stiffness and preload. To accurately analyze the effects and apply the results to precision machine design, mathematical modeling of the friction force is required. In this paper, accurate formulation of the friction force due to rolling, viscous, and slip frictions is conducted for LM ball guides. To verify the reliability of the developed friction model, experiments are performed under various assembly, load and velocity conditions. Effects of frictional components are analyzed through the formulated friction model.

Multiple Pounding Tuned Mass Damper (MPTMD) control on benchmark tower subjected to earthquake excitations

  • Lin, Wei;Lin, Yinglu;Song, Gangbing;Li, Jun
    • Earthquakes and Structures
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    • v.11 no.6
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    • pp.1123-1141
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    • 2016
  • To explore the application of traditional tuned mass dampers (TMDs) to the earthquake induced vibration control problem, a pounding tuned mass damper (PTMD) is proposed by adding a viscoelastic limitation to the traditional TMD. In the proposed PTMD, the vibration energy can be further dissipated through the impact between the attached mass and the viscoelastic layer. More energy dissipation modes can guarantee better control effectiveness under a suite of excitations. To further reduce mass ratio and enhance the implementation of the PTMD control, multiple PTMDs (MPTMD) control is then presented. After the experimental validation of the proposed improved Hertz based pounding model, the basic equations of the MPTMD controlled system are obtained. Numerical simulation is conducted on the benchmark model of the Canton Tower. The control effectiveness of the PTMD and the MPTMD is analyzed and compared under different earthquake inputs. The sensitivity and the optimization of the design parameters are also investigated. It is demonstrated that PTMDs have better control efficiency over the traditional TMDs, especially under more severe excitation. The control performance can be further improved with MPTMD control. The robustness can be enhanced while the attached mass for each PTMD can be greatly reduced. It is also demonstrated through the simulation that a non-uniformly distributed MPTMD has better control performance than the uniformly distributed one. Parameter study is carried out for both the PTMD and the MPTMD systems. Finally, the optimization of the design parameters, including mass ratio, initial gap value, and number of PTMD in the MPTMD system, is performed for control improvement.

Fatigue Life Analysis of Rolling Contact Model Considering Stress Gradient Effect (응력 구배 효과를 고려한 구름 접촉 모델의 피로수명해석)

  • Cho, InJe;Yu, YongHun;Lee, Bora;Cho, YongJoo
    • Tribology and Lubricants
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    • v.31 no.6
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    • pp.272-280
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    • 2015
  • Recently, Luu suggested fatigue life equation that uses every term of the Crossland equation with stress gradient effect. Luu’s model, however, has a limit of being unable to coverage small radii that are less than a specified length. Furthermore, rolling model has a very small contact area compared to the rolling element size, and fatigue failure occurs on the small radius such as surface asperity by cyclic loading. Therefore, it is necessary to modify fatigue life equation in order to enable fatigue analysis for a small radius. In this paper, the fatigue life considering a stress gradient effect in rolling contact was obtained using Luu’s modified equation. Fatigue analysis was performed to study the effect of stress gradient on the fatigue life using newly adopted equation and to compare the results with pervious models. In order to do this, a series of simulation such as surface stress analysis, subsurface stress analysis, and fatigue analysis are conducted for two rolling balls of same size that contact each other. Through such a series of processes, the fatigue life can be calculated and equation that is proposed in this paper evaluates the fatigue life in case the contact area is small.