• JSTS:Journal of Semiconductor Technology and Science
• /
• v.16 no.2
• /
• pp.153-158
• /
• 2016

The elastic material constants, stiffness constants ($c_{11}$, $c_{12}$, and $c_{44}$), are three unique coefficients that establish the relation between stress and strain. Accurate knowledge of mechanical properties and the stiffness coefficients for silicon is required for design of Micro-Electro-Mechanical Systems (MEMS) devices for proper modeling of stress and strain in electronic packaging. In this work, the stiffness coefficients for silicon as a function of temperature from $-150^{\circ}C$ to $+25^{\circ}C$ have been extracted by using the experimental measurements of Poisson's ratio (${\nu}$) of silicon in several directions.

• Tribology and Lubricants
• /
• v.14 no.1
• /
• pp.14-22
• /
• 1998

This paper describes the effects of exciting frequency on the stiffness and damping coefticients of a 5-pad tilting pad journal bearing, LOP (load on pad) type. The stiffness and damping coefficients are investigated experimentally under the different values of exciting frequency, bearing load and shaft speed. These coefficients are estimated by measuring the response of the relative displacement between the bearing and the shaft and acceleration of the bearing due to the known exciting loads acting on the bearing. In order to analysis the response of exciting load, displacement and acceleration, a FFT analyzer is used. It is shown that the variation of exciting frequency has a little effect on both the stiffness and damping coefficients. Both the stiffness and damping coefficients in the loading direction are decreased by the increase of shaft speed but increased by the increase of bearing load.

• The KSFM Journal of Fluid Machinery
• /
• v.2 no.2 s.3
• /
• pp.32-38
• /
• 1999

An experimental study is performed to investigate the frequency effects of the excitation force on the linear stiffness and damping coefficients of a LOP (load on pad) type five-pad tilting pad journal bearing with the diameter of 300.91 mm and the length of 149.80 mm. The main parameter of interest in the present work is excitation frequency to shake the test bearing. The excitation frequency is controlled independently, using orthogonally mounted hydraulic exciters. The relative movement between the bearing and shaft, and the acceleration of the bearing casing are measured as a function of excitation frequency using the different values of bearing load and shaft speed. Measurements show that the variation of excitation frequency has quite a little effect on both stiffness and damping coefficients. Both direct stiffness and damping coefficients in the direction of bearing load decrease by the increase of shaft speed, but increase with the bearing load.

• 유체기계공업학회:학술대회논문집
• /
• 1998.12a
• /
• pp.173-179
• /
• 1998

An experimental study is performed to investigate the frequency effects of the excitation force on the linear stiffness and damping coefficients of a LOP (load on pad) type five-pad tilting pad journal bearing with the diameter of 300.91 mm and the length of 149.80 mm. The main parameter of interest in the present work is excitation frequency to shake the test bearing. The excitation frequency is controlled independently, using orthogonally mounted hydraulic exciters. The relative movement between the bearing and shaft, and the acceleration of the bearing casing are measured as a function of excitation frequency using the different values of bearing load and shaft speed. Measurements show that the variation of excitation frequency has quite a little effect on both stiffness and damping coefficients. Both direct stiffness and damping coefficients in the direction of bearing load decrease by the increase of shaft speed, but increase with the bearing load.

• Tribology and Lubricants
• /
• v.31 no.6
• /
• pp.294-301
• /
• 2015

In this paper, we predict the rotordynamic force coefficients of tilting pad journal bearings (TPJBs) with rocker-back pivots, and we compare the predictions to recently published predictions and test data. The present TPJB model considers the rocker-back pivot stiffness calculated based on the Hertzian contact-stress theory, which is nonlinear with the application of a force . For the five-pad TPJB in load-between-pad and load-on-pad configurations, the predictions show the pressure- and film-thickness distributions, the deflection and stiffness of the individual pivots, and bearing stiffness and damping coefficients. The minimum film thickness and peak pressure occur at the bottom pad on which the applied load is directed. Because of the preload, the pres- sure is positive even at the upper pad in the opposite direction to the applied load. The pivot deflection and stiff- ness are maximum at the bottom pad that receives the heaviest pressure load. The predicted stiffness coefficients increase as the static load and rotor speed increase, while the damping coefficients decrease as the rotor speed increases, but increase as the static load increases. In general, the predicted stiffness coefficients agree well with the test data. The predicted damping coefficients overestimate the test data, particularly for large static loads. In general, the current predictive model considering the pivot stiffness improves the accuracy of the rotordynamic performance compared to previously reported models.

• Structural Engineering and Mechanics
• /
• v.51 no.3
• /
• pp.377-402
• /
• 2014

In this study, optimal distribution of springs which supports a cantilever beam is investigated to minimize two objective functions defined. The optimal size and location of the springs are ascertained to minimize the tip deflection of the cantilever beam. Afterwards, the optimization problem of springs is set up to minimize the tip absolute acceleration of the beam. The Fourier Transform is applied on the equation of motion and the response of the structure is defined in terms of transfer functions. By using any structural mode, the proposed method is applied to find optimal stiffness and location of springs which supports a cantilever beam. The stiffness coefficients of springs are chosen as the design variables. There is an active constraint on the sum of the stiffness coefficients and there are passive constraints on the upper and lower bounds of the stiffness coefficients. Optimality criteria are derived by using the Lagrange Multipliers. Gradient information required for solution of the optimization problem is analytically derived. Optimal designs obtained are compared with the uniform design in terms of frequency responses and time response. Numerical results show that the proposed method is considerably effective to determine optimal stiffness coefficients and locations of the springs.

• Computers and Concrete
• /
• v.29 no.3
• /
• pp.127-144
• /
• 2022

To investigate the flexural stiffness of the steel-composite beam, the contributions of the concrete slab and steel beam to the stiffness were considered separately. The method for flexural stiffness of the composite beam, considering the stiffness of the concrete slab and steel beam, was proposed in this paper. In addition, finite element models of the composite beams were established and validated. Parametric analyses were carried out to study the effects of different parameters on the neutral axis distance reduction factors of the concrete slab and steel beam. Afterward, the neutral axis distance reduction factors were fitted, and the stiffness combination coefficients of the two parts were solved. Based on the stiffness combination coefficients, the flexural stiffness of the composite beam can be obtained. The proposed method was validated by the tested and analyzed results. The method has a simple form and high accuracy in predicting the flexural stiffness of the steel-concrete composite beam, even though the degree of shear connection is less than 0.5.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
• /
• 1997.04a
• /
• pp.91-100
• /
• 1997

In this paper the linearzed stiffness and damping coefficients of tilting pad thrust bearing are calculated by the perturbation method. The coefficients are obtained for a wide range of pivot positions. The effects of exciting frequency and pad mass on stiffness and damping coefficients are investigated. Critical frequencies due to the tilting motions of the pad are presented and are shown to be strongly influenced by the pivot position and pad mass.

• Tribology and Lubricants
• /
• v.13 no.3
• /
• pp.33-41
• /
• 1997

In this paper the linearized stiffness and damping coefficients of tilting pad thrust bearing are calculated by the perturbation method. The coefficients are obtained for a wide range of pivot positions. The effects of exciting frequency and pad mass on stiffness and damping coefficients are investigated. Critical frequencies due to the tilting motions of the pad are presented and are shown to be strongly influenced by the pivot position and the pad mass.

• Tribology and Lubricants
• /
• v.30 no.2
• /
• pp.77-85
• /
• 2014

This study set out to predict the load capacity and rotordynamic coefficients of tilting-pad journal bearings, taking the pivot stiffness into account. The analysis uses rocker-back (cylindrical) and ball in socket (spherical) pivot models, both of which are based on Hertzian contact stress theory. The models ascertain the non-linear elastic deformation of the pivots according to the applied load, pivot geometry, and material properties. At present, the Reynolds equation for an isothermal, isoviscous, and incompressible fluid is used to calculate the film pressure by using the finite-element method, after which the Newton-Raphson method is used to simultaneously find the journal center location, pad angles, and pivot deflections. The bearing analysis, excluding the pivot models, is validated using predictions those are readily available in the literature. As the rotor speed increases, the predicted journal eccentricity and damping coefficients decrease, but the stiffness coefficients increase, as expected. Most importantly, the implementation of the pivot models increases the journal eccentricity but significantly decreases the stiffness and damping coefficients of the tilting-pad journal bearings.