2nd Bending Mode Research Articles

Prediction of Vertical Tail Buffet Using CFD/CSD Coupling Method

The vertical tail buffet induced by the vortex breakdown flow is numerically investigated. The unsteady flow is calculated by solving the RANS equations. The structural dynamic equations are decoupled in the modal coordinates. The radial basis functions (RBFs) are employed to generate the deformation mesh. The buffet response of the flexible tail is predicted by coupling the three sets of equations. The results show that the presence of asymmetry flow on the inner and outer surface of the tail forced the structural deflection offsetting the outboard. The frequency of the 2nd bending mode of the tail structure meets the peak frequency of the pressure fluctuation upon the tail surface, and the resonance phenomenon was observed. Therefore, the 2nd bending responses govern the flow field surrounding the vertical tail. Finally, the displacement of the vertical tail is small, while the acceleration with a large quantitation forces the vertical tail undergoing severe addition inertial loads.

Numerical Calculation of Hip Squeak Over the Normal Gait Cycle

This paper present the numerical and analytical hip squeak model using the normal gait data acquired from the experiment. The axis of the ground reaction force is defined on the hip joint at the successive position of the right hip during the gait cycle. The contact pressure and its distribution on the ball are calculated by the Hertz theory at the corresponding cycle. The eigenvalue sensitivity analysis is conducted at the quasi-static state of the successive position of the right hip for both the full lubrication and the mixed lubrication. For the full lubrication case, the hip joint system becomes dynamically unstable only when the hip extends. In the mixed lubrication, the 2nd bending mode has the very high squeak propensity and its frequency drastically varies with the gait cycle.

Direct Determination of Dynamic Elastic Modulus and Poisson’s Ratio of Timoshenko Rods

In this paper, the exact solution of the Timoshenko circular beam vibration frequency equation under free-free boundary conditions was determined with an accurate shear shape factor. The exact solution was compared with a 3-D finite element calculation using the ABAQUS program, and the difference between the exact solution and the 3-D finite element method (FEM) was within 0.15% for both the transverse and torsional modes. Furthermore, relationships between the resonance frequencies and Poisson’s ratio were proposed that can directly determine the elastic constants. The frequency ratio between the 1st bending mode and the 1st torsional mode, or the frequency ratio between the 1st bending mode and the 2nd bending mode for any rod with a length-to-diameter ratio, L/D ≥ 2 can be directly estimated. The proposed equations were used to verify the elastic constants of a steel rod with less than 0.36% error percentage. The transverse and torsional frequencies of concrete, aluminum, and steel rods were tested. Results show that using the equations proposed in this study, the Young’s modulus and Poisson’s ratio of a rod can be determined from the measured frequency ratio quickly and efficiently.

Modeling and Analysis of Piezo-Elastica Energy Harvester in Computer Hard Disk Drives

In this paper, design and analysis of an energy harvester named piezo-elastica energy harvester (PEEH) to harvest wasted mechanical energy generated by flex cable kinetic and vibratory motions are presented. A coupled piezo-elastic model is developed for the harvester with focus given to understanding piezoelectricity generated by its PVDF layer over its underlying largely deformed flex cable elatica structure. Design for manufacturing for the proposed harvester is detailed in this work. Numerical finite element simulations and laboratory measurements using noncontact laser interferometry validate the mode with respect to the PEEH's profiles, natural frequencies and mode shapes as well as electric energy generated resulted from flex cable's dynamics. It is observed that about 25% of the power consumed by disk drive's voice coil motor can be harvested by the proposed design. Among harvested energy, it is found that 58% comes from significant change of PEEH's profile when rotary actuator swings between disk's outer diameter and inner diameter regions, 33% from PEEN's 2nd bending mode, and 9% from its 1st bending mode. The work presented in this paper suggests the possibility of scavenging and converting flex cable's mechanical vibrations and dynamics into electrical form for power conservation inside computer hard disk drives.

Study on Micro-energy Harvesting Device Using Iron-Gallium Alloy

We propose a micro-energy harvesting device using an iron gallium alloy (Galfenol) that is capable of providing electrical energy through environmental vibrations. Galfenol is a ductile magnetostrictive material with high piezomagnetic constant, good machinability, and a large inverse magnetostrictive effect in which the magnetization can be varied by mechanical stress. The proposed device consists of two columns of Galfenol those ends are connected at the end with iron yokes, coils and a bias magnet. When bending force is applied on the mover with the other end fixed like a cantilever, the magnetization in one column increases because of tensile force due to the inverse magnetostrictive effect, and the other decreases due to compression. The time variation of the magnetization generates voltage on the wound coils. This energy harvesting device is advantageous over other types such as those using piezoelectric material, in size, high robustness, and low electrical impedance. In addition, the two columns structure requires low mechanical force to provide sufficient stress to change the magnetization. We fabricated a prototype using stress-annealed Galfenol with 314 coil turns and in experiments verified a maximum voltage of 0.48 V at forced vibration with a frequency of 333 Hz. The frequency response was also measured to understand the behavior at resonances of the 1st and 2nd bending modes as well as the effect of additional weight.

A piezoelectric ultrasonic linear micromotor using a slotted stator

A novel ultrasonic micro linear motor that uses 1st longitudinal and 2nd bending modes, derived from a bartype stator with a rectangular slot cut through the stator length, has been proposed and designed for end-effect devices of microrobotics and bio-medical applications. The slot structure plays an important role in the motor design, and can be used not only to tune the resonance frequency of the two vibration modes but also to reduce the undesirable longitudinal coupling displacement caused by bending vibration at the end of the stator. By using finite element analysis, the optimal slot dimension to improve the driving tip motion was determined, resulting in the improvement of the motor performance. The trial linear motor, with a weight of 1.6 g, gave a maximum driving velocity of 1.12 m/s and a maximum driving force of 3.4 N. A maximum mechanical output power of 1.1 W was obtained at force of 1.63 N and velocity of 0.68 m/s. The output mechanical power per unit weight was 688 W/kg.

3202 扇形圧電振動子を用いた薄型マイクロ超音波モータの駆動特性の解析と評価(J22-1 次世代アクチュエータシステム(1),ジョイントセッション,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

A low-profile micro ultrasonic motor has been designed and fabricated. This motor has two sector shaped vibrators. The vibrators generate elliptical motion by the 1st longitudinal mode and the 2nd bending mode. They are supported by planar elastic structure that combined with preload mechanism. Three types of pre-load systems were designed and evaluated. The diameter and thickness of one type was 9.8[mm] and 0.6[mm]. These vibrators have been oscillated around 340 [kHz]. The maximum rotation speed was 1.2 x 10^3 [rpm] and the maximum starting torque was 98.8[μNm] when the applied voltage was 20[V_<p-p>].

A Q-value Measurement for Damping Evaluation and Rotational Test of Over-Hung Rotor Supported by AMBs

In recent years, Active Magnetic Bearings (AMBs) characterized by non-contact support without mechanical loss have been applied in industrial rotors. The purpose of this research is to develop a flexible, overhanging rotor supported by AMBs to pass smoothly the 2nd bending mode critical speed. This paper deals with the following topics : (1) Controller design based on the phase adjustment method and the evaluation of the designs using sensitivity functions, (2) Evaluation of the designs using a new method, called Q-value function, and (3) Application of modal balancing method to pass the 2nd bending mode critical speed.

The Evaluation of the Damping Characteristics of a Hard Coating on Titanium

Engine failures due to fatigue have cost the Air Force an estimated &amp;dollar;400 million dollars per year over the past two decades. Damping treatments capable of reducing the internal stresses of fan and turbine blades to levels where fatigue is less likely to occur have the potential for reducing cost while enhancing reliability. This research evaluates the damping characteristics of magnesium aluminate spinel, MgO+Al2O3, (mag spinel) on titanium plates from an experimental point of view. The material and aspect ratio were chosen to approximate the low aspect ratio blades found in military gas turbine fans. In the past, work has generally been performed on cantilever supported beams, and thus the two‐dimensional features of damping were lost. In this study plates were tested with a cantilevered boundary condition, using electrodynamic shaker excitation. The effective test area of each specimen was 4.5 in × 4.5 in. The nominal plate thickness was 0.125 in. Mag spinel was applied to both sides of the plate, at a thickness of 0.01 in, and damping tests were run at room temperature. The effect of the coating was evaluated at the 2nd bending mode (mode 3) and the chord wise bending mode (mode 4). A scanning laser vibrometer revealed the frequency and shape of each mode for the plates. Sine sweeps were used to characterize the damping of the coated and uncoated specimens for the modes tested. The coating increased damping nonlinearly for both modes tested in which the general outcome was similar to that found in beams.

Identification of reactor internals' vibration modes of a Korean standard PWR using structural modeling and neutron noise analysis

The vibration characteristics of a Korean standard PWR reactor internals have been estimated through a three-dimensional finite element analyses and verified by using the mode separated power spectral density functions obtained from the ex-core neutron noise signals. Also the natural vibration modes of the fuel assembly have been identified measuring both the ex-core and the in-core neutron noise signals which are close to each other. As a result, the fundamental bending mode frequency of the reactor internal structure is found to be around 8 Hz and the fundamental shell mode frequency 14.5 Hz, respectively. It is also shown that the fundamental bending mode frequency of the fuel assembly is 2.3 Hz and the 2nd bending mode frequency 5.8 Hz, respectively. These results can be used for the supplements of the Korean standard PWR's CVAP (Comprehensive Vibration Assessment Program) data.