Vibration Of Assembly Research Articles

Dynamic stiffness matrix of a rectangular plate for the general case

The dynamic stiffness matrix of a rectangular plate for the most general case is developed by solving the bi-harmonic equation and finally casting the solution in terms of the force–displacement relationship of the freely vibrating plate. Essentially the frequency dependent dynamic stiffness matrix of the plate when all its sides are free is derived, making it possible to achieve exact solution for free vibration of plates or plate assemblies with any boundary conditions. Previous research on the dynamic stiffness formulation of a plate was restricted to the special case when the two opposite sides of the plate are simply supported. This restriction is quite severe and made the general purpose application of the dynamic stiffness method impossible. The theory developed in this paper overcomes this long-lasting restriction. The research carried out here is basically fundamental in that the bi-harmonic equation which governs the free vibratory motion of a plate in harmonic oscillation is solved in an exact sense, leading to the development of the dynamic stiffness method. It is significant that the ingeniously sought solution presented in this paper is completely general, covering all possible cases of elastic deformations of the plate. The Wittrick–Williams algorithm is applied to the ensuing dynamic stiffness matrix to provide solutions for some representative problems. A carefully selected sample of mode shapes is also presented.

Assessment of Solder Joint Fatigue Life Under Realistic Service Conditions

The behavior of lead-free solder alloys under complex loading scenarios is still not well understood. Common damage accumulation rules fail to account for strong effects of variations in cycling amplitude, and random vibration test results cannot be interpreted in terms of performance under realistic service conditions. This is a result of the effects of cycling parameters on materials properties. These effects are not yet fully understood or quantitatively predictable, preventing modeling based on parameters such as strain, work, or entropy. Depending on the actual spectrum of amplitudes, Miner’s rule of linear damage accumulation has been shown to overestimate life by more than an order of magnitude, and greater errors are predicted for other combinations. Consequences may be particularly critical for so-called environmental stress screening. Damage accumulation has, however, been shown to scale with the inelastic work done, even if amplitudes vary. This and the observation of effects of loading history on subsequent work per cycle provide for a modified damage accumulation rule which allows for the prediction of life. Individual joints of four different Sn-Ag-Cu-based solder alloys (SAC305, SAC105, SAC-Ni, and SACXplus) were cycled in shear at room temperature, alternating between two different amplitudes while monitoring the evolution of the effective stiffness and work per cycle. This helped elucidate general trends and behaviors that are expected to occur in vibrations of microelectronics assemblies. Deviations from Miner’s rule varied systematically with the combination of amplitudes, the sequences of cycles, and the strain rates in each. The severity of deviations also varied systematically with Ag content in the solder, but major effects were observed for all the alloys. A systematic analysis was conducted to assess whether scenarios might exist in which the more fatigue-resistant high-Ag alloys would fail sooner than the lower-Ag ones.

Isotropic Design Method of Suspension System of Dithered RLG Strapdown Inertial Measurement Unit

The dithered ring laser gyro (DRLG) strapdown inertial navigation system (SINS) is widely used in many applications, including military and commercial systems for the advantages such as high accuracy, wide dynamic range and bandwidth, outstanding scale factor stability over temperature, compactness and lower cost. However, the dither motion introduced to eliminate the lock-in error which is the inherent phenomena in the ring laser gyro also brought the adverse disturbance to the inertial measurement unit (IMU). Meanwhile, the installation environment of the SINS may also bring undesirable vibration and shock. For these reasons, a feasible and reliable suspension system is required to provide decoupling of the translational and rotational vibrations of the inertial sensor assembly (ISA) and attenuating the outside vibration and shock. Based on this, the isotropic design method of suspension system of DRLG strapdown IMU is proposed in this paper. The method consists four principles: 1) the input axes of sensors should be placed symmetrically along the ISA symmetric axes which are also the principle inertial axes; 2) the mass center of ISA is also the center of the geometric structure; 3) the elastic center of the suspension system is overlapped on the mass center by placing mounting isolators in the ISA structure corner in the isotropic manner and 4) the first mode frequency of ISA structure should be twice or more higher than the maxim mechanical dither frequency of DRLG triad. Following these principles, a design practice is implemented. The simulation and the experiment result show that the IMU using isotropic design method is proved to be feasible and reliable even in the extreme temperature ambiance.

A novel method for in-situ estimation of time constant for core temperature monitoring thermocouples of operating reactors

Core temperature monitoring system is an important component of reactor protection system in the current generation fast reactors. In this system, multiple thermocouples are housed inside a thermowell of fuel subassemblies. Response time of the thermocouple assembly forms an important input for safety analysis of fast reactor and hence frequent calibration/time constant estimation is essential. In fast reactors the central fuel subassembly is provided with bare fast response thermocouples to detect under cooling events in reactor and take proper safety action. On the other hand, thermocouples in thermowell are mainly used for blockage detection in individual fuel subassemblies. The time constant of thermocouples in thermowell can drift due to creep, vibration and thermal fatigue of the thermowell assembly. A novel method for in-situ estimation of time constant is proposed. This method uses the Safety Control Rod Accelerated Mechanism (SCRAM) or lowering of control Rod (LOR) signals of the reactor along with response of the central subassembly thermocouples as reference data. Validation of the procedure has been demonstrated by applying it to FBTR.

A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part I: Theoretical Basis

In this paper, a reduced order model for the vibrations of bladed disk assemblies was achieved. The system studied was a 3D annulus of shroudless, “custom-tailored,” mistuned blades attached to a flexible disk. Specifically, the annulus was modeled as a spectral-based “meshless” continuum structure utilizing only nodal data to describe the arbitrary volume in which the system's dynamical energy was minimized. An extended Ritz variational procedure was used to minimize this energy, subjected to constraints imposed by an assumed 3D displacement field of mathematically complete, orthonormal “blade-disk” polynomials multiplied by generalized coefficients. The coefficients were determined by constraining the polynomial series to satisfy the extended Ritz stationary equations and essential boundary conditions of the bladed disk. From this, the governing equations of motion were generated into their usual dynamical forms to calculate upper-bounds on the actual free and forced responses of bladed disks. No conventional finite elements and element connectivity or component substructuring data were needed. This paper, Part I, outlines the theoretical foundation of the present model, and through extensive Monte Carlo simulations, establishes the analytical basis, predictive accuracy, and re-analysis efficiency of the present technology in the prediction of 3D maximum response amplitude of mistuned bladed disks having increasing numbers of nodal diameter excitations. Further applications validating the 3D approach against conventional finite element procedures of free and forced response prediction of a mistuned Integrally-Bladed Rotor used in practice is presented in a companion paper, Part II (Fang, McGee, and El-Aini, 2013, “A Reduced-Order Meshless Energy Model for the Vibrations of Mistuned Bladed Disks—Part II: Finite Element Benchmark Comparisons, ASME J. Turbomach., to be published.

The Research of the Servovalve Noise

Use Gambit and Fluent to the servo valve armature component of squeak problem undertook CFD is analyzed, simulates the flow field distribution in internal circuit structure, found in the servo valve armature component whistle when fluid in the inner of the product, produced a marked a negative pressure zone, and in this context the armature assembly stress sharply change, causing the armature assembly vibration squeal, changing the internal structure of the product again CFD simulation, negative pressure area disappeared, the pressure change tends to be steady, the structure of the product was the actual through pressure liquid servo valve test, howling problem solved.

Active Control on Flow-Induced Vibration of the Head Gimbals Assembly in Hard Disk Drives

An active control method has been applied for the flow-induced vibration (FIV) of the head gimbals assembly (HGA) in working hard disk drives (HDDs) through suppressing the pressure fluctuations around the HGA. Firstly, the HGA off-track vibrations and the pressure fluctuations around the HGA are measured. The results show a high correspondence between the pressure fluctuations and the HGA off-track vibration. Secondly, a feedback control architecture, based on numerical simulations, is proposed for the FIV of the HGA by introducing virtual pressure sensors into the airflow regions around the HGA. The numerical results show that the FIV of the HGA can be successfully controlled when the pressure fluctuations are actively suppressed around the HGA. Finally, an experiment has been conducted to demonstrate the proposed feedback control method for the FIV of the HGA, in which the FIV on the HGA was detected by a laser Doppler vibrometer and used as the feedback error signals.

Active Control of Flow-Induced Vibrations on Slider in Hard Disk Drives by Suppressing Pressure Fluctuations With Virtual Sensing

This paper presents numerical simulations on a feedback active control strategy for flow-induced off-track vibration of a head gimbals assembly (HGA) bearing a slider in hard disk drives (HDDs). In the proposed active control strategy, a physical pressure sensor is assumed on the HDD cover to detect the pressure fluctuations and a pressure actuator is on the inner surface of the HDD cover to actuate feedback acoustic pressures to suppress pressure fluctuations in airflow turbulence around the HGA. A virtual sensing method is employed to enable the system feedback signal changeable from the physical pressure sensor to specific “virtual pressure sensors” closely around the HGA. The performance of the proposed active control strategy has been numerically examined based on a turbulence model of a 2-D channel flow with large eddy simulation. The results show that successful active control on the HGA off-track vibration can be achieved if the feedback signal is configured by virtual sensing to minimize the pressure fluctuations at specific positions closely around the HGA. It is also shown that the wake zone of the HGA is a typical virtual sensing position for pressure fluctuations in the feedback control system in order to achieve suppression on the HGA off-track vibration.

Analytical investigation of the properties of the neutron noise induced by vibrating absorber and fuel rods

Abstract Analytical solution methods for the neutron noise in a one-dimensional multi-region system in two-group theory, which have so far been based on the adjoint function technique, are extended here to using the forward Green's function technique. The forward Green's functions were calculated analytically for a noise source in a core surrounded by reflector regions at both sides. It is shown that with symbolic computation methods, the forward Green's function can be used for the calculation of the space- and frequency-dependent noise in the first order approximation for arbitrary noise sources which have an analytical representation. The properties of the induced neutron noise were investigated for vibrations of both absorbers and fuel assemblies, with two representations of the noise sources: a point-like source which corresponds to the vibrations of a fuel rod, and a finite width source which corresponds to vibrations of a fuel assembly. The contributions of the components induced by the fluctuations of the various types of macroscopic cross sections in the total noise are also discussed and the information content of the noise in the fast group is explored for the identification of fuel assembly vibrations.

Pressure Fluctuations and Flow-Induced Vibration Measurements in a Hard Disk Drive under Different Rotation Speeds

Flow-induced vibration (FIV) of a head gimbals assembly (HGA) in hard disk drives (HDDs) limits the positioning accuracy of magnetic head in the HGA for higher HDD magnetic recording density. The pressure fluctuations characterize turbulent fluctuations exciting the HGA off-track vibration (HGA-OTV). In this paper, experimental studies have been carried out to investigate the spectrum characteristics correspondence between pressure fluctuations around an HGA and the simultaneous HGA-OTV under different HDD rotation speeds. A practical and effective experimental setup has been implemented to enable the simultaneous measurements on both the pressure fluctuation and HGA-OTV signals, where pressure fluctuations are measured with a pressure transducer through a small hole on the HDD top cover and the direct HGA-OTV signals are detected through a laser Doppler vibrometer. Results under conditions of three different HDD rotation speeds of 7200, 9000, 10800 rpm have been investigated and compared. It is shown that the HGA off-track vibration spectra are highly associated with those of the pressure fluctuations in terms of principal peaks in four frequency bands around 1.8 kHz, 2.5-3.5 kHz, 7-7.5 kHz and 11.5-12.5 kHz. With increasing HDD rotation speed, it is shown that the spectrum magnitudes of both the pressure fluctuation and the HGA off-track vibration increase correspondingly, while the principal peak positions in spectra of either pressure fluctuation or the HGA off-track vibration always hold the line. This study demonstrates a causal nexus from the pressure fluctuation to the HGA off-track vibration and suggests the feasibility of controlling the HGA-OTV through suppression of pressure fluctuations around the HGA.

SELF-TUNING VIBRATION ABSORBER

A self-tuning vibration absorber including a carrier rod assembly having operatively connected thereto a mounting mechanism for mounting the carrier rod assembly to a primary system and a hollow shafted motorized tuning mechanism for tuning a phase difference between vibration of the primary system and vibration of the carrier rod assembly to 90 degrees, the carrier rod assembly further including a detecting mechanism for detecting the vibration of the primary system and the vibration of the carrier rod assembly, and a controller in electrical connection with the detecting mechanism and the tuning means for controlling the tuning mechanism based on the vibration of the primary system and the vibration of the carrier rod assembly detected. A method of vibration dampening, a method of controlling a self-tuning vibration absorber, and a method of reducing hunting motion in railcars.

1301 カーシェイク向上のためのタイヤホイール組立体の起振力予測技術(OS2-1 自動車ダイナミクスのモデリング,OS2 交通・物流システムのダイナミクス,オーガナイズド・セッション(OS))

Car shake is one of many kinds of vehicle vibration that causes customer dissatisfaction. Uniformity of tire and wheel assembly affects the vehicle vibration including car shake. In this study, the authors developed the estimation method to calculate the radial force vibration of tire and wheel assembly. The parameters used in this method are the radial force variation of tire, the radial runout of wheel, and so on. This estimation method is based on the complex functions and the Monte Carlo calculations. The complex functions are used to study the assembly condition of a tire and a wheel. The Monte Carlo calculations are applied to calculate the parameters from their statistical data such as averages and standard deviations. The estimated results are in good agreement with the experimental results. The authors concluded that this method is an effective tool to reduce car shake.

Dynamic Characteristics Analysis of Abnormal Vibration for Power Assembly of Diesel Engine of SUV

With regard to the problem of abnormal vibration for power assembly of diesel engine of the Sport Utility Vehicle in working rotation speed conditions, the method of test mode combined finite element simulation analysis was adopted, the dynamic characteristics of the power assembly were studied in all conditions. First vibration modal testing of the power assembly was carried out in whole vehicle condition and in test bed, the cause of abnormal vibration of the power assembly was found out, the bending stiffness was low, then a kind of actual finite element simulation model of the power assembly was set up, the constraint mode was calculated. The rationality of finite element simulation model of the power assembly was validated. Integrated modal testing and simulation analysis showed that the low stiffness of flywheel shell led to the low first modal frequency of power assembly which was easily in the excitation frequency range of diesel engine working rotational speed, and resulted in system resonance of the power assembly

Analysis of slip characteristics between dimple and flexure in hard disk drives

A mobile hard disk drive (HDD) is often faced with inevitable mechanical problems because of the portability of the drive. Then, almost HDD use much faster emergency parking system to protect the system from these problems. However, very fast emergency parking causes a large ramp contact, which could create dimple-flexure interactions such as a dimple-flexure slip, head-gimbal assembly vibration, unexpected slider motion. These dimple-flexure interactions largely affect the flyability of a slider. As such, dimple-flexure interactions are one of the most important factors in designing a mobile HDD. Therefore, in this study, we characterized the dimple-flexure slip among dimple-flexure interactions and analyzed it using a combination of experiments and finite element modeling. We evaluated the feasibility of dimple-flexure slip and verified the main cause of dimple-flexure slip. We also investigated the relationship between dimple-flexure slips and ramp contact during emergency parking. Finally, we designed the finite element ramp contact simulation, and analyzed dynamic characteristics for the dimple-flexure slip.

Analysis of Experimental Stand for Surface Acoustic Wave Vibrations Sensors

The analysis of vibrations excitation in surface acoustic wave vibrations sensors is the aim of our work. The sensors are parts of electronic warning system which is intended to be mounted at fences of guarded object. The vibration excitation with expected acceleration is needed during experiments. Elements of fences are replaced by tense strings for experimental purposes and the surface acoustic wave vibration sensors are fastened to these strings. Analysis of the assembly string-sensor takes into account not only the mass of sensor but its moment of inertia, too. Free vibrations of string-sensor assembly are considered. The standard excitation by pulling off string in chosen point causes vibrations. The normal vibrations of assembly (frequencies, orthogonal set of normal functions) are calculated and used for calculations of free vibrations. The spectrum of the standard free vibrations is calculated. The results will be used in the experimental stand. The calculations enable excitation of vibrations with expected spectrum. The stand enables tests of the whole warning system. The thresholds of detection and reaction at concurrent intruder alarm will be investigated at this laboratory stand.

Technology Focus: Bit Technology and Bottomhole Assemblies (December 2010)

Technology Focus Performance Drilling—System Approach Will Yield Sustainable Improvements The industry continues to develop new tools, technologies, and processes to help drive down drilling costs. This commitment to improve drilling efficiency and reliability, through effective questioning of relevant data, also has strong positive effects on drilling operations. Strides have been made, but there is more to be done. In most instances, efforts to understand and develop sustainable-improvement strategies tend to isolate and focus on specific components [e.g., drill bit, drilling fluid, bottomhole assembly (BHA), and drive system]. In relating to these components, we usually are guided by past experiences and “rules of thumb.” Without a doubt, it is clear that the effect and value of our experiences are immeasurable. However, we need to shape our data-questioning processes around our experiences to challenge the rules of thumb. We have tools that will speed up this process. First, we need a system approach to performance drilling. Extensive research has contributed to the development of high-performance positive-displacement motors and turbines. In addition, development of rotary-steerable tools has been extended successfully into slimhole applications. Earlier limitations of these tools, in terms of torque vs. revolutions-per-minute relationship, as well as product reliability, have seen tremendous improvements. What usually is missing is the selection analysis from a drilling-system perspective rather than as an individual component. BHA design and modeling, a critical part of the system approach, must be practical and field driven. Negative effects of vibrations, with regard to downhole-tool life, borehole quality, and overall drilling performance, have been clearly established. As a means to vibrations mitigation, sources and specific modes must be identified. BHA design, as part of the system approach, must be cognizant of the drilling system’s functional requirements. In addition, performance-improvement discussions must focus on practical aspects of the application. System-based solutions will ensure consistent and sustainable improvements. We have the key, let’s open the door. Bit Technology and Bottomhole Assemblies additional reading available at OnePetro: www.onepetro.org SPE 128767 • “Decoupling Stick/Slip and Whirl To Achieve Breakthrough in Drilling Performance” by Sean Xianping Wu, Smith Technologies, et al. SPE 128211 • “High-Frequency Downhole Dynamic Measurements Provide Greater Understanding of Drilling Vibration in Performance-Motor Assemblies” by Andrew D. Craig, SPE, NOV, et al. SPE 134488 • “Downhole-Vibration Measurement, Monitoring, and Modeling Reveal Stick/Slip as a Primary Cause of PDC-Bit Damage in Today’s Applications” by L.W. Ledgerwood III, SPE, Baker Hughes, et al.

Effect of Prebent Deflection on Lateral Vibration of Stabilized Drill Collars

Summary An effective modulation of lateral vibration of a bottomhole assembly (BHA) is that some prebent deflection is made on the lower stabilized section of drill collars. This is because the restorable deflection of a drill collar confined in a borehole depends on the prebent deflection. If the prebend nears the limit that the borehole can contain, there will be no sufficient restorable deflection to produce restoring force for lateral vibration. To understand the nature of this phenomenon, a dynamic model for lateral vibration of a stabilized prebent drill-collar section in an inclined well is presented. The governing nonlinear equations are obtained by using a Lagrangian approach, which are characterized by a prebend-dependent nonlinear bending stiffness term. They also include the effects of clearance/friction of stabilizers with borehole wall, contact friction of drill collar with borehole wall, axial forces from weight-on-bit (WOB) and bit/formation interactions, and hydrodynamic damping of drilling mud. The gyroscopic moments are proved to be negligibly small terms within a range of operating conditions of drilling. Poincaré map bifurcation diagram, phase diagram, Liapunov exponent, and power spectrum analysis are used to evaluate the dynamic behaviors. Simulation results both in a vertical well and in an inclined well show that lateral vibration is sensitive to the prebent deflection in some degree, presenting periodic motion, chaotic motion, or alternating in turn as usual. However, when prebent deflection is more than 87% in a vertical well and more than 45% in a 20°-inclined well (of the average clearance between the drill collar and the borehole), lateral vibration will vanish. Such a characteristic is crucially important for practical applications. For example, we may effectively prevent a drill string in an inclined well from severe whirling motion with a properly designed prebent drill collar.

Copper trace fatigue models for mechanical cycling, vibration and shock/drop of high-density PWAs

When assessing the mechanical durability of electronic assemblies, the focus is generally on the solder interconnects. However, in many package styles, such as ball grid arrays (BGAs), land grid arrays (LGAs), micro lead frame (MLFs) and quad flat no-lead (QFNs), the Cu trace emanating from the solder pad may be the weakest failure site, especially if the solder joint is copper-defined rather than mask defined. This is particularly true in situations with cyclic mechanical loading, such as cyclic quasi-static bending, vibration and repetitive drop/shock. This study focuses on quasi-static mechanical cycling durability of LGA assemblies with copper-defined pads. Specimens were cycled to failure under zero-to-max, three-point bending and failure statistics were collected. The failure mode was confirmed to be fatigue cracks in copper traces emanating from the corner solder pads, just at the edge of the solder mask where the solder joint ends. The cracks were identified by lateral polishing after desoldering the component. The cyclic bending of this assembly was modeled with 3D, elastic–plastic, large deformation finite element analysis. Due to the complexity of the geometry, a global–local approach was used to identify the strain history and the mean stress at the failure site. A generalized strain-based fatigue model was used to characterize these failures, and preliminary model constants were iteratively estimated by ensuring that they were simultaneously compatible with both the durability test data and the copper stress–strain curves used in the FEA (finite element analysis). These preliminary model constants were then refined by separately modeling the initiation and progression history of fatigue damage in the cyclic bend tests. Damage progression was modeled in this study by using a technique of ‘successive initiation’ developed earlier by this research group. In this method, finite element simulations are used to progressively ‘kill’ elements that have accumulated sufficient fatigue damage to lose their load-carrying capacity. When the killed elements span the entire cross-section of the copper trace, the trace is assumed to electrically fail. This calibrated model is then used to demonstrate its ability to predict copper trace failures in other situations such as quasi-static four-point bending of LGA assemblies and vibration of BGA assemblies. More important, we demonstrate its use for re-designing of BGA assemblies to prevent copper trace failures under drop/shock loading. The important impact of this study includes insight into copper trace failures in Printed Wiring Assemblies (PWAs) under mechanical cycling, a quantitative model to predict its occurrence, and validated guidelines to prevent it by design.

Nonlinear Vibration of the Double-Beams Assembly Subjected to A.C. Electrostatic Force

In this study, the mathematical model of double-beams assembly subjected to the a.c. electrostatic force is established. This is helpful for designing sensors and actuators. The boundary condition of this system is nonlinear and timedependent. Obviously, this system is very complicated. A new solution method is here developed to derive the analytical solution. Because the a.c. electrostatic force includes the static and harmonic forces, the system is divided into the nonlinear static and dynamic subsystems. The exact static solution is presented. In the other hand, the boundary conditions of the dynamic subsystem are nonlinear and time-dependent. First, using the balanced method the system with time-dependent coefficients is transformed into one with time-independent coefficients. Further, the analytical solution of the transformed dynamic subsystem is derived. It is found that there exists great difference between the linear and nonlinear spectrums. Moreover, the effects of several geometry and material parameters on the frequency spectrums of this system are significant.

A study on the grid-to-rod fretting wear-induced fuel failure observed in the 16×16KOFA fuel

The burnup-dependent grid-to-rod gap combined with the fluid-induced vibration may generate grid-to-rod fretting wear-induced fuel failure for some fuel assemblies in a certain burnup range. The systematic grid-to-rod fretting wear-induced fuel failure occurred at the 16×16 Korean Optimized Fuel Assembly loaded in the 2-loop Westinghouse type plant in Korea. Prior to various tests and some measurements for investigating its root causes, they were assumed to be self-excited fuel assembly vibration caused by hydraulic-unbalanced mixing vane design, excessive cross-flow between fuel assemblies during the transition core, or relatively large grid-to-rod gap formation during in-reactor irradiation that may be caused by excessive initial spring force loss of fresh fuel during a fuel rod loading process and/or a fuel assembly transport to a plant and by excessive cladding creep-down. A wide spectrum of tests and some measurements were performed to find out root cause(s) of the grid-to-rod fretting wear-induced fuel failure. Based on these tests and measurements, it is concluded that the self-excited fuel assembly vibration is the primary root cause, while excessive initial spring force loss during the fuel rod loading process is the second major root cause.