Random Vibration Test Research Articles

Force limited vibration testing: an evaluation of the computation of C<sup>2</sup> for real load and probabilistic source

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the load (test item), <TEX>$C^2$</TEX> is a very important parameter for FLVT. A number of computational methods to estimate <TEX>$C^2$</TEX> are described in the literature, i.e., the simple and the complex two degrees of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of <TEX>$C^2$</TEX> to perform a representative random vibration test based on force limitation, when the adjacent structure (source) description is more or less unknown. Marchand discussed the formal description of getting <TEX>$C^2$</TEX>, using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between load and source. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected, consisting of modal effective masses and the spring stiffness's associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter <TEX>$C^2$</TEX>. When no mathematical model of the source can be made available, estimations of the value <TEX>$C^2$</TEX> can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value <TEX>$C^2$</TEX> can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature have been analyzed and discussed to get more knowledge about the applicability of the probabilistic method.

Experimental study on on-orbit and launch environment vibration isolation performance of a vibration isolator using bellows and viscous fluid

Operation of various actuators on a satellite such as reaction wheels, cryocoolers, etc. produces micro-vibration which may have adverse effects on the performance of high precision payloads. In order to protect the high precision payloads from the vibration disturbances, vibration isolators are often applied in the vibration propagation path. Vibration isolators developed for on-orbit space application should be able to isolate micro-vibration when in orbit, and also withstand severe launch vibration environment. In this paper, on-orbit and launch environment isolation performance of a vibration isolator using bellows and viscous fluid is evaluated. For the on-orbit environment test, a test setup was prepared inside a thermal-vacuum chamber and the transmissibility of the vibration isolator was measured to examine the effects of on-orbit space environment on the isolation performance of the developed isolator. The isolation test performed in a vacuum condition revealed problems caused by the elongation of the bellows due to the pressure difference which were addressed by sealing the viscous fluid inside the bellows at a vacuum condition. The effect of temperature variation on the isolation performance was found to be confined to the narrow frequency region around the isolator's resonant frequency due to the isolator's three parameter configuration. This result implies that the isolation performance of a vibration isolator having temperature dependent damping can be made less sensitive to the temperature variation by implementing three parameter configuration. The developed vibration isolator is designed to survive large deformation without being permanently deformed to guarantee the structural safety of the isolator in the launch environment. The structural safety of the isolation system is evaluated through sine and random vibration and shock tests. The on-orbit and launch environment test results indicate that the developed isolator can provide effective isolation for the small amplitude vibration disturbances on-orbit and also survive the large amplitude vibration during launch without any damage.

Force limited random vibration testing: the computation of the semi-empirical constant $$C^2$$ C 2 for a real test article and unknown supporting structure

To prevent over-testing of the test-item during random vibration testing Scharton proposed and discussed the force limited random vibration testing (FLVT) in a number of publications. Besides the random vibration specification, the total mass and the turn-over frequency of the test article (load), \(C^2\) is a very important parameter for FLVT. A number of computational methods to estimate \(C^2\) are described in the literature, i.e. the simple and the complex two degree of freedom system, STDFS and CTDFS, respectively. The motivation of this work is to evaluate the method for the computation of a realistic value of \(C^2\) to perform a representative random vibration test based on force limitation, when the description of the supporting structure (source) is more or less unknown. Marchand discussed the formal description of obtaining \(C^2\), using the maximum PSD of the acceleration and maximum PSD of the force, both at the interface between test article and supporting structure. Stevens presented the coupled systems modal approach (CSMA), where simplified asparagus patch models (parallel-oscillator representation) of load and source are connected. The asparagus patch model consists of modal effective masses and spring stiffnesses associated with the natural frequencies. When the random acceleration vibration specification is given the CSMA method is suitable to compute the value of the parameter \(C^2\). When no mathematical model of the source can be made available, estimations of the value \(C^2\) can be find in literature. In this paper a probabilistic mathematical representation of the unknown source is proposed, such that the asparagus patch model of the source can be approximated. The chosen probabilistic design parameters have a uniform distribution. The computation of the value \(C^2\) can be done in conjunction with the CSMA method, knowing the apparent mass of the load and the random acceleration specification at the interface between load and source, respectively. Data of two cases available from literature has been analyzed and discussed to get more knowledge about the applicability of the probabilistic method.

Fretting in Electrical Connectors Induced by Axial Vibration

A series of experiments were performed to investigate fretting behavior of electrical connectors subjected to axial vibration input. A random vibration test used to study vibration behavior of the connector systems revealed that multiple transverse modes were excited by the axial input. Through tests with single-frequency vibration inputs, the threshold behaviors at various frequencies for the onset of fretting corrosion were identified. It is demonstrated that the threshold amplitudes are at micrometer scale for these types of connectors. The results also exhibit that the thresholds vary with vibration frequencies, and at the frequency of one mode, the threshold is lowest over the testing spectrum. Threshold amplitudes at this mode of the connector systems with various wiring tieoff lengths were also tested. Based on the understanding of the dynamics of the connector systems, a discrete vibration model was developed to predict the threshold behavior at this mode. The estimated threshold amplitudes correlate well with the experimental results through a parametric best fit of the vibration transfer functions.

Using a Random Vibration Test Specification to Cover a Shock Requirement via a Pseudo Velocity Fatigue Damage Spectrum

Aerospace and military components must be designed and tested to withstand shock and vibration environments in terms of shock response spectrum (SRS) and power spectral density (PSD) specifications. Shock tests are usually more difficult to configure and control in the test lab. Furthermore, some lower and mid-level SRS specifications may lack the true damage potential to justify shock testing. The purpose of this paper is to demonstrate a comparison method based on the fatigue damage spectrum (FDS) to determine whether the random vibration test covers the shock requirement. This method is found to be effective within a framework of assumptions.

Vibration testing of vehicle components by random excitations with increased kurtosis

Non–Gaussian random vibration testing with kurtosis control is considered in the paper as a way of introducing realistic high peaks into shaker drive signals, thereby increasing the excitation crest factor. This is required for more accurate simulation of ground vehicle vibrations. Implementing kurtosis, not the crest factor itself, as an additional test specification along with the PSD, leads to closed–form expressions for the non–Gaussian simulation criteria and allows for analytical solutions as a result. An approach of subjecting Gaussian signals to polynomial transformation is simple but has an inherent tendency of introducing frequency distortions jeopardising the PSD simulation. There is no such difficulty with the IFFT phase manipulation approach because the power spectrum is not influenced by the phases. A phase selection procedure capable of modelling random excitations with high kurtosis has been developed and it also works for the opposite case of decreasing kurtosis. Because of the analytical solution advantage, the methods proposed in the paper meet time restrictions critical for closed–loop operation of shaker controllers. Numerical simulations of automobile vibrations with severe time history peaks and experimental work with a complete shaker testing setup were carried out.

1 N급 단일추진제 추력기 개발모델의 장기수명 연소시험 -Part I: 환경시험 및 연속모드 성능 특성

1 N급 단일추진제 하이드라진 추력기 개발모델에 대한 인수수준 랜덤 진동시험과 장기수명 연소시험이 수행되었다. 랜덤 진동시험 결과로부터 1 N급 추력기 개발모델로 구성된 이중추력기모듈의 고유 진동수는 부품수준 요구조건(100 Hz)을 상회하였으며, 구조적으로 강건함을 확인하였다. 또한 20 kg 이상의 추진제가 사용된 장기수명 연소시험 결과 연속모드 추력 감소는 약 7% 이하, 추력 불안정 현상은 <TEX>${\pm}5%$</TEX> 이내로 나타났다. 컴퓨터단층촬영을 이용해 추력기 내부의 촉매를 촬영한 결과 촉매의 손실은 약 7% 이하로 추력기 개발모델의 설계가 적절함을 보여주었다. Acceptance level random vibration and life firing test for development model of 1 N-class monopropellant thruster have been performed. From the results of random vibration, the natural frequency of the dual thurst module composed of 1 N-class development model thrusters was higher than the part level requirement(>100 Hz) and the structural robustness was verified. Thrust decrease of steady sate was below 7% and thrust instability was within <TEX>${\pm}5%$</TEX> in the life firing test using over 20 kg propellant throughput. The computerized tomography for catalyst bed showed a less than 7% of catalyst loss and it revealed the design appropriateness of the current thruster development model.

Characteristics of spaceborne cooler passive vibration isolator by using a compressed shape memory alloy mesh washer

Cryogenic coolers produce undesirable micro-vibrations during on-orbit operation, which may seriously affect the image quality of high-resolution observation satellites. Micro-vibrations can be easily isolated by mounting the cooler on a vibration isolator with low stiffness to attenuate the vibration transmitted to the satellite structure. However, the structural safety of a cooler supported by an isolator with low stiffness cannot be guaranteed under the much more severe vibration condition of a launch environment. In this study, to guarantee vibration isolation performance in a launch environment while effectively isolating the micro-vibrations from the cooler on-orbit, a new type of passive vibration isolation system by using a compressed shape memory alloy mesh washer was proposed and investigated. The basic characteristics of the isolator were measured in static and free vibration tests of the isolator, and a simple equivalent model of the isolator was proposed. The effectiveness of the isolator design in a launch environment was demonstrated through sine vibration, random vibration, and shock tests.

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.

On the Optimum Placement of Dissipators in a Steel Model Building Subjected to Shaking-Table Tests

The following research presents the numerical and experimental results obtained on a reduced scale steel model of a medium-rise building structure dynamically protected with energy dissipaters. The steel-steel friction dissipates energy as the structure undergoes interstory drifts. A preliminary numerical analysis is performed to determine the best position of the friction dampers in the longitudinal frames. All the nodes of the numerical model have been assumed with the same bending stiffness. Shaking table tests have been performed, both in random vibration tests (to determine the natural periods and the dynamic characteristics of the model) and in earthquake simulation tests (to study the dynamic behaviour of the model with and without dampers). The results have been compared to those achieved during a previous experimental study based on the same model protected with only one friction damper for each longitudinal frame.

Fatigue Life Prediction and Verification for HIC Hermetical Sealing under Random Vibration Loading

This work aims to predict fatigue life of hybrid integrated circuit (HIC) hermetical metal sealing structure mounted on PCB under random vibration loading. The prediction method consists of following steps. Firstly, finite-element model was developed to obtain model parameters (including natural frequencies and mode shapes) and power spectral density (PSD) of the critical part of sealing structure by ANSYS workbench. Secondly, modal test and random vibration test were conducted to verify the results of simulation. Thirdly, the Von Mises stress PSD was transformed into time-history data through inverse Fourier transform with Matlab program after calculating from the FEA results. The rainflow-counting algorithm was employed to evaluate cumulative damages of the critical part. The material’s S-N curve, Palmgren-Miner’s damage accumulation rule and rainflow-counting algorithm were used to predict fatigue life. A specially designed fixture and board with heat sink were used in the experiment to verify the first five mode shapes and response spectrum of the six critical points with hammer excitation. The calculation result of in this study is 70.3 hours which could be a reference for structural design of hybrid integrated circuit hermetical metal sealing under vibration conditions.

Role of Distribution Function in Vibration Related Error of Strapdown INS in Random Vibration Test

In this paper, a detailed investigation of the random vibration test is presented for strapdown inertial navigation systems (INS). The effect of the random vibration test has been studied from the point of view of navigation performance. The role of distribution functions and RMS value is represented to determine a feasible method to reject or reduce vibration related error in position and velocity estimation in inertial navigation. According to a survey conducted by the authors, this is the first time that the effect of the distribution function in vibration related error has been investigated in random vibration testing of INS. Recorded data of navigation grade INS is used in offline static navigation to examine the effect of different characteristics of random vibration tests on navigation error.

Dynamic Load Test and Data Analysis of Tiansheng Bridge

This test took dynamic strain detection method depending on time history curve of the dynamic deflection or the dynamic strain analysis of moving load in the control section to obtain impact factor. Using the method of environmental random vibration testing tested vibration response signals of L / 4 section of bridge test span , the cross section and 3 L / 4 section to identify the dynamic characteristics parameters of the overall vibration of Bridge, so that to determine current situation of application , assess the carrying capacity of bridge and test design load bearing capacity. According to the results of load test,the bearing capacity of Tiansheng bridge meets the requirements of "road - grade I" load level.

형상기억합금 메쉬 와셔를 이용한 우주용 냉각기 진동절연기의 발사 진동 및 충격 저감 성능검증

ABSTRACT Micro-vibration induced by on-board equipments such as fly-wheel and cryogenic cooler with me-chanical moving parts affects the image quality of high-resolution observation satellite. Micro-vi-bration isolation system has been widely used for enhancing the pointing performance of observation satellites. In general, the micro-vibration isolation system requires a launch locking mechanism addi-tionally to guarantee the structural safety of mission payloads supported by the isolation system with low stiffness under launch environment. In this study, we propose a passive launch and on-orbit vi-bration isolation system using shape memory alloy mesh washers for the micro-vibration isolation of spaceborne compressor, which does not require the additional launch locking mechanism. The basic characteristics of the isolator were measured in static and free vibration tests of the isolator, and a simple equivalent model of the isolator was proposed. The effectiveness of the isolator design in a launch environment was demonstrated through sine vibration, random vibration and shock tests.

Vibration Testing by Non-Gaussian Random Excitations with Specified Kurtosis. Part II: Numerical and Experimental Results

This paper is a follow-up to a preceding paper (Part I) in which two methods of non-Gaussian random vibration testing with adjustable kurtosis were introduced and motivation for kurtosis control as a way of increasing or decreasing the excitation crest factor was discussed. The current paper (Part II) adds numerical examples of automobile vibration simulation and experimental results for a kurtosis upgrade implemented in the same form of closed-loop control as in industrial shaker controllers. It was observed in experiments that the dynamic range of a kurtosis controller based on the polynomial transformation method was reduced and the handling of resonances worsened notably. These problems also arise with the sigma clipping technique of crest factor limiting. However, there are no such difficulties with the non-Gaussian method of phase manipulation in the inverse fast Fourier transform (IFFT). When using this method, the signal-to-noise ratio, the controller’s dynamic range, and the stabilization time are as good as in standard Gaussian random testing. Evaluation of the performance of the proposed phase selection algorithm has shown that for increased kurtosis it ensures realistic variability of high peaks in terms of their amplitudes and positions, as well as the number of severe peaks per data block. Because of the analytical solution advantage, both methods, the polynomial transformation and the phase selection, meet time restrictions critical for the operation of shaker testing controllers.

Method Based on Bi-Spectrum Research on Driving Signal Generation in Multi Random Vibration Test

A new method based on bi-spectrum for generating random driving signal in time domain is presented for multi shakers in random vibration test. Firstly, the equivalent relationship of amplitudes and phases between auto-spectrum and bi-spectrum are established, Secondly, MIMO linear system are supposed, relations between driving bi-spectrum and response bi-spectrum are set up, inverse operation are used for calculating the driving bi-spectrum, Finally, the equivalent relationship are obtained, random driving signal in time domain according with reference requests are got. A numerical example is done, the result show existence of the equivalents. At the same time, random vibration experiment about cantilever beam is made to prove the effective aspects of the method.

Random vibration testing with controlled samples

This paper proposes a novel experimental test procedure to estimate the reliability of structural dynamical systems under excitations specified via random process models. The samples of random excitations to be used in the test are modified by the addition of an artificial control force. An unbiased estimator for the reliability is derived based on measured ensemble of responses under these modified inputs based on the tenets of Girsanov transformation. The control force is selected so as to reduce the sampling variance of the estimator. The study observes that an acceptable choice for the control force can be made solely based on experimental techniques and the estimator for the reliability can be deduced without taking recourse to mathematical model for the structure under study. This permits the proposed procedure to be applied in the experimental study of time-variant reliability of complex structural systems that are difficult to model mathematically. Illustrative example consists of a multi-axes shake table study on bending-torsion coupled, geometrically non-linear, five-storey frame under uni/bi-axial, non-stationary, random base excitation. Copyright (c) 2014 John Wiley & Sons, Ltd.

A MEMS Based Electrochemical Vibration Sensor for Seismic Motion Monitoring

This paper presents a micro-electro-mechanical system (MEMS) based electrochemical vibration sensor for seismic detection. Simulations were conducted to analyze the effect of the insulating spacers thickness on the sensitivity of the devices. Then, devices with different insulating spacers thicknesses were fabricated based on MEMS processes. The devices sensitivity was confirmed by a customized experimental platform, verifying the simulation results. In addition, the device performance was characterized with a quantified bandwidth of 0.2-5 Hz with sensitivity of 30.2 V/(m/s2) and a linear voltage output as a function of the input vibration amplitude (up to 10 mg). The devices noise was determined as -140 dB at 1 Hz. A random-vibration testing in the laboratory environment was conducted, where response correlations among seven devices were calculated as 0.976±0.017, suggesting high device repeatability. A field test was conducted right above a subway line to detect the seismic motion caused by the train and test results showed that the performance of the proposed devices was comparable with that of the commercial product MET-1001. A field test was also conducted in a prairie to monitor natural seismic motions and experimental results indicated that the proposed electrochemical sensors can detect seismic motions in a lower frequency domain with an energy peak at around 0.3 Hz compared with conventional moving-coil seismic sensors with an energy peak at 3 Hz. This newly proposed vibration sensor may function as a promising seismic motion detecting device in the field of geophysical prospecting where low-frequency seismic motion detection is requested.

Vibration Testing by Non-Gaussian Random Excitations with Specified Kurtosis. Part I: Discussion and Methods

Non-Gaussian random vibration testing with kurtosis control is considered in the paper as a way of increasing or decreasing the excitation crest factor. An increase of crest factor is required for more accurate simulation of ground vehicle vibrations and the opposite action of crest factor decrease is useful in other applications, such as modal testing. Implementing kurtosis as an additional test specification leads to closed-form solutions for the requirement of the excitation high peak behavior being controlled simultaneously with the traditional power spectral density (PSD) control. A method of subjecting Gaussian signals to polynomial transformation is simpler but has an inherent tendency of introducing frequency distortions jeopardizing the PSD simulation. There is no such difficulty with another approach of phase manipulation in the inverse fast Fourier transform since the power spectrum is not influenced by the phases. A universal phase selection procedure capable of modeling non-Gaussian random excitations with a high or low kurtosis has been developed. Because of the analytical solution advantage, the proposed phase method can be implemented in automatic shaker testing systems with closed-loop control. This paper is the first in a series of two publications. Part II will present numerical and experimental results.

랜덤진동환경에서 솔더접합부의 인쇄회로기판내 위치에 따른 내구수명 변화 연구

A vibration test coupon is prepared with nine plastic ball grid array packages on a printed circuit board using SnPb solders, and a random vibration test is conducted on the coupon. Life data from the test are analyzed, and it is shown that over the board, life data is location-dependent. For investigating this location dependency, a finite element model is developed and the equivalent stresses, which are defined based on the stress response functions at each node, are investigated. It is shown that one of the corner solder balls has the maximum equivalent stress at a package during the test. Finally, it is demonstrated that the maximum equivalent stress and durability life are inversely proportional.