Random Vibration Test Research Articles

Vibration lifetime estimation of PBGA solder joints using Steinberg model

The work studies the vibration lifetime modeling of Sn37Pb soldered plastic ball grid array (PBGA) assemblies on the basis of vibration tests, finite element analysis (FEA) and Steinberg's empirical formulation. The test vehicles for the vibration tests consist of twelve PBGA components with built-in daisy-chained circuits, which are assembled on a printed circuit board (PCB) symmetrically. First, the natural frequencies of the test vehicle were determined by modal tests. The first three natural frequencies were obtained using FEA, which were compared with those from the modal test. Then, narrow-band sinusoid vibration tests were conducted at the first natural frequency of the test vehicle using constant-amplitude excitation, and the number of failure cycles was recorded by monitoring the overall electrical resistance. FEA was performed to obtain the stress of the critical solder joints under various levels of sinusoidal vibration loadings. To construct the stress versus failure cycles (SN) curve of the solder joints, the stresses of solder joints were used in conjunction with the lifetime obtained from the sinusoidal vibration tests. The random vibration test was conducted on the test vehicle to assess the lifetime of the solder joints subjected to broad-band excitation. Random vibration analyses were performed numerically to obtain the displacement responses of the PBGA assembly. Finally, a fatigue life prediction based on Steinberg's model was deduced from all these procedures. A comparison of the lifetime between the experimental results and the prediction suggests that the methodology is valid and practicable in predicting the vibration lifetime of PBGA solder joints.

Weibull analysis for normal/accelerated and fatigue random vibration test

AbstractIn this paper, the formula to estimate the sample size n to perform a random vibration test is derived only from the desired reliability (R(t)). Then, the addressed n value is used to design the ISO16750‐3 random vibration test IV for both normal and accelerated conditions. For the normal case, the applied random vibration stress (S) is modeled by using the Weibull stress distribution [W(s)]. Similarly, for the testing time (t), the Weibull time distribution [W(t)] is used to model its random behavior. For the accelerated case, by using the over‐stress factor fitted from the W(t) and W(s) distributions, four accelerated scenarios are formulated with their corresponding testing's profiles. Additionally, from the W(s) analysis, the stress formulation to perform the fatigue and Mohr stress analysis is given. Since the given Weibull/fatigue formulation is general, then the formulas to determine the W(s) parameters, which correspond to any principal stresses values and/or vice versa, are given. Although the application is performed to demonstrate R(t) = 0.97 by testing only n2 = 6 parts, the guidelines to use the values given in columns n, S, and t of the Weibull analysis table to generate several accelerated testing plans are given.

Finite Element Model Updating and Verification of Satellite-borne Slot Waveguide Based on Random Vibration Test

For an axial free-floating slot waveguide, finite element model updating and verification based on the vibration data are studied. The slot waveguide and the free-floating side are modeled by shell element and spring element respectively. The two slot waveguide structures are applied to modal and random vibration test getting the modal frequencies, root mean square of acceleration. The finite element are first verified by tested modal data, and then the connecting stiffness will be updated by random vibration test data. These results show that the analytical dynamic responses of the updated finite element are well compared with the test responses, and the maximum error is 3.8%. The spring element could also model the free-floating side well and verify the accuracy for dynamic analysis.

Development of 6 U CubeSat’s Deployable Solar Panel with Burn Wire Triggering Holding and Release Mechanism

In the present work, a deployable solar panel based on a burn wire triggering holding and release mechanism was developed for use of 6 U CubeSat. The holding and release mechanism was designed based on a nichrome burn wire cutting method widely used for CubeSat applications. However, it provides a high loading capability, reliable wire cutting, multiplane constraints, and handling simplicity during the tightening process of wire. A demonstration model of a printed circuit board-based solar panel stiffened by a high-pressure fiberglass-laminated G10 material was fabricated and tested to validate the effectiveness of the design and functionality of the mechanism under various test conditions. The structural safety of the solar panel combined with the mechanism in a launch vibration environment was verified through sine and random vibration tests at qualification level.

A rotary variable admittance device and its application in vehicle seat suspension vibration control

In this paper, a novel semi-active variable admittance (VA) concept is proposed, and a seat suspension prototype with a magnetorheological fluid damper based rotary VA device is designed, manufactured, and experimentally validated. The conventional inerter with a single flywheel has a constant inertance, which can effectively improve the suspension performance by being integrated into a mechanical network with springs and dampers. The proposed rotary VA device comprises a gear reducer, two flywheels and a variable damping (VD) device which is used to connect the two flywheels. With carefully designing, the rotary VA device is compacted and is similar with a VD device in size. The rotary VA device is installed in the centre of a seat suspension's scissors structure to form a VA seat suspension. According to the test results, the equivalent inertance of the seat suspension can vary from 11.3 Kg–76.6 Kg with a 3 Hz frequency and 5 mm amplitude sinusoidal movement by changing the current from 0 A–1 A. By analysing the system characteristics, a hybrid controller with two acceleration feedbacks is proposed. Thereafter, the seat suspension and controller are validated in experiments by comparing the performance with a conventional passive seat suspension. The random vibration test shows the excellent performance of the proposed seat suspension; the frequency weighted root mean square acceleration of the seat is reduced by 43.6%, which indicates a great improvement of the ride comfort. The VA device shows great prospect in the suspension application.

Development of Stirling-type pulse tube cryocooler

Stirling type pulse tube cryocoolers are very attractive for cooling of diverse application because it has it has several inherent advantages such as no moving part in the cold end, low manufacturing cost and long operation life. A moving magnet type linear motor of dual piston configuration is designed, and this compressor could be operated with the electric power of 100 W at the operating frequency of 50 Hz. A pulse tube cold finger with a double segmented inertance tube was designed for the desired cooling capacity. The coiled inertance tube was assembled inside the reservoir. In experiment, the pulse tube cryocooler is capable of providing the cooling capacity of 2.0 W at 80 K with power consumption of 99.1 W. Random and sinusoidal vibration tests have been conducted to evaluate their performance characteristics and structural integrity.

Vibration and acoustic radiation of bogie area under random excitation in high-speed trains

Based on the experiments on a platform with real vehicle structure and finite element simulation, the vibration and interior acoustic radiation under random excitations of high-speed trains’ bogie area were studied. Firstly, combined with line tests, a vehicle body with a length of 7 m was used as the research object. By comparing the results of experiment and simulation, the accuracy of the finite element model was verified. Secondly, the power spectral density curves at typical measuring points in bogie area were obtained by processing and calculating the line test data, which was measured when the vehicle ran at high speeds, and the standard vibration spectrum of the bogie area was obtained by the extreme envelope method. Furthermore, the random vibration test and simulation prediction analysis of the real vehicle structure were carried out to further verify the accuracy of the noise and vibration prediction model. Finally, according to the vibration and acoustic radiation theory, the indirect boundary element method was adopted to predict the acoustic response of the real vehicle. The analysis shows that the simulated power spectral density curves of acceleration and sound pressure level are highly consistent with the experimental ones, and the error between the simulated prediction and the experimental result is within the allowable range of 3 dB.

A frequency domain approach in residual stiffness estimation of composite thin-wall structures under random fatigue loadings

Based on the constant-amplitude fatigue experiment, a new residual stiffness model combining with power spectral density is proposed to adapt random stress states. The random loading process can be divided into multi-level variable amplitude loadings. All stiffness degradation increments can be integrated to obtain the stiffness degradation by using a numerical integral method. Fatigue damage accumulation of composite thin-wall structures subjected to random cyclic loadings is investigated by using the proposed method, which is also verified by random vibration tests with limited-bandwidth excitation. The influence of local stiffness damage on the fundamental frequency of the experiment specimen is calculated by using finite element method, which is in good agreement with the experimental results. The life predictions based on the proposed residual stiffness model are more conservative in comparison of that with linear damage accumulation rule.

Research on control method on super-Gaussian random vibration test

This paper studies the control of super Gaussian random vibration test. Experiments show that based on the proposed super Gaussian random vibration control strategy, the output power spectrum and kurtosis can be highly accurate and meet the requirements. The super Gaussian random vibration control system can significantly accelerate the fatigue failure process of the fan, improve the test efficiency, reduce the cost, and shorten the product development cycle.

Venting Analysis of the Payload Fairing of Korea Space Launch Vehicle II

Our study involved an investigation of the venting analysis of payload fairing of Korea Space Launch Vehicle II with vent valves. Two types of vent valves with a spring-loaded door were developed for a payload adapter and compartments of Korea Space Launch Vehicle II. First, the performance of the vent valves was evaluated through three-axis random vibration tests and flow tests. Structural robustness of the vent valves was validated through random vibration tests. Flow characteristics were investigated through flow tests. The cracking pressure of the vent valves for the payload adapter was in the range of 74–86 Pa, whereas the cracking pressure of the vent valves for compartment was in the range of 384–447 Pa. The results of flow tests were used to determine valve models of the vent valves for the venting analysis. Subsequently, venting analysis was conducted to predict the maximum pressure difference and pressure drop rate of payload fairing, and the results were compared with those of other space launch vehicles. The maximum values of the pressure difference were and 1.27 kPa. The maximum pressure drop rate was 4.68 kPa/s. The values were lower than the maximum values of other space launch vehicles. Consequently, the vent valves were suitable for Korea Space Launch Vehicle II.

Multiple-input multiple-output non-stationary non-Gaussian random vibration control by inverse system method

Abstract This paper investigates the control method for multi-input multi-output non-stationary non-Gaussian random vibration test with the specified references composed of stationary power spectra, moving root mean square distributions and moving kurtosis distributions. The objective of random vibration test is to force the response signals of test structure to satisfy the specified references within tolerances. An inverse system method in time domain is used to guarantee the control of response time-frequency characteristics independently and simultaneously. The evolutionary spectrum theory is utilized to establish the matrix representation of non-stationary non-Gaussian input-output relationships of a linear dynamic system in frequency domain. To analyze a non-stationary non-Gaussian vibration signal, two sets of random numbers named moving root mean square and moving kurtosis are used to modulate a stationary random signal. The transformation process theory is utilized to obtain moving root mean square and moving kurtosis by a moving root mean square distribution and a moving kurtosis distribution respectively. The control algorithms are presented to update the drive signals according to the deviations between responses and references. A numerical example by a cantilever beam and a biaxial vibration test are carried out and the results demonstrate the feasibility and validity of the proposed methods.

Robustness and lifetime of the bone conduction implant - a pilot study.

ObjectivesThe objective of this study was to develop methods for evaluating the mechanical robustness and estimating the lifetime of the novel bone conduction implant (BCI) that is used in a clinical study. The methods are intended to be applicable to any similar device.Materials and methodsThe robustness was evaluated using tests originally developed for cochlear implants comprising a random vibration test, a shock test, a pendulum test, and an impact test. Furthermore, magnetically induced torque and demagnetization during magnetic resonance imaging at 1.5 T were investigated using a dipole electromagnet. To estimate the lifetime of the implant, a long-term age-accelerated test was performed.ResultsOut of all the tests, the pendulum and the impact tests had the largest effect on the electro-acoustic performance of the BCI implant, even if the change in performance was within acceptable limits (<20%). In comparison with baseline data, the lower and higher resonance peaks shifted down in frequency by 13% and 18%, respectively, and with a loss in magnitude of 1.1 and 2.0 dB, respectively, in these tests.ConclusionA complete series of tests were developed, and the BCI passed all the tests; its lifetime was estimated to be at least 26 years for patients who are using the implant for 12 hours on a daily basis.

Random fatigue damage accumulation analysis of composite thin-wall structures based on residual stiffness method

The damage accumulation and life prediction for C/SiC composite panels subjected to random vibration loading was studied by using the residual stiffness model in combination with critical failure stiffness ratios in the different stress levels. According to the results of stiffness degradation and material S-N curves for constant-amplitude fatigue loadings, a new residual stiffness model was established and extended to adapt random stress states by using an equivalent damage ratio algorithm in time domain. The stiffness degradation and material S-N curves were obtained by using constant amplitude fatigue experiments. Random vibration tests with limited-bandwidth excitation were conducted to verify the prediction model. Good agreement is observed compared with the results of 2D plain-woven C/SiC composite panel subjected to random vibration loadings.

Maximally stationary window design for overlap-add based random vibration synthesis

Abstract The accurate synthesis of realistic waveforms conforming to certain specifications is a fundamental step in random vibration testing. Since real-time implementation of digital signal processing systems for random vibration and noise synthesis necessarily operates frame by frame, the overlap-add (OLA) method, by which frames are windowed and overlapped, is widely used in practice to avoid artifacts at frame boundaries. When a wide-sense stationary random signal is desired, however, the OLA method presents a shortcoming, because the inherent periodicity of the frame-by-frame process unavoidably produces a cyclostationary signal, i.e., its statistics present an undesired periodic behavior. We analyze the impact of the window coefficients in the cyclostationarity properties of the synthetic process, and then present algorithms for window design with the goal of maximizing a measure of its stationarity, considering both second- and fourth-order statistical properties. The proposed designs are shown to significantly improve the stationarity properties when compared to commonly used windows.

Vibration testing of vehicle components by fatigue damage spectrum control

Random vibration testing with increased kurtosis introduces high peaks into shaker drive signals to simulate land vehicle vibration more accurately or to shorten duration of fatigue damage testing. For the latter, the kurtosis control method must be able to pass high kurtosis values from the generated shaker vibration into the stress response of the tested component. It was verified and confirmed in the paper that the method of phase manipulation based on the analytical relationship between the IFFT phases and kurtosis was capable of doing so if the resonance frequency of the component is known. However, the fatigue damage spectrum model used for evaluation of time-to-failure considers not just one but a number of resonance frequencies constituting a certain test profile which cannot be simulated by the kurtosis control alone. For this purpose, the phase manipulation method was developed further and verified for operational vibrations of a railway vehicle.

Multi-exciter stationary non-Gaussian random vibration test with time domain randomization

Abstract This paper presents a new control method for multi-input multi-output stationary non-Gaussian random vibration test using time domain randomization. The control objectives are composed of response skewnesses, kurtoses and power spectral densities. The generation process of stationary and coupled reference non-Gaussian signals by specified reference skewnesses, kurtoses and spectra is analyzed. The reference non-Gaussian signals combined with system frequency response functions are then utilized to obtain the desired drive signals for dynamic inputs, in which the inverse system method in the frequency domain is employed. The primary advantages of the proposed methods are the high computational efficiency and simultaneous control of the time-frequency characteristics of response signals. In consideration of system cross coupling characteristics manifested in coherence and phase coefficients, the skewness and kurtosis tuning steps for each control channel are formulated by using a sequential phase modification method. The relationships between reference skewnesses, kurtoses and spectra are discussed and they reveal that the reference spectra have an influence on the settings of reference skewnesses and kurtoses, which implies that proper settings of reference skewnesses, kurtoses and spectra are necessary. A numerical example and a triaxial vibration test are provided and the results show the validity and feasibility of the proposed method.

Comparison study on simulation effect of improved simulation methods for packaging random vibration test

In general, existing testing methods for packaging design employ Gaussian distributions to represent vibration induced by road profiles. However, the actual road vehicle vibration is non‐Gaussian. The key limitation is that the simulated Gaussian vibration cannot reconstruct the shock events buried in the vibration, which will result in inaccurate reliability evaluation of cushion packaging. A new simulation technique called shock extraction has been proposed and validated in our earlier study. This article is a further study of our previous research. The shock extraction method has been compared with other three representative simulation methods including the single‐level PSD, three‐way split spectral, and wavelet decomposition in terms of simulation effect. Signal simulated by the shock extraction method possesses the same vibration intensity, duration, approximate statistical characteristics, and PSD plots with the original signal. The results show that the simulation effect of the shock extraction method is the best, and the worst is the single‐level PSD. The wavelet decomposition and three‐way split spectral are somewhere in the middle.

Vibration Testing of Absolute Pressure Sensor for a Flush Air Data System (FADS)

ABSTRACT Flush Air Data Sensing System (FADS) is an important subsystem required for a winged re-entry vehicle. It essentially makes use of surface pressure measurements located at a suitable position in the vehicle for deriving the air data parameters of the vehicle such as angle of attack, angle of sideslip, Mach number, etc. These air data parameters are used by the control and guidance system for carrying out gain scheduling, trim scheduling of control surfaces and overall flight management. The accuracy of the pressure sensors used in FADS is critical in achieving the targeted accuracy of the air data parameters. In the FADS system considered in this paper, piezoresistive MEMS-based pressure sensors are used. The FADS system is located in the nosecone of the vehicle which is a region prone to vibration during transportation as well as during flight. It is essential that the pressure sensors perform with the desired accuracies in spite of the vibration environment. Sine and random vibration testing are carried out as part of qualification testing of the vibration sensors of FADS. Analysis of the test results shows that the accuracies demanded by the system are provided by the pressure sensors under the vibration environment.

Effect of Cycling Amplitude Variations on SnAgCu Solder Joint Fatigue Life

Reliability of conventional electronic assemblies in real service applications is typically limited by fatigue failure of a single solder joint in reversed cyclic loading. Fatigue damage accumulation in a lead-free solder joint is still not well understood, especially not for cycling with a varying amplitude; i.e., random vibration testing is not representative of realistic service conditions and the common reliability models fail to offer relatively accurate life predictions. Developing or modifying a fatigue life model should, of course, consider the interactive effect of stress amplitude variations, which is found to be substantial. Cycling real individual SnAgCu solder joints with systematically varying stress amplitudes allowed understanding of the fatigue damage accumulation through monitoring of the plastic work dissipation during cycling. The results show a significant amplification in the work dissipation compared to what was expected based on fixed stress amplitude cycling results. Cycling with combinations of 16- and 20-MPa stress amplitudes leads to amplification of the work (more fatigue damage) at the 16-MPa amplitude, but no significant change in damage accumulation at the 20-MPa amplitude. Cycling with combinations of three or more stress amplitudes leads to work amplification at the lowest amplitude, no change at the higher amplitude, and slight to moderate amplifications at the intermediate amplitudes. In addition, the value of the work amplification at any stress amplitude depends on the sequence of higher amplitudes applied immediately before it. It is also found that any high amplitude does not affect subsequent work at a lower amplitude if an even higher amplitude was applied just before it.

Failure study of Sn37Pb PBGA solder joints using temperature cycling, random vibration and combined temperature cycling and random vibration tests

In this paper, the tin-lead (Sn-37wt%Pb) eutectic solder joints of plastic ball grid array (PBGA) assemblies are tested using temperature cycling, random vibrations, and combined temperature cycling and vibration loading conditions. The fatigue lives, failure modes for the solder joints and the typical locations of the failed solder joints for single-variable loading and combined loading conditions are compared and analyzed. The results show much earlier solder joint failure for combined loading than that for either temperature cycling or pure vibration loading at room temperature. The primary failure mode is cracking within the bulk solder under temperature cycling, whereas the crack propagation path is along the intermetallic compound (IMC) layer for vibration loading. The solder joints subjected to combined loading exhibit both types of failure modes observed for temperature cycling and vibration loading; in addition, cracking through the IMC and the bulk solder is observed in the combined test. For temperature cycling and vibration loading, the components in the central region of the printed circuit board (PCB) have more failed solder joints than other components, whereas for combined loading, the number of failed solder joints in the components in different locations of the PCB is approximately the same.