Sinusoidal Vibration Test Research Articles

Multi-condition adaptive detail characterization model of magnetorheological dampers and experimental verification

The theoretical model for predicting the damping characteristics of magnetorheological dampers (MRDs) is significant for enhancing the design efficiency of the control algorithm. However, some existing theoretical models face limitations in characterizing MRD damping characteristics simultaneously in terms of nonlinear detail characterization and adaptability to variable working conditions. Therefore, this paper proposed the Composite Double-Boltzmann (CDB) model combining the Double-Boltzmann (DB) function widely used in the field of biology and chemistry for its strong nonlinear characterization capability. Utilizing this model to fit the sinusoidal vibration testing data of the MRD prototype under variable combination working conditions, obtaining quantitative relationships between the undetermined parameters in the CDB model and the excitation current, vibration frequency, and amplitude to enable the model to address both the nonlinear details characterization of MRDs and adaptability to variable working conditions. Subsequently, the validity of the quantitative relationships were verified by comparing the calculated parameter values using the quantitative relationships with the original accurate parameter values. In order to verify the validity of the CDB model, extensive unknown working condition vibration tests were conducted on the MRD prototype under variable excitation currents, vibration frequencies, amplitudes and random excitation working conditions, employing the CDB and Tanh models to predict the damping characteristics, to compare to demonstrate the CDB model’s capability of adapting to variable working conditions while accurately characterizing the nonlinear details of MRD damping characteristics.

Evaluation of viscous damper on the vibration transmission to the piping system and the support structure exposed to sinusoidal vibration in vertical, horizontal, and lateral directions.

Viscous dampers have been shown to be a potential solution to addressing piping vibration problems. The primary objective of this study is to confirm the ability of viscous dampers in addressing piping vibration problem in a piping system at different supporting structural stiffness. The piping systems were fabricated and arranged horizontally, vertically, and axially with respect to the direction of the input vibration force. Input force was applied to the piping system using an electromagnetic shaker. A sinusoidal vertical vibration at a 5 Hz frequency (21 mm/s RMS) was applied at one end of the piping system. The use of viscous damper was varied from no viscous damper to one, two and three dampers. Results showed that having three viscous dampers installed caused the piping vibration at point P2 showed the maximum reduction in vibration of up to 80% for three axes, respectively. For the case of structural vibration, the measurement results showed that point S1 experienced the highest vibration exposure before the installation of the viscous dampers, in all axes. With the three viscous dampers installed, the maximum vibration reduction for the sinusoidal vibration test case at point S1 were 86% and 91% for the x- and z-axes, respectively. In conclusion, viscous dampers able to reduce both the piping and structural vibration in multiple axes. This study also highlights the importance of positioning dampers in reducing piping vibration and vibration transmitted to the structure, with reduction up to 90% amplitude for sinusoidal input and 80% for random input.

An Analysis of the Vibration Transmission Properties of Assemblies Using Honeycomb Paperboard and Expanded Polyethylene.

In the process of logistics, shock and vibration are the most important factors contributing to product damage. Assembling honeycomb paperboard and EPE is commonly used to provide cushioning and anti-vibration effects to materials. Therefore, it is necessary to study the vibration transmission properties of this kind of assembly in the anti-vibration process. The aim of this paper was to experimentally determine the vibration transmission properties of assemblies with honeycomb paperboard and expanded polyethylene (EPE). Through a sinusoidal sweep vibration test of this assembly, the vibration transmission characteristic curves of assemblies with honeycomb paperboard and EPE of different thicknesses were obtained and compared. Assuming the assembly and mass block as a single degree of freedom with a small damping linear system, the damping energy dissipation of the assembly and the resonance frequency were obtained. The vibration transmission property curves of the assembly can be divided into four regions. With an excitation acceleration of 0.5 g and a honeycomb paperboard with a thickness of 60 mm (F60), the vibration transmission rate and the resonance frequency-of the material dampened with EPE at a thickness of 60 mm (E60), and the assembly (F30/E30) with a 30 mm thick honeycomb paperboard and 30 mm thick EPE-increased by -2.5% and -17.5%, -86.9% and 79.3%, and -95.9% and -85.7%, respectively. Compared to the assembly with 20 mm thick honeycomb and 20 mm thick EPE (F20/E20), the vibration transmission rate, the resonance frequency, and the material damping and damping energy dissipation of F40/E20, F30/E30, and F20/E40 increased by 75.6%, 48.3%, and 66.1%; 1.2%, -21.5%, and -38.9%; 241.5%, 82.8%, and 13.3%; and 12.5%, 98.9%, and 106.8%, respectively. Compared to F60 and E60, the damping energy dissipation of F30/E30 increased by 2816.7% and 133.3%, respectively. The assembly of F30/E30 has the smallest vibration transmission rate and the most vibration energy dissipation among these assemblies. This means that the assembly of F30/E30 absorbs the most external vibration energy, while the acceleration that is transmitted to the internal product is minimal. Therefore, in the design of cushioning packaging, according to the characteristics and natural frequency of the internal products, an appropriate assembly can be selected, which should have a lower vibration transmission rate and more vibration energy dissipation, and should not resonate with the internal product. This will provide a theoretical basis for the design of cushioning packaging.

Random vibration fatigue behavior of directionally solidified superalloy: Experiments and evaluation of life prediction methods

Vibration is closely related to structural dynamics, and the study of random vibration fatigue loads is typically conducted in the frequency domain. In this study, various frequency domain methods were employed to predict the random vibration fatigue life of DZ125L directionally solidified superalloy under different vibration signal intensities. Experimental analysis was used to examine the fatigue life and random vibration response of DZ125L alloy specimens under different vibration signal intensities. The S-N curve derived from sinusoidal vibration tests was used to replace the traditional S-N curve obtained from tension-compression tests in random vibration fatigue analysis, leading to improved life prediction accuracy. Additionally, an intensity function fξ was established using the spectral width parameters α1 and α2 of the random process and the vibration signal intensity ξ, which was used to modify the traditional Rayleigh method. A new vibration fatigue life prediction model based on frequency domain method is obtained. The results indicate that the intensity function fξ emphasizes the elastic or plastic stage of the specimen during the random process, leading to highly accurate life prediction values using the Modified Rayleigh method across different vibration signal intensities, with all prediction points are within 1.5 times the scatter band.

Research on the Influence of the Closing Amount of Electrical Connector Contacts on Fretting Wear under a Vibration Environment

As a key component for transmitting electrical signals, the electrical contact performance of electrical connectors is directly affected by the closing amount of the socket. It is urgent to explore the relationship between contact resistance and the closing amount of cylindrical groove electric connectors, as well as the range of the closing amount when their comprehensive performance is optimal in vibration environments. Based on Hertz contact theory, the long- and short-axis parameters of the contact elliptical surface were obtained using the Boussinesq solution and the contact deformation coordination equation. An electrical contact resistance (ECR) theoretical model was obtained using Holm’s electric contact theory and the GW contact model. According to the ECR and long- and short-axis parameters of the contact elliptical surface and the theoretical model of contact resistance, an ECR model based on changes in the initial closing amount (deflection) of the socket spring was established by introducing the cantilever beam model of the socket spring. Then, the failure mechanism of fretting wear and the change mechanism of the ECR of the electrical connectors under a vibration environment were analyzed using the sinusoidal vibration test of electric connectors. The optimal range of the initial closing amount of the cylindrical-groove-closing-type electrical connector socket spring was determined, providing a reference for the reliability designs of electrical connectors.

A vibration-powered self-contained node by profiling mechanism and its application in cleaner agricultural production

The vibration-based electromagnetic energy harvester offers a cost-effective and promising renewable energy approach. With the rapid development of autonomous agricultural production, advanced agricultural machinery equipped with multiple sensors is of significant importance. In the hilly areas of southwest China, the driver of the pennisetum sinese roxb harvester must frequently adjust the height of the stripping header to adapt to the terrain height variation and it leads to high labor intensity. Because of the harness environment of the working condition, the arrangement of wires for sensors is almost impossible. Thus, a self-powered sensor node by profiling mechanism with a vibration energy harvester is proposed. This paper presents theoretical and experimental research on a profiling mechanism using a vibration energy harvester, with which a detailed theoretical model is established to perform the dynamic simulation study. Diverse excitation conditions such as sinusoidal sweeping vibration tests, fixed frequency vibration and stochastic road spectrum tests of agricultural machinery were implemented to verify the power generation capacity. The simulation results agree well with the experimental data. Experimental results show the peak-peak voltage and power of the proposed device reach about 44 V and 113 mW under low frequency and large displacement excitations. The vibration test justifies the feasibility of the proposed profiling mechanism in the application scene for powering the range sensor applied in agricultural production.

Effect of Relative Humidity on Main Resonance Frequency for Paper Honeycomb Packaging System

Paper honeycomb sandwich plate is often used as transport packaging for the good cushioning and vibration isolation properties. However, the change of relative humidity has a great influence on the vibration performance of paper honeycomb sandwich plate because of its strong water vapor absorbing characteristics. In order to avoid the system resonance and reduce the product vibration damage, the main resonance frequencies for the paper honeycomb packaging system were evaluated by the sinusoidal vibration tests, further the effects of relative humidity, static compression stress, and the geometric parameters of honeycomb core on the main resonance frequencies were investigated. The results show that the main resonance frequency decreases with the increase of relative humidity, static compression stress, honeycomb cell length, and plate thickness.

Rail corrugation inspection by a self-contained triple-repellent electromagnetic energy harvesting system

Rail corrugation, a widely distributed periodic wear pattern of the railway track, is a severe rail defect that could cause high-pitched noises and vibrations of the ground and nearby buildings. The current rail corrugation inspection trolley can only be employed offline, whereas online monitoring devices require external batteries that depend heavily on manual maintenance. This paper presents a novel approach by monitoring the rail corrugation online using a self-contained energy harvesting system. The mechanics of the magnetic-floating energy harvester was improved by a triple-magnet configuration, and differences between repellent and attractive configurations were investigated. Comprehensive broad-band (5–2000 Hz) sinusoidal sweeping vibration tests and stochastic vibration tests were conducted based on the measured railway track spectra. The wavelet theory was used to carry out time–frequency analysis and identify the defects of the rail corrugation. The results indicate that the proposed system could collect the rail vibration energy across a wider frequency range as well as identify the rail corrugation by the induced voltage of the energy harvesters. This study offers a new sustainable approach toward rail corrugation monitoring by the self-contained energy harvesting system that could eliminate environmentally-unfriendly batteries and reduce manual involvement for railway track inspection.

Application of High-Speed Photography in Amplitude Measurement of a Satellite Antenna

Spacecraft antenna is an antenna loaded on the spacecraft and an indispensable part of the spacecraft system. It is particularly important to measure the assembly accuracy of the antenna. A certain type of satellite needs to test the amplitude of antenna A and B in sinusoidal vibration test. Because the distance between antenna A and antenna B is very close to the fairing, it is necessary to measure the amplitude of antenna A to verify the spatial compatibility of antenna A with carrier fairing and antenna B in the test process. By comparing four kinds of antenna measurement technology, this paper chooses high-speed photography technology to measure the amplitude of the antenna, uses recognition processing computing technology to binarize the image, changes the image into calculable coordinate value, obtains the amplitude data of X-direction and Y-direction, and verifies the space composite compatibility requirements between antenna A, carrier fairing and antenna B under vibration conditions. There will be interference and collision.

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.

Stiffness design of cantilevered structure with space optics load

Considering the low stiffness and strength for cantilever motor on the pitching shafting of a wide-angle aurora imager, a solution is proposed for setting up the motor-auxiliary-support, a stiffened plate, between the base and the motor. Firstly, the material, support position and structure form were determined. Secondly, the structural topology optimization was accomplished from the layout of stiffeners and the parameters of stiffeners by using the finite element simulation method. Then the structural design of the motor-auxiliary-support was determined. The simulation analysis and mechanical tests of the camera were carried out. It was found that the finite element analysis results were in agreement with the test results. After installed the motor-auxiliary-support, the frequency of the camera was increased by 14.58%, and the acceleration response of the sinusoidal vibration test on the motor was decreased by 79.32%. The structural ability to resist space mechanics environment had been improved significantly. The motor-auxiliary-support had a remarkable effect on improving the stiffness and strength of the structure.

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.

3D-encapsulated VHF MEMS resonator with high frequency stability and low vibration sensitivity

Frequency stability of 3D encapsulated VHF MEMS resonators with Q factor of 10,000 is systematically studied. The long-term frequency stability results of the resonance frequency variation were ±1 ppm and ±0.95 ppm. The noise floors of Allan Deviation were 26 ppb and 40 ppb, which were comparable to these of the typical quartz resonators. The thermal cycling test between −40 °C and 85 °C was carried out and the results show that the resonant frequency drifts were less than 1.5 ppm and no detectable hysteresis was observed. Finally, a series of sinusoidal vibration tests were done and the measured acceleration sensitivity is comparable with the AT-cut quartz resonator.

Accelerated Vibration Reliability Testing of Electronic Assemblies Using Sine Dwell With Resonance Tracking

In this work, a sinusoidal vibration test method with resonance tracking is employed for reliability testing of circuit assemblies. The system continuously monitors for changes in the resonant frequency of the circuit board and adjusts the excitation frequency to match the resonant frequency. The test setup includes an electrodynamic shaker with a real-time vibration control, resistance monitoring for identifying electrical failures of interconnects, and vibration logging for monitoring changes in the dynamic response of the assembly over time. Reliability tests were performed using the resonance tracking sinusoidal test method for assemblies, each consisting of a centrally mounted ball grid array (BGA) device assembled with 63Sn37Pb and SAC105 solder alloys. These tests show that the resonance tracking method gives more consistent failure times. Failure analysis for the tested devices shows the primary failure mode is “input” trace crack first, followed by fatigue through the solder for complete failure. A finite element (FE) model, correlated with experimental modal analysis, is shown to accurately estimate the circuit board deflection estimated from the harmonic vibration data. This provides a means of estimating the stresses in the electronic interconnections while accounting for the variability between test parts. These fine-tuned vibration measurement techniques and related FE models provide the building blocks for high cycle solder fatigue plots (i.e., S–N curves).

Fatigue life prediction of Package-on-Package stacking assembly under random vibration loading

This paper presents a general methodology to predict the fatigue life of the Package-on-Package (PoP) under random vibration loading by means of vibration tests and finite element (FE) simulation. The behavior of the critical solder joints of the PoP under vibration loading was accurately described by FE model using ANSYS software and confirmed by modal analysis and linear sweep tests. The stress-life (S-N) curve of the PoP solder joints was obtained by the sinusoidal fatigue vibration tests and FE simulations to characterize the fatigue properties of the PoP under vibration. The comparison of the S-N curves of the SAC305 solder joints in different structures indicates the S-N curve of the SAC305 solder joints depends on the package structure. With the same fatigue cycles, the stress levels for the current 3D package is the smallest compared with the other 2D package due to the stacked structure of the PoP. Spectrum analysis for the random vibration tests was performed by the FE simulations to acquire the stress response power spectral density (PSD) of the critical solder joint. A specific frequency domain approach based on the Palmgren-Miner's rule was established to predict the fatigue life of the PoP under random vibration. Results show that simulated fatigue life matches well with the random vibration test results, which implies that this approach could be a potential method for the predication of fatigue life of the 3D packaging under random vibration.

How Mitigation Techniques Affect Reliability Results for BGAs

Abstract Since 2006 RoHS requirements have required lead free solders to take the place of tin-lead solders in electronics. The problem is that in some environments the lead free solders are less reliable than the older tin-lead solders. One of the ways to solve this problem is to corner stake, edge bond or underfill the components. When considering what mitigation technique and material to use, the operating conditions must be characterized. The temperature range is important when selecting a material to use since the glass transition temperature (Tg) and coefficient of thermal expansion (CTE) are important properties. If improperly chosen, the mitigation material can cause more failures than an unmitigated component. This study focused on 208 I/O BGAs on a 4 layer FR4 board. There were three solders tested; two lead free (SAC305 and SN100C) and one leaded (SnPb). Three mitigation techniques were tested: corner staking, edge bonding, and underfilling. Each of these techniques had two mitigation materials tested. One material was reworkable and the other was not. The boards were subjected to mechanical shock testing and sinusoidal vibration testing until failure. The results of the testing show that no one mitigation technique is best for all of the conditions tested. The same is true for the mitigation material. The best choice of mitigation technique and material is application dependent.

How Mitigation Techniques Affect Reliability Results for BGAs

Since 2006 RoHS requirements have required lead free solders to take the place of tin-lead solders in electronics. The problem is that in some environments the lead free solders are less reliable than the older tin-lead solders. One of the ways to solve this problem is to corner stake, edge bond or underfill the components. When considering what mitigation technique and material to use, the operating conditions must be characterized. The temperature range is important when selecting a material to use since the glass transition temperature (Tg) and coefficient of thermal expansion (CTE) are important properties. If improperly chosen, the mitigation material can cause more failures than an unmitigated component. This study focused on 208 I/O BGAs on a 4 layer FR4 board. There were three solders tested; two lead free (SAC305 and SN100C) and one leaded (SnPb). Three mitigation techniques were tested: corner staking, edge bonding, and underfilling. Each of these techniques had two mitigation materials tested. One material was reworkable and the other was not. The boards were subjected to mechanical shock testing and sinusoidal vibration testing until failure. The results of the testing show that no one mitigation technique is best for all of the conditions tested. The same is true for the mitigation material. The best choice of mitigation technique and material is application dependent.

Multiple Sinusoidal Vibration Test Development for Engine Mounted Components

Durability testing is required before vehicle launching to prevent failure before designed life. Limited publications were found on specifying vibration testing to validate durability and reliability of engine mounted components. These published test methods did not consider engine firing order effects and oversimplified the vibration profiles. In this paper, a new ordered multiple sinusoidal vibration test method is proposed to improve the existing procedures. The test method is designed to fulfill an infinite life durability requirement for engine mounted components subjected to a four-stroke internal combustion engine vibration. An innovative test development procedure, based on engine vibration field data, is illustrated in details in this paper. The ordered multiple sinusoidal vibration test method covers the choice of sweep type, sweep time, frequency range, vibration magnitude and profile, and test duration. Instead of obtaining the vibration magnitude directly from order analysis results, vibration magnitudes are determined by fully analyzing the vibration data in both time domain and frequency domain. Test profiles designed by enveloping method are proposed for a better represent of the engine excitations.

Development of Vibration Data Processing Program

The program for vibration data processing is developed based on MATLAB software. Different methods are used to extract the important information from the random, sinusoidal vibration and shock test. Some main codes in the program are listed in the paper, and the examples for the random and sinusoidal vibration data processing are also shown. Results indicated that the program can help the analyzer to exactly catch the test information and automatically generate the report document.

Dynamical Simulation about Buffer Packaging of Computer <sup> </sup>

A host computer packaging cushion is designed, including deflection, buffering capacity, creep checking. Then g a three-dimensional model of the host buffer packaging systems is established Simulation of the system, including static analysis, modal analysis, harmonic analysis and transient dynamic analysis. Finally, the physical system is used to do the sine frequency, fixed-frequency sinusoidal vibration test. the vulnerability of the buffer package sinusoidal frequency calculate by the computer modal analysis larger than the resonance frequency of the measured test values This is due to host the actual shell of the computer by each side made of thin steel plate riveting, and list them in the computer simulation as a whole in the shell, so that the overall stiffness of the system become larger, so that the analysis of the inherent frequency than the actual value. Transient dynamic analysis of the computer meets the fixed-frequency sinusoidal test results，which are all happened in the prophase of vibration in the balance position. This vibration last a period causing fatigue, so that the acceleration package increases slowly and the product damage.