Random Vibration Loading Research Articles

Assessment of the Fatigue Parameters from Random Vibration Testing: Application to a Rivet Joint

In order to estimate a structure's fatigue life when excited with an acceleration profile the fatigue parameters must be known. However, material's fatigue exponent and fatigue strength are not always readily available, especially for complex structures that include riveted or welded joints for which additional fatigue tests are needed. This study introduces a new fatigue-parameter assessment method based on random vibration loading and its application to a blind-hole rivet joint that diminishes the need for additional fatigue tests. The presented procedure requires a simple experimental setup; however, a more extensive analysis of the experimental results is necessary. The method of fatigue parameter assessment is presented and applied on real, experimentally obtained data from vibration tests of rivet-joint specimens, excited with a random base-vibration load in the frequency range of a single natural frequency. Special attention was given to the modelling of the rivet joint and the uncertainties arising from the riveting process were considered. With the presented procedure it is possible to obtain the fatigue parameters solely from the results of random-vibration testing with different acceleration profiles and therefore diminishing the need for additional classic fatigue tests. The obtained fatigue parameters indirectly include the stress concentration factor and the damping-loss-factor increase during the damage accumulation. Additionally, by applying the random-vibration load the influences of the natural-frequency shift and the small nonlinearities of the structure are reduced, which can present a major issue in classic harmonic-vibration fatigue testing.

Application of particle damper on electronic packages for spacecraft

Particle damping is an effective method of passive vibration control, which is of recent research interest. This paper presents a novel application of particle damper on an electronic package of a spacecraft, tested at ISRO Satellite Centre. The effectiveness of particle damper on the random vibration response of electronic package for spacecraft application exposed to random vibration environments experienced during the launch is studied. The use of particle damper under shock environments are also demonstrated. Optimal particle damper parameters were used based on the design guidelines derived from previous publications of the authors. The comparison of particle damper effectiveness under random vibration loads with respect to the shape of the particle damper capsule and packing ratio are also examined.

Design and Development of Vibration Testing Fixtures

This paper deals with the Design of Vibration Testing Fixtures for Random Vibration loads as specified by the MIL 810 military standards. Following selection of the right material and configuration of the fixtures, CAD models are generated and numerically checked for natural frequencies and mode shapes using Finite Element Analysis. Based on these results, the response of the fixtures to the MIL 810 standard Random Vibration profile input is measured using Finite Element Analysis and the transmissibility is calculated.Finally, the fixture is tested experimentally for to the MIL 810 standard Random Vibration profile input and based on these values; transmissibility of the fixture is computed. The experimental result is compared to the Finite Element results and thus, found that the fixture can be used for testing missile packages at the Defense Research and Development Laboratory (DRDL), Hyderabad.

Numerical simulation and fatigue life estimation of BGA packages under random vibration loading

This work investigates finite element (FE) simulation and fatigue life prediction of ball grid array (BGA) under random vibration loading. The printed circuit board (PCB) assemblies are tested under random vibration loadings. The center displacement responses of PCB assemblies and the time to failure are recorded. A three-dimensional FE model of the PCB assembly is established using ABAQUS software, and spectrum analysis specified for random vibration is performed numerically to obtain the response power spectral density (PSD) of the PCB assembly. Simulation results show good correlation with experimental data in terms of center displacement responses in actual random vibration testing, validating the effectiveness of the proposed FE model. In particular, the root mean square (RMS) values of the maximum peeling stress under different loading conditions are calculated and compared. Different pre-tightening force levels and vibration intensities are applied to study their influence on solder joint reliability. Finally, the fatigue life of BGA solder joints under random vibration loading is determined in terms of Miner's rule and random vibration theory, and it is experimentally verified that the predicted fatigue life of BGA solder joints matches the experimental results with reasonable accuracy. It is concluded that solder joints at the four outermost corners of BGA packages have higher peeling stress values than others, especially at the both sides of solder joints near PCB and BGA. The stress responses of critical solder joints increase with the increase of vibration loading. BGA packages would be more prone to damage and failure when the screws became looser. This research will provide a guide for investigating the dynamic characteristics and optimization design of PCB assemblies, and predicting the fatigue life of BGA solder joints.

Coupling effects of mechanical vibrations and thermal cycling on reliability of CCGA solder joints

The microstructures and crack propagation behavior of CCGA (ceramic column grid array) solder joints after sinusoidal vibration loading, random vibration loading, and thermal cycling test have been discussed in this study. The failure mechanism of solder joints was analyzed using an experimental method and finite element analysis. It was found that the failed solder joints mainly distributed at the peripheral area in the solder column arrays and the crack initiation was mainly caused by mechanical vibrations. The deformation of PCB (printed circuit board) introduced by mechanical vibrations brought the outermost solder columns in CCGA devices with significant stress concentration and induced the initiation of cracks. Furthermore, cracks propagated during the process of mechanical vibrations and thermal cycling. The cracks propagated rapidly and the solder joints finally failed. The structure of the PCB holder was improved to relieve the vibration response from the peripheral joints. No visible crack was found in the solder joints after the same mechanical vibrations and thermal cycling test. The reliability of solder joints have been greatly improved with the new PCB holder.

Vibrational Fatigue and Structural Dynamics for Harmonic and Random Loads

The presented study experimentally and theoretically researches vibrational fatigue of an aluminum-alloy specimen for harmonic and random loads. The main aim of this study is to determine the influence of modal parameter changes that occur during the experimental fatigue test, on the correctness of the numerical fatigue life prediction. Firstly, the material’s fatigue parameters were obtained with harmonic base excitation of the specimen near its natural frequency. During the harmonic fatigue testing the changes in the specimen’s natural frequency and damping loss factor were monitored as the fatigue damage was accumulated at the fatigue zone. Secondly, with a validated numerical model of the specimen the stress transmissibility was obtained for the case of the random-vibration base excitation. Finally, by respecting the stress response along with the experimentally obtained material fatigue parameters the vibration fatigue life was estimated for the case of the random vibration load. The numerically predicted fatigue life was compared to the experimental results, obtained with the electro-dynamic shaker. From this comparison the influence of the damping-loss-factor changes on the calculated fatigue life was clearly shown. For the case of the observed specimen, the damping loss factor included in the fatigue life estimation should be increased by more than 100 percent to give reliable prediction of the fatigue life. The presented research shows new possibilities and critical aspects in the area of accurate high-cycle vibration fatigue life-estimation of dynamic structures.

Failure study of solder joints subjected to random vibration loading at different temperatures

In this paper, the combined test of temperature and vibration is conducted to statistically analyze the influence of temperature (25, 65, 105 °C) on lifetime and failure mode of SAC305 solder joint subjected to random vibration loading. Results indicate that vibration resistance of solder joint is greatly improved with temperature increase. Mean lifetime of solder joint at 65 and 105 °C is increased by 70 and 174 % respectively compared to that of solder joint at 25 °C. Failure modes are analyzed using scanning electron microscope. Different crack paths are observed at elevated test temperature. Results show that crack propagation path gradually changes from the interface of intermetallic compound (IMC)/Cu pad to bulk solder with temperature rise. Failure mechanism is remarkably transformed from brittle fracture to ductile fracture.

PBGA packaging reliability assessments under random vibrations for space applications

In this study, experimental and numerical analyses on the solder joint reliability of plastic ball grid array under harsh random vibration and thermal loadings were presented. The chips were assembled on the daisy chained circuit boards for the test samples preparation, and a half of the samples were processed for underfill to investigate the underfill effects on the solder failures. Two consequential steps of the random vibrations, named as acceptance level and qualification level, were applied. Overall required root mean square (rms) of the power spectrum densities of the steps were 22.48grms for one minutes and 31.78grms for two minutes, respectively. A thermal shock test was then performed after the vibration tests. It was found that the samples did not show any solder failure under the test requirements, demonstrating the robustness of the packaging structure for potential space applications. The samples were further tested to induce the failures, and finite element analyses were performed to analyze the sample vibration behaviors and the solder stresses to compare the results with the test data. Finally, a simple analytical calculation for the natural frequency estimations was introduced to overcome the complex finite element modeling efforts.

Study on Random Vibration Response Analysis for the Sphere Cylinder Assembly in Aerospace Vehicle

To assess the structural strength of spherical cylinder, the finite element model was constructed by the NX NASTRAN software. Firstly,the basic principle of random vibration response analysis was introduced, then the random vibration response analysis of the cylinder assembly was analyzed. The simulation result shows that the stress of the joint between spherical cylinder clamp and the base is larger than other areas in conditions of a given random vibration load. The spherical cylinder structure is safe and that the maximum RMS stress is about 20 MPa.

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.

Vibrational Fatigue and Structural Dynamics for Harmonic and Random Loads

The presented study experimentally and theoretically researches the vibrational fatigue analysis of the aluminium-alloy specimen at harmonic and random loads. The relation between vibrational fatigue for deterministic and random vibration loads is demonstrated with presented experiments and standard frequency-based counting methods. Firstly, a new fatigue testing methodology is proposed to obtain the material fatigue parameters with harmonic base-vibration excitation. With the developed methodology it is possible to monitor in real-time the principal stress amplitude at the specimen as well as to track the natural frequency shift and the increase of the structural damping of the specimen due to the accumulated fatigue damage. Secondly, with a validated numerical model of the specimen the mechanical stress transmissibility of the structure was obtained for the case of the random-vibration base excitation. Finally, by respecting the mechanical stress response along with experimentally obtained material fatigue parameters the vibration fatigue life was estimated for the case of random vibration load. The numerical fatigue life is in good accordance with the experimental one (obtained with the electro-dynamic shaker). The presented research shows new possibilities in the area of accurate high-cycle vibration fatigue life-estimation of dynamic structures.

Fatigue behavior of aluminum stiffened plate subjected to random vibration loading

Vibration tests were carried out on three types of stiffened aluminum plates with fully clamped boundaries under random base excitation. During the test, the response of the specimens was monitored using strain gauges. Based on the strain history, the accumulation of fatigue damage of the stiffened plates was estimated by means of the rainflow cycle counting technique and the Miner linear damage accumulation model in the time domain. Utilizing the change of natural frequencies, a nonlinear model was fitted for predicting the fatigue damage of plate and then the foregone failure criterion of 5% reduction in natural frequency is improved. The influence of section and spacing of the stiffeners on the vibration fatigue behavior of the aluminum plate was investigated. The results show that the fatigue life of aluminum plate increases with adding either T or L section riveted stiffeners. With the same cross-sectional area of stiffener, the T section stiffened plate shows longer fatigue life than L section stiffened plate. Meanwhile, the vibration fatigue life also shows great sensitivity to the spacing between the stiffeners.

Investigating the effect of road roughness on automotive component

Suspension systems are one important part of automotive chassis that impact the level of passenger comfort and vehicle aerodynamics is clearly. So, a good suspension design is considered all vehicle designers in automotive industry. Suspension systems are composed 4 main components such as springs, shock absorbers, suspension mechanism and its interface of connections that its mainly tasks are isolation of a car body from road roughness to comfort passenger travel and establish a permanent contact between tire and road conditions to the proper performance tire is in motion. Therefore, suspension testing that has a direct impact on passenger safety and comfort is essential and important. Given the high cost and time of testing should be used different ways to study it.This paper presents used a quarter car model in according road classification ISO 2631-1 is achieved road roughness as PSD function in a constant speed of car by using Matlab Code. in continually, study effect of random vibration and variable amplitude loading (VAL) on the suspension system performance. Finally, has been studied tire adhesion to the ground.

Random vibration reliability of BGA lead-free solder joint

Solder joint fatigue failure under vibration loading has been a great concern in microelectronic industry. High-cycle fatigue failure of lead-free solder joints has not been adequately addressed, especially under random vibration loading. This study aims to understand the lead-free solder joint behavior of BGA packages under different random vibration loadings. At first, non-contact TV Laser holography technology was adopted to conduct experimental modal analysis of the test vehicle (printed circuit board assembly) in order to understand its dynamic characteristics. Then, its first order natural frequency was used as the center frequency and narrow-band random vibration fatigue tests with different kinds of acceleration power spectral density (PSD) amplitudes were respectively carried out. Electrical continuity through each BGA package is monitored during the vibration event in order to detect the failure of package-to-board interconnects. The typical dynamic voltage histories of failed solder joints were obtained simultaneously. Thirdly, failed solder joints were cross-sectioned and metallurgical analysis was applied to investigate the failure mechanisms of BGA lead-free solder joints under random vibration loading. The results show that the failure mechanisms of BGA lead-free solder joint vary as the acceleration PSD amplitude increases. Solder joint failure locations are changed from the solder bump body of the PCB side to the solder ball neck, finally to the Ni/intermetallic compound (IMC) interface of the package side. The corresponding failure modes are also converted from ductile fracture to brittle fracture with the increase of vibration intensity.

Dynamic Analysis of Support System of Permanent Magnet Traction Motors for High-Speed Trains

During the operation, the high speed train will be subject to random vibration load induced by the roughness of the rail and will cause the vibration. Traction motor is critical component of traction system for high-speed train. It is subject to not only static loads, but also random vibration load. This kind of random vibration load may easily lead to fatigue damage of the structure, which will finally cause adversely effect to the motor. Thus, in this paper, a 3-dimension model of the support system of traction motors in high-speed train applications is built, and the static and modal analyses are undertaken using finite element calculation software. The simulation results confirm that the support system is robust enough to meet the design requirements of strength and stiffness. Furthermore, it has a larger margin of safety in a typical case which meets the technical requirements for safe operation of the high-speed train.

Optimal Design of LCD Module under Random Vibration

Random vibration is being specified for acceptance tests, screening tests and qualification tests by manufacturers of electronic equipment meant for military applications, because it has been shown that random vibration more closely represents the true environment in which the electronic equipment must operate. In this paper, the simulation of the LCD panel subjected to random vibration load is done by the rectangle plate to represent the panel, the deformation and stress of LCD is analyzed by FEM method. Combined the simulation result and Taguchi optimization algorithm, we analyzed the relationship between the geometric dimensions of LCD and the dynamic response.

Dimensional stability of materials subject to random vibration

High precision stable structures are potentially vulnerable to dimensional instability induced by exposure to random vibration. There appears to have been little work in the literature to understand or mitigate structural dimensional instability induced by random vibration. To gain more insight into this issue, a novel test was recently developed to assess the plastic strain response in the 10−5 to 10−6 range for structural materials subjected to specific random vibration loads. The test was based on a four-point bending configuration with an applied random base excitation. Two types of material were tested – an Al alloy and a CFRP. This paper presents the test setup and results in detail. The Al alloy samples were found to grow slightly in length during testing, due to a small non-symmetry in the applied load. An FEA model of the test setup was solved in the time domain for a sequence of cyclic loads whose amplitude was based on their probability of exceedance in the random environment. This model, using nonlinear kinematic hardening, was able to predict the residual strain response observed during testing with good accuracy. The main implication of this finding is that ultra stable structures subject to random vibration should be assembled in the most strain-free state possible to avoid loss of dimensional stability due to cyclic hardening.

Percentiles of von Mises Stress from Combined Random Vibration and Static Loading by Approximate Noncentral Chi Square Distribution

Firstly, a calculation for percentiles of von Mises stress in linear structures subjected to Gaussian random loads is extended to the case of Gaussian random loads having nonzero mean values, i.e.,the inclusion of static loads. The development is restricted to the case of plane stress. The method includes calculation of a given percentile of von Mises stress to any desired accuracy, a rapid estimate of the percentile, and upper and lower bounds on the von Mises stress. The calculation expands the cumulative distribution function of the von Mises stress as a series of noncentral chi-square distributions. Summation of a sufficient number of terms of the series calculates the percentile to the desired accuracy. The rapid estimate of the percentile interpolates the distribution of the von Mises stress in a small number of inverse noncentral chi-square2 distribution functions. The upper and lower bounds on the percentiles take advantage of the noncentral chi-square distribution of summations of normally distributed stress components. Second and third calculation methods arise from approximations of the distribution of quadratic forms of noncentral normal variables, or equivalently, linear combinations of noncentral chi-square variables. These methods provide rapid estimates of percentiles of von Mises stress in linear structures under random loads having nonzero mean values. The accuracy and computational efficiency of the methods are reviewed and compared. The methods are expected to have wide application in design of and prognostics for components subjected to constant structural loads coupled with random loading arising from vibrations caused by wind, waves, seismic events, engines, turbulence, acoustic noise, etc.

Numerical Simulation of Subway Train Vertical Random Vibration Load in Time Domain

It is of importance to identify the subway train random vibration load correctly. On the basis of the in-situ dynamic response measurement, the deterministic data for vertical acceleration of rail were obtained. The problem of identifying the random vibration load of subway train was solved in Matlab, according to the simplified vibration model of vehicle system, and in Newmark-β method. Then the time curve and the amplitude spectrum curve of the vertical random vibration train load were obtained. Compared with Fast Fourier Transform method, Newmark-β method is more simple and practical to simulate the train vertical random vibration load directly in the time domain.

불규칙 진동하중을 받는 쇽 타워의 피로수명을 고려한 점용접 위치 최적설계

In this paper, optimal spot weld layout design for a shock tower structure is presented. This design increases the fatigue life of the spot-welds thereby increasing the fatigue life of the shock tower itself. In order to predict the fatigue life, a quasi-static analysis has been conducted then a fatigue analysis was performed through the application of random vibration loads. In order to optimize the spot weld layout, the design variables that have an effect on the spot weld fatigue life were determined. A spot weld fatigue analysis was then conducted based on the experiment design. Finally, a response surface model was made using the fatigue analysis results and an optimized spot weld layout model, one that increases the fatigue life of the spot welds and thereby the fatigue life of the shock tower, was developed.