Random Vibration Loading Research Articles

Fatigue life prediction based on modified narrowband method under broadband random vibration loading

The vibration fatigue life and vibration response signal at the dangerous position of each specimen were obtained by the broadband random vibration fatigue test for 7075-T651 aluminum alloy, and the stress amplitude probability distribution of vibration response signal was counted by rainflow counting method. By comparing the probability density distribution functions of broadband random vibration signal by frequency-domain method and analyzing the fitting accuracy of different distribution models for rainflow distribution, a new model for frequency-domain fatigue life prediction based on modified narrowband distribution model was proposed. The proposed model takes the second-order spectral width parameter of vibration signal as the weight coefficient, and the life prediction results are more accurate and less dispersive.

Fatigue of composite honeycomb sandwich panels under random vibration load

The fatigue test of composite honeycomb sandwich panels has been carried out under random vibration load in this investigation. The test results show that, the failure mode of the honeycomb sandwich structure under random vibration load is the same as that under constant-amplitude load, both of which are core shear failure and the resulting face-core delamination. Based on the test results and the S-N curve of honeycomb sandwich panel under constant-amplitude load, a method has been proposed to predict the fatigue life of composite honeycomb sandwich structures under random vibration load. The core shear stress is taken as the fatigue damage parameter. The validity of the proposed method has been verified by comparing the predicted results with the test results.

Notch fatigue behavior of needled C/SiC composite under random vibration loading

In order to study the properties of needled C/SiC composite under random vibration loading, a kind of plate specimen with arc notch was designed. Random vibration tests were carried out on a vibration table, the vibration fatigue life and vibration response signal at the dangerous position of each specimen were obtained. The strain amplitude probability distribution of vibration response signal was obtained by rainflow counting method, which can be approximately described by the Dirlik distribution. The attenuation history curve of natural frequency for the specimen presented obvious nonlinearity. In addition, the microscopic fracture morphology of failed specimens showed that the major failure mode of fibers in axial and transverse direction are pull-out and splitting, respectively. And the fiber bundles adhering strongly to the matrix can form a neat fracture surface.

Fatigue-based reliability in assessing the failure of an automobile coil spring under random vibration loadings

The paper presents an assessment of fatigue-based reliability in measuring failure random vibration loadings due to unexpected loads under various road conditions. Random loads were the main cause of fatigue failure in a component durability analysis. Acceleration signals were measured during a road test held on rural and highway road surfaces. These signals were captured from an accelerometer placed on a vehicle’s lower arm suspension system in a locally made sedan-type automobile. This arrangement enhanced the capacity for collecting acceleration signals using multi-body dynamics simulation, which would minimise the need for actual acceleration data measurements. Modal analysis was conducted to determine the natural frequencies and mode shapes of the geometry of a coil spring so that strain signals based on each mode shape could be obtained. As modal parameters occurred within the frequency range of road excitation, fatigue life prediction was not affected by instances of dynamic behaviour in the components in time domain. Fatigue life was analysed using the Dirlik, Lalanne and narrowband approaches in frequency domain. The Dirlik method predicted a good correlation for the measured acceleration and generated strain signals at 2.32 × 108, 2.55 × 108 and 1.51 × 108 blocks to failure, indicating that a coil spring could withstand the uneven road surface without failing prematurely. Hence, fatigue-based reliability can evaluate the hazards of rate-reliability, based on predictions of fatigue life data on component durability.

Random vibration analysis of composite plate

Random vibration analysis is one of the major type of dynamic load which are having multiple amplitudes with multiple frequencies at a given particular time. The aerospace structure which contains Printed circuit board [PCB] fails frequently due to the high accelerations, high Stresses levels and high deformations under dynamic loads. So it is very important to analyse the PCB (Composite Plate) under dynamic load conditions. In the present research work, rectangular plate with composite materials which acts as PCB is analysed under random vibration load with different boundary conditions 2 faces fixed using Copper foil and Epoxy E Glass UD materials. The geometry of the rectangular plate is modelled in the FEA Software ANSYS. Proper fine mesh is done for the rectangular plate. Plate with [1/1], [2/2], [2/4] and [4/4] layups are designed in the Ansys ACP pre-module and later assigned the different properties of the composites to the rectangular plate and performed random vibration analysis by applying PSD G acceleration load to the fixed supports. A total number of 9 critical points are selected on the plate for calculating the PSD responses [Acceleration, displacement and normal stresses] to the random vibrations which are given to the rectangular plate. Based on the results, critical point is located and best material and best layup sequence is selected for the composite plate.

Influence of External Factors on Airborne Missile’s Horizontal Backward Launching

This paper studies the influence of different external disturbance factors on the horizontal backward separation of airborne missiles on large transport aircraft. The method of comparison with experiment was adopted to verify the accuracy of the finite element model during the ejection process. By comparing the finite element model, it was confirmed that the all rigid body model and partly rigid body model are inaccurate in calculating the pitch angle and pitch velocity of the missile separation. Finally, the influences of ejection force, random vibration, and missile loading position on the ejection process are analyzed. The analysis found that the ejection force and the sliding distance will increase the vibration of the launching platform, therefore increase the separation pitch angle and the pitch velocity of the missile, but the influence of random vibration on platform is much greater than the other two factors, and it will also introduce randomness into the movement of the missile.

Reliability Analysis of Solder Joints on Rigid-Flexible Printed Circuit Board for MEMS Pressure Sensors Under Combined Temperature Cycle and Vibration Loads With Continuously Monitored Electrical Signals

Abstract The reliability of lead-free solder joints on flexible printed circuit board (PCB) has created significant new challenges in the industry, especially in automotive electronics, and possibly for future wearable electronics. In the automotive industry, thermal cycling test and random vibration test need to be conducted to certify every electronic product to be used in harsh automotive environments. In order to accelerate the testing time, we may need to subject the electronic components, in particular, sensors to both loadings such as thermal cycling and vibration. During all the experiments, the electrical signals of each specimen were continuously monitored by using an event detector. One advantage of this method is that any individual soldering interconnect failure will result in the diagnostic signal of the circuit, which could be detected in real-time. A simulation was used to confirm the possibility of the stress concentration location caused by the vibration and thermal cycling loads. The influence of vibration frequency and acceleration on the vibration fatigue life of solid joints was investigated. In this paper, the submodeling technique was used to construct the finite element model of the rigid-flexible printed circuit board (rigid-flexible PCB) coupled with a MEMS pressure sensor subjected to temperature cycle and random vibration loadings. The research results are helpful to effectively characterize the performance of the MEMS sensors under both thermal cycling test and vibration test. Two kinds of land shapes and two kinds of PCB assemblies were selected. In order to investigate the crack growth in the solder joint, the solder joint is sliced and the crack on the cross section of the solder joint was observed. Results of finite element modeling analysis were consistent with the experimental results. Two design parameters have been identified in our research as being important to soldering usage in automotive environments: pad type (teardrop versus nonteardrop) and pad size (big versus small, matching size for Cu-wire and pad). Experimental results also showed that the solder joint with a big land shape presented a relatively good thermal fatigue resistance.

A multiaxial fatigue life prediction method for metallic material under combined random vibration loading and mean stress loading in the frequency domain

A spectral method for the determination of the critical plane is proposed for metallic material under random vibration loadings based on the criterion of maximum shear stress amplitude, where the direction of critical plane is obtained by solving the maximum value of a function using mathematical optimization method and the fatigue critical location of the structure can be determined. A multiaxial fatigue damage parameter is proposed for combined random vibration loading and mean stress loading cases based on Susmel’s criterion, which is a Power Spectral Density (PSD) of the equivalent shear stress and can be adopted for fatigue life evaluation. The fatigue life estimation of structures under multiaxial random vibration loadings with mean stresses in the frequency domain could be carried out based on this damage parameter constructed at the fatigue critical location with the spectral method for random vibration fatigue life. The multiaxial random vibration fatigue experiment with mean stress loadings is conducted on the notched plate specimens made of 2297-T87 aviation grade aluminum alloy, and the initiation sites of the fatigue cracks as well as the experimental fatigue lives are compared with those calculated by the proposed models, where satisfactory prediction capabilities on both the fatigue crack initiation locations and fatigue lives of the models are demonstrated.

Equivalent Spectral Method to Estimate the Fatigue Life of Composite Laminates Under Random Vibration Loadings

The power spectral density (PSD) of an equivalent stress is proposed to analyze the fatigue life of composite laminates under random vibration loadings using the Tsai–Hill criterion. The vibration fatigue life can be estimated based on the rainflow amplitude probability density function p(S) of the equivalent stress, which is obtained from this PSD, combined with the S-N curve of the materials. The fatigue life analysis of a random vibration fatigue experiment of composite laminates was carried out, and the calculation results were in accordance with experimental data, which indicates that the fatigue life analysis model proposed gives a satisfactory prediction accuracy.

Research on Wiener Degradation Model and Failure Mechanism of Interconnect Solder Joints Under Random Vibration Load

Electronic packaging solder joints are the key parts of mechanical fixation and electrical interconnection between electronic chips and printed circuit boards, which are prone to failure and lead to electronic device failures under the action of vibration environment stress. In regard to the failure characterization and degradation modeling of electronic packaging solder joints under vibration load, this paper adopts environmental stress tests, builds a vibration failure test platform, designs a vibration load excitation spectrum, and obtains solder joint degradation data under vibration stress; it uses the square root amplitude, form factors, and kurtosis factors to characterize the solder joint degradation process, which effectively identify the solder joint degradation node, and improve the data monotonicity of the solder joint degradation process; the Wiener process is used to build a solder joint multi-stage degradation model. Based on the EM algorithm, the hyperparameters of the degradation model have been optimized, and the universal test of the Wiener degradation model with multiple samples is carried out in accordance with the LB index. The analysis shows that the effectiveness of different samples is as high as 87.5%, which verifies the universality of the Wiener degradation model; Based on the crack morphology subject to the solder joint test and the features of the solder joint in the multi-stages, the paper analyzes the crack propagation behavior of the solder joint, and clarifies the failure mechanism of the solder joint.

Frequency-domain characterization of varying random vibration loading by a non-stationarity matrix

Spectral analysis constitutes an essential technique for random vibration fatigue. The power spectral density (PSD) provides an efficient, statistically unique characterization of stationary Gaussian loading which can be effectively processed via linear systems theory and load-spectrum estimators such as the Dirlik formulation. The PSD represents vibration loading by its averaged intensity for frequency. However, if the intensity varies throughout a dataset, i.e. the loading is non-stationary, the PSD has a fundamental flaw – it conceals any information about its evolution. Consequently, the PSD is not qualified to describe non-stationary loading and thus cannot represent instantaneous highly damaging events in a fatigue assessment. Therefore, this article proposes a statistical characterization particularly formulated for the specifications of non-stationary random vibration fatigue. We introduce a non-stationarity matrix defined as the auto-correlation matrix of short-time Fourier transforms, which describes the average variation and interaction of intensity by frequency. This characterization can directly be related to fourth-order statistics (kurtosis, trispectrum, etc.) and allows to be processed via linear systems theory. Thereby the influence of a loading’s non-stationarity structure on structural responses, and thus fatigue damage, can be assessed. Furthermore, this article provides the basis for an accompanying article in which the non-stationarity matrix finds application to efficiently perform fatigue analyses for non-stationary loading via a statistical approach using load-spectrum estimators.

STRUCTURAL DESIGN AND ANALYSIS OF MAIN AERO CRAFT STRUCTURE AND COMPARISON OF DIFFERENT MATERIALS IN DIFFERENT CONDITIONS.

The project deals with the structural design and analysis of Main Aero craft structure (Skin, Floor mounting, Support Lugs) for assembling of electronic packages in a flight vehicle section. The flight vehicle consists of various sections assembled to form an integrated vehicle. Different types of electronic packages to meet the requirements are assembled in different flight vehicle sections based on the flight vehicle configuration. One such type of flight vehicle section needs to be assembled with different electronic packages. The packages have to be rigidly mounted on a mounting structure in the flight vehicle section. The high random vibration loads imparted on vehicle by the electronic packages during launch create an adverse design requirement that all hardware have a natural frequency greater than that of the vehicle, in order to avoid damage and failure due to dynamic coupling. Maximizing natural frequency is generally accomplished by creating as stiff and lightweight a design as possible. However, designing for the resultant high loads also requires a high strength intermediate structure for mounting the various components and subassemblies to the vehicle structure. These two opposing design requirements drive an optimization between a lightweight and high strength structure. The project comprises of design and analysis of the Aero craft structure (Skin, Floor mounting, Support Lugs). The Aero craft (Skin, Floor mounting, Support Lugs) structure has to be designed to withstand the loads generated by the electronic packages. It also includes the design of mounting plate and brackets to withstand the given loads using CAD and CAE tools. CATIA software is used for modeling the flight vehicle section, packages and the mounting plate with brackets. The mounting plate and brackets are imported to ANSYS software for structural analysis. The mounting plate with brackets is applied with specified loads in different flight conditions like Pitch, Yaw and Roll moments. A finite element model was created to manually iterate several aspects of the design, such as geometric characteristics like thicknesses and fillet radii, to analyze the effects on weight and stress and converge on a successful design. The project eludes in detail the methodology adopted for the analysis of Aero craft structures (Skin, Floor mounting, Support Lugs) for flight vehicles and comparison of different materials (Aluminium alloy (2025), Aluminum alloy (23435), Titanium Alloys (Ti4Al4Mo2Sn).

Durability of lithium-ion 18650 cells under random vibration load with respect to the inner cell design

Lithium-ion batteries undergo random vibrations in automotive applications, for example due to rough road surfaces. So far, no investigation based on random vibration has considered the influence of the inner cell design and the influence of cyclic aging on vibration durability. Therefore, in this study, 18 different 18650 cell types from seven different manufacturers are tested, using two random vibration load profiles. The applied vibration profiles are the random profile according to the standard SAE J2380 and another upscaled, more severe profile. The SAE J2380 test is carried out using both new and electrically pre-cycled cells. All cell types are analyzed by computed tomography in terms of their inner design with a focus on inner mandrel, spacer and tab design. The performance of the cells is checked in terms of capacity, electrochemical impedance spectroscopy and post-vibration computed tomography. None of the cells shows significant electrical performance degradation due to the vibration. Post-vibration computed tomography reveals mechanically damaged negative current collector tabs inside of two cell types due to a loose mandrel in the case of the upscaled profile. These cell types have the lowest ratio of mandrel diameter to inner jelly roll diameter, emphasizing the importance of the inner cell design for vibration durability.

Experimental study on vibration fatigue of a certain chassis

The chassis is the structure for installing and protecting various circuit units, components and mechanical components inside the electronic device. Vibration fatigue damage is a major form of structural damage, and the vibration fatigue life prediction of the chassis structure is of great significance. The theoretical calculation of structural vibration fatigue life has frequency domain method and time domain method, but it has certain limitations. The theoretical calculation method can not accurately obtain the vibration fatigue life of the structure. According to the actual structure of a chassis, this paper designs and processes a test model of a chassis, applies a random vibration load to the vibration table, and performs vibration fatigue test to predict the vibration fatigue life of a chassis structure. The results show that the vibration fatigue life of the chassis is 40 hours, and fatigue fracture occurs first at the pin.

Dynamic Response Characteristics and Fatigue Life Prediction of Printed Circuit Boards for Random Vibration Environments

The study focuses on the analysis of the surface mounted components of the printed circuit boards (PCB) under random vibration loading. The surface mount technology used for the study involves ball grid arrays. In order to predict the fatigue life of the component under certain defense and automotive applications, modal analysis is done by using the finite element method. The results are verified experimentally using JEDEC standards to validate the finite element design used for the study, and random vibration experiments were performed with finite element analysis. The fatigue life of PCB under different random vibration environments is predicted and compared. The fatigue life of PCB is least with jet cargo environment and is maximum with rail cargo environment. The analysis reveals that under the jet cargo environment, more numbers of natural frequency excitations are present. It was found that upon loading, maximum stress was found to be induced at the corner of solder balls for packages mounted in the center of the PCB. Hence, it is suggested to incorporate design modification such that the central area of the PCB must not contain any packaging designs.

Lubrication and Wear Characteristics of Mechanical Face Seals under Random Vibration Loading.

The service life of mechanical face seals is related to the lubrication and wear characteristics. The stable analytical methods are commonly used, but they cannot address effects of random vibration loading, which, according to experimental studies, are important factors for lubrication and wear of mechanical face seals used in air and space vehicles. Hence, a dynamic model for mechanical face seals is proposed, with a focus on the effects of random vibration loading. The mechanical face seal in the axial direction is described as a mass-spring-damping system. Spectrum analysis specified for random vibration is then performed numerically to obtain the response power spectral density (PSD) of the mechanical face seal and calculate the root mean square (RMS) values under random vibration conditions. A lumped parameter model is then developed to examine how dynamic parameters such as stiffness and damping affect the lubrication regimes of mechanical face seals. Based on the dynamic model and Archard wear equation, a numerical wear simulation method is proposed. The results elucidated that the increase of input acceleration PSDs, the decrease of axial damping, and the increase of axial stiffness lead to the probability of the mechanical face seal operating under full film lubrication regime increase and finally the decrease of wear. This research provides a guideline for improving the adaptability of mechanical face seals under random vibration environments.

Multi-Degrees-of-Freedom Energy Analysis for Identification of Failure Risk in Structural Components Subjected to Random Vibration and Shock Loading

AbstractWhen designing or analyzing a mechanical system, energy quantities provide insight into the severity of shock and vibration environments; however, the energy methods in the literature do not address localized behavior because energy quantities are usually computed for an entire structure. The main objective of this paper is to show how to compute the energy in the components of a mechanical system. The motivation for this work is that most systems fail functionally due to component failure, not because the primary structure was overloaded, and the ability to easily compute the spatial distribution of energy helps identify failure-sensitive components. The quantity of interest is input energy. That input energy can be decoupled modally is well known. What is less appreciated is that input energy can be computed at the component level exactly, using the component effective modal mass. We show that the steady-state input energy can be decomposed both spatially and modally and computed using input power spectra. A numerical example illustrates the spatial and modal decomposition of input energy and its utility in identifying components at risk of damage in random vibration and shock environments. We show that the modal properties of the structure and the spectral content of the input must be considered together to assess damage risk. Because input energy includes absorbed energy as well as relative kinetic energy and dissipated energy, it is the recommended energy quantity for assessing the severity of both random vibration and shock environments on a structure.

Reliability of PBGA Solder Joints under Random Vibration Load

Reliability of PBGA Solder Joints under Random Vibration Load

Random vibration fatigue life analysis of electronic packages by analytical solutions and Taguchi method

This paper provides an analytical solution to solve for the electronic assembly random vibration problem. Additionally, this paper employs Taguchi method to investigate the fatigue life performance of electronic vehicles subjected to random vibrations loadings. The current work adopted and modified as necessary a previously published analytical solution to solve for the electronic assemblies random vibration problem. This solution is also used to solve for BGA's axial deflections, strains and stresses. In combination with Taguchi method, this was solution employed to investigate the printed circuit board (PCB) and the integrated circuit (IC) component geometries as well as ball grid array (BGA) solder ball dimensions on solder axial stresses and related that to fatigue life performance of electronic packages under random vibration loading. The results of this newly developed analytical solution are in great match with FEA results in terms of the solder joint axial deflections power spectral density (PSD) function. Also, the stress analysis results of Taguchi method showed that the smaller and thicker PCB as well as larger and thicker IC's might reduce solder stresses and hence improve the fatigue performance. Also solder dimensions, compared to PCB and IC, have minor effects on solder stresses and fatigue life behavior. Finally, an optimal design for best fatigue performance was suggested.

Characterizing non-Gaussian vibration loading using the trispectrum

This paper addresses the use of higher-order spectra to study the non-Gaussian nature of random vibration loading. Since the power spectral density is only a full description for stationary Gaussian processes, specifying non-Gaussian random vibration loading requires a sophisticated statistical description. In recent research higher-order statistical moments such as skewness and kurtosis have been used to define non-Gaussian properties of vibration loading. However, useful information contained in the spectral representation of these moments is neglected. This paper introduces the trispectrum as a tool for analyzing vibration loading. It is the spectral representation of the fourth-order moment and thus extends the information content of the kurtosis. For demonstration several common methods for generating non-Gaussian loading are reviewed and used to derive loads that reproduce the power spectral density and kurtosis of a real in-service loading. These loads are analyzed using Fatigue Damage Spectra and trispectra to relate structural response behavior to their non-Gaussian nature. The results suggest that the trispectrum is a valuable tool for analyzing and classifying non-Gaussian random loading.