Random Vibration Fatigue Life Analysis of Aeroengine Bolts Using the Frequency-Domain Method

Based on the frequency-domain method, the influence factors of vibration fatigue life of aluminum alloy beam with a hole was analyzed. Firstly, the finite element model of aluminum alloy beam with a hole was established, and modal analysis was performed to obtain the natural frequency and mode shape of each order. And then, harmonic response analysis was employed to determine the direction and natural frequency of vibration that has the greatest impact on the structure. After that, fatigue life of the structure was studied. The in-fluence of model method, power spectral density, natural frequency order, frequency band, bandwidth and other factors on fatigue life was analyzed by changing excitation load conditions. Through the simulation, the results indicate that: Fatigue life calculated by Steinberg and Lalanne method is more conservative than that calculated by Dirlik method under the same excitation load. The accelerated fatigue life test can be performed by changing the power spectral density value. The power spectral density value of the excitation load at the first natural frequency plays a major role in the fatigue life. The quantitative relationship between central band fatigue and full frequency fatigue is established.

<div class="section abstract"><div class="htmlview paragraph">Rubber isolators are widely used under random vibrations. In order to predict their fatigue life, a study on the fatigue analysis methodology for rubber isolators is carried out in this paper. Firstly, taking a mount used for isolating air conditioning compressor vibrations as studying example, accelerations versus time of rubber isolator at both sides are acquired for a car under different running conditions. The acceleration in time domain is transformed to frequency domain using the Fourier transform, and the acceleration power spectral density (PSD) is the obtained. Using the PSD as input, fatigue test is carried for the rubber isolator in different temperature and constant humidity conditions. A finite element model of the rubber isolator using ABAQUS is established for estimating fatigue life, and model validity is verified through static characteristic testing. Dynamic responses of the rubber isolator at frequency domain are calculated if a unit load is applied. The estimated dynamic responses are then imported into Fe-safe for calculating fatigue analysis of the rubber isolator. The proposed methods in this paper are validated by comparing the calculated with the measured fatigue life. To enhance the fatigue life of the rubber isolator, structural optimization is carried out by optimizing main spring parameters. Fatigue life calculation of the optimized rubber isolator is then carried out and it is shown that the isolator meets design requirements. A frequency-domain calculation method of fatigue life proposed in this study can be used for assessing the fatigue life of rubber isolators under random vibration.</div></div>

A composite hydrogen storage vessel (CHSV) is one key component of the hydrogen fuel cell vehicle, which always suffers random vibration during transportation, resulting in fatigue failure and a reduction in service life. In this paper, firstly, the free and constrained modes of CHSV are experimentally studied and numerically simulated. Subsequently, the random vibration simulation of CHSV is carried out to predict the stress distribution, while Steinberg's method and Dirlik's method are used to predict the fatigue life of CHSV based on the results of stress distribution. In the end, the optimization of ply parameters of the composite winding layer was conducted to improve the stress distribution and fatigue life of CHSV. The results show that the vibration pattern and frequency of the free and constrained modes of CHSV obtained from the experiment tests and the numerical predictions show a good agreement. The maximum difference in the value of the vibration frequency of the free and constrained modes of CHSV from the FEA and experiment tests are, respectively, 8.9% and 8.0%, verifying the accuracy of the finite element model of CHSV. There is no obvious difference between the fatigue life of the winding layer and the inner liner calculated by Steinberg's method and Dirlik's method, indicating the accuracy of FEA of fatigue life in the software Fe-safe. Without the optimization, the maximum stresses of the winding layer and the inner liner are found to be near the head section by 469.4 MPa and 173.0 MPa, respectively, and the numbers of life cycles of the winding layer and the inner liner obtained based on the Dirlik's method are around 1.66 × 106 and 3.06 × 106, respectively. Through the optimization of ply parameters of the composite winding layer, the maximum stresses of the winding layer and the inner liner are reduced by 66% and 85%, respectively, while the numbers of life cycles of the winding layer and the inner liner both are increased to 1 × 107 (high cycle fatigue life standard). The results of the study provide theoretical guidance for the design and optimization of CHSV under random vibration.

The flexible positioning platform is a critical structural component in the ultra-high acceleration macro–micro motion platform, enabling precise positioning across multiple scales. However, under high-frequency start–stop cycles and prolonged multi-condition operation, it is prone to fatigue damage induced by random vibrations, which poses a threat to system reliability. This study proposes a method for evaluating and optimizing the platform’s performance under random vibration based on power spectral density (PSD) analysis. In accordance with the IEC 60068-2-64 standard, representative load spectra from Tables A.8 and A.6 were selected as excitation inputs. Frequency-domain analyses of stress, strain, and displacement were conducted using ANSYS Workbench 2022R1 in conjunction with the nCode platform, incorporating the Gaussian three-sigma probability interval. The results reveal that stress and deformation are highly concentrated in the hinge region, indicating a structural vulnerability. Fatigue life predictions were carried out using the Dirlik method and Miner’s linear damage rule under various PSD loading conditions. The findings demonstrate that hinge stiffness is a key factor influencing vibration resistance and service life. This research provides theoretical support for the design optimization of flexible structures operating in complex random vibration environments.

<div class="htmlview paragraph">In this paper, a CAE (Computer-Aided Engineering) methodology to simulate the vibration test and predict fatigue life of head lamp bulb shield is presented. A modal analysis is performed first to determine the critical elements from the strain energy density distribution patterns. A random vibration frequency response analysis is then performed to monitor the stress response power spectral densities (PSDs) for critical elements due to the g-load input PSDs, measured at the mounting point in all three directions. Fatigue life can be estimated based on the stress response PSDs and material S-N curve by using Dirlik's method. The fundamentals for frequency domain fatigue analysis are reviewed and a case study with test correlation is then presented.</div>

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

Failure of the light beam direction adjusting mechanism (LDAM) of an automotive headlight might occur after hundreds of driving hours, though the strength of components conforms to the requirement specified in the random vibration bench test standard. In order to determine the causes of the failure, fatigue life prediction and failure analysis based on numerical method of the LDAM exposed to random loading both in bench test and field experiment were carried out. In the bench test analysis, the Dirlik method was utilized to calculate the lifetime by taking the power spectrum density in the frequency domain. In the fatigue analysis for the field experimental loading, to consider the effect of nonuniform temperature distribution, a numerical process in time domain is developed to calculate the lifetime of the LDAM subjected to the random vibration caused by road surface roughness. As a result, the predicted life and failure locations are in good agreement with real life and actual failure regions, respectively.

During the Launch phase, Spacecraft structures are submitted to heavy acoustic excitation mainly generated by the engines and the aerodynamic forces over the whole the vehicle. The acoustic excitation creates a vibration environment that must be characterized to correctly design the secondary structure for a multimission operational profile. Various design approaches for predicting the random fatigue life of structural items have been proposed and developed. These methods generally include predicting the random loads, estimating the fluctuating stress response of the structures and predicting the life from stress versus cycles to failure curves for the relevant material. As the random loads increase, the stress response and the structures fatigue behaviour become more non linear and very difficult to predict with the classical computation methods, because the theory of non linear random vibration has not reached a good state of maturity. Although many methods of solution exist, there can be no general rule about the suitability and reliability of any methods. Moreover, the fatigue process which reduce strength in composite materials are generally very complex, involving the accumulation of multiple damage modes which may combine in a variety of way to produce numerous failure modes. For the fatigue life assessment, in the literature there are many methodologies based on simple analysis for evaluating response prediction, using fundamental mode approximation for estimation of induced stress and strain caused by random loads. The derived stress levels in rms form for particular load cases, are used together with rms stress endurance data to estimate fatigue damage for each case. The overall structural damage can then be used to obtain the fatigue life of the relevant component. However, life estimates are not so accurate and often factors correlating predictions with tests are enough large. Possibly reasons for these discrepancies might be first the use of rms levels in the damage analysis; they cannot be expected to reflect the more complex behaviour of the range of stresses they are representing. Second cause might be the use of available endurance design data to cover a too wide range of structural geometry. A probabilistic model for damage accumulation in composite is therefore the most suitable one. Consequently, probabilistic concepts and methods are needed for an assessment of the safety and reliability of metallic and composite under fatigue. In the CEE BRITE EURAM RESEACH “AMADEUS”, an analytical formulation based on a statistical method has been proposed to evaluate the “expected” fatigue damage on structures subjected to random loads during their service life. The target of the present paper is to show the reliability of the simulation techniques based on Finite Element Method (FEM) and the statistical Energy Analysis (SEA) modelling, adopted for the derivation of spacecraft Random Vibration Environment (RVE) integrated with a newly developed algorithm to predict the multiaxial Random fatigue for structural panels models. Based on this Design verification approach ,the potential Design criticality can be identified in the early design stage of a project and where required local structural modifications can be implemented during the development phase ,resulting in an optimized design at reduced cost.

This paper presents fatigue life prediction of an engine exhaust manifold, this approach developed an exhaust manifold prediction model which used neural network technology and finite element analysis model. Firstly, Modern exhaust systems should withstand severe cyclic mechanical and thermal loads throughout the whole life cycle. Thermos-Fluid-Structure coupling analysis established the prestressed conditions and identified the potential fatigue risk area, this area was under cycle fatigue. Secondly, several cycles the fatigue micro cracks would appear in this region. random vibrations were applied in the fatigue life evaluation, and a life prediction model was established and trained to improve the prediction efficiency. Finally, the model showed that the predicted life of parts approached the actual life, the prediction error of fatigue life was controlled within 10%. This method emphasized the advantages of the model which combined neural networks with finite element analysis model to accurately and effectively, and the lifetime of this part can be determined through the modeling analysis instead of only experiment.

The reliability of electronic components has persistently posed challenges for engineers. This study addresses the critical need of understanding the impact of random vibration on the reliability of lead-free solder as thermal interface materials (TIM) within electronic components. ANSYS software was deployed to design, develop, and simulate the electronic model, with a focus on the TIM. SAC405 lead-free solder served as the TIM, its thickness was varied between 0.01 to 0.06 mm (at 0.01 mm intervals). The results from this investigation reveal relevant correlations. As the TIM thickness increases, there's a noticeable reduction in stress and strain while the deformation increases. Remarkably, a direct relationship emerges between TIM thickness and fatigue life; thicker TIM correlates with increased fatigue life. In addition, at a TIM thickness of 0.01 mm, the fatigue life measurements were 2.76 x 104, 1.63 x 104, and 0.792 x 104 for Equations 1, 2, and 3, respectively. These findings carry profound implications for engineers, serving as a guiding framework to aid in the selection of optimal TIM thickness for electronic components if lead-free solders are used as TIM. Understanding these trade-offs between stress, strain, deformation, and fatigue life is pivotal, empowering engineers to make informed decisions during electronic system design and development, ultimately enhancing overall reliability. Using lead-free solders as TIM in electronic applications is proposed by this study due to the thermal and reliability benefits presented.

Failure analysis on the axial-connected bolts of the thin-walled cylinder under random vibration loading

Fatigue life prediction model for accelerated testing of electronic components under non-Gaussian random vibration excitations

A new fatigue damage formulation has been developed to include the full stress energy distribution of a broad band stress spectrum with one or more peaks. The formulation was based on the general probability distribution of stress peaks associated with stress spectra for various sea-states. The conventional approach was to assume a Rayleigh probability distribution applicable only to a narrow band spectrum. The main conclusions were that:–Assumption of Rayleigh probability distribution leads to over conservative results.–Accurate fatigue life estimation is possible without the use of stress time history and rainflow cycle counting.–Reduction in fabrication steel cost. INTRODUCTION Several years of experience in the design of offshore steel platforms (rigid and compliant) has shown that fatigue is a major and in some cases the governing design criterion. Over the past years fatigue life calculation technique has advanced from simple deterministic to a more realistic spectral fatigue method. However, the actual spectral formulation, in most of the cases, is limited to the use of assumed conservative Rayleigh probability distribution of the stress peaks. This is because accurate spectral fatigue method requires the generation of lengthy stress-time histories and combining the damages caused in each stress cycle, a very expensive method indeed. Recent development of compliant and floating structures has resulted more and more accurate dynamic stress responses over the whole frequency range and their associated stress spectra. Yet, the accuracy of the fatigue life calculation has not been improved for the input to spectral fatigue formulation has been narrow banded spectrum, even though stress spectra of even a lightly damped structure are broad banded, often, with more than one peak. Assumed narrow banded spectrum means that the fatigue damage formulation only uses the area of the spectrum in the form of R.M.S. value, square root of the area of a spectrum. The effect is that all the information of the stress energy distribution is ignored, which leads to a more conservative fatigue life estimation. This paper describes a spectral fatigue damage formulation that was based on the generalized probability distribution of stress peaks associated with any stress spectrum. The objective was to obtain an accurate fatigue damage without the use of lengthy stress-time histories and cycle by cycle damage counting. The proposed damage formulation was correlated and verified with the model test results of large scale tubular joints and rainflow cycle damage counting of computer simulated stress-time histories. Finally, a typical TLP has been considered to assess the contribution of the proposed formulation both in terms of calculated fatigue life and the relative savings in the cost of steel fabrication. PROPOSED SPECTRAL DAMAGE FORMULATION Fatigue damage calculations are usually based on number of stationary sea-states of short durations, known as scatter diagrams. Number of such sea-states, concentrated scatter diagram, for North Sea environment are presented in Table,. Stress spectra associated with the sea states in Table, were obtained for a typical offshore structure by using the following analytical expression:1

This article verifies a method of predicting the fatigue life of materials under random vibration containing nonlinear loading. We approximated stress frequency distribution in nonlinear range by exponential function. Next, fatigue lives were predicted with stress frequency distribution calculated by Dirlik's method and mathematically-formulated frequency in nonlinear range. As the result of the comparison, the error in the predicted fatigue lives calculated by Dirlik's method to those calculated by proven Rainflow method was within 50 percents. In addition, the predicted fatigue lives calculated by Dirlik's method were 1.79 times as much as those resulted from random fatigue tests with sheet welding test pieces in average (Rainflow method was 1.93 times). We indicated this improved method could predicted the fatigue live with same precision with Rainflow's method.

The present work concerns solving Noise, Vibration and Harshness (NVH) and fatigue based on Power Spectrum Density (PSD) analysis of a landing gear's leg for an Un-Manned Aerial Vehicle (UAV). This analysis includes random vibration and high-cycle fatigue analysis in a random vibration environment. In this analysis, the cumulative damage ratio is computed using material S-N (Stress-Number of cycles) fatigue curve. Dirlik method is used for the analysis of lifetime as it is proven to provide accurate results for large number of applications, both in automotive and aerospace industry. It is also compared to other methods that have been developed in LS-DYNA® as well. The input acceleration PSD data are provided through measurements. The obtained analysis results shows that although the landing gear design is safe according to dynamic and static load, its service life is about 3037 hours due to random vibration effect.