Rain-flow Method Research Articles

Demonstrative irregular fatigue cycle counting by rainflow method implementation using a Python program

Demonstrative irregular fatigue cycle counting by rainflow method implementation using a Python program

Dynamic fatigue damage calculation for a high-speed train bogie frame considering the three-dimensional gear meshing

A three-dimensional rigid-flexible coupling model of a high-speed train has been developed incorporating both the elastic bogie frame and the gear meshing within the drivetrain system. Notably, both the wheel polygonisation and dynamic nonlinear internal excitation forces induced by the time-varying gear meshing stiffness and errors of the gear meshing are systematically taken into account. By virtue of the finite element scheme, the real-time and time-varying cumulative fatigue damage of the bogie frame is achieved based on the rainflow method and Miner’s damage summation rule. Numerical results demonstrate that the impacts of nonlinear internal excitation forces and wheel polygonisation on the fatigue damage of the bogie frame are significant. Compared to the case without nonlinear internal excitation forces, the fatigue damage at some critical positions of the bogie frame drastically increases, specifically, the damage of the most dangerous position increases by approximately 106.09%. Whether the dynamic internal excitation forces are exit or not, the fatigue damage of the bogie frame increases with the increasing amplitude of the polygonal wheel. The effect of nonlinear internal excitation forces on the fatigue damage of the bogie frame is more pronounced at lower amplitudes of the polygonal wheel.

Sizing of Battery Energy Storage Systems for Firming PV Power including Aging Analysis

The variability of solar radiation presents significant challenges for the integration of solar photovoltaic (PV) energy into the electrical system. Incorporating battery storage technologies ensures energy reliability and promotes sustainable growth. In this work, an energy analysis is carried out to determine the installation size and the operating setpoint with optimal constant monthly power through an iterative calculation process, considering various operating setpoints and system parameters. A degradation model is integrated according to the curves offered by battery manufacturers and the charge–discharge cycles are calculated using the rainflow method to guarantee a reliable analysis of the plant. Through massive data analysis in a long-term simulation, indicators are generated that allow for establishing a relationship between the energy unavailability of the system and the BESS dimensions.

Estimating the optimal duration of random loading as part of machine part durability research

Aim. Making an informed decision regarding the durability of machine parts requires information on the operational load that needs to be measured on a representative section of the track. It should not be too long as well. Thus, it is required to determine the optimal duration of implementation. The duration of implementation that is optimal in terms of the reliability of load registration is defined for a process that is stationary in a special sense. Stationarity in a special sense is defined specifically for the task of assessing the durability of a specific part. Methods. The use of spectral theory for the study of random processes is probably not the best way of examining non-stationary loading processes in the context of durability assessment. We believe it would be optimal to use a cycle counting procedure (rain flow method) with subsequent calculation of durability. A lemma and a theorem were formulated on the sufficient duration of implementation for a process that is stationary in a special sense. A sufficient duration of implementation is defined as a limit past which its increase will not lead to a noticeable change in the calculated durability. Results. The matters of stationarity of a process in a narrow sense and the required duration of implementation will help in planning operational tests to measure and record random processes of machine part loading. Both matters were examined in terms of fatigue damage accumulation using Miner linear damage rule, as well as the adjusted linear damage summation hypothesis taking into account the fatigue curve slope parameter m. Some practical engineering problems were examined, including the problem of the optimal duration of implementation of a mining machine whose loading process is characterized by a high degree of irregularity and the problem of finding the required duration of implementation of load recording in a rolling stock component. Conclusion. A theorem on the required and sufficient duration of implementation was formulated. In order to test the method, Markov transition matrix-based model processes were used. In addition, the method and theorem were tested using examples of some experimental processes obtained from operational tests of vehicles and production machines.

Physics-Aware Degradation Model of Lithium-ion Battery Energy Storage for Techno-Economic Studies in Power Systems

Power system operation and planning decisions for lithium-ion battery energy storage systems are mainly derived using their simplified linear models. While these models are computationally simple, they have limitations in how they estimate battery degradation, either using the energy throughput or the Rainflow method. This paper proposes a hybrid approach for lithium-ion battery system modeling suitable for use in power system studies that enhances representation of battery degradation at a reasonable computational cost. The proposed hybrid model combines a physics-based model for improved degradation estimates with a simple and linear energy reservoir model commonly used to represent a battery storage system. The advantage of constructing the battery model with this vision is that it allows its smooth integration into the mixed-integer optimization frameworks. The proposed model is evaluated using both power- and energy-based use cases from the electrical grid. The simulations demonstrate that degradation could be reduced by 45% compared to other modeling strategies while generating the same level of operation profits. The net result of using the proposed hybrid model could be an extended lifespan through better informed planning and operating decisions for energy storage assets.

Prediction of Fatigue Crack Growth in Vacuum-Brazed Titanium Alloy

The assessment of fatigue is a crucial concern in welded components and structures. This study investigates the fatigue properties and models for predicting fatigue crack growth in Ti-6Al-4V titanium alloy when processed by vacuum brazing with TiCuNi filler. Fatigue properties and the impact of the stress ratio were determined through constant amplitude fatigue tests. By utilizing the results obtained from variable amplitude fatigue tests, various prediction models for fatigue crack growth were examined: modifications for load interaction, residual stress, and crack closure. The results indicate that the microstructures in the brazed zone consist of numerous fine, elongated needle-like Widmanstätten structures. In terms of cycle counting methods, the rainflow method outperforms the simple-range method. In the stable crack growth rate region, fatigue crack growth rate increases with the rise in stress ratio in a manner similar to high-strength steels. The Paris model without any modification obtains good predictions. For models modified with crack closure, the Elber model yields slightly better prediction results than the Schijve model. Among fatigue crack growth prediction models, the Willenborg model with residual stress modification produces the best results. Fracture surfaces within fatigued specimens’ brazed zones exhibit ductile failure characteristics, where fatigue striations and secondary cracks were observed.

Modeling and Verification of Rolling Resistance Torque of High-Speed Rubber Track Assembly Considering Hysteresis Loss

Due to the viscoelasticity of rubber materials, hysteresis loss due to deformation is the main reason for the rolling resistance of high-speed rubber tracks. Since the structure and material of high-speed rubber track assemblies are different from traditional tires and metal tracks, the rolling resistance theory of traditional wheeled and tracked vehicles is not applicable. Therefore, in order to determine the rolling resistance scientifically and accurately, the mechanism research of the rolling resistance of high-speed rubber track assembly is the key to the design of high-speed rubber crawler vehicles. In this paper, the stress-strain characteristics of rubber track under the action of compression, tension, bending, and driving were studied. The strain load spectrum of rubber tracks was established, and the strain cyclic load was extracted by the rainflow method. The temperature model of the rubber track was developed based on its dynamic characteristics. On the basis of energy conservation, the hysteresis loss of rubber is equivalent to the energy consumption of rolling resistance, and the theoretical model of rolling resistance of high-speed rubber track assembly is established. In accordance with the model above, the key influencing factors and changing trends of rolling resistance are analyzed, which provides a theoretical basis for the performance optimization of high-speed rubber track assembly.

Fatigue life prediction of a Durga flyover bridge at vijayawada using wireless sensors

It is essential to inspect and assess any fatigue damage to the components of a structure in order to determine how long it will last. This is necessary for constructions such as concrete bridges, which are subjected to fluctuating loads with high intensity and frequency. This study presents a computer application method for calculating the fatigue life of the Durga flyover (reinforced concrete) bridge. The damage to bridge components can be evaluated based on the dynamics of the interaction between the bridge and vehicles caused by actual traffic. The computer code initially calculates the fluctuation of stresses caused by the passage of various types of vehicles in a given segment of a bridge. The other module has a continuous set of loads to measure the strains and calculate the stress variations across the section components. The rainflow method is used to count stress cycles owing to the fact that the peak intensities of the stress cycles are not steady, and the appropriate S-N curves are utilized to determine the damage caused by each cycle. In this analysis, the stress range amplitude waveform and fatigue toughness characteristics of bridge elements were employed to systematically detect continuous bridge girder fatigue damage. The most severe flexural stresses induced by vehicles were detected, and a stress-range frequency waveform was created while accounting for the total traffic volume. Linear damage accumulation theory was used to calculate the cumulative damage index and bridge fatigue life. The Miner's rule was used to calculate the overall damage caused by the passage of the vehicles. The major factors affecting the fatigue life are the effects of the span, pavement quality, increase in the speed of operation, weight, and suspension characteristics of the bridge.

Fatigue life evaluation of automotive mechanical components by using smart design algorithm

AbstractThe aim of this work is to develop a so‐called “smart design” in MATLAB™ environment. The design process consists of an innovative and automatic algorithm aimed at rapidly evaluating the fatigue damage of automotive mechanical components, starting from the load cycle that the component is subjected. In this work, the target component is the front halfshaft of a sport utility vehicle. The algorithm works as follows. A driving cycle has been acquired through an experimental setup consisting of a control unit, a GPS and an OBD port. A mathematical model of the vehicle, based on longitudinal vehicle dynamics, has been developed in Simulink™ environment to evaluate the traction torque at the wheel. A torsional fatigue tests campaign has been carried out on nine front halfshafts of the vehicle to evaluate the torque amplitude–number of cycles curve of the component. The output histories, computed with the rainflow method, have been referred to a load ratio R = −1, according to the experimental fatigue tests, by the application of three different mean stress fatigue criteria: Goodman, Gerber, and Morrow. At the end, cumulative fatigue damage on the component has been evaluated by the application of the Palmgren–Miner rules. The results show that the Goodman criteria, with a fatigue damage value of around 20%, represents the most precautionary criteria for the fatigue design of an automotive component.

Angle measurement stability and cycle counting accuracy of hours-long duration IMU based arm motion tracking with application to normal shoulder ADLs

BackgroundInertial measurement units are increasing used for monitoring joint motion, but there is a need to demonstrate their suitability during hours-long continuous use, as well as a need for validated methods to count arm cycles and provide descriptions of typical cycles. Research questionDo IMU sensors and rainflow counting have sufficient accuracy for tracking and cycle counting of hours-long continuous arm motion? If so, what are the cycle rates of normal arm ADL and is there a representative cycle that can serve as a ‘gait cycle’ for the arm? MethodsIMU sensors continuously tracked a robot performing 8 h of simulated cyclic arm motion. Error in the angle measurements was regressed against time to determine the rate of error and the total accumulated error. Additionally, the cycle count accuracy of rainflow, peak/valley, and Fourier transform counting methods was evaluated. ResultsOver 8 h the IMU measurements accumulated a maximum 0.473° of error and the rainflow method counted cycles with less than 1% error. Applying rainflow counting to normal shoulder ADL resulted in an average rate of 533 elevation cycles per day.Tabulating the ADL cycles by mean and range values into a matrix and calculating the centroid, the single best values representing arm elevation cycles were a mean of 22.4° and a range of 21.6°. SignificanceIMU sensors can track arm motion for 8 h with little increase in error, though during longer durations error may reach unacceptable levels. For normal arm ADL, the rainflow determined count of arm elevation full-cycles differed from previous estimates based on peak/valley counting. From the rainflow counting, a single cycle representation of cycle mean and range was determined that can be used as a ‘gait cycle’ for the shoulder

Procedure for defining of the equivalent vehicle mileage and the procedure approbation results

Introduction (problem statement and relevance). Automotive manufacturers and research engineers around the world are actively engaged in improving the methods of checking the safety and durability of the vehicle, vehicle components and systems. Testing and evaluation methods play an important role in solving this problem. This article reveals the issues of using the methods for determining the equivalent mileage of a vehicle in accordance with accumulation of pseudodamage, which includes well-known methods and procedures, and also describes the results of applying the methods in practice.The purpose of the research is development of the program of accelerated durability testing of the М1С category vehicle based on the application of the methods for determining the equivalent mileage.Methodology and research methods. The method is based on the approaches of the material fatigue curve definition, the rule of linear damage accumulation, the theory of counting the number of loading-unloading hysteresis cycles with the rain flow method approach and subsequent comparative analysis according to values of accumulated pseudo damage.Scientific novelty and results. The main results were obtained in the form of a program of accelerated durability testing of the М1С category vehicle, in addition, the features of using the method for determining the equivalent mileage of a vehicle based on the accumulation of pseudo-damages are disclosed.Practical significance. The obtained result is applicable in the field of studies of the durability of the load-bearing components of the vehicle and its subsystems using the capabilities of the test base and mathematical modeling tools, in addition, the results are of practical importance in the development of accelerated durability testing of competing vehicles, similar in weight and size parameters to the studied.

Investigation on runner resonance and fatigue life of a high–head pump–turbine

The structural stability and fatigue of the runner of a high-head pump-turbine was explored by conducting a numerical simulation of the entire flow passage under different working conditions. A two-way fluid-structure interaction calculation method was used, which captured the values for 5.75 fn, 9 fn, 13 fn, 18 fn, and 20 fn ( fn is rotational frequency) in pressure fluctuation. The resonance of the runner was compared with the results of the modal analysis. The rain flow and damage accumulation methods were used to predict the fatigue life. The study found that the 13 fn pressure fluctuation of the fluid in the flow passage of the pump-turbine is the primary cause of the resonance of the runner blade. The main frequency of vibration is the third natural frequency of the runner. The vibration form is up and down along the Z–axis, and there are some high-order resonances. The most vulnerable part of the entire runner is located at the T-shaped connection between the blade inlet edge and the runner crown and bottom ring. The excitation force under the small flow condition is more complicated than that under the large flow condition, which is more likely to cause fatigue damage to the runner. In addition, the damage extent of the high-stress amplitude to the runner is obviously greater than the influence of the number of stress cycles, accounting for approximately 60% of the total damage. The research results can provide a reference for the operational stability and life prediction of a high-head pump-turbine runner.

Seismic fatigue evaluation method based on vibration velocity of pipeline

In previous reports, a new seismic fatigue evaluation method based on the vibration velocity was proposed. In this study, the cumulative fatigue damage was evaluated by the rain flow method as well as the new method for the case where the seismic input acts on the cantilever pipe with the concentrated mass at the tip. When the cumurative fatigue damage was relatively large, both results were shown to be in good agreement, especially at the peak values of the response spectra. It was shown that quantitative fatigue evaluation is possible using the new method.

ПРОЦЕДУРА ТА АЛГОРИТМ ВИЗНАЧЕННЯ КОЕФІЦІЄНТА ЗАПАСУ МІЦНОСТІ ВАНТАЖНОГО ВАГОНА З УРАХУВАННЯМ СУЧАСНИХ ВИМОГ

Improving the reliability of test results is achieved by applying more advanced methods of recording and processing the results. Therefore, an important part of the study of the strength of freight wagons is the choice of methods for obtaining, processing and analyzing experimental data. The article outlines the procedure and algorithms for determining the equivalent stresses under longitudinal and dynamic loads acting during operation. It is shown that algorithms for determining stresses generated by dynamic longitudinal and vertical forces are significantly different due to various load application schemes. Thus, the testing of freight wagons under dynamic longitudinal loads is carried out by the impact against an experimental wagon, and testing under dynamic vertical forces is performed during the wagon motion in the composition of the experimental train on the characteristic, pre-selected (planned) sections of the railway track at specified speeds. To estimate the level of loading of the freight wagon structureunder vertical dynamic loads, a method based on the replacement of a real random process is used by some schematized process, which in terms of the fatigue damage accumulation should be equivalent to a real process. From the whole variety of schematic methods, two methods stand out, i.e., the full cycle method and the rainflow method, which most fully represent the real process.The advantage of the rainflow method is the ability to process the process in real time. However, the algorithm of the rainflow method is quite complicated and does not allow processing large amounts of information. In this regard, a method of maximum discharge was proposed, which is a kind of full cycles method and allows you to process an unlimited amount of information online. An example specified in GOST 25.101 was used for a comparative analysis of the rainflow and maximum discharge methods. Analysis showed a satisfactory matching of both methods. Based on the procedure outlined, the block structure of the computational process is proposed to determine the equivalent reduced voltage amplitude. Each block displays the impact of the forces depending on the loading condition, that is, longitudinal impact force and dynamic forces when the wagon is moving on straight track sections, curves and switches of the railway track. Key words: wagon car, process, dynamic load, longitudinal load, voltage, amplitude, algorithm, equivalent stress, safety margin, strength.

Comparative Study of a Powerplant Life Consumption Rate When Installed in Two Different Aircraft Variants

The Hellenic Air Force (HAF) operates both EMB-145 and EMB-135 LR versions of Embraer aircraft, used in surveillance and civil missions respectively. These aircraft are equipped with the same version of Rolls Royce, AE 3007 turbofan engine. This study aims to quantify and compare the life consumption rate of this engine when installed in each of the two aircraft variants. Two typical missions, one for each variant, were constructed based on mission profile data dictated by the aircraft commanders. For each mission profile segment, corresponding engine data were matched out of the engine recordings archives held by the Hellenic Air Force. The life consumption rate was based on the Low Cycle Fatigue (LCF) and creep cumulative detrimental effect on the rotor blades of the 1st High-Pressure Turbine stage. For the LCF, the rainflow method was used to determine the respective loading cycles, whereas the Larson - Miller parameter method was used to determine the consumed life fractions due to creep. The main conclusion of the study was that the engine when installed in the EMB-145 military variant, is much more loaded. Despite the fact absolute life consumption values could hide a great level of uncertainty, the comparative outcomes wherein errors are, to a certain extent, cancelled out, could be used as a rule of thumb when monitoring engine life consumption rates.

An efficient fatigue analysis for the nonbonded flexible riser

ABSTRACT This paper presents an efficient fatigue analysis for the non-bonded flexible riser. This fatigue analysis is based on well approved methodology including stochastic analysis of sea states, global response analysis of riser and local stress analysis of individual tensile wires followed by rain flow and Palmgren-Miner methods for calculating the fatigue damage and fatigue life. For the global response analysis, the nonlinear hysteresis relationship between bending moment and curvature of riser is coupled for accurately allocating the bending stiffness in the corresponding curvature range. For the local stress analysis, the simplified bending moment model is applied for describing the stick-slip behavior, which is efficient for calculating axial stress of individual tensile wires when 3D effects along the pipe is not considered. Sensitivity studies with respect to the flooded condition of tensile annulus layer and friction coefficient are further carried out for investigating the associated effects on the fatigue life.

Fatigue crack growth prediction model under variable amplitude loading conditions

Crack size prediction under variable amplitude loading is a very complex process, which is also important for life prediction in engineering. A crack growth model considering different stress ratio for fatigue remaining life prediction is proposed in this paper. The model utilizes stress ratio to describe the variable loading sequences, which makes the calculation greatly simplified. The rain-flow method is utilized to characterize the load sequence effects under variable amplitude loading. In addition, particle filter is utilized to estimate the model parameters describing the crack growth. Finally, case study indicates that the proposed approach is efficient in predicting crack growth and fatigue remaining life.

Study on Quasi-Static Loading Protocols considering the Action Characteristics of Long-Period Ground Motions

Due to abundant low-frequency components of long-period ground motions (LPGMs), long-period structures are susceptible to severe damage. The corresponding time-history displacement responses have significant “large-displacement” and “long-duration” characteristics. These action characteristics essentially reflect the different loading paths imposed on structures of LPGMs from ordinary ground motions (OGMs). Hence, revealing the influence mechanism of the action characteristics on the seismic performance of structural components is the key to investigating the influence of LPGMs on the whole structure. This paper presents a kind of quasi-static loading protocol considering the action characteristics of LPGMs. Firstly, nonlinear time-history analyses on structural systems subjected to 50 selected representative LPGMs were conducted. Inelastic cycles and corresponding amplitudes of time-history displacement responses under LPGMs were statistically analyzed through the rainflow method. Then, considering two of the most significant factors, structural period and target ductility, a prediction model of cycle number and cycle amplitude was obtained by regression. On this basis, the quasi-static loading protocol considering the action characteristics of LPGMs was developed. Proposed protocols can be directly applied to experimental investigations on the seismic performance for structural components under LPGMs.

Nominal stresses to assess damage in notched additively manufactured steel subjected to constant and variable amplitude multiaxial fatigue loading

The present paper reports on the use of the Modified Wöhler Curve Method (MWCM) applied along with nominal stresses to estimate lifetime of notched additively manufactured metallic materials subjected to constant and variable amplitude multiaxial fatigue loading. The MWCM is applied by defining the critical plane via the direction that experiences the maximum variance of the resolved shear stress. In this setting, owing to the fact that the shear stress resolved along this direction is a monodimensional stress quantity, fatigue cycles are counted directly by using the standard Rain-Flow method. Based on a large data set taken from the literature, the validation exercise being performed strongly supports the idea that the MWCM used in conjunction with nominal stresses is successful in estimating fatigue damage also in notched 3D-printed metallic materials subjected to constant/variable amplitude multiaxial load histories.

Varied approaches to loading assessment in fatigue studies

In this paper, the authors want to draw readers’ attention to one long-standing question: which approach is preferable for estimation longevities in fatigue problem, the time domain approach (Rainflow) or the frequency domain one (Dirlik and others)? This question is important in engineering problems, particularly in problems of prolongation of the guaranteed service life. The discussion here is restricted by the longevity evaluation only at the post-processing stage of unidirectional loaded machine parts. It means the realizations might be recorded.Some experimental and speculative evidence of preferable use the Rainflow method is shown. Taking into account the huge computer's power nowadays, the question of the irrelevance of appellation to the calculation accelerating using the spectral methods is specially discussed.There are areas, where the spectral methods are really necessary. There is only a need to recommend the restriction of their application scope to these special situations. It seems there is no need in inventing new spectral complicated algorithms only to stress out at the end, that their result coincides with the Rainflow outcome. That might be confusing for the practicing engineers.Currently, the main attention among supporters of spectral methods is focused on non-stationary and non-Gaussian random processes. (to estimate the spectral density is impossible for non-stationary processes, according to definition). These researchers seem to have forgotten, that even for these complicated situations the decision has already existed: that is the Rainflow and its analogues.The paper shows extensive laboratory experiment results of random fatigue testing of aluminum flat specimens under regular (to build the fatigue curve) and irregular (random) loading. The fatigue life curve (Gassner curve) has been built. These results allowed to compare the existing computation methods of longevity estimation. In the particular situation of narrow-band process, the methods seem to provide comparative results.Considered are methodological issues related to the assessment of the necessary and sufficient realization length, the influence of RMS, cycle counting methods and some possibilities of computing resources saving when using the Rainflow method. The stability of the Rainflow estimates is confirmed. Some problems with the choice of parameters during the longevity assessment by the Dirlik method were noted.