Rainflow Cycle Counting Method Research Articles

Online Optimization of Vehicle-to-Grid Scheduling to Mitigate Battery Aging

The penetration of electric vehicles (EVs) in vehicle-to-grid (V2G) interaction can effectively assist the grid in achieving frequency regulation and peak load balancing. However, the customer perceives that participating in V2G services would result in the additional cycling of the battery and the accelerated aging of the EVs’ power battery, which has become a major obstacle to the widespread adoption of V2G services. Most existing methods require long-term cycling data and battery parameters to quantify battery aging, which is not suitable for the V2G scenario with large-scale and short-time intervals. Consequently, the real-time and accurate quantification of battery aging for optimization remains a challenge. This study proposes a charging scheduling method for EVs that can accurately and online quantify battery aging. Firstly, V2G scheduling is formulated as an optimization problem by defining an online sliding window to collect real-time vehicle information on the grid, enabling online optimization. Secondly, battery aging is more accurately quantified by proposing a novel amplitude-based rain-flow cycle counting (MRCC) method, which utilizes the charging information of the battery within a shorter time period. Lastly, an intelligent optimization algorithm is employed to optimize the charging and discharging power of EVs, aiming to minimize grid fluctuations and battery aging. The proposed method is validated using a V2G scenario with 50 EVs with randomly generated behaviors, and the results demonstrate that the proposed online scheduling method not only reduces the EFCC of the battery by 8.4%, but also achieves results close to global optimization.

Nonlinear thermo-acoustic response and fatigue prediction of three-dimensional braided composite panels in supersonic flow

In this paper, a novel aerodynamic-acoustic coupling model to investigate the influence of aeroelastic effects on the thermo-acoustic response of three-dimensional, four-directional braided composite panel is proposed, and the fatigue life under the combined aerodynamic load and acoustic load is discussed by using a rainflow cycle counting method. Assuming that the fibers are transversely isotropic and the matrix is isotropic, the fiber inclination model was used to predict the effective stiffness matrices of the composite panels. The piston theory and Gaussian random acoustic excitation were used to simulate the aerodynamic load and acoustic load, the thermal load is assumed to be a uniform distribution in steady state, and the material properties are assumed to be independent of temperature. Based on the von-Karman strain–displacement relation, the governing equations of the panel were formulated, and the response solutions of the four sides simply supported panel were obtained using Galerkin method and Runge-Kutta method. The aeroelastic effect on the thermos-acoustic response of the braided composite panel was investigated in time and frequency domains, and the life of different load conditions was predicted. The results show that the aeroelastic not only transforms the movement form, but also affects fatigue life of the panel.

A study on the fatigue crack growth behaviour of GTM718 nickel based super alloy under cold-TURBISTAN spectrum loads

In this study, the fatigue crack growth (FCG) behavior of GTM718 nickel base super alloy subjected to cold-TURBISTAN spectrum load sequence was determined by three different methods i.e., (i) Experimental, (ii) Analytical prediction using cycle-by-cycle method and, (iii) Prediction by finite element analysis (FEA). In the experimental method, a standard compact tension (CT) specimen was prepared and pre-cracked to produce a sharp fatigue crack at the notch root. Then, the specimen was subjected to spectrum load blocks repeatedly and crack growth was measured as a function of applied number of flights. Two such tests were carried out in a servo-hydraulic universal test machine with triangular waveform and at an average frequency of 2 Hz. In the second analytical method, the individual load cycles in cold-TURBISTAN spectrum block were separated through rain flow cycle counting method. For each of this counted cycle, the crack extension was determined using crack growth law which was based on two-parameter crack driving force, ΔK*. An in-house MATLAB code was written and used to determine the FCG behavior by cycle-by-cycle method. In the third FEA method, a global model of CT specimen of GTM718 was created in HYPERMESH and a local model with a pre-crack was created in FRANC3D. The FCG behavior under spectrum load was determined using FRANC3D in conjunction with MSC NASTRAN. Two different types of ‘FCG law - stress ratio effect’ combinations were employed i e., Paris’-Walker (P-W) and Bi-linear-Walker (B-W). The required constants for these laws were derived from the available experimental data of the material. It was observed that the predicted FCG behavior by analytical and FEA methods, although conservative, were fairly good when compared to experimental results.

A case study investigation into the risk of fatigue in synchronous flywheel energy stores and ramifications for the design of inertia replacement systems

Flywheels are an attractive energy storage solution for many reasons; high turnaround efficiencies, long cycling lives and high “ramp-up” power rates have all been noted in the literature. Novel flywheel based hybrid energy storage systems have also been suggested by several authors which, due to the inherent partitioning of power sources in the system architecture, provide capacity for flywheels to deliver/receive energy over a comparatively large range of time scales and loading frequencies. Accommodating grid power fluctuations at the millisecond to second time scale is an ever growing problem that almost all grids undergoing de-carbonisation are facing. Synchronous flywheel energy storage systems have the attractive capability of being able to replace “real” (passively controlled) inertia with “real” inertia in a cheap and very robust manner. Flywheel design at the grid scale warrants careful consideration, as for static energy storage applications (i.e. those not used in transportation) the main driving factor is the reduction of manufacturing and material costs. It is paramount that material is used effectively, i.e. it is sufficiently stressed such that the flywheel is not oversized (and therefore expensive) while simultaneously guarding against the likelihood of catastrophic failure during service. Fatigue has the potential to be a serious life limiting mechanism due to fluctuating rotational speeds, however in depth analysis is lacking in the literature. The present work looks to quantify the severity of fatigue in flywheels which re-establish grid inertia by applying fatigue design methods (such as the rainflow cycle counting method and the generalised strain amplitude methods of Ince and Glinka for fatigue lifing) to loading scenarios that represent grid frequency fluctuations. Importantly flywheels are sized based on different limit stress criteria, thereby enabling differing levels of structural capacity usage between designs. For the realistic design cycles considered in the present work (representative of a large scale grid undergoing normal frequency fluctuations) all projected lives are extremely large, suggesting that fatigue is not a limiting factor and that any of the tested design methodologies is viable. Significant improvements in energy density and cost per unit of energy stored may however be achieved if elastic–perfectly-plastic (Tresca based) design criteria are implemented over simple strictly elastic variants. Neglecting containment costs for simplicity, improvements in energy density of ≈74% and cost per unit of energy stored of ≈290% are demonstrated to be achievable.

Stress and fatigue analysis of the hydraulic motor shaft and conveyor joints of a tractor-mounted Chinese cabbage collector

Deflection and fatigue damage in a tractor-mounted Chinese cabbage collector might occur due to continuous operation. Therefore, the objective of this study is to predict the service life of the material used for the hydraulic motor shaft and conveyor joints based on stress and fatigue analysis. The torque produced by the motor was measured using the torque sensor for various tractor forward speeds and rotational speeds under unloaded and loaded conditions with three iterations. The relevant shear stress with the S – N curve on fatigue life was determined using the Smith – Watson – Topper equation and rain flow cycle counting method. Additionally, the severity level was investigated using Miner’s rule. Design variables of the shaft diameter and conveyor’s joints were incrementally increased by 0.02 m. The experimental results of deflection and shear stress of the components were found to be negligible. The result of fatigue lifecycles was also generated over 107. The maximum severity level of the motor shaft, conveyor joints 1 and 2 were 4.27 and 4.48, 4.26 and 5.58, and 4.12 and 4.46, respectively under unloaded and loaded conditions. When the values of design variable components were increased incrementally, shear stress and deflection decreased gradually but the fatigue life increased. Nevertheless, the results indicated that this machine could be safely used in the field.

Application of Spectral Method for Vibration-Induced High-Cycle Fatigue Evaluation of an High-Pressure Turbine Blade

Abstract A method of fluid–structure interaction coupling is implemented for a forced-response, vibration-induced fatigue life estimation of a high-pressure turbine blade. Two simulations approaches; a two-way (fully coupled) and one-way (uncoupled) methods are implemented to investigate the influence of fluid–solid coupling on a turbine blade structural response. The fatigue analysis is performed using the frequency domain spectral moments estimated from the response power spectral density (PSD) of the two simulation cases. The method is demonstrated in relation to the time-domain method of the rainflow cycle counting method with mean stress correction. Correspondingly, the mean stress and multi-axiality effects are also accounted for in the frequency domain spectral approach. In this case, a multiplication coefficient is derived based on the Morrow equation, while the case of multi-axiality is based on a criterion which reduces the triaxial stress state to an equivalent uniaxial stress using the critical plane assumption. The analyses show that while the vibration-induced stress histories of both simulation approaches are stationary, they violate the assumption of normality of the frequency domain approaches. The stress history profile of both processes can be described as platykurtic with the distributions having less mass near its mean and in the tail region, as compared to a Gaussian distribution with an equal standard deviation. The fully coupled method is right leaning with positive skewness while the uncoupled approach is left leaning with negative skewness. The directional orientation of the principal axes was also analyzed based on the Euler angle estimation. Although noticeable differences were found in the peak distribution of the normal stresses for both methods, the predicted Euler angle orientations were consistent in both cases, depicting a similar orientation of the critical plane during a crack initiation and propagation process. Finally, the fatigue life estimation was shown to be conservative in the fully coupled solution approach.

Application of the S-N Curve Mean Stress Correction Model in Terms of Fatigue Life Estimation for Random Torsional Loading for Selected Aluminum Alloys.

The paper presents the experimental fatigue test results for cyclic constant amplitude loading conditions for the case of the torsion of the PA4 (AW-6082-T6), PA6 (AW-2017A-T4) and PA7 (AW-2024-T3) aluminum alloy for a drilled diabolo type test specimen. The tests have been performed for the stress asymmetry ratios R = −1, R = −0.7, R = −0.5 and R = −0.3. The experimental results have been used in the process of a fatigue life estimation performed for a random generated narrowband stress signal with a zero and a non-zero global mean stress value. The calculations have been performed within the time domain with the use of the rainflow cycle counting method and the Palmgren−Miner damage hypothesis. The mean stress compensation has been performed with the S-N curve mean stress model proposed by Niesłony and Böhm. The model has been modified in terms of torsional loading conditions. In order to obtain an appropriate R = 0 ratio S-N curve fatigue strength amplitude, the Smith−Watson−Topper model was used and compared with literature fatigue strength amplitudes. The presented solution extends the use of the correction model in terms of the torsional loading condition in order to obtain new S-N curves for other R values on the basis of the R = −1 results. The work includes the computational results for new fatigue curves with and without the mean stress effect correction. The results of the computations show that the mean stress effect plays a major role in the fatigue life assessment of the tested aluminum alloys and that the method can be used to assess the fatigue life under random conditions.

Elastomeric Component Fatigue Analysis: Rubber Fatigue Prediction and Correlation Comparing Crack Initiation and Crack Growth Methodologies

<div class="section abstract"><div class="htmlview paragraph">Many elastomeric components in automotive industry applications are subjected to dynamic service loads. Fatigue must be a consideration in the design of these components.</div><div class="htmlview paragraph">The two approaches in rubber fatigue analysis discussed in this study are the conventional crack initiation approach, based on continuum mechanics parameters versus life, and the crack growth approach, based on fracture mechanics parameters. These methodologies are demonstrated for a passenger vehicle engine mount here. Temperature effects are not considered since testing was performed at ambient room temperature and with a low frequency, typically less than 5 Hz.</div><div class="htmlview paragraph">The promising methodology for fatigue life prediction, discussed in this paper, is a critical plane approach based on crack energy density. Rainflow cycle counting method and Miner’s damage rule are used for load cycle characterization and damage accumulation respectively. A fracture mechanics approach is implemented based on specimen crack growth data.</div><div class="htmlview paragraph">This methodology is validated with component testing under constant amplitude experiments. Results are investigated through analysis of critical stress locations hot spots, life values, and strain states. Comparative results are presented. Numerical results show reasonable correlation with experimental data.</div></div>

A computational model of wind turbine blade erosion induced by raindrop impact

This research focuses on developing a computational model for analysing wind turbine blade erosion induced by raindrop impact. A stochastic rain texture model is used to simulated realistic rain events determined by a rain intensity and a rain duration. A new smoothed particle hydrodynamic approach is implemented to study the influence of the raindrop size, impact speed, impact angle, and raindrop shape on the impact stress. In addition, a stress interpolation method is proposed to accurately and efficiently calculate the impact stress under a random rain event. The fatigue damage of the top coating material is evaluated under a rain event based on the rainflow cycle counting method and the Miner’s rule.

Multiaxial high-cycle fatigue life prediction under random spectrum loadings

A multiaxial fatigue life prediction model under general multiaxial random loadings is proposed in this paper. First, a brief review for existing multiaxial fatigue models is given with a special focus is on the Liu- Mahadevan critical plane concept, which can be applied to both brittle and ductile materials. Next, the new model development based on the Liu-Mahadevan critical plane concept for random loading is presented. The key concept is to use two-steps to identify the critical plane: identify the maximum damage plane due to normal stress and calculate the critical plane orientation with respect to the maximum damage plane due to normal stress. Multiaxial rain-flow cycle counting method with mean stress correction is used to estimate the damage on the critical plane. Equivalent stress transformation is proposed to convert the multiaxial random load spectrum to an equivalent constant amplitude spectrum. The equivalent stress is then used for fatigue life predictions. The proposed model is validated with both literature and in-house testing data generated using an Al 7075-T6 alloy under various random uniaxial and multiaxial spectrums. Comparison between experimental and predicted fatigue life lives shows good agreements; thus, demonstrating efficacy of the proposed model. Finally, concluding remarks and future work based on the results obtained are discussed.

A Micropitting Study Considering Rough Sliding and Mild Wear

Micropitting is a typical surface contact fatigue in rolling–sliding contact. The kinematic sliding is of great significance in the initiation and progression of micropitting. A numerical surface fatigue model considering rolling–sliding contact and surface evolution is developed based on mixed-EHL (elastohydrodynamic lubrication) theory, rainflow cycle counting method and Archard’s law. Surface evolution is evaluated using Archard’s wear law based on measured teeth surface topography. Surface damage is determined via the Palmgren–Miner line rule and Goodman diagrams. The effect of rolling speed and surface roughness are discussed in detail. Results show that stress micro-cycles are introduced by rough sliding in the rolling–sliding contact. The mild wear reduces the height of asperities, the maximum pressure and alleviates subsurface stress concentration. For rolling–sliding contact, the faster moving surface dominates the composite height of asperities, then decides the fluctuations of pressure, as well as stress ranges. The combination of surface topography should be considered in the surface design.

Effects of Damaged Fiber Ropes on the Performance of a Hybrid Taut-Wire Mooring System

Abstract In this study, effects of damage levels of fiber ropes on the performance of a hybrid taut-wire mooring system are investigated. The analysis is performed using a numerical floating production storage and offloading (FPSO) model with a hybrid mooring system installed in 3000 m of water depth. An in-depth study was conducted using the numerical model, the dynamic stiffness equation of damaged fiber ropes, the time-domain dynamic theory, the rainflow cycle counting method, and the linear damage accumulation rule of Palmgren-Miner. Results indicate that, in a mooring line with an increasing damage level, the maximum tension decreases, while the offset of the FPSO increases. Particularly, when a windward mooring line failure occurs, in addition to the significant increase in the offset of the FPSO, the maximum tension, tension range, and annual fatigue damage levels of the remaining lines adjacent to the failed also increase significantly. The present work can be of great benefit to the evaluation of the offset of the floating platform, the tension response, and the service life of the hybrid mooring systems.

Stochastic battery energy storage scheduling considering cell degradation and distributed energy resources

The penetration of distributed energy resources (DERs) greatly raises the risk of distribution network operation such as peak shaving and voltage stability. Battery energy storage (BES) has been widely accepted as the most potential application to cope with the challenge of high penetration of DERs. To cope with the uncertainties and variability of DERs, a stochastic BES scheduling model and its algorithm are proposed. The overall economy is achieved by fully considering the cell degradation, DERs, electricity purchasing, and active power losses. The rainflow algorithm-based cycle counting method is incorporated in the BES scheduling model to capture the cell degradation, greatly extending the expected BES lifetime and achieving a better economy. DER power scenarios are generated to consider the uncertainties and correlations based on the Copula theory. To solve the BES scheduling model, we propose a Lagrangian relaxation-based algorithm, which has a significantly reduced complexity with respect to the existing techniques. For this reason, the proposed algorithm enables much more scenarios incorporated in the BES scheduling model and better captures the DER uncertainties and correlations. Finally, numerical studies for the day-ahead BES scheduling in the IEEE 123-node test feeder are presented to demonstrate the merits of the proposed method. Results show that the actual BES life expectancy of the proposed model has increased to 4.89 times compared with the traditional ones. The problems caused by DERs are greatly alleviated by fully capturing the uncertainties and correlations with the proposed method.

Comparative Study of Ramp-Rate Control Algorithms for PV with Energy Storage Systems

The high variability of solar irradiance, originated by moving clouds, causes fluctuations in Photovoltaic (PV) power generation, and can negatively impact the grid stability. For this reason, grid codes have incorporated ramp-rate limitations for the injected PV power. Energy Storage Systems (ESS) coordinated by ramp-rate (RR) control algorithms are often applied for mitigating these power fluctuations to the grid. These algorithms generate a power reference to the ESS that opposes the PV fluctuations, reducing them to an acceptable value. Despite their common use, few performance comparisons between the different methods have been presented, especially from a battery status perspective. This is highly important, as different smoothing methods may require the battery to operate at different regimes (i.e., number of cycles and cycles deepness), which directly relates to the battery lifetime performance. This paper intends to fill this gap by analyzing the different methods under the same irradiance profile, and evaluating their capability to limit the RR and maintain the battery State of Charge (SOC) at the end of the day. Moreover, an analysis into the ESS capacity requirements for each of the methods is quantified. Finally, an analysis of the battery cycles and its deepness is performed based on the well-established rainflow cycle counting method.

Multiaxial high-cycle fatigue modelling for random loading

In this paper, a multiaxial fatigue life prediction model is proposed under general multiaxial random loadings. First, a brief review for existing multiaxial fatigue models is given and special focus is on the LiuMahadevan critical plane concept, which can be applied to both brittle and ductile materials. Next, new model development based on the Liu-Mahadevan critical plane concept for random loading is presented. The key concept is to use two-steps to identify the critical plane: identify the maximum damage plane due to normal stress and calculate the critical plane orientation with respect to the maximum damage plane due to normal stress. Multiaxial rain-flow cycle counting method with mean stress correction is used to estimate the damage on the critical plane. Equivalent stress transformation is proposed to convert the multiaxial random load spectrum to an equivalent constant amplitude spectrum. The equivalent stress is used for fatigue life prediction. Following this, experimental design and testing is performed for Al 7075-T6 under various different random uniaxial and multiaxial spectrums. The developed model is validated with both literature and in-house testing data. Very good agreement is observed for the investigated material. Finally, conclusion and future work is given based on the proposed study.

Fatigue damage mitigation of offshore wind turbines under real wind and wave conditions

Offshore wind turbines (OWTs) subjected to combined wind and wave loadings experience excessive vibrations which will increase fatigue loadings on the structure and reduce the fatigue life. In this paper, a three-dimensional pendulum tuned mass damper (3d-PTMD) is attached to the OWT to mitigate the bi-directional vibrations resulting from wind-wave misalignment so as to increase the fatigue life. An analytical model of the offshore wind turbine coupled with the 3d-PTMD is established using the Euler-Lagrangian equation. To predict long-term metocean condition, a statistical analysis for different properties of wind and wave loading such as, wind-wave misalignment, significant wave height and wind velocity is carried out. The aerodynamic wind loading is calculated using the blade element method and the wave loading is computed using the JONSWAP wave spectrum and Morison equation. Dual linear tuned mass dampers (TMDs) deployed in the side-side and fore-aft directions are used for comparison. The NREL monopile 5 MW baseline wind turbine is used to examine the performance of 3d-PTMD in a realistic metocean condition. The fatigue damage is estimated based on the rain-flow cycle counting method and Miner’s rule. Results indicate that the 3d-PTMD can increase the wind turbine tower fatigue life by more than 50% in comparison with the dual TMDs.

Load sequence effects and variable amplitude fatigue of superelastic NiTi

Fatigue behavior of superelastic NiTi alloys under variable amplitude loading is experimentally studied and two energy-based fatigue models were used to analyze the fatigue behavior. Cyclic tests were conducted in strain-controlled condition. Load sequence effects are studied by performing fatigue testing under load paths consisting of two steps of constant amplitude loading. Both low-high (LH) and high-low (HL) load paths were considered in experimentations. Variable amplitude load paths were also generated at a constant strain rate using random values, which resulted in reversals of different strain amplitudes and mean strains. Analysis of the fatigue results was carried out using two energy-based fatigue models that have been shown to appropriately account for the effects of mean strain and stress. The energy-based total-fatigue-toughness parameter, ∑Wt, together with the Rainflow cycle counting method provided satisfactory fatigue life predictions for this alloy. Based on this combination of the fatigue parameter and cycle counting technique, the predicted fatigue lives fall within prediction bands of 2.5 for all the different variable amplitude loading paths.

An integrated methodology for fatigue life prediction of carbon fiber-reinforced polymer matrix composites under constant and variable R-ratio loadings

The progress in the anisomorphic constant fatigue life (CFL) diagram approach for efficiently identifying the fatigue of carbon fiber-reinforced composites under constant waveform loading over the whole range of mean stress is reviewed. The asset of this approach is the concept of critical stress ratio. The anisomorphic formulation of CFL diagram is flexible enough not only to increase the number of segments to accommodate the transient change in sensitivity to mean stress, but also to take a generalized form that considers the effect of temperature as well as the effect of variability in fatigue life. The anisomorphic approach is shown to succeed in describing the asymmetric and nonlinear CFL diagrams for carbon fiber composites of different kinds. It is suggested that the classic procedure for prediction of spectrum loading fatigue life of composites using the Miner rule with the rain flow cycle counting method is powered by integrating with the anisomorphic CFL diagram approach.

Failure analysis of crankshafts used in maritime V12 diesel engines

Abstract Maintenance of equipment requires constant monitoring of the components that constitute a mechanical system, as well as the monitoring of the conditions of service, among others. One first indication of failure in a crankshaft is given by the low-pressure value of the lubrication circuit. This is mainly due to the accumulation of debris in the lubrication channels, which causes the oil filters to be clogged. As such, this will cause poor lubrication of the crankshaft, which can consequently cause its catastrophic failure, and frequently originates damage propagation to other components of the engine, namely crankcase, bearing shells, connecting rods, pistons and other mechanical parts. In the 4-stroke internal combustion maritime V12 diesel engine herein studied, there has been a frequent failure of crankshafts. The seven cases of failure of the crankshafts reported in the last 25 years are presented in the paper and several causes of failure were listed. From those, the influence of initial imperfections in the material was discussed in the article, as well as the influence of the loadings applied to the crankshaft. Hence, the theoretical dimensioning of the crankshaft was firstly assessed assuming the conservative Soderberg criterion and the crankshaft model was then analysed using the Finite Element Method, during a complete combustion cycle, at several stress concentration regions. The Rainflow cycle counting method was applied to determine the stress cycles induced during functioning and a stress-life equation was then used to estimate the fatigue lifespan of the crankshaft. Additionally, a modification to the crankshaft's geometry was suggested and a significant reduction of the induced stresses was obtained.

Variable amplitude fatigue behavior of neat and short glass fiber reinforced thermoplastics

Variable amplitude fatigue behavior of injection molded thermoplastics was investigated. A neat thermoplastic (polypropylene impact co-polymer) and a thermoplastic composite made of polybutylene terephthalate (PBT) with 30wt% short glass fibers were used for the experimental study. Fatigue tests were conducted on both un-notched and notched specimens using plate-type specimens. For the notched specimens, a circular hole was drilled in the center of the specimens. Two-step loading (high-low and low-high) tests at two cycle ratios of 0.2 and 0.5 and stress ratios of R=0.1 and −1 were conducted to investigate load sequence and mean stress effects, as well as the accuracy of linear damage rule. Periodic overload and service load history tests were also conducted to investigate the effect of overloads, cycling frequency, small stress cycles, and maximum stress level. A strengthening effect of increased frequency was observed for both materials and the effect of small stress cycles was found to be negligible. A general fatigue damage model along with the rainflow cycle counting method and linear damage rule were used for life predictions of variable amplitude service load history tests. More than 89% of the life predictions based on the modeling procedure used were within a factor of 3 of the experimental lives for both materials.