Rainflow Counting Research Articles

On load assumptions for self-propelled forage harvesters

This article describes investigations into the subject of load assumptions on a self-propelled forage harvester. A measurement campaign during the maize harvest in hilly regions in Germany and the corresponding evaluations are presented. The investigations analyse both the usage profile of the machine and the load data for the chassis. The used sensors enable the acquisition of wheel forces and moments as well as the identification of different driving states. The wheel loads at the front axle are calculated to an auxiliary quantity (dimension of stress at the axle) for a summarised comparison of different load conditions. The stress signal is counted by a rainflow algorithm to implement a damage calculation. In addition to the known rainflow counting, information on the temporal reference of the hystereses within the load-time sequence is detected to assign damage values to defined driving states. The calculated damage values serve as relative comparison criteria for the different driving states.

Fatigue Life Prediction of a Pump Turbine Runner

The working environment of the runner of a hydro-turbine unit is complex, and it is subjected to relatively large and variable water pressure. Fatigue cracks may occur after a long period of work, and even cause the runner to lose its working ability. The fatigue crack problem of hydraulic turbines should be paid attention to. This paper introduces the nominal stress method which is often used to analyse the fatigue life of a hydraulic turbine unit. Modelling and numerical calculation are carried out for a pump turbine unit. Stress concentration points and load spectra are calculated for different working conditions of the turbine. The load spectra are processed by rain flow counting method. The fatigue life of the runner under different working conditions is carried out by Miner criterion. The results show that the fatigue life of the unit tends to be infinite under steady working conditions, and the fatigue life under variable working conditions is far less than that under steady working conditions. Therefore, from the point of view of fatigue life, the working process under variable working conditions should be minimized to improve the service life of the unit.

Big Data Fast Analysis Method of Random Stress Spectrum for Crane Equipment

With the increase of service time, the random stress spectrum of crane equipment causes cumulative damage. Cumulative damage induced crack initiation is one of the important failure modes of crane equipment. Through the rapid analysis of the random stress spectrum obtained in real time by the structural health monitoring system of lifting equipment, the cumulative damage of the structure can be analyzed and the remaining life of the structure can be predicted. In this paper, based on the traditional rain flow counting method, the big data fast analysis method of random stress spectrum is studied by adopting stack data structure. The program of fast rain flow counting method based on stack structure with two parameters is compiled. The fast rain flow counting method based on stack structure is used to analyze and calculate the big data of stress monitoring collected by the structural health monitoring system of metallurgical crane, and the stress amplitude-mean-frequency matrix of the hot spot area of fatigue damage of the main girder is obtained, which lays an important foundation for the health status diagnosis of metallurgical crane equipment.

A frequency-time domain method for ship fatigue damage assessment

Ships in ocean waves are suffered from cyclic wave loads which can cause fatigue damage to ship structures. Classification societies require owners to carry out fatigue assessment for ship structure for its potential great loss caused by fatigue failure. Currently there are many fatigue assessment methods including simplified method, deterministic method, spectral-based method and time domain method. But none of them predict fatigue life precisely and effectively. Based on linear superposition theory and the assumption that a linear relationship occurred between waves and ship structural response, some scholars proposed the hybrid frequency-time domain method. This method avoids the imprecise narrow band approximation in spectral-based method and adopts rainflow counting instead. However, the hybrid method is not applied extensively on ship fatigue assessment because relevant research is insufficient. In this paper, aiming to validate the hybrid method, a segmented ship model test is carried out, and the short-term fatigue damages of a 4600TEU container forecasted by hybrid method and traditional methods are compared. Results shows that the hybrid method forecasts the closest fatigue damage prediction to time domain analysis and owns enough efficiency. But in some area located at midship, hybrid method may predict lower fatigue damage than time domain method.

Dynamic analysis of elliptical vibrating screen based on disc motor

ABSTRACT According to the requirements of the current drilling fluid vibrating screen for high efficiency, high reliability and low energy consumption, an elliptical vibrating screen based on disk motor is proposed. The dynamic analysis model of the vibrating screen of the three-excited motor is established, and the dynamic characteristics of the whole system and key structures are studied by multi-body dynamics and finite element method. The dynamic stress response characteristics of the rigid flexible coupling system of screen box are mainly analysed. Based on the deformation and stress of the flexible body damage node analysis results, through the fatigue cumulative damage theory and rain-flow counting method against casing load surface fatigue life prediction, verifying the reliability of fatigue life of screen box. The result shows that: Three Eccentric Rotors elliptical vibrating screen can achieve balanced elliptical vibration track, meeting the requirements of high stable amplitude vibration, and its natural frequency, structural strength and fatigue life all meet the engineering requirements, verifying the feasibility and effectiveness of the design scheme.

APPLICATION OF RAINFLOW TECHNIQUES TO THE DESIGN AND OPERATION OF PORT INFRASTRUCTURE

The concept of rainflow comes from the fatigue damage field where it has demonstrated its appropriateness (see Johannesson, 1999). In port engineering, rainflow counting has shown some serious advantages over traditional methods such as the zero-downcrossing method but it is not widely used. This work aims at showing some applications of this technique to problems detected in port operation and reliability after briefly introducing the concept.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/_gwjsDd3yiE

Multiaxial stress mapping and fatigue failure prediction of aircraft hydraulic pipes

Frequent fatigue failures of aircraft hydraulic pipes were caused by a stress concentration site in the form of a circumferential groove at the constrained pipe ends. The grooves were formed as a result of the crimping of a metallic sleeve on the pipes. Internal hydraulic pressure fluctuations during aircraft flight resulted in multiaxial and alternating stresses at the constrained (fractured) end. The complete stress state was found using FEM ‘Frame 3D’ MATLAB® code and analytical stress concentration factors. The calculated stresses not only mapped well with the fractured patterns of a failed pipe but also correlated to the computational stress analysis performed separately in an FEA software. The stress calculations were further utilised for fatigue life estimation of the pipe with and without the presence of circumferential groove. The load spectrum of the pipe was developed using 73 flying hours data of hydraulic fluctuations and converting those into stresses. Various stress amplitudes and load ratios were segregated from the cyclic stresses using the rainflow counting method. A linear constant lifeline diagram and Miner’s rule of damage accumulation were used for fatigue life estimation. A significant decrease (from 12,500 to 165 flying hours) in the service life of the pipe was predicted due to the presence of the stress concentration. The predictions matched well with the observed failure trend (life) of the pipe.

Study on the economic benefits of retired electric vehicle batteries participating in the electricity markets

The lithium-ion batteries of battery electric vehicles are generally replaced when their capacity decays below 80% of the rated capacity. In this way, a large number of retired electric vehicle batteries (REVB) will be produced in a short time and cause new environmental pollution if REVB are not treated properly. To address this problem, one of the major solutions is to realize the echelon utilization of REVB based on the requirements of different application scenarios. Therefore, this study investigates the economic benefits of REVB participating in different Danish electricity markets. The objective function maximizes the profit in the different markets with considering REVB life loss cost in the operational process. Rainflow counting method is employed to accurately estimate the REVB life loss cost, leading to a strong nonlinearity of the optimization problem. Afterward, simulated annealing based particle swarm optimization (SAPSO) method is used to solve the nonlinear problem and find the optimal operational strategies of the REVB. Finally, a case study with considering different situations is provided to analyze the economic benefits of applying REVB in different markets. The results reveal: 1) SAPSO method performs best in finding the optimal results compared with particle swarm optimization and simulated annealing methods, and 2) It is more likely and beneficial to invest in REVB to participate in the regulation market than the day-ahead market. This significance of the study can be summarized as: 1) Theoretically, apart from proposing a simple, cheap and eco-friendly green strategy, i.e., the echelon utilization of REVB in Danish electricity market, we advance the knowledge and call for attention about under which conditions that performing a green strategy can allow environmental-economic benefits simultaneously achievable. 2) The study provides new business opportunities for energy storage and new energy industries, and can help to realize sustainable development to improve people’s life and environmental quality.

Truck Platooning to Minimize Load-Induced Fatigue in Steel Girder Bridges

Truck platooning has been demonstrated to possess several advantages in relation to energy savings. To implement this technology in the future, a better understanding of the effects of truck platooning on bridges is needed in relation to safety, serviceability, and remaining service life. This research aims at investigating the effects of truck platooning on the fatigue of steel girder bridges. Different types of platoons are simulated in line girder analysis for simple spans and two-equal continuous spans bridges. Then the rainflow counting method is applied to obtain the stress ranges and cycles. Miner’s rule is used to quantify the fatigue damage. The fatigue damage of different platoons is normalized by American Association of State Highway Transportation Officials Load and Resistance Factor Design Fatigue Load for comparison. The effects of the number of trucks and gap distances of truck platoons are further investigated. In some cases, truck platooning helps decrease the fatigue damage since, although truck platooning brings higher load effects, it also decreases the number of cycles. For platoons with different truck wheelbases, there are specific span to wheelbase ratios, beyond which fatigue damage decreases as gap distance increases. In addition, depending on the platoon configurations, there are ranges of span lengths where it is more beneficial to travel as truck platoons rather than traveling individually in relation to fatigue damage.

Surrogate Models for Wind Turbine Electrical Power and Fatigue Loads in Wind Farm

Fatigue damage of turbine components is typically computed by running a rain-flow counting algorithm on the load signals of the components. This process is not linear and time consuming, thus, it is non-trivial for an application of wind farm control design and optimisation. To compensate this limitation, this paper will develop and compare different types of surrogate models that can predict the short term damage equivalent loads and electrical power of wind turbines, with respect to various wind conditions and down regulation set-points, in a wind farm. More specifically, Linear Regression, Artificial Neural Network and Gaussian Process Regression are the types of the developed surrogate models in this work. The results showed that Gaussian Process Regression outperforms the other types of surrogate models and can effectively estimate the aforementioned target variables.

Cumulative Damage Modeling of Fuel Cell Membranes

The strongly varying humid environment under which fuel cell membranes operate introduces detrimental mechanical stresses that inflict damage to the membrane1. The damage incurred by the membrane during each humidity cycle when accumulated over time may lead the membrane to fatigue failure. The residual fatigue life of the membrane is determined here by using a cumulative-damage model2. A time-temperature-humidity dependent constitutive model and a multi-physics fuel cell finite element model are first developed to characterize the material properties and estimate the coupled mechano-hygral-thermal stress field in the membrane. Using this multi-level modeling approach, and with the aid of experimentally obtained fatigue data, fail-safe regions (see Figure) are identified for the case of accelerated stress test loading. For general loads simulating fuel cell operation, the distribution of stress-reversals is calculated for the load history using rain-flow counting algorithm. The regions of membrane that are more susceptible to fatigue damage are identified. It is also found that high amplitude stress cycles with low occurrence percentage are more detrimental than high occurrence low-amplitude cycles.This work was supported by Natural Sciences and Engineering Research Council of Canada, Simon Fraser University Community Trust Endowment Fund, Canada Research Chairs, Mitacs through the Mitacs Accelerate program, and Ballard Power Systems. 1 Borup, R., et al., Scientific aspects of polymer electrolyte fuel cell durability and degradation. Chemical Reviews, 2007. 107(10): p. 3904-3951. 2 Fatemi, A. and L. Yang, Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. International Journal of Fatigue, 1998. 20(1): p. 9-34. Figure 1

Impact Characteristics and Fatigue Life Analysis of Multi-Wire Recoil Spring for Guns

Recoil spring is a key part in automatic or semi-automatic weapons re-entry mechanism. Because the stranded wire helical spring (SWHS) has longer fatigue life than an ordinary single-wire cylindrically helical spring, it is often used as a recoil spring in various weapons. Due to the lack of in-depth research on the dynamic characteristics of the current multi-wire recoil spring in recoil and re-entry processes, the fatigue life analysis of the current multi-wire recoil spring usually only considers uniform loading and does not consider dynamic impact loads, which cannot meet modern design requirements. Therefore, this paper proposes a research method for fatigue life prediction analysis of multi-wire recoil spring. Firstly, based on the secondary development of UG, a three-wire recoil spring parameterized model for a gun is established. Secondly, ABAQUS is used to carry out a finite element analysis of its dynamic response characteristics under impact, and experimental verification is performed. Then, based on the stress-time history curve of the dangerous position obtained by finite element analysis, the rain flow counting method is used to obtain the fatigue stress spectrum of recoil spring. Finally, according to the Miner fatigue cumulative damage theory, the fatigue life prediction of the recoil spring based on the S-N curve of the material is compared with experimental results. The research results show that the recoil spring has obvious transient characteristics during the impact of the bolt carrier. The impact velocity is far greater than the propagation speed of the stress wave in the recoil spring, which easily causes the spring coils to squeeze each other. The maximum stress occurs at the fixed end of the spring. And the mean fatigue curve (50% survival rate) is used to predict the life of the recoil spring. The calculation result is 8.6% different from the experiment value, which proves that the method has certain reliability.

Research on Bench Fatigue test method of frame under torsion condition

In order to predict the fatigue life of frame, a new bench test method of the frame torsion fatigue is proposed, which can approximately reflect the results of enhanced road test. The frame finite element model was established and the simulation was carried out to determine the dangerous position of fatigue life failure. The load spectrum of the fatigue dangerous position was collected, and the fatigue damage value was analyzed by the rain-flow counting method and Miner criterion. The equivalent conversion relationship of the fatigue life between bench test and road test was established. The mean error between theoretical calculation result and bench test result is 5.2 %; The mean error between theoretical calculation result and road test result is 3.85 %. The results showed that the bench test method of frame torsion fatigue can improve the precision and reliability of the frame fatigue life prediction.

Modelling of load spectra containing clusters of less probable load cycles

When the load is stochastic and the service life is a consequence of the fatigue process, the loading histories are transferred into load spectra using rainflow counting. Once the empirical densities of load cycles are known, their probability density is estimated. Here, different probability density mixtures and algorithms for their estimation have been compared according to their ability to model rainflow matrices. The estimated probability density should also consider loading cycles with a small probability. The main scientific contribution of this article is that procedures were identified, which enable more thorough consideration of those clusters with less probable load cycles.

Simulation of Random Processes in the Fatigue Problem under Variable Loading

The method is proposed to generate random processes with stable integral characteristics of cumulative distributions, which at the same time are random in nature. The algorithm consists of the two steps. The first one is generation of the random extrema sequence using the objective Markovian matrix, completed with in-service loading data. The extrema and their sequence are shown to be of importance for the metal fatigue assessment. Therefore, random testing with extrema control is more advantageous as compared to testing with the generation of spectral densities. The next step is the random process generation with its first continuous derivative. The concatenation procedure was proposed to create the continuous function reconstruction with the pointwise specification (local maxima and minima sequence). The regression analysis of two random variables was used to evaluate the frequency component. Spectral analysis of such a continuous process results in the spectral density function, which finds its application in some methods of random fatigue estimation. The major trait of the proposed method is the coincidence of the rain-flow cycle counting characteristics of the initial and resulting processes.

A parametric study on fatigue life of plate girder railway bridge with varying velocity of rolling stock

It is important to measure the fatigue life of a structure as it helps in finding the probable life of a structure before its failure. It also helps in making cost effective decision on existing structure regarding replacement or rehabilitation in time. In this study deterministic approach is used for the estimation of fatigue life of a plate girder railway bridge. Finite element analysis is carried out using software to find the critical region of fatigue failure and the stress developed there. Number of cycles of different stress range during the movement of train is evaluated with the help of S-N curve. The S-N curve is selected based on type of welds and type of stress considered. Rain flow counting method is used for evaluating the number of cycles corresponding to each stress range. The fatigue damage is then evaluated by using Palm Miner damage accumulation rule and corresponding fatigue life is evaluated. The fatigue life corresponding to different velocity of train ranging from 30 kmph to 140 kmph is generated similarly and compared to find the influence of velocity of moving load on fatigue life of structure.

Fatigue Crack Growth Prediction under Spectrum Load in an Aluminium Alloy using Crack Driving Force K*eff Approach

Fatigue Crack Growth (FCG) behaviour in a Single-Edge-Notched Tension (SENT) specimen of 2024-T3 aluminium alloy under a standard mini-FALSTAFF spectrum load sequence was experimentally determined. Further, the FCG behaviour was predicted using cycle-by-cycle method and compared with experimental results. Prediction procedure involved are rain-flow counting of fatigue load cycles, estimation of crack driving force for each of the counted cycle and prediction of crack extension per cycle from constant amplitude crack growth rate equation. In the present work, a new crack driving force (CDF) K*eff involving Kujawski’s crack driving force K* in conjunction with Elber’s crack closure concept was used to account for load interaction effects. FCG prediction was also made using conventional CDF ΔKeff (Elber’s) approach. A good correlation was observed between experimental and predicted FCG behaviour under spectrum loads by the proposed K*eff approach. Also, this prediction was observed to be better than that predicted by conventional ΔKeff approach.

How to Experimentally Monitor the Fatigue Behaviour of Vibrating Mechanical Systems?

Fatigue damage and, in general, fatigue behaviour is not simple to observe or estimate during the operational life of a generic vibrating mechanical system. There are a lot of theoretical or numerical methods that allow to evaluate it or by knowing a priori the loading conditions and obtaining output stress states by adopting numerical models of the mechanical system or by directly experimentally measuring and acquiring stress/strain states. A few examples of instruments (e.g. rain flow recorders) or measurement chains dedicated to estimate it in time domain or frequency domain are found in the literature but none that fully both observes the system dynamic behaviour and estimates the related actualized cumulated damage, and, thus, none that can estimate the residual life of the system itself. In this paper, a simple time-domain method, designed to monitor the instantaneous fatigue behaviour by definition of the instantaneous and cumulated potential damage or of equivalent damage signal amplitude is presented, based on rain-flow counting method and a damage linear cumulation law and starting from system dynamics signals. This methodology was designed to overestimate real damage to alert the system manager before any crack starts and to be simply translated into electronic boards that can be mounted on generic mechanical systems and linked to one of the sensors that usually monitor system functionality. Keywords: fatigue; damage; rain flow counting; random loads

Experimental study on the fatigue damage of designed T-type specimen with high-low frequency superimposed loading

The nonlinear synthetic bending moment caused by springing and whipping can be simplified as the superposition of high-frequency load components and low-frequency load components. In order to investigate the influence of this high-low frequency superimposed loading on the fatigue performance of hull structure, the high-low frequency superimposed fatigue tests under different frequency ratios, amplitude ratios and mean stresses were carried out for the time domain response characteristics of nonlinear vertical bending moments in the wave load model test of River-Sea-Going-Ship. Combined with the rain-flow counting method and Goodman correction method, the cumulative damage of small loads under fatigue limit and the effect of high-low frequency coupling damage on the fatigue life were analyzed, a fatigue life prediction model suitable for high-low frequency superimposed loading was proposed. The analysis results show that the high-frequency, small-amplitude loads have a significant impact on the fatigue life of the structure. The threshold that the high-low frequency coupling damage causes the reduction of fatigue life is closely related to the combined effects of the amplitude ratio and the frequency ratio.

RETRACTED: Fatigue reliability assessment for hangers of a special-shaped CFST arch bridge

Abstract The main bridge of the Yingzhou Bridge is a special -shaped concrete-filled steel tubular (CFST) arch bridge. As a key load-carrying member, the safety of a hanger affects the service life of arch bridges. This paper presents a comprehensive frame work for fatigue reliability analysis of hangers in CFST arch bridges. A simplified finite element (FE) model is established to satisfy the fatigue analysis accuracy. The mathematical model for traffic flow of the Yingzhou Bridge is simulated using the Monte Carlo method. Then the stress time history of the hanger is calculated. The rain flow counting method is used to obtain the stress range values and the number of cycles. Based on the Miner cumulative damage rule, considering the effect of mean stress, the fatigue reliability for hangers with and without corrosion is calculated using the Monte Carlo Importance Sampling method. It is found that the reliability index of inclined hangers is lower than that of vertical hangers. Inclined hangers have a higher probability of failure earlier. The reliability index of the inclined hanger X3 in the position where the stiffness changes is the lowest, which should be paid greater attention to in daily maintenance. The reliability index of hangers with corrosion is significantly lower than that of hangers without corrosion, and the decline rate of the reliability index is increased with time.