Rainflow Counting Technique Research Articles

A double load spectrum extrapolation for drill pipe of rotary drilling rig considering load sequence

The load spectrum of rotary drilling rig’s drill pipe is used for drill pipe design, simulated fatigue testing, and reliability assessment. However, the proper extrapolation of the drill pipe double load is challenging, especially to meet the requirements of both load sequence and load strengthening. In this paper, an extrapolation technique for a double load of drill pipe is proposed. The time sequence rainflow counting technique is proposed to keep the torque and pressure sequence. Meanwhile, the individual distributions of the loads are accurately estimated. Finally, the torque and pressure are simulated and extrapolated by the percentile extrapolation method. The results show that the proposed extrapolation method for maintaining the load sequence enriches the dynamics and diversity of the loads while ensuring the load sequence.

Spatial wind speed interpolation using Isoparametric shape functions for structural loading

This study developed a spatial interpolation technique using Isoparametric finite element shape functions to derive wind speed records for all unsampled Kansas counties from actual data recorded at 17 city locations within and around Kansas. A computational method using the Kaimal spectrum is presented for generating artificial time histories of wind speeds. This is done to extract wind-cycle distribution using the Rainflow counting technique, which can be used as input for fatigue analysis procedures of highway sign structures. Comprehensive validation, verification and benchmarking has been performed in this paper at all spatial and time span levels to guarantee the accuracy and efficiency of the algorithm developed. The comparison of the validation measures strongly suggests a very accurate interpolation scheme that can be confidently used in further fatigue computations and analysis. A user-friendly software was designed using C# to extract wind-speed cycles for all Kansas counties related to different time spans. This software is expected to facilitate fatigue-life prediction because it generates a full range of wind-loading.

The influence of wellhead stick-up on the analysis of critical stress points on conductor casing

During the subsea well construction and workover, a subsea well is connected to the drillship through the blowout preventer (BOP) and the drilling riser. Environmental loads acting on the drilling riser and the drillship are transferred to the wellhead, conductor, and casings, which can cause fatigue issues at critical points such as at the casing couplings. The main function of a subsea wellhead system is to perform the interface between the BOP and the well, ensuring its integrity throughout its operational life. Factors such as the increase in the weight and height of the BOP on 6th generation platforms contributed to the increased risk of failure due to fatigue. The system in this work is represented by a 3D finite element model including internal cement, conductor, and surface casings. Although simplifications were adopted in the modeling, the essence of the well physical behavior remains. The work addresses the influence of the wellhead stick-up on the maximum stress in the conductor below the seabed, comparing analyses of two wellhead stick-up and including horizontal displacement resulting from the integration of the platform/riser dynamics. These horizontal loads are transferred to the top of the wellhead system as a bending moment and shear force. A time series containing riser horizontal loadings is utilized to obtain the von Mises stress. This information is used to count cycles with the rainflow counting technique. The number of cycles resulting for the two wellhead stick-up is compared and demonstrates how wellhead stick-up can be influenced by an increase in dynamic loads acting on the wellhead top. An influence can be observed on the maximum stress point of the conductor located below the seabed. From these results, it was possible to conclude the wellhead stick-up can influence the depth of a critical point in the conductor below the seabed.

Intelligent approach for accurately predicting fatigue damage in overhead highway sign structures

Full-span overhead sign support structures can be found along any major highway across the US. Such structures experience different wind loading scenarios varying with time. As a result, these structures start to build up fatigue cracks within their members near the end of their fatigue life. Due to economic realities, the needed routine fatigue inspections on such highway structures can not be performed regularly. This paper is intended to present a comprehensive tool to accurately predict the remaining fatigue life of full-span overhead highway sign support structures subjected to a long and sustained wind fluctuation. Synthetic wind time histories were developed by superimposing cosine waves over a range of frequencies of 3–300 Hz and randomly generated phase angles. Kaimal spectrum was utilized to build a database of wind time histories for each daily mean wind speed along a period of 45 years in the State of Kansas. Moreover, each wind time history was modified to capture both the mean speed and high speed in each given day. After that, the wind speed vs. the number of cycle relationship, for a given time span, was extracted from the synthetic wind time history using the Rain Flow counting technique. Fatigue evaluations were conducted using axial truss member stresses extracted from a finite element solution corresponding to each wind speed in any given time range. Potential fatigue failure was assessed for each structural member after amplifying the stress range using an average dynamic amplification factor generated by integrating the frequency-response curve of harmonic excitations. These assessments evaluate the ratio of consumed fatigue cycles to ultimate fatigue cycles using Miner’s rule to estimate the fatigue life. A computationally affordable simulation package was developed to carry out the generation of wind time histories, cycle counting, structural modeling, and fatigue life calculations. This package was used to evaluate the fatigue life of a non-cantilever sign structure in Wichita, Kansas. The software predicted the end-of fatigue life of two members in this structure. Accordingly, inspections of these two members revealed the existence of unnoticed severe fatigue cracks while other members did not show any sign of distress.

Prevention of low-cycle fatigue damage using adaptive control approach and magnetorheological dampers

Studies conducted after Northridge and Kobe earthquakes have shown that brittle failures in connections and members of structures led to extensive and catastrophic damage. Consequently, evaluation of critical points in a structure, controlling, and mitigating the seismic responses of structures, and avoiding structural damage such as low-cycle fatigue are needed. In this study, an adaptive control algorithm is used to reduce the low-cycle fatigue damage in two benchmark structures equipped with MR dampers. First, optimum parameters of the adaptive control method, called the Simple Adaptive Control Method (SACM), are calculated. The effectiveness of using SACM to mitigate the structural response of a three-story benchmark structure and a twenty-story benchmark structure under earthquake is studied. Finally, reducing fatigue damage on those structures subjected to various earthquakes is examined to extend the fatigue life of the structures.To calculate the cumulative fatigue, the rain-flow counting technique is used. In order to validate the developed nonlinear models, natural frequencies and displacement response of a three-story structure subjected to three different earthquakes are compared with the values presented in the reference studies. A numerical search method is used to minimize the ratio of cumulative fatigue and maximum ratio of roof displacement in each structure. The results show that the adaptive control system can reduce fatigue damage in elements, and fatigue life could be extended in structures. Also, the effects of using the semi-active adaptive control approach on dynamic characteristics of a structure are studied.

Noise limits on ITER plasma vertical stabilization system imposed by tungsten divertor monoblock thermal fatigue

Abstract Tokamak plasmas with vertically elongated cross-sections are unstable due to vertical displacements. Feedback stabilization of the ITER plasma current centre will be performed using the speed of its vertical displacements, dZ/dt, as input. Inevitable noise in the diagnostic signal for dZ/dt leads to “noisy” components in the feedback voltage and current in the stabilizing coils. This leads to noisy components in the vertical position of the plasma current centre and the divertor strike points. For burning plasma conditions on ITER, these strike point displacements may be a concern for thermal fatigue at the water cooling interface of the tungsten monoblocks constituting the divertor targets. A study is presented here in which this concern is examined for the first time. The baseline 15 MA scenario (fusion power of 500 MW with a 500 s flattop and fusion power gain, QDT = 10) is simulated with the DINA code, assuming low frequency noise in the dZ/dt diagnostic signal. The noise has uniform spectrum with a given root mean square (RMS) value ( =0.6 ms−1 or 0.2 ms−1) in the frequency band (0, 1 kHz). The results of these DINA simulations are combined with dissipative divertor plasma solutions obtained with the SOLPS-ITER plasma boundary code to provide a time dependent divertor target heat flux density profile. The latter is then imposed on a finite element model of the target monoblocks to assess the temporal evolution of the 3D temperature field in the block, including the Cu-W and Cu-CuCrZr joints at the cooling interface. These joints represent the points of the Cu and CuCrZr materials that see the largest temperature changes and are thus at greatest risk of failure. To evaluate an acceptance criterion on the non-cyclic and non-uniform thermal loads at the joints, an approach is developed which combines a Rainflow counting technique with Palmgren-Miner’s rule for fatigue accumulation. Analysis of the temperature evolution at the Cu-W joint shows that the RMS value of noise ∼0.6 ms−1 is unacceptable from the point of view of thermal fatigue for the expected total exposure time under burning plasma conditions that the first ITER divertor must survive. The lower value ( ∼0.2 ms−1) is found to be acceptable. A subsequent parametric study concludes that ≲ 0.44 ms−1 is just consistent with fatigue lifetime for the prescribed divertor power flux density profile, but should be kept lower than this to allow for some margin. Regarding the monoblock surface temperature, the natural power spreading caused by the separatrix movements is found to be beneficial from the point of view of recrystallization. For the level of noise in the dZ/dt diagnostic required to stay below joint fatigue limits, the average surface temperature on the most loaded monoblocks is reduced by ∼100 °C compared to the case with stationary strike points and the amount of time spent at this temperature at any one block by over 80 %.

Numerical study of fatigue damage under random loading using rainflow cycle counting

PurposeThe purpose of this scientific work is to simulate the fatigue damage under random loading taking into account the mean stress effect on fatigue lifetime and using the rainflow counting technique to assess the fatigue damage.Design/methodology/approachThe study of fatigue under random loading is based on same concepts which as constant loading with addition of damage summation. The damage of materials due a stress cycle depends not only on the alternating stress but also on the mean stress.FindingsThe cycles counting simulation method allows quantifying the hysteresis loops, even if for small amplitude stresses.Originality/valueThe cycles are low or medium; the damage occurs most often, the higher values of alternating stresses cause the most failure of materials.

Numerical study of fatigue damage under random loading using Rainflow cycle counting

PurposeThe purpose of this scientific work is to simulate the fatigue damage under random loading, taking into account the mean stress effect on fatigue lifetime and using the Rainflow counting technique to assess the fatigue damage by the Ansys software. The used material is aluminum alloy 6082-T6. A comparison with literature results has confirmed this investigation in this paper.Design/methodology/approachThe study of fatigue under random loading is based on the same concepts as constant loading with the addition of damage summation. The proportion of damage caused by a stress cycle depends not only on the alternating stress but also on the mean stress.FindingsAnalysis of the fatigue damage shows that the number of relative damage due to each cycle.Originality/valueThis paper aims to simulate the fatigue damage under random loading for aluminum alloys.

Experimental investigation on short-term fatigue damage of slack and hybrid mooring for wave energy converters

Two mooring systems, namely a slack mooring and a hybrid mooring are proposed for the application of wave energy converters’ station keeping. The performance of these two mooring systems are assessed by hydrodynamic model tests on a point absorber-mooring system. Totally, four sea states are considered, including two operational and two survival wave conditions. The snap events are found in slack mooring when point absorber operates in survival conditions. Besides, the snap loads are closely related to the significant wave height and wave peak period. The hybrid mooring shows good performance in preventing snap loads. The short term mooring fatigue damage is estimated by the T-N curve method, while the load cycles are counted by the rainflow counting technique based on the measured mooring tension time series. The effects of T-N curve as well as snap loads on mooring fatigue damage are discussed, and the fatigue results of these two mooring systems are compared. In the last part of this study, the uncertainties in mooring fatigue estimations are discussed.

Out-of-plane bending stiffness and hotspot stress based on advanced numerical analysis techniques

ABSTRACTThis paper aims to presents an integrated procedure to reach the out-of-plane bending (OPB) moment-induced hotspot stress distribution for the mooring chains of an 8MW class floating offshore wind turbine platform (FOWT). Three-link models of the mooring chains were used to obtain the OPB stiffness, mid-span stress distribution, hotspot stress, and stress concentration factor based on the prescribed rotation approach (PRA), direct tension approach (DTA), and empirical formula. Multi-link analyses were also conducted to build a tension angle-interlink angle relationship between two successive links at a given tension level. A combination of three-link and multi-link analyses produced the relation of the hotspot stress-tension angle. After a stress interpolation procedure for the hotspot stress history, the hotspot stress range distributions were presented using rainflow counting technique. The tension-induced stress range distribution well followed the Rayleigh distribution, while the OPB moment elevated the hotspot stress which will seriously affect the fatigue accumulation.

The frequency domain estimate of fatigue damage of combined load effects based on the rain-flow counting

Based on the rain-flow counting technique, a frequency domain method is developed for calculating the fatigue damages caused by the combined loads, which can be linear or nonlinear and Gaussian or non-Gaussian loads. Firstly, the new method is developed for the fatigue damage estimates of the combination of high and low frequency Gaussian loads, by which the ranges of the small rain-flow cycles are obtained as high frequency cycles with considering the reduction effect of low frequency loads on them; the ranges of the large rain-flow cycles are determined by means of Turkstra's rule of load combination. Secondly, the method is extended to calculate the fatigue damages caused by the nonlinear Morison load which is the combination of linear inertial and nonlinear drag forces. The method is benchmarked against the rain-flow damage estimates and compared with the existing ones. The numerical analyses show that the damages estimated by the new method are close to the rain-flow damages.

Discretized Markov chain in damage assessment using Rainflow cycle with effects of mean stress on an automobile crankshaft

We studied the effect of mean stress correction factor using the Rainflow counting technique to assess the fatigue damage of an automobile crankshaft under service loading by considering the stochastic process of the Markov chain. The failure of the crankshaft will cause serious damage to the engine and also to other connecting subcomponents. The service loading is computationally generated from the Discrete Markov chain model and the fatigue cycle is counted using the Rainflow counting technique with the consideration of the local minima and maxima load. To quantify the fatigue damage, the strain-life curve using the fatigue mean stresses was used to model the fatigue failure of the material used in for the crankshaft at Nf = 106. The fatigue mean stresses were used to estimate the effects of the mean stress on the fatigue strength of the component under service loading condition. Statistical verification with the boundary condition of the 90% confidence level was performed to observe the difference between the stochastic algorithms when compared towards the fatigue life behavior of the ductile cast iron material. We concluded that for the practical application, the proposed stochastic model provides a highly accurate assessment of fatigue damage prediction for improving the safety and controlling the risk factors in terms of structural health monitoring.

Computationally efficient approaches to fatigue analysis of deepwater risers

Riser long-term fatigue performance is an important design consideration. Although extensive application of irregular sea analysis in time domain with the rainflow counting technique for post-processing is regarded as the most accurate of the approaches for fatigue analysis, it does suffer from some limitations, such as the computational effort. For this reason, two computationally efficient approaches are employed to perform the fatigue analysis of a deepwater top-tensioned riser, based on the Longuet-Higgins distribution and time domain scaling respectively. With Longuet-Higgins distribution irregular wave sea states are expanded into their individual wave bins. These regular wave simulations are of short duration and consequently run quickly. Using the time domain scaling technique, the number of irregular wave runs can be performed for a comparatively small number of load cases and hence reduces the calculation time. The results showed a reasonable accuracy and significant efficiency for both approaches, compared with those from the equivalent rainflow analysis. With much less computational effort and disk storage requirement, the approaches outlined in this paper can therefore be used for the fatigue assessment of deepwater risers in industry practice.

Fatigue behavior of laminated composites with a circular hole under in-plane uniaxial random loading

A modified fiber failure fatigue model is presented to evaluate the behavior of laminated composites with a central circular hole under in-plane uniaxial random/block loading. The analytical model presented is based on minimum strength model and fiber failure criterion under static loading available in the literature. The analysis starts with the determination of location of a characteristic curve around the hole and the stress state along the characteristic curve under in-plane uniaxial fatigue loading. Number of cycles to failure and location of failure are determined under given fatigue loading condition. Based on ply-by-ply analysis, ultimate fatigue failure and the corresponding number of cycles are determined. Degradation of material strength as a function of applied number of cycles is considered in the model presented. Random loading case is analyzed based on rainflow counting technique. Analytical predictions are compared with the experimental results for uniaxial block loading.

A New Software Framework for Fatigue Life Prediction of Composite Materials under Irregular Loading

A new software framework for fatigue life prediction of composite materials under irregular loading is presented herein. The entire work is based on a well established methodology for the life prediction of GRP laminates under variable amplitude complex stress states. The process consists of the sequential execution of four main tasks, each one of which copes with a single subproblem in a straight forward manner. The aim of this on-going work is to create a generic software framework that will enable rapid prototyping of various life prediction schemes. Based on the software design, a software library is under development. In the current paper, the software framework is analytically presented. Two different modules are prepared for the first task of the entire methodology. Cycle counting of two different variable amplitude spectra is performed by rainflow counting technique and by simple range-mean technique. Results of both analyses are then processed by routines that solve subsequent steps of the entire methodology in order to predict time up to failure of the material system under consideration, a [0/(±45)2/0]T multidirectional laminate. Theoretical predictions are plotted against experimental data for comparison, and pros and cons of each one of the cycle counting algorithms are discussed.