Dirlik Method Research Articles

Contributions to the Analysis of Mining Equipment Fatigue Through the Dirlik Method and Spectral Analysis

Abstract The paper analyses the phenomenon of mining machinery fatigue, focusing on the Bucket Wheel Stacker-Reclaimer KsS 5600/3800x40 machine. To evaluate fatigue cycles under variable and non-periodic force conditions specific to this type of machine, Dirlik method and spectral analysis are applied. Dirlik method provides an innovative approach to stress spectrum analysis, taking into account the complex distribution of stress amplitudes during coal stacking operations and their deposition on the conveyor belt. Spectral analysis provides detailed insight into the frequency distribution in the dynamic response of Bucket Wheel Stacker-Reclaimer. This analysis allows the identification of the dominant frequencies associated with the charging and discharging cycles. The results obtained have significant implications for the optimisation of operations and the effective management of fatigue within this specific equipment.

Using Computer Technique for Developing Method for Vibration Damage Estimation Under Combined Random and Deterministic Loading

Abstract This paper is focusses on developing a novel method for vibration damage estimation for military helicopters, fighter aircrafts and any other aircraft exposed to combined stochastic and deterministic loading. The first stage of the research focused on frequency domain damage prediction, which is the legacy method proposed by Bishop and developed by Sweitzer, Schlesinger, Woodward, Kerr, Murthy, Datta and, Atkins. The mentioned frequency domain-based method is used in commercial software, e.g., MSC CAE Fatigue. Frequency domain damage prediction is based on superposition of spectral moments and Dirlik method of Rainflow Cycle Counting algorithm in frequency domain. The first phase of the research showed the legacy algorithm based on transfer function developed using FEM (Finite Element Method) method in Abaqus environment and is very conservative. The second stage of the research aims to develop a novel method which allowing for more robust and accurate damage estimation. For this purpose, the Monte Carlo method for retrieving random signal in the time domain from signal in frequency domain was used. To obtain the system transfer function, – the 1 g load harmonic system response was obtained using FEM analysis. It was subsequently scaled linearly by the PSD input curve for random loading and sine wave, or sine sweep function for deterministic loading to calculate the cumulative system response of the linear system. The research allows the development of a novel method to precisely estimate vibration damage using combined time and frequency domains approach, based on effective frequency domain FEM analysis of the linear system. The new proposed method can be also used for precise replication of test conditions via considering signal clipping and frequency resolution used for real testing.

Fatigue life analysis of welded joints in the frequency plane in a structure designed for the defense industry

Welded joints are used in many industrial products and evaluations against static and dynamic stresses are important in terms of structure and life safety. It is very difficult to predict and model the vibration fatigue life of welded joints in the frequency plane under dynamic stresses. In this study, fatigue life estimation was made in the welded joint on a structure under vibration stresses in the frequency plane. Vibration characteristics for modes up to 1000 Hz were determined by modal analysis of the structure. In the MIL-STD 810G standard, power spectral density (PSD) is offered for composite wheeled vehicles, which are products of the defense industry. Random vibration analyzes were performed by defining PSD data as analysis input. With the effective notch stress approach, geometry and material S-N definitions were made and evaluations were carried out according to the Dirlik method. As a result of this study, the fatigue life of welded joints was determined as 4.582e+11 seconds. Approaches for structural reliability in a welded joint structure designed for the defense industry are proposed.

Using computer techniques for vibration damage estimation under stochastic loading using the Monte Carlo Method for aerospace applications

The main focus of this article is a review of legacy methods for vibration damage estimation under stochastic loading and extending research made by Dirlik and Bendat using two combined methods: FEM and Monte Carlo simulation, for which we used Python programming for aerospace applications. For some aircraft, regulated by the RTCA international aviation standard DO-160G (Environmental Conditions and Test Procedures for Airborne Equipment), stochastic loading is defined as one of the requirements. This article will focus on the stochastic loading impact on the fatigue life assessment made on a dummy sample, and frequency and time domain damage estimation shall be considered in parallel to compare both results. Additionally, dummy PSD responses shall be defined in the frequency domain for signal statistical parameters research. The article introduces Rainflow Cycle Counting methods in the frequency domain for procedures used commercially in aerospace applications. The first method introduced and developed further is the Dirlik method of Rainflow Cycle Counting in the frequency domain, which is the most popular method in commercial use. The second technique introduced and developed further was established by Bendat — the Narrow Band Method. The new empirical equation presented in this paper is the modification of the Narrow Band Method fitted for general use (narrow band, wide band, and white noise signals). A new approach for the integration of spectral moments is introduced in this paper, allowing for an accurate evaluation of the signal statistic parameters in the frequency domain for use in the modified Dirlik and Narrow Band methods. Research results also revealed new phenomena not researched by Dirlik, such as high vibration damage variation from stochastic loading, which depends on the frequency resolution (the block size used in Inverse Fourier Transformation). This discovery will be the subject of further study. Research results presented in this paper will also be utilised to combine stochastic and deterministic loading scenarios for military helicopters, as well as fighter aircraft, and will be the subject of further research.

РАСЧЁТНО-ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ ВЛИЯНИЯ ДЕМПФИРОВАНИЯ КОНСТРУКЦИИ НА ЕЁ ДОЛГОВЕЧНОСТЬ ПРИ СЛУЧАЙНОМ НАГРУЖЕНИИ

Mechanical engineering products are often subjected to dynamic impact during operation. The analysis of the durability of structures functioning under random multi-frequency loading requires taking into account their dynamic parameters (natural frequencies and vibration forms, damping, etc.). This paper analyzes the influence of the damping coefficient on the durability of a structurally similar specimen using a method for the narrow-band process and the Dirlik method. A computational scheme based on a finite element model determines the stress spectral density. The study defines the range of the damping coefficient variation by experiment and calculates the durability of the damping coefficient. The influence of damping on durability is analyzed by different methods. The calculations are experimentally verified.

Response spectrum method for fatigue damage assessment of mechanical systems

In this paper, a new response spectrum method is proposed for high-cycle fatigue damage assessment of a linear multi-degree-of-freedom system subjected to random base acceleration. Mode damage response can be accessed by separating the modal participation factor and stress mode from the contribution of a mode to the total damage, assessed by the Single Moment method. The fatigue damage response spectrum is defined as the family of curves formed by the mode damage response with the variation of the frequency and modal damping ratio, which is irrelevant to the spatial characteristics of the load and structure. Three calculation formats of the response spectrum method are formed by considering different cross-correlation hypotheses of each mode (i.e. the Complete Quadratic Combination format, the Square Root of the Sum of Squares format, and the Modified Square Root of the Sum of Squares format). The proposed method has higher computational efficiency than other frequency-domain methods because of avoiding the calculation of power spectral density function and spectral moment of stress responses. The spatial and frequency information of the structure are decoupled from each other in the implementation, which can effectively reduce the computational cost of reanalysis. Compared to the result of the Dirlik method (self-compiled program and MSC.Patran/Nastran) and the Single Moment method, the correctness and efficiency of the proposed method are verified, and the influences of the material and load spectrum form on the response spectrum method are investigated.

Experimental study on vibration-induced clamping force reduction in fuel cell structures

When applied to transportation systems, fuel cell structures are exposed to external mechanical disturbance including shocks and harmonic excitations from operating components. To minimize performance degradation from machine operations, the fuel cell structure needs to be examined via vibration reliability tests. In this study, the reduction in the clamping force of the stack by random vibrations was investigated by experiments. The stack mass and gasket were clamped with bolts for vibration tests. The vibration induced shear movements between clamped stacks. To estimate the vibration input magnitudes, the Dirlik method was used. The reduction in the stack clamping force was estimated using the Basquin's power law. The clamping force decreased by the shear vibration input to the stack structure. The degree of clamping force reduction was larger for the heavier stack. When the stacks were separated by the gasket the reduction became smaller. Through the Dirlik method, the vibration reliability of the stack was evaluated. This information provides severity of the external vibration on the stack functionality.

Fatigue-based reliability in assessing the failure of an automobile coil spring under random vibration loadings

The paper presents an assessment of fatigue-based reliability in measuring failure random vibration loadings due to unexpected loads under various road conditions. Random loads were the main cause of fatigue failure in a component durability analysis. Acceleration signals were measured during a road test held on rural and highway road surfaces. These signals were captured from an accelerometer placed on a vehicle’s lower arm suspension system in a locally made sedan-type automobile. This arrangement enhanced the capacity for collecting acceleration signals using multi-body dynamics simulation, which would minimise the need for actual acceleration data measurements. Modal analysis was conducted to determine the natural frequencies and mode shapes of the geometry of a coil spring so that strain signals based on each mode shape could be obtained. As modal parameters occurred within the frequency range of road excitation, fatigue life prediction was not affected by instances of dynamic behaviour in the components in time domain. Fatigue life was analysed using the Dirlik, Lalanne and narrowband approaches in frequency domain. The Dirlik method predicted a good correlation for the measured acceleration and generated strain signals at 2.32 × 108, 2.55 × 108 and 1.51 × 108 blocks to failure, indicating that a coil spring could withstand the uneven road surface without failing prematurely. Hence, fatigue-based reliability can evaluate the hazards of rate-reliability, based on predictions of fatigue life data on component durability.

Analysis of random vibration fatigue of aluminum alloy beam with a hole based on frequency domain method

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

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.

Representative Environmental Condition for Fatigue Analysis of Offshore Jacket Substructure

The 20-year cumulative fatigue damage of an offshore jacket substructure was estimated under the long-term local environmental conditions in the Taiwan Strait. Because of the nonlinearity of wave load for slender members of the structure, time-domain simulations of the dynamic finite element model were conducted for each sea state. By utilizing the Dirlik method to process the stress signals, the fatigue damages of joints were computed. Concerning the computational time, we propose a probability-based method of using a representative combination of environmental conditions in this study, which can considerably reduce the required number of evaluations prior to determining fatigue damage, thereby improving the process of preliminary design. The results show that only three sea states among 120 can represent 28% of the average damage ratio, and up to 17 sea states fully resolved the fatigue life.

INVESTIGATION OF TIME AND FREQUENCY DOMAIN FATIGUE LIFE CALCULATION METHODS USING FINITE ELEMENT METHOD

Maruz kalınan titreşim nedeni ile meydana gelen yorulma hasarı ve ömrünü tespit etmek için zaman düzleminde ve frekans düzleminde hesaplama yapan yöntemler bulunmaktadır. Bu yöntemler sonlu eleman analizleri ile birlikte kullanılarak mekanik tasarımın şekillendirilmesi sürecinde kritik rol oynamaktadır. Bu çalışmada zaman düzleminde yorulma hesaplayan Rainflow yöntemi ve frekans düzleminde yorulma hesaplayan Dirlik yöntemi sonlu elemanlar analizleri yardımı ile incelenmiş ve minimum yorulma ömrünü Dirlik metodunun verdiği görülmüştür. Herhangi bir test ile tasarım doğrulama imkânı bulunmadığında ve tasarım yalnızca sonlu elemanlar yöntemi ile değerlendirileceğinde, Dirlik metodu sonuçları referans alınarak yapılacak tasarımın en güvenli tasarımı vereceği için en avantajlı yöntem olduğu tespit edilmiştir.

주파수 영역 피로해석에서 PSD 분석 방식 비교

If fatigue failure occurs during aircraft operation, it can cause catastrophic injuries. So, it is necessary to study fatigue failure at the design stage. Frequency domain fatigue analysis is used to predict fatigue failure. During frequency domain fatigue analysis, results can be calibrated by PSD analysis. In this study, fatigue failure is predicted by the Dirlik method, Lalanne method and Steinberg method. Regarding results, life determined by the Dirlik method, Lalanne method and Steinberg method were 8.737, 8.314, and 7.901 times the standard life, respectively. The Steinberg method is the most conservative but the difference with other methods was approximately 10%. In the cycle histogram, the Dirlik method had more counts than the Lalanne method in lower stress range. However, it does not affect the life of material used in this study. However, if material has a lower fatigue limit or stronger PSD data is used, life difference will occur.

Fatigue assessment method of marine structures subjected to two Gaussian random loads

Fatigue assessment is a critical issue for marine structures which usually encounter a combination load of a low frequency and a high frequency component. Furthermore, two components are commonly analyzed separately. In a strict sense, each of two components cannot be considered as narrowband processes. Recently, the authors proposed a combination of fatigue damage method (Han-Ma method) for predicting fatigue damage on the assumption of two well-separated and narrowband Gaussian components. The method is extended to non-narrowband and frequency overlapped cases in this paper. In addition, the application of existing combined spectrum method with dual narrow-banded correction factor (such as Jiao-Moan method, Low's bimodal method, Low-2014 method) and combination of fatigue damage method (such as DNV method, Huang-Moan method) is also investigated. These methods are also compared with some general wide-band spectral methods such as Dirlik method, single-moment method, Benasciutti-Tovo method and Park method. The results show that Jiao-Moan method, Low's bimodal method, Low-2014 method and Han-Ma method can still provide very accurate fatigue damage estimation when two Gaussian processes are separately non-narrowband and have overlapped frequencies. In particular, the accuracy of Low-2014 method and Han-Ma method is very close to that from some general spectral methods in the case that two Gaussian components have overlapped frequencies.

Fracture mechanics analysis for a mooring system subjected to Gaussian load processes

An investigation on the fracture mechanics (FM) analysis using various load combination methods for a mooring system subjected to Gaussian load processes is conducted in this paper. Low frequency (LF) and wave frequency (WF) tensions of mooring lines are predicted by a frequency-domain analysis taking into account environmental effects including wind, wave and current. The LF and WF load processes are regarded as two random processes. The narrow-band method, general wide-band methods (Dirlik method and Tovo and Benasciutti method), and dual narrow-band methods (Jiao and Moan method, Fu and Cebon method and modified Fu and Cebon method) are used for predicting the combined load induced by LF and WF motions in the FM analysis. A comparison between mooring fatigue lives predicted by the FM analysis using these load combination methods is performed and the results show that the FM analysis based on the narrow-band method generally offers the most conservative fatigue life prediction and the difference of fatigue lives of mooring chains estimated based on general wide-band methods and dual narrow-band methods is not significant. However, in some cases, the FM analysis based on Dirlik method, Jiao and Moan method, Fu and Cebon method or modified Fu and Cebon method even provides more conservative results compared with the narrow-band method.

Fatigue life evaluation and failure analysis of light beam direction adjusting mechanism of an automobile headlight exposed to random loading

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

Fast Estimation of the Damage Equivalent Load in Blade Geometry Multidisciplinar Optimization

Designing blade geometry as a multidisciplinary optimization presents important challenges due to the increment in the number of design variables and computational cost of calculating the constraints and objective function. Blades have an important impact on loads because they capture the kinetic energy in wind and transfer it to the rest of the wind turbine components. Thus, consideration of the fatigue response is necessary in the optimization problem. However, the calculation of the damage equivalent loads (DELs) implies time-consuming simulations that restrict the number of design variables due to the increment of the search space. This article proposes a frequency domain method to estimate the fatigue response, which produces an advantage in terms of computational cost. The method is based on wind turbine model linearization by means of an aero-elastic code and the subsequent calculation of a frequency response function (FRF), which serves to estimate the response of the wind turbine. The Dirlik method is then applied to infer the damage equivalent loads. This process, which is useful for variables that have a stochastic nature, provides rapid approximate prediction of the fatigue response. An alternative estimation is proposed for loads subjected to an important periodic component. The results show that the method is useful in the initial stages of design.

Topology optimization considering fatigue life in the frequency domain

This research develops a new topological optimization (TO) method to assess dynamic fatigue failure in the frequency domain for random excitation forces. Besides static failure, fatigue life (or fatigue failure) is an important design criterion for the safety of mechanical and building structures. Therefore, many assessment theories and computational approaches have been proposed, and they can be divided into two categories: time domain and frequency domain. Although both approaches have been successfully applied for engineering purposes, they are rarely considered in structural TO. To consider fatigue failure caused by stochastic mechanical loads in structural TO, this research adopts fatigue assessment approaches in the frequency domain, such as narrow band solution, the Wirsching and Light method, the Ortiz and Chen method, and Dirlik method. For TO, we perform an adjoint sensitivity analysis with those fatigue assessment methods. We consider some two-dimensional benchmark problems and show that the present design method successfully constrains fatigue.

Experimental, theoretical and numerical fatigue damage estimation using a temperature modified Dirlik method

This article describes experimental, theoretical and numerical fatigue damage estimation using a temperature modified Dirlik method. The method enables an estimation of high cycle fatigue damage for uniaxial loadings caused by random vibrations directly from power spectral analyses with the temperature effect. Preliminary investigations of high cycle fatigue properties of high pressure die-cast aluminium alloy AlSi9Cu3 have been carried out at elevated temperatures. Standard and non-standard fatigue tests have been performed to determine the temperature dependent S–N curves. Simultaneously, fatigue damage estimation was carried out numerically with commercial programmes Ansys Workbench and LMS Virtual.Lab using finite element methods. Finally, the numerical simulation results are compared with both experimental and theoretical results. The temperature modified Dirlik method enables a computationally fast fatigue damage estimation of random stress loadings and temperature histories.

Failure and fatigue life estimate of a pre-stressed Aircraft seat support tube

There have been increasing reports of annoyance, fatigue, and even neck and back pain during prolonged operation of troop propeller aircraft, where persistent multi-axis vibration occurs at higher frequencies. A claim from failure of the 2024-T3 aluminum tube used as a seat support tube (SST) for troop seat – wall style – construction. A failure occurs after about 85 flight hours. A numerical static analysis model for the tube with its holders shows that it is safe, even with impact loading. In the present work, a random vibration analysis is conducted to calculate the lifetime of the SST. First, a static analysis is performed using a pressure load on part of the tube that represents the seating location, followed by random vibration analysis. A contact algorithm is added in order to transfer the support’s movement to the tube. Dirlik method is used for the analysis of lifetime as it is proven to provide accurate results for large number of applications, both in automotive and aerospace industry. The predicted service life is in a good agreement with the real actual life.