Frequency-based fatigue analysis of non-stationary switching random loads

The service loadings in real systems are not only random, but also non-stationary. The spectral methods based on a frequency-domain characterization of random loads, which have been used in alternative to classical time-domain approaches, cannot be applied to non-stationary loads, because the conventional spectral density spectrum is not able to capture the evolutionary frequency characteristics of non-stationary loads. This clearly restricts the applicability of the existing frequency-based methods only to loads which are stationary. At the same time, it is also very difficult to propose general models valid for all types of load non-stationarity encountered in practice. Therefore, a practical approach is to restrict the analysis to a specific class of non-stationary loads; in this work, we consider particular non-stationary loads (i.e. switching loads), which are piecewise stationary in their variance. A frequency-domain analysis of such loads is proposed, which is based on a combination of the frequency-based analysis of each adjacent stationary segment, which can be either Gaussian or non-Gaussian. Numerically simulated load histories, as well as loads measured on mountain bikes in special tracks, are analysed to validate the proposed methodology. The presented results also show the correlation between load non-stationarity and non-Gaussianity.     

White noise excitation of road vehicle structures

Heave and pitch motions of road vehicle structures affect the comfort and the safety of passengers. Excitation of these vertical vibrations is due to road surface roughness. Road vehicle structures are modelled as mechanical systems characterized by their inertia, damping and stiffness, and represented as state equations. This paper deals with the influence of random road profiles on the vertical dynamics of road vehicles characterized by stochastic processes. Switching from road profile displacement to road profile velocity results in white noise excitation facilitating mathematical analysis. Some fundamentals of power spectral density analysis and covariance analysis are reviewed. A quarter car model is used to show the advantages of the covariance analysis resulting immediately in standard variations characterizing the vehicle’s performance. A list of symbols is given at the end of the paper This paper is dedicated to Prof R N Iyengar of the Indian Institute of Science on the occasion of his formal retirement.     

Survey of fatigue failures in helicopter components and some lessons learnt

The paper presents a comprehensive review of the failure investigations carried out within AgustaWestland Limited (AWL) over the last 30 years. The results of this survey show that fatigue accounts for approximately 55% of all failures in helicopter components. Although fatigue failures can occur in a wide range of components the types of factors responsible for initiation differ depending on the application of the part. This paper identifies the most common fatigue prone areas in the helicopter, how design considerations and certain key factors such as fretting can influence fatigue life. The importance of aircraft maintenance and quality control in the supply chain will also be discussed. Based on the survey, the paper will also illustrate several instances where fatigue failures have been eliminated through the application of novel surface engineering techniques, improvements in material & processes and modifications to the original design.     

Lightweight design of vehicle components based on strengthening effects of low‐amplitude loads below fatigue limit

A new lightweight design method for vehicle components is proposed based on the strengthening effects of low‐amplitude loads below the fatigue limit. The new method is technically based on the strength feature of strengthening and damaging of vehicle components under loading spectrum, while combining dynamic strength equations with the residual strength of vehicle components. It ensures the maximum exploitation of the material's strength potential and fully realises the lightweight design of vehicle components at a low cost. As an application of the new lightweight design method, a light truck's front axle was redesigned. The lightweight potential of the front axle was first estimated by fatigue and static strength experiments of four‐point bending. Then the lightweight design was realised by finite element analysis and experimental results. The weight of this front axle was reduced by 5.5 kg.     

Changes in mechanical properties of vehicle components after strengthening under low-amplitude loads below the fatigue limit

Changes in the mechanical properties of vehicle components were investigated after strengthening under low-amplitude loads below the fatigue limit (SLAL). The strengths of vehicle components including fatigue strength, static strength and yield strength were significantly increased by SLAL. The surface hardness of the front axle, composed of a kind of low strength steel without heat treatment, was enhanced with increased strengthening and damaging. The change of surface hardness was reversed completely for the transmission gear, composed of a kind of high strength steel with surface heat treatment. The natural frequency of the transmission gear was appreciably increased by SLAL.     

Random multiaxial fatigue: A comparative analysis among selected frequency and time domain fatigue evaluation methods

Fatigue analysis of mechanical components subjected to random loads has been recently upgraded through several developments of calculation procedures, with the scope to support the designer within the loading condition numerical simulation. Under such scenario, the frequency domain approach is characterized by interesting features, which support its adoption in alternative or in conjunction with the classic time-domain approach, especially when the frequency domain is applied for the individuation of the component critical locations. The major goal of this paper consists of an overview about the strength and weaknesses of frequency approach with respect to the time domain one by comparing the reference time domain methods with their frequency domain translation. A significant test case development will be shown, representing a classic automotive one (chassis validation). Promising results of the frequency method application will be presented, encouraging its adoption on large scale.     

Multiaxial fatigue and failure analysis of helical compression springs

Multiaxial fatigue criteria are applied to the analysis of helical compression springs. The critical plane approaches, Fatemi–Socie and Wang–Brown, and the Coffin–Manson method based on shear deformation, were used to predict fatigue lives of the springs under constant amplitude loading. Experimental fatigue lives are compared with the multiaxial fatigue criteria predictions. The stress analysis was carried out in the finite element code ANSYS, and the multiaxial fatigue study was performed using the fatigue software nCode. A failure analysis was conducted in order to determine the fatigue crack initiation point and a comparison of that location with the most damaged zone predicted by the numerical analysis is made. The Fatemi–Socie critical plane approach gives a good prediction of fatigue life. While the Wang–Brown criterion overestimates spring fatigue life, the Coffin–Mason model gives conservative results.     

全向车测量轮导引方式的设计与仿真

针对全向车位姿检测中由于麦克纳姆轮驱动打滑引起的整车运行精度测量误差大的问题,提出了测量轮自主导引方式,建立数学模型,并对AGV系统结构进行了阐述.设计方案中的整车六轮布局,采用四驱两从动,俩从动轮作为测量轮,运用差速原理获取自动导引全向车的路径信息,同时解决了现有单测量轮全向车原地回转状态下位姿无法精确检测的难题.提出浮动三自由度测量轮结构设计,实现实时接触地面,保证位姿检测的准确性,并对直线、曲线、原地自转三种典型运动状态下的位姿检测进行了ADAMS仿真,结果表明,此种导引方式可满足灵活设置路径下全向车位姿的精确检测,适用范围广.     

成型砂轮廓形设计的CAD法

将作图法和计算法相结合,提出成型砂轮廓形的CAD设计方法。该方法以啮合原理为根据,采用反求设计的思路;通过做一系列垂直于砂轮轴线的截面,得到相应的砂轮与螺旋槽的接触点,连接这些接触点得到接触线,将接触线绕砂轮轴线旋转360°,即是成型砂轮的廓形。该方法具有简单直观、结果准确的特点。以球头铣刀螺旋槽的成型磨削为实例,对用CAD法设计成型砂轮的过程进行说明。该方法可用于各种按展成原理进行加工的成型工具的轮廓设计。     

Generation and validation of loading profiles for highly accelerated durability tests of ground vehicle components

Accelerated durability tests are designed to quantify the life characteristics of ground vehicle components under normal use conditions by testing at a higher stress level to accelerate the occurrence of failure. Presently, conducting durability tests with a high acceleration factor has become increasingly demanding for the reduction of the time and the cost involved in long period field/durability tests. In previous work, to accelerate the field test, the standard ‘test tailoring approach’ has been modified due to the limitations of testing implementation and required high acceleration factors. In this modified approach, a full period durability loading profile has to be shortened to an equivalent partial period test loading profile, which is repeated in the tests keeping the same amount of damage contents. To apply this new modified approach to industrial durability tests, it needs to be validated. In this work, a computer-aided testing method is developed for the validation of this modified ‘test tailoring approach’. Hence, a new test-piece has been designed by a conjugative approach involving the finite element technique and fatigue analysis for a specific durability life. Afterwards, the loading profiles with various acceleration factors synthesized via the modified approach have been applied on the designed test-piece and the fatigue lives have been simulated to verify the effectiveness of those loading profiles. Simulation results show that, loading profiles with high acceleration factors can be successfully generated with the accuracy above 95%. In addition, synthesized accelerated loading profiles result failure from the identical locations determined using the proposed conjugative approach.     

Cumulative fatigue damage and life prediction of elastomeric components

Elastomeric components are widely used in many applications due to their good damping and energy absorption characteristics. The type of loading normally encountered by these components in service is variable amplitude cyclic loading. Therefore, fatigue failure is a major consideration in their design. In this work capabilities of Rainflow cycle counting procedure, maximum principal strain as a damage criterion, and Miner's linear cumulative damage rule are evaluated with both specimen and component tests. An automotive cradle mount is used as an illustrative component. Comparison of predicted and experimental fatigue lives in both specimen and cradle mount variable amplitude load tests indicate satisfactory predictions in both cases.     

Measurement and analysis of vibration levels for express logistics transportation in South China

Trunk transportation and terminal distribution are two important parts of express delivery in China. Heavy truck and medium truck are two main vehicles of trunk transportation. Mini van and two‐wheel electric bicycle are widely used for terminal distribution. Four vehicles mentioned previously and a sedan car were chosen for vibration level measurement and analysis in this paper. The results revealed that vibration levels were significantly higher in the vertical axis, and decreased with the increase of payload, and increased with the increase of speed again. Similar power spectral density peak frequencies were found in a comparison study with previous results in the low‐frequency region (1‐10 Hz), occurred at approximately 2 Hz in the van and sedan car and at 3 to 4 Hz in the truck and at 4 to 5 Hz in the two‐wheel electric bicycle. Except the two‐wheel electric bicycle, the second peak frequency occurred at approximately 20 to 30 Hz in the sedan car and at 10 to 20 Hz in the mini van and at 20 to 40 Hz in the heavy truck, which were also similar to the previous studies. Vibration levels of the sedan car were the lowest, and the trunk transportation vehicles (heavy truck, medium truck) were the highest. The terminal distribution vehicles (mini van, two‐wheel electric bicycle) were somewhere in the middle.     

A method for the random analysis of linear systems subjected to non-stationary multi-correlated loads

The paper shows a procedure for evaluating the correlation matrix and the evolutionary power spectral density matrix of the response of linear structural systems subjected to random non-stationary multi-correlated vector processes. The approach reduces this problem to the solution of some corresponding stationary problems. It is shown that the assumption of a modulating matrix function, whose elements are the sum of exponential functions, allows to transform the initial non-stationary problem into a stationary one. This stationary problem can be solved by well-known unconditionally stable step-by-step numerical procedures in the time domain, and, in closed form, in the frequency domain. The comparison of the results obtained using the proposed approach with those obtained by Monte Carlo Simulations (MCS) has revealed a very good level of accuracy.     

微弹性啮合轮的传动力及失效分析

 根据大变形梁原理推导出微弹性啮合轮传动力的计算公式,结合计算和实验结果研究弹性杆的传动力与变形程度、啮合深度之间的关系,分析微弹性啮合轮发生传动失效的原因.计算结果表明,传动力的大小随弹性杆倾斜变形角度的增大而增加;实验表明,弹性杆啮合越深,机构产生的传动力越大;失效分析表明,微弹性啮合轮传动失效的主要影响因素包括变传动力、振动冲击和弹性啮合轮的微细制造工艺等.     

空间时间域路面行驶车辆的演变随机响应分析

介绍在空间频率——时间域计算随机路面行驶车辆演变随机振动响应功率谱的方法。根据积分变换调制路面对行驶车辆的随机激励,利用行驶车辆的行程与持续时间的确定性关系确定随机激励与响应的功率谱,在实数域用确定性振动响应分析结果预测演变随机响应功率谱。给出随机路面行驶四轮车在空间频率——时间域的激励功率谱矩阵和计算机仿真结果。研究表明：只要车辆的行驶速度是持续时间的确定性函数,就能将路面对车辆在空间域的平稳激励转化为在时间域的演变随机过程;在实数域预测行驶车辆演变随机振动响应功率谱的方法是可行的。     

Measurement and analysis of delivery van vibration levels to simulate package testing for parcel delivery in Hungary

In the past several decades, there continues to be an increase in both domestic and international online and catalogue shipments that requires an increase in shipments and handling of parcels by single parcel delivery companies. This study measured the vibration levels that occur in parcel delivery shipments from pickup to delivery, especially the sections involving delivery vans and small vehicles over ground road transportation in Hungary. Goods that were shipped in the regions studied almost always travel at least once by van on varying road conditions such as motorways, main, side or city roads to deliver parcels to the final destination. The aim of this paper was to provide an understanding of vibration levels that occur during van transportation that can be used to pre‐shipment test new packages to prevent damage. The measured acceleration‐time data were analyzed in terms of power spectral densities (PSDs) and presented with statistical data to provide an understanding of the variability of intensity. The separated and averaged vibration levels that were measured in this study were compared with the American Society of Testing and Materials and the International Safe Transit Association vibration profiles for pickup and delivery vehicle in the form of PSD spectrums. Based on the analyzed data of this study, PSD spectra were provided for various route conditions as well as composite spectra, which can be used to simulate the measured vibration conditions representing van shipments.     

Fatigue analysis of unidirectional GFRP composites under combined bending and torsional loads

Fatigue behavior of unidirectional glass fiber reinforced polyester (GFRP) composites at room temperature under in-phase combined torsion/bending loading was investigated. All fatigue tests were carried out on constant-deflection fatigue machine with frequency of 25 Hz. A 30% reduction from the initial applied moments was taken as a failure criterion in the combined torsion/bending fatigue tests of the composite materials. A series of pure torsional fatigue tests were conducted to construct the failure contour of GFRP composites using different failure theories. The obtained S–N curves from combined torsion/bending tests were compared with both, pure torsion fatigue test results and published results of pure bending fatigue tests of GFRP rods. Pictures by scanning electron microscope were used to closely examine the failure mode of the tested specimens under combined torsion/bending loading.

The results showed that, the unidirectional glass fiber reinforced polyester composites have poor torsional fatigue strength compared with the published results of pure bending fatigue strength. Endurance limit value (calculated from S–N equation at N = 10⁷ cycles) of GFRP specimens tested under combined torsion/bending loading equals 8.5 times the endurance limit of pure torsion fatigue. On the other hand the endurance limit of combined torsion/bending fatigue strength approximately half the fatigue limit of pure bending fatigue strength. The predicted values of combined torsion/bending fatigue strength at different number of cycles, using the published failure theory are in good agreement with the experimental data. For the investigated range of fiber volume fractions (V_f) it was found that higher stress levels are needed to produce fatigue failure after the same number of cycles as V_f increases.     

Fracture and fatigue analysis of an agitator shaft with a circumferential notch

This paper is concerned with the fracture analysis of an agitator shaft of a large vessel and predicting its high cycle fatigue life. The agitator shaft has a circumferential notch around it and is subjected to remote bending and torque created by the mixing operation. The problem is comprised (i) the analyses of the bending force and torque acting on the agitator by using the analytical method, (ii) calculation of stress intensity factors under mode I and III loading conditions by using finite element method and, (iii) fatigue analysis of the agitator shaft failed in service.An agitator model is set up and data obtained from the agitator are processed to make more realistic approximations for bending forces, since they form a base for stress analysis, in which mode I stress intensity factors are evaluated. Mode I stress intensity factors obtained by finite element analysis are compared with the results provided by using the body force method.     

The research on failure analysis of fluid cylinder and fatigue life prediction

To analyze the reasons of fluid cylinders’ rupture, macro-analysis, SEM, composition inspection, metallographic analysis, hardness test and mechanics performance test of fluid cylinders materials were implemented. Two different kinds of fatigue life prediction methods have been proposed which are based on total life analysis and strain–life methodology. The results indicate that: the failure cylinders’ material quality is satisfactory. Fatigue damage caused by high working, stress and corrosion is the main reason of cracking. The fatigue life prediction illustrates that strain–life methodology is well adapted to fluid cylinders.