This study investigates the role of the tribo-dynamic behavior in the contact fatigue crack nucleation for spur gears. To describe this fatigue phenomenon, a six-degree-of-freedom (DOF) lumped parameter dynamics formulation is coupled with a set of mixed elastohydrodynamic lubrication (EHL) governing equations. The former provides the dynamic tooth force to the EHL analysis, and the latter yields the gear mesh damping as well as the friction excitations that are required in the gear dynamics simulation. The converged tribo-dynamic surface normal pressure and tangential shear are then used to determine the multi-axial stress fields using the potential theory based closed-form stress formulation for half space. Lastly, the stress means and amplitudes are implemented in a multi-axial fatigue criterion to assess the fatigue damage.

The fatigue life of a component is defined as the total number of cycles or time to induce fatigue damage and to initiate a dominant fatigue flaw which is propagated to final failure.(Shigley & Mischke 2002) The aim of this project is to calculate the total fatigue life of metallic structures under cyclic loading by applying equations found by Basquin and Manson-Coffin. The local stresses and strains necessary for the calculation are determined by the finite element method. Former studies concerning this subject have used analytical methods to find the local conditions at the critical section. The analytical methods, based on Neuber and Molski-Glinka’s approaches, permit the calculation of the local stresses and strains at the critical section of the structure’s geometry as a function of the nominal stress (forces) applied. For the finite elements method, ABAQUS is used to determine the local conditions at the critical section of a T-shaped model.

In the case of variable amplitude loading, fatigue damage accumulation theory is closely related to loading histories, such as load sequences, load interactions, and so on. Due to the lack of load histories, there may be a large deviation with the reality for linear damage rule (Miner rule). Although many non-linear fatigue damage accumulation models can deal with the effect of load sequences, load interaction effect cannot be ignored and it plays an important role in damage accumulation behavior. This paper describes the damage evolution behavior based on nonlinear damage rule under variable amplitude loading. A new method to describe the load interaction effects is proposed, it is assumed that the load ratio between adjacent stress levels is used to present this phenomenon. Thereafter, the method is introduced to a non-linear damage model, and a modified model is developed to predict the residual lifetime. Four categories of experimental data sets from literatures are employed to investigate the validity of the proposed model. The results indicate that the modified model shows a good agreement between experimental data and theoretical results. It is also found that the modified model demonstrates an improvement in prediction accuracy over the primary model and Miner rule. Furthermore, the modified model can be easily implemented with the use of Wöhler curve only.

Fatigue damage analysis is critical for systems under stochastic loadings. To estimate the fatigue reliability at the design level, a hybrid reliability analysis method is proposed in this work. The First Order Reliability Method (FORM), the inverse FORM, and the peak distribution analysis are integrated for the fatigue reliability analysis at the early design stage. Equations for the mean value, the zero upcrossing rate, and the extreme stress distributions are derived for problems where stationary stochastic processes are involved. Then the fatigue damage is analyzed with the peak counting method. The developed methodology is demonstrated by a simple mathematical example and is then applied to the fatigue reliability analysis of a shaft under stochastic loadings. The results indicate the effectiveness of the proposed method in predicting fatigue damage and reliability.

A new dynamic model of fatigue evolution in structures is presented. The analytical model is derived for an Euler-Bernoulli beam with a fatigue crack. This model captures the coupling between the crack propagation dynamics and the beam oscillations. Hamilton’s Principle and Paris’ Law are used to advance the coupled field model in which a new characteristic of the beam motion is introduced as a loading parameter to fatigue model. The resulting fatigue damage model is validated by experimental data.

Estimating and tracking dynamics of crack growth is essential for fatigue failure prediction. A new experimental system coupling structural and crack growth dynamics was used to show fatigue damage accumulation is different under chaotic and stochastic loading, even when both excitations have similar spectral and statistical signatures. Furthermore, conventional rain-flow counting method considerably overestimates damage in case of chaotic forcing. Important nonlinear loading characteristics are identified to guide the new fatigue model development.

Many structural applications of adhesive joints experience vibration loads. The dynamic loads due to vibration motions are therefore one of the primary causes for structural damage, especially when the outside cyclic stir vibration frequency is adjacent to the natural frequencies of the adhesive joint frame. This is so called the vibration fatigue. In this paper, the fatigue behavior of adhesively bonded single lap joint (SLP) subject mainly to normal stresses induced by vibration excitations is investigated. Combining with static tests, the NI PXI-1045 vibration measurement and analysis system are used to analyze the effect of vibration loading on the fundamental modal frequency with long-term fatigue cycle. Furthermore, a virtual fatigue analysis approach for the fatigue damage prediction of adhesive joints subject to vibration loads is performed in this study. It is found that the joint stiffness decreases with the cyclic durations under which the vibration loads are applied. As a result, a stable decrease of the fundamental resonance frequency of the joint structure is observed during the tests. The experimental data demonstrate a significant correlation between the shear strength of adhesive joints and the vibration cycling time. A gradual decrease in the shear strength with increasing load cycles is seen in vibration fatigue, the maximum shear strength of adhesively bonded joints drops about 12% after 1.35e8 cycles. Based on the test data, a new approach called virtual fatigue analysis modeling (VFAM) is proposed for the fatigue damage of the adhesive joints under vibration loads. The VFAM shows that the fatigue damage occurs first at the end of the overlap area of the adhesive layer.

In this paper, we present techniques for fatigue damage evaluation using spectral methods and a model taking into account elasto-plastic behaviour. The model is associated with a non linear fatigue law, covering the whole endurance domain (low cycle and high cycle fatigue). It uses Neuber’s method and is valid for limited plasticity. To validate this modeling, we perform a correlation between spectral methods, modified spectral methods and experimental data. We present here, the results obtained in the case of narrowband random vibrations.

In recent years, Subsynchronous Resonance (SSR) and Subsynchronous Oscillation (SSO) are increasingly attracting more and more researchers’ interests in China. The network is encountering great changes and large-scale networks are increasingly implemented for long distance power transmission as well as various kinds of power electronic devices. Several SSO phenomena were monitored in a fossil-fired power plant in China in 2008. They were determined as complex factors’ co-activation between the network and the turbine generator. Multi-mode torsional vibration is one significant feature of torsional vibration caused by SSO. The paper simulates the multi-mode SSO based on the practical situation in China. The torsional vibration is studied to analyze the torsional vibration features under multimode SSO and the differences caused by different peak values and phases of electromagnetic torques. Based on some type of 600MW steam turbine generator, the fatigue damage of the shafts is studied.

In seeking to simplify fatigue life calculations for components of fitness equipment, this paper develops a general expression for the user weight L e which, in N T cycles, generates the same fatigue damage as a set of user weights {L i } described by a probability density function f i = N i /N T , where each L i gets applied for N i cycles and Σ N i = N T . The derivation of the method goes beyond the textbook development of equivalent load by retaining geometric, material, and loading parameters throughout the derivation. The expression allows exploration of the effect of the geometry of the mechanical component, material properties, and loading on the value of the user weight L e which simulates the set of user weights {L i }. The paper explores a range of stress-life exponent b typical of common steels. The paper explores the complete range of stress ratio R ∈ (-1, 1). The paper explores the combined effect of the component’s ultimate tensile strength and the ratio between applied load and stress. These last two parameters determine the user weight L b which causes single-cycle fracture of the component. The results indicate a strong dependence of L e on stress ratio R, stress-life exponent b, and on breaking weight L b . The paper proposes guidelines for assignment of L e in the special case where the {L i } arise from body weights of the US population.

The detection of damage in early stage of fatigue is important for a reliable evaluation of gear life and strength. From this point of view, the variation of strain distribution in a tooth due to cyclic load contains useful information because the fatigue crack will initiate as a result of the accumulation of plastic strain. Meanwhile, digital image equipments are widely used in our life and the performance is in progress. We took digital pictures of cyclic loaded tooth by the digital camera and compared with the picture of no load to find displacement. The strain distribution of tooth is calculated by the correlation method using those pictures. The initiation of a micro crack is observed by the method. It is also confirmed by the detection of acoustic emission wave with higher energy. The variation of stress-strain diagram in fatigue process is presented, and this illustrates the increase of strain in the final stage of fatigue.

The fatigue failure mechanism was investigated for the rubber CVT (continuously variable transmission) belts. There are three major crack initiation modes in the rubber CVT belts, namely the adhesive rubber crack, the backing rubber crack and the bottomland crack. Especially, the mode of the adhesive rubber crack is important to strengthen the rubber CVT belts, because the crack is the most difficult to find out during the driving. In this study, the failure morphology of the damaged belts was observed using an optical microscope and a X-ray CT scan after some fatigue tests. Moreover, the failure mechanism of the adhesive rubber crack was discussed basing on the FEM and simplified mechanical analyses. The fatigue damage was accumulated along the interface between the cog rubber and the adhesive rubber. The interface was de-bonded by the shearing strain, which was induced by the dishing deformation of the belt within the pulley groove.

In this paper, a dynamical systems approach to material damage identification is presented. This methodology does not depend on knowledge of the particular damage physics of material fatigue. Instead, it provides experimental means to determine what are practically observable and observed facts of damage accumulation, thus making it possible to develop or experimentally verify appropriate damage evolution laws. The procedure implicitly uses the fact that the system undergoing fatigue damage accumulation possesses time scale separation, where damage accumulation occurs on a much slower time scale than the observable dynamics of a system. Damage tracking is achieved using a two-time-scale modeling strategy based on phase space reconstruction. Fast-time oscillation data is collected and used to estimate a damage tracking function by calculating the short time reference model prediction error. Tracking metrics based on these estimates are used as feature vectors. Damage identification is achieved either by applying proper orthogonal decomposition or optimal tracking methods to these vectors. The method is experimentally validated using an elasto-magnetic system, in which a harmonically forced cantilever beam in a nonlinear magnetic field accumulates fatigue damage. The damage tracking results were virtually identical for both identification schemes. In both cases tracking data showed power-law type monotonic trends. These results were in good agreement with the Paris fatigue crack growth model during the time-period of macroscopic crack growth. In addition, the tracking provides much needed insight into the incipient or early damage accumulation process, where only one scalar damage variable is needed to describe the incipient or early damage accumulation process.

The evaluation of the fatigue damage performed by using the Power Spectral Density function (PSD) of stress and strain state is proving to be extremely accurate for a family of random processes characterized by the property of being stationary. The present work’s original contribution is the definition of a methodology which extracts stress and strain PSD matrices from components modelled using a modal approach (starting from a finite element modelling and analysis) within mechanical systems modelled using multibody dynamic simulation and subject to a generic random load (i.e. multiple-input, with partially correlated inputs). This capability extends the actual stress evaluation scenario (principally characterised by the use of finite element analysis approach) to the multibody dynamic simulation environment, more powerful and useful to simulate complex mechanical systems (i.e. railway, automotive, aircraft and aerospace systems). As regards the fatigue damage evaluation, a synthesis approach to evaluate an equivalent stress state expressed in terms of the PSD function of Preumont’s “equivalent von Mises stress (EVMS)”, starting from the complete stress state representation expressed in terms of PSD stress matrix and easily usable in the consolidated spectral methods, is proposed. This approach allows and has allowed the use of the above methods such as the Dirlik formula as a damage evaluation method. An additional result is the conception and implementation of a frequency domain method for the component’s most probable state of stress, allowing quickly identification of the most stressed and damageble locations. The described methodologies were developed and embedded into commercial simulation codes and verified by using as a test case a simple reference multibody model with a simple flexible component.