Vibration diagnostics of fatigue cracks

The diagnostics of fatigue cracks in a rotor system is based on the investigation of vibration signals measured in bearing housings with fatigue cracks of different depths. The obtained results can be used for the diagnostics of the state of a rotor system, in particular, to detect fatigue cracks in machines used in general engineering.     

含多条裂纹梁的模态与振动疲劳寿命分析

基于Paris公式,提出了一种含多条裂纹梁疲劳寿命预估的方法。在模态分析中,基于传递矩阵方法,利用无质量的弯曲弹簧等效裂纹,提出一种求解含有多条裂纹梁固有振型的方法,分析裂纹数目、裂纹位置、裂纹深度对裂纹梁固有频率的影响。在振动疲劳分析中,研究了在简谐激励作用下裂纹数目对裂纹尖端应力强度因子的影响。通过Paris疲劳裂纹扩展方程和同步分析法,考虑裂纹梁振动与裂纹扩展的相互作用,分析了裂纹数目和裂纹位置对裂纹梁疲劳寿命的影响。结果表明,裂纹数量、裂纹位置和深度对梁的模态参数和疲劳寿命有重要影响。     

疲劳小裂纹的萌生和扩展形态研究

本文通过对35SiMnMoV复相钢的常温疲劳试验研究和GH4049镍基高温合金的高温疲劳试验研究,获得了大量的试验数据和得出了相应的裂纹扩展行为规律。采用对比分析方法,从疲劳小裂纹的萌生和扩展形态出发,归纳总结了疲劳小裂纹的扩展规律。     

Rolling contact fatigue of alumina ceramics sprayed on steel roller under pure rolling contact condition

The rolling contact fatigue of sprayed alumina ceramics with a nominal composition of Al₂O₃–2.3 mass% TiO₂ was studied with a two-roller test machine under a pure rolling contact condition with oil lubricant. The influence of undercoating of sprayed Ni-based alloy on the rolling contact fatigue was investigated. The failure mode of all sprayed rollers was spalling caused by subsurface cracking. The undercoating did not contribute to the improvement of the rolling contact fatigue life. The elastic modulus of the alumina sprayed layer evaluated with the nano-indentation method was around 85 GPa. The depths of the observed subsurface cracks corresponded approximately to the depths where the orthogonal shear stress or the maximum shear stress calculated with two-dimensional FEM became maximum.     

Surface fatigue failure of nitride-hardened aluminium-chromium-molybdenum steel rollers under pure rolling and sliding-rolling contacts

To study surface failures of nitride-hardened gears, rolling fatigue tests were performed using nitride-hardened steel rollers as gear-tooth surface models. Surface failure of nitride-hardened rollers was by subsurface-initiated spalling under all contact conditions, nitriding depths and Hertzian stresses used. Cracks leading to spalling initiated at the case/core boundaries. White etching areas (WEA) were observed along spalling cracks. Electron probe microanalysis revealed that the WEA material was carbide. It is considered that there is a relation between the initiation of spalling cracks and the formation of WEA.     

Three-dimensional weld toe magnification factors for various welded joints

To effectively calculate the stress intensity factors in welded components, a weld toe magnification factor is introduced here that will allow for the influence of geometrical effects. This factor was derived from the data obtained in a parametric study performed by FEM. Several sets of weld toe magnification factor solutions have been presented, but these are applicable only to non-load-carrying cruciform or T-butt joints, due possibly to the requirement of very complicated calculations. In the majority of cases for various welded joints such as cruciform, cover plate and longitudinal stiffener joints, the currently used weld toe magnification factors do not adequately describe the behavior of weld toe cracks. In the present study, the weld toe magnification factor solutions with exponents and fractions that have polynomial functions in terms of a/c and a/t ?? i.e., crack depths normalized by corresponding crack lengths and specimen thickness ?? were developed through a parametric study using 3-dimensional finite elements for the above mentioned three types of welded joints. These weld toe magnification factor solutions showed a tendency to increase at a/t < 0.2. Meanwhile, for 0.2 < a/t < 0.7, the effect of the attachment on the weld toe magnification factor decreased asymptotically. When the a/t ratio exceeded this range, the weld toe magnification factor became almost one of unity. The fatigue crack propagation life was evaluated by using the proposed weld toe magnification factor and by considering the propagation mechanisms of multiple-surface cracks, and it showed good agreement-to within a deviation factor of 2-between the experimental and calculated results for the fatigue crack propagation life for all welded joint.     

Fretting fatigue crack initiation and propagation behavior of Inconel 690 alloy

Several studies have been conducted on the fretting fatigue limit characteristics of Inconel alloy tube material used in steam generators of nuclear power plants. Nevertheless, additional research on fretting fatigue crack initiation and propagation behavior is necessary in order to evaluate its fretting fatigue life more accurately. In this study, crack growth tests of fretting fatigue are conducted, and the characteristics of fatigue crack initiation and propagation are analyzed on Inconel 690 alloy. Also, plain fatigue crack growth tests are performed on the same material, and the results are compared with those of fretting fatigue crack growth tests. From both of the plain and fretting fatigue crack growth test results, the ΔK-da/dN diagrams are obtained and the crack growth rates are compared. It is found that the crack growth rate for fretting fatigue tests is faster than that for plain fatigue tests under a certain value of DK. However, over this value of DK, the crack growth rate for fretting fatigue tests becomes slower than that for plain fatigue tests due to debris which is produced by fretting and trapped in the propagated cracks. Finally, the fracture surfaces examined by an optical microscope, and the initiation angles of the oblique cracks are determined under various applied stresses. Also, the microstructure of the fracture surfaces is observed by a Scanning electron microscopy (SEM).     

带内表面裂纹的组合厚壁筒装配应力强度因子研究

由于过盈配合组合厚壁筒内会产生装配应力。文中用权函数方法导出组合厚壁筒带半椭圆形表面裂纹的内壁在装配应力下的应力强度因子公式。这些公式可用于计算组合厚壁筒在不同裂纹深度、形状和不同材料、过盈量、尺寸情况下的应力强度因子。研究装配应力强度因子随表面裂纹深度和形状的变化规律。     

Numerical studies on crack growth in a steel tubular T-joint

The results of a numerical investigation on fatigue crack growth of an offshore tubular T-joint under the action of axial, in-plane and out-of-plane bending loads are presented in this paper. Extensive stress analysis has been carried out to determine the location of the hot spot stress along the brace—chord intersection for each load case. Semi-elliptical cracks with varying crack lengths and crack depths were introduced at the hot spot location by means of line spring elements for stress intensity factor evaluation. The line springs were properly constrained to prevent the problem of crack surface penetration. The stress intensity factors obtained are then used in a crack growth law for life estimation.     

梁类结构多裂纹微弱损伤的小波有限元定量检测方法

提出了一种定量检测梁类结构多裂纹参数的方法。利用适宜求解奇异性问题的小波有限元法,从动力学正问题入手,对裂纹梁进行有限元建模,获得裂纹故障在结构固有频率上反映的本质征兆,并利用曲面拟合技术绘制出以裂纹位置和深度作为变量的固有频率变化率曲面,然后对整个裂纹梁进行剖分,迭代求解出每个剖分单元上的结构损伤系数。损伤系数为正的单元诊断为裂纹单元,在每个裂纹单元上求出裂纹对应的前三阶固有频率变化率,并分别将其作为输入参数代入固有频率变化率曲面,做出前三阶模态的频率变化率等高线,最后通过三条等高线的交点预测出裂纹存在的位置和深度,算例分析验证了该算法的有效性。     

Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms

In this paper, a crack detection approach is presented for detecting depth and location of cracks in beam-like structures. For this purpose, a new beam element with an arbitrary number of embedded transverse edge cracks, in arbitrary positions of beam element with any depth, is derived. The components of the stiffness matrix for the cracked element are computed using the conjugate beam concept and Betti’s theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain precise natural frequencies and mode shapes of the beam knowing the cracks’ characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results and available experimental measurements. Moreover, by knowing the natural frequencies and mode shapes, an inverse problem is established in which the location and depth of cracks are determined. In the inverse approach, an optimization problem based on the new finite element and genetic algorithms (GAs) is solved to search the solution. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam. The proposed approach is verified through a cracked beam containing various cracks with different depths.     

用振动信号分析诊断齿轮齿根疲劳裂纹

对运行中的齿轮箱进行轮齿根部早期疲劳裂纹的诊断在许多领域中有重要意义。这种诊断的一种简单、快速方法就是振动信号分析。本文通过理论分析和实验验证讨论了三种齿根部疲劳裂纹诊断的振动信号分析方法。     

Fatigue growth simulation for cracks in notched and unnotched round bars

Fatigue crack growth for various cracks in both unnotched and notched round bars is directly modelled by using an automated numerical technique, which calculates the stress intensity factors at a set of points on the crack front through the three-dimensional finite element method and then applies an appropriate fatigue crack growth law to this set of points to obtain a new crack front. This technique also has the capability of automatic remeshing so that the crack propagation can conveniently be followed. The crack geometries modelled in the present paper include a small internal crack near the free boundary and several initially part-elliptical or irregular surface cracks in a smooth round bar under tension, a surface crack in different semi-circularly notched bars under both tension and bending, a surface crack initiated from the root of a V-notched bar and an initially twin crack configuration within a smooth tension bar. Some fatigue growth characteristics relevant to each type of cracks are also revealed. It is demonstrated that the fatigue growth analyses of various cracks commonly occurring in bars can reliably be made by using the automated finite element technique proposed.     

Effects of environment on fretting fatigue

Fretting fatigue tests of a carbon steel and an aluminum alloy were carried out in various environments and the effects of oxygen and water vapor were investigated by tangential force measurements, the initiation and propagation of cracks and hardness and structural changes of the damaged surface layer. With carbon steel the effect of water vapor is negligible but oxygen has a deleterious effect on the initiation and propagation of fretting fatigue cracks. However, with an aluminum alloy the effect of oxygen is small but water vapor accelerates the initiation and propagation of cracks. Environmental effects are more dominant than the stress conditions with an aluminum alloy; material softening and structural change of the surface layer occur.     

Numerical and experimental method for the prediction of the propagation life of fatigue crack on metallic materials

A prediction method for the propagation life of fatigue crack for cracked components was provided and verified in this study to predict the propagation life of fatigue cracks on components in engineering applications conveniently and directly. In the simulation aspect, a finite element (FE) model of cracked specimen was created to obtain the stress intensity factor range ΔK. The FE model was verified by comparing simulated ΔK to a formulary calculated one. The simulated ΔK could be used for studying the relationship with crack size. In the experimental aspect, the fatigue crack propagation test was conducted on three specimens. The material coefficients C and m were fitted according to Paris’ law. The load cycles with different crack depths were recorded in the testing process. The propagation life of fatigue cracks of specimen was predicted via the relationship between ΔK and crack size a according to Paris’ law. The comparison between predicted life and experimental life of specimens indicated the feasibility of the method. The proposed prediction method in this study for the propagation life of fatigue cracks can be used in engineering applications.     

Torsional vibration of cracked beams of non-circular cross-section

The equation of motion and associated boundary conditions are derived for a uniform beam of non-circular cross-section which is subjected to torsional vibration and which contains one or more pairs of symmetric cracks. The procedure is to use the Hu-Washizu variational principle which requires plausible assumptions about the displacement, momentum, strain and stress fields to be chosen. The perturbation in the stress and strain distributions of the beam due to the presence of the cracks is incorporated through local functions which have their maximum value at the cracked section and which decay exponentially from the crack location. The rate of exponential decay can be evaluated from experimental tests. The fundamental torsional frequency of the beam is computed for various depths of crack using the theoretical model. These predictions are then compared with results obtained from experiments on beams which contain cuts to simulate the cracks. It is found that the theoretical predictions closely match the experimental results.     

A stress analysis of a shaft with a press-fitted hub subjected to cyclic axial loading

This paper presents a calculation of the stress distribution in a shaft with a press-fitted hub subjected to axial fretting fatigue. Both normal contact stresses and frictional shear stresses at the shaft-hub interface are included in the model. The solution of Airy's function is obtained by means of Fourier integrals. The results are presented for different combinations of hub length, shaft radius and non-slip area and for various values of the coefficient of friction. Special consideration was given to the axial component of the stress, σ_z, as this is the most important stress component in the initiation and propagation of fatigue cracks. Finally, the paper deduces the implications arising from the stress analysis on the fretting fatigue of the junction studied.     

大型混流式水轮机转轮叶片裂纹及其成因分析

大型混流式水轮机转轮计片裂纹故障是水电站普遍存在的问题，它严重影响了水电站的安全稳定运行。转轮叶片裂纹是多种因素综合作用造成叶片材料疲劳．导致叶片疲劳开裂。叶片的各种制造缺陷是裂纹萌生的始点，而各种水力激振因素引发的流固耦合共振是转轮叶片疲劳开裂的根本诱因。     

Metallographic analysis of fretting fatigue damage in Ti-6Al-4V MA and 7075-T6 aluminum

Fretting fatigue tests were conducted utilizing axial fatigue load application at various maximum fatigue stress levels and normal pressures. Materials investigated were titanium Ti-6A1-4V mill annealed (MA) and aluminum 7075-T6. Subsequent to testing, the specimens were sectioned and metallographically examined to investigate the relationship between fretting damage, fretting induced cracking and reduction of specimen fatigue life.At all maximum fatigue stress levels investigated a given amount of fretting damage was required before any fatigue life reduction occurred. Presumably, the damage leads to the development of cracks in the fretted areas. Metallographie studies of the fretted areas have revealed that multiple cracks form and are propagated by fatigue. Some evidence was found to indicate that fretting debris is forced into the microcracks as they develop, thus explaining, in part, the significant reduction in life caused by the fretting.     

Initiation and propagation of fretting fatigue cracks

Fretting fatigue tests of a carbon steel were carried out. Fatigue cracks were measured by means of electrical resistance and observed with a scanning electron microscope. The mechanism of fretting fatigue failure is discussed from the experimental results. Small fatigue cracks are initiated early in life and some grow to be propagating cracks. Cracks grow to a given depth by tangential stress combined with repeated stress and then propagate with repeated stress alone, causing a knee point in the propagation curve. Fretting fatigue damage is saturated in the first 20–25 % of life which coincides with the knee point. The condition of non-propagating cracks is also known.