Impact of Multi-cracks on the Breathing Mechanism of a Rotating Shaft
Table of contents
Abstract 4-5
Introduction 6 – 7
Research gap 8
Objective 9
Literature Review 10 -1 8
Methodolgy 1 9
Reference 20-21
Abstract
Rotating shafts often experience fatigue cracks that result in severe machine failure that incur significant losses. This problem is most pronounced in factories that use rotor dynamic equipment including, oil, nuclear, aerospace, and transportation industries, to mention a few. It is, therefore, prudent to say that popper and efficient methods must be devised to detect any cracks in rotating machinery. Numerous concerned establishments have invested a significant amount of time and money to this end. It is worth noting that failures in machinery are not only detrimental to a specific company but also to the subject industry at large through a chain of connected impacts such as referred damages, repairs costs, and downtime. Another salient point is that regular visual inspections of machinery may affect a company negatively as they demand the dismantling of the said equipment, which is both costly and time-consuming. Therefore, the most potent way of dealing with crack-induced failure in rotating shafts is through the establishment of a process that can be used to project, detect, and locate the said damages without compromising the functioning of machinery. Such a method also ensures that the concerned equipment is serviced effectively in a timely manner and within the desired schedule.
Cracks are very significant to industries that employ rotor dynamic equipment as they cause serious downtime during maintenance. It is prudent to say that the study of the elliptical cracks is extremely necessary as it is a more frequent and natural occurrence on most rotating shafts. Also multi-crack is one of the most common factor that causing failure in a rotating shaft. Even more Dynamic loads are very important factor to study the stability and the vibration response when the shaft rotates. The crack location inherent that proper 3-dimension Finite Element model should be established to represent accurately the aforementioned lacking area of research. This research aims to investigate the effect of multi-cracks, crack location and unbalance force on the crack breathing mechanism of a cracked rotating shaft. This will be investigated by using ABAQUS software to simulate a model.
Introduction
The spreading of fatigue cracks is the main cause of most machine failures, which may incur significant property and financial losses coupled with risks of personnel injury. The said form of failure mostly occurs on spinning shafts because of excessive loading, torsion, and vibrations induced by mass turbulence and rotation. It is worth noting that the shafts are crucial components of gyrating machinery used across numerous industries, which emphasizes the significance of fatigue crack-based failure. The propagation of a crack in mechanical machine parts may change their functionality in several ways, including the amelioration of displacements coupled with the lowering of the frequency as a result of augmented component flexibility (Dimarogonas & Papadopoulos, 1983). Besides, machine failure may induce referred damages in other elements of the affected equipment and may incur economic losses when the machinery in dormant. Therefore, this research aims to establish non-intrusive methods to detect crack propagation in a shaft, which would ensure timely response and repair.
The crack breathing mechanism is defined as the process through which a crack opens and closes once per revolution of a shaft. The process is caused by the dynamic and static loadings on the said machine component, which creates strains and stresses around the region of failure. According to the existing literature, this activity has been modeled in four typologies, namely the gaping, switch, sine, and transient models. The gaping kind is the most basic form that is based on the assumption that a crack would always manifest in a fully open position regardless of the angle of shaft rotation. The main advantage of this model is that it uses relatively simple analysis, but it is unpopular as it does not portray the actual open and close action of a crack. The switch model is the second simplest typology, and it assumes a crack to either be in a fully open or closed position with no gradual change between the two states. Although it facilitates the investigation of open and closed states of a crack, it is drawn back by the fact that it is based on the assumption of a drastic change between the phases rather than a progressive transition. This shortcoming is negated by the sine model of crack breathing mechanisms that represents the crack open area percentage as a sine wave with rises and falls. Notably, this typology assumes that a crack would take a fully open or closed position for only a single instance in each shaft rotation.
The transient model is the most accurate of the four typologies, and it is regarded as an amalgamation of the sine and switch models. This concept allows for a smooth transition between states and shows that a crack maintains a fully closed or open position for a longer and more realistic time. This research aims to explain by the 3-dimension Finite Element model impact of unbalanced forces and crack location on breathing processes through the execution of a transient crack breathing model. Another worthy remark is that this study is based on the gap in knowledge in the existing literature into the fatigue-induced crack failure in machinery.
Research Gap
Cracks are extremely detrimental to industries that employ rotor dynamic equipment as they cause significant downtime in the course of maintenance and destructive inspections. The said failure may also place workers in the vicinity of affected machinery at serious risks of injury. This stresses the need for proper methods of crack diagnostics, prediction, and prevention. Most of the existing studies have neglected to investigate elliptical cracks; instead, they focus on straight crack fronts. It is prudent to say that the study of the elliptical is extremely necessary as it is a more frequent and natural occurrence on most rotating shafts. Multi-crack is one of the most common factor that causing failure in a rotating shaft. However, researchers ignored the effect of the multi-cracks due to the configuration of multi-cracks are very complicated. Moreover, it is worth noting that most of the existing literature regarding cracked rotors are based on the premise of static loadings. Dynamic loads are very important factor to study the stability and the vibration response when the shaft rotates. Researchers also ignored the effect of crack location. Thus, it is inherent that proper 3-dimension Finite Element model should be established to represent accurately the aforementioned lacking area of research.
Research Objectives
This research aims to investigate the effect of multi-cracks under the unbalance force on the crack breathing mechanism of a cracked rotating shaft. This will be investigated by using ABAQUS software to simulate a model, which will be used to assess the crack status at various locations along the shaft and rotating angles.
The main objectives of this thesis are:
1. Develop a 3-dimension Finite Element model for a cracked rotor system with multi-cracks.
2. Analysis the multi-cracks breathing mechanism under the static loads.
3. Analysis the multi-cracks breathing mechanism under the dynamic loads.
4. Analysis the multi-cracks locations along the shaft length on breathing mechanism.
Literature Review
Shafts are the machine components with the highest risk of crack defects, which is attributed mainly to the fact that they function under severely harsh conditions. Such failures often manifest with minimal warning, resulting in substantial losses. Shafts are susceptible to fatigue cracks because of the presence of manufacturing flaws, large variations in operating temperatures, rapid variation of the bending stresses and deformation, incident shaft loadings, and the corrosive stimulation from the surrounding environment. In rotating shafts, cracks spread in a transversal manner to their longitudinal axes because of the fatigue generated by the cyclic loads, and they often take an elliptical or slanted shape (Carpinteri, Brighenti & Vantadori, 2006; Carpinteri & Brighenti, 1996) Numerous studies have been conducted to establish appropriate methods to initially detect cracks and, consequently, determine their location, shape, and size. However, most of the existing research focuses on the connection between the mechanical performance of a component and the presence of a crack with a straight front. Thus, the proposed methods are limited as they fail to reproduce the actual behavior of cracked shafts adequately.
As mentioned earlier, crack breathing is among the most critical process in fatigue-induced cracking of shafts. This mechanism has been modeled in several manners, with the most practical one being the transient breathing typology that is based on the postulation that during shaft rotation, a crack transitions from open to close positions gradually. Another crucial note is that this model considers a crack to shut and open when it gets to the compression and tension zones of a shaft respectively. Figures 1 and 2 are graphical representations of crack breathing, with the latter showing a scaled shaft deformation.
Figure 1: Crack breathing mechanism
Figure 2: Crack in upper (a) and lower (b) positions.
The first model of the nature of fatigue-induced cracks in a rotating shaft is the gaping model that was proposed by several researchers, including (Bachschmid, Pennacchi & Tanzi, 2008; Darpe, Gupta & Chawla, 2004; Dimarogonas & Papadopoulos, 1983). This concept assumes a crack to always be in an entirely open position that is not impacted by the rotational angle of the shaft. Mathematically, this model is defined by considering the local stiffness of the affected component as a fraction of the cracked part over a full revolution of the affected shaft. The gaping concept is common as it is the simplest method of estimating the properties of a crack in an operational shaft. It is worth noting that gaping failures are somewhat different from notches as their width is assumed to be insignificant. Thus, these cracks are often not considered in experimental testing, which instead uses notches as they can be manufactured, controlled, and quantified easily. Figures 3 and 4 show the pie chart and line graphs for the gaping model respectively.
Figure 3: Gaping model pie chart
Figure 4: Gaping model line graph.
The second common model used to describe fatigue-induced failures is the switch crack typology as proposed by Chan and Lai. This mechanism is an improvement on the gaping concept and assumes a crack to be in either a fully open or closed position. However, it is limited to a binary variable in the location of cracks and, as such, it is an unrealistic explanation of the characteristics of a cracked shaft. Figures 5 and 6 how the pie chart and line graph for the switch model respectively.
Figure 5: Switch model pie chart
Figure 6: Switch model bar graph
The third model for modeling cracks is the transient crack breathing typology that accurately defines the progressive transition of the said failure between open and closed phases. This concept assumes that the small lots of shaft rotation are in an entirely open or closed state while all the rotational angles are taken to include partial forms of the said phases. Consequently, this makes the transient model the most accurate and realistic modeling technique of crack breathing processes. Figures 7 and 8 show the pie chart and line graph of this concept respectively.
Figure 7: The transient model pie chart
Figure 8: The transient model line graph.
Another critical component process in fatigue-induced cracking is the propagation of the said forms of failure, which is defined as the enlargement and lengthening of an existing crack. This development is extremely risky as it augments vibration significantly, creating several undesired forces that may damage equipment. Several factors may foster the propagation of cracks, including operating faults, metallurgical conditions, residual and thermal stresses, as well as environmental conditions, to mention a few. If mass eccentricity is subjected opposite to the position of a minute crack, the failure cannot open and, thus, would never propagate. Conversely, if the said derivative is oriented in the same direction as the location of the small crack, the failure would always open, resulting in its propagation. Progressive spreading of cracks in a shaft eventually causes its failure, which occurs when the said part can no longer handle subjected loads and breaks into at least two pieces. This may manifest in several forms beginning with transverse and longitudinal cracks that appear perpendicular and parallel to the length of the shaft, respectively.
Another form of failure is slant cracking, which occurs at an angle to the shaft axis and impacts the torsional character of a shaft similar to other cracks. However, the resultant effect is moderate. These forms of failure are detected through a basic processes such as dye-penetration and visual inspection. Similar to longitudinal damages, slant cracks are difficult to detect and, as such, they are the least studied type of cracks on rotating shafts. Additionally, failures may manifest below the surface of a rotating; they are referred to as sub-surface cracks. Such damages may be discovered through several methods, including magnetic particle, ultrasonic, shaft voltage drop, and radiography. It is noteworthy that surface cracks impact the vibration character of a rotating shaft more that their sub-surface counterparts. Finally, there may be gaping cracks or notches that always maintain an open position.
As mentioned earlier, the detection of cracks in their early stages of propagation is extremely important to prevent machine damage. However, this is quite challenging as cracks disturb their surrounding fields in a manner that is proportional to their respective sizes and, thus, would be discovered once they have propagated over a large area (Staroselsky & Cassenti, 2002). The first potential method of detecting the said forms of failure includes vibration techniques that employ shaft vibration feedbacks. According to Adams et al., the natural frequency of longitudinal vibrations can be used to determine the damage caused in a shaft in a one-dimensional manner. More recent studies, however, exploit all characteristics of cracks to facilitate more accurate detection. For example, Barad, Sharma, and Vyas employed all the known relationships held between the crack size and location coupled with a rotational spring constant to propose more accurate procedures for detecting cracks in a cantilever beam. It is worth noting that this method can be used effectively to detect failures in a rotating shaft.
Another popular non-destructive method used to detect cracks is modal testing, which exploits the variations in modal properties. Most the proposed procedures in this respect are only effective when a shaft is stationary, while just a few need the said component to rotate at a very low speed. For example, Gounaris and Papadopoulos (1983), proposed a technique of modal assessment where three clusters of radial excitation are subjected on one end on a spinning shaft and the equivalent axial displacements on the opposite end are gauged. Consequently, the position and depth of existing cracks can be established graphically. Other studied methods of detecting cracks in rotating shafts include borescope inspection, fuzzy logic, neural networks, and complex processing techniques. However, few researchers have investigated the applicability of these methods, but they remain a significantly potent area of study and application. One of the most informing works in this respect was conducted by Adewusi and Al-Bedoor (2002), who argued that a 2-neuron network can detect the propagation of a crack, while a 3-neuron typology could even identify non-propagating cracks.
Based on the preceding postulations, it is prudent to say that the subjects of crack breathing, initiation, propagation, and cracking are topics of high interest and have been studied for several decades. Numerous methods have been proposed over the years to detect cracks along with their characteristics. However, no single research has developed a single holistic process to detect and quantify the said failures without interrupting the operation of affecting machines significantly. It is, therefore, prudent to say that a more in-depth understanding of crack behavior can potentially result in the development of new and better detection and analysis techniques. Generally speaking, continued research into these topics may eventually augment the efficiency of crack detection in rotating shafts, which may realize significant industrial cost savings coupled with ameliorated worker safety.
Please write here 10 more pages following same procedure of citation and referencing
Research Methodology
This research will be a progressive study that will demand different methodologies at various stages. To begin with, the project topic, “Effects of Multi-cracks on the Breathing Mechanism of a Rotating Shaft,” will be discussed with the research supervisors. It is noteworthy that the primary focus of this efforts will be on the nature of cracks at different locations and angles along a rotating shaft. Another crucial point is that the model that will be used to this end will be defined in relation to the information sourced from various literature reviews and research gap regarding the visual simulation shaft failure induced by crack formation and propagation. Specifically, the model to be set up will be a pin beam shaft that resembles a rotating shaft, which is appropriate since it has two supports and is subject to different forces along its length. Preferably, this model will have a radius of 6.35mm and will be fixed at both ends. What is more, the main forces will be subject on the shaft at about 181mm from each terminal. Another crucial remark is that the shaft will have a total length if 726 mm, and a crack will be simulated in the middle of the said component, thus manifesting the initiation and propagation of an elliptical crack. As mentioned earlier, the simulation software that will be used in this study is the ABAQUS standard program. It is worth noting that the virtual shaft simulated using the program will comprise two forces replacing the rotating disc. What is more, both ends of the model will be fixed in all axial plane orientations, which will facilitate the calculation of the work on the bearing support of the model shaft. Notably, the ABAQUS software uses a chain of sequences to solve the 3-D non-linear element model: part, property, assembly, step, load and boundary conditions, mesh, job, and results. Moreover, this study will be conducted in detail to simulate and explain the data generated from the ABAQUS software, therefore providing insights into the deflection, stress, and strain on the model shaft.
References
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Adams, R. D., et al. 1978 “A vibration technique for non-destructively assessing the integrity of structures.” Journal of Mechanical Engineering Science, vol.20, no.2, pp.93-100.
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Barad, KH, Sharma, D and Vyas, V 2013, ‘Crack detection in cantilever beam by frequency based method’, Procedia Engineering, vol. 51, pp. 770-5.
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Carpinteri, A, Brighenti, R and Vantadori, S 2006, ‘Surface cracks in notched round bars under cyclic tension and bending’, International Journal of Fatigue, vol. 28, no. 3, pp. 251-60.
Chan, R and Lai, T 1995, ‘Digital simulation of a rotating shaft with a transverse crack’, Applied Mathematical Modelling, vol. 19, no. 7, pp. 411-20.
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Fonte, M, Reis, L, Romeiro, F, Li, B and Freitas, M 2006, ‘The effect of steady torsion on fatigue crack growth in shafts’, International Journal of Fatigue, vol. 28, no. 5, pp. 609-17.
Gounaris, G. D., C. A. Papadopoulos, and A. D. Dimarogonas 1996 “Crack identification in beams by coupled response measurements.” Computers and structures, vol.58, no.2, pp.299-305.
Liu, Chao, and Dongxiang Jiang 2017 “Dynamics of slant cracked rotor for a steam turbine generator system.” Journal of Engineering for Gas Turbines and Power, vol.139, no.6, pp. 062502.
Muñoz-Abella, B., et al. 2012 “Study of the breathing mechanism of an elliptical crack in a rotating shaft with an eccentric mass.” Proceedings of the World Congress on Computational Mechanics, Sao Paulo, Brasil.
Staroselsky, Alexander, and Brice N. Cassenti 2002 “Thermal—Vibration Method of Crack Detection.” International journal of fracture, vol.116, no.2, pp.35-40.
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