Dissertations / Theses on the topic 'Shafting'

This work presents a novel methodology for evaluation of in service loads applied to the output shafts of automatic transmissions. It also presents a novel methodology of data reduction for shaft load signals as an alternative to the cycle counting methods. Current durability testing of automatic transmission output shafts uses 50 000 stall torque cycles from zero to wide open throttle. In the majority of cases, these requirements lead to an over design that can result in an unnecessarily bulky transmission system. As a solution to this problem a novel methodology for evaluation of loads applied to the output shafts of automatic transmissions was developed. The methodology is based on real world loading conditions and therefore leads to a more realistic estimation of the fatigue life of shafts. The methodology can be used as a tool for shaft optimisation in different drive conditions. Using the developed methodology the effects of different road conditions on the fatigue life of a transmission output shaft were compared. Four routes having differing driving conditions were investigated and of those routes, the route with most stop-start events resulted in the greatest reduction in fatigue life. A novel methodology of data reduction for shaft load signals was also developed. The methodology is based on knowledge of the bandwidth and dynamic range of the expected in-service load signal. This novel methodology allows significant reduction of the volume of data to be acquired. It preserves the time sequence of peaks and valleys of the signal, which is vital in the case of fatigue analysis. This is in contrast to current methods based on cycle counting. Cycle counting methods achieve high data reduction but do not preserve the time sequence of the signal. The developed novel methodology has been validated on the newly developed data acquisition system capable of real time data acquisition and compression of shaft torque signal. The performed tests show that the proposed one-channel low cost system equipped with 1 GB compact flash card can store well over 10 000 hrs of load history.

Condition monitoring of rotating shafts is gaining importance in industry due to the need to increase machine reliability and decrease the possible loss of production due to machine breakdown. In this work, the use of vibration signals for the detection of a crack within a shaft was investigated. The research involved the measurement of vibration signals during laboratory tests on a long rotating shaft rig. The focus of the experimental work was on the effect of cracks on the dynamics and the initiation and growth of cracks in the shaft. Measurements were taken from the shaft system both with simulated cracks (notches) cut at 45° and 90° to the shaft axis and with real propagating cracks initiated by a pre-crack cut. All defects were located at the mid- point along the shaft. The vibration responses and stresses were measured for different depths of crack. The vibration responses of the three different defects were compared using PSDs of the data to identify the change in position and magnitude of the peaks in the spectrum under each defect. Experiments to study the effect of defect depth at different shaft rotation speeds were also carried out. Finally, a shaft with a breathing crack (continuously opening and closing as the shaft rotates) was also studied experimentally, with the crack growing under normal steady state operating conditions. After completing the experiment work, the shaft was broken and the type of fracture studied. The results for both simulated and actual crack growth showed that vibration frequencies decreased as a crack progressed, indicating the possibility of using the vibration signal for crack detection. A significant relationship was found between the stage of crack growth and the vibration results. A finite element (FE) model was constructed to explore the relationship between the natural frequencies and crack depth and position along the shaft and to explain and validate the results of the experimental work. The FE model showed similar trends to the experimental results and also allowed the effect of different crack positions to be explored. The PSD data was fed into an artificial neural network after a feature extraction procedure was applied to significantly reduce the quantity of data whilst at the same time retaining the salient information. Such an approach results in a considerably reduced training time for the network due to the reduced complexity. The proposed scheme was shown to successfully identify the different defect levels. This method greatly enhances the capacity of an automated diagnostic process by linking increased capability in signal analysis to the predictive capability of the artificial neural network.

A unique multifrequencied transfer matrix method performs three-dimensional harmonic, steady-state response calculations on geared-rotor systems. The full six degrees-of-freedom method includes physical branching to accommodate multiple shafting and frequency branching to simultaneously accommodate multiple frequencies and their interdependence resulting from time-varying mesh stiffness. Areas of emphasis include development of a modified transfer matrix to handle multiple frequencies and shafting; description of the time-varying stiffness tensor representing the involute spur gear mesh based on bending, shear, compression, and local contact deformation; development of the mesh transfer matrix; development of an automatic system solver to allow the engineer to analyze systems of arbitrary construction; and the development of a matrix solver to efficiently handle large systems. A computer analysis demonstrates the significance of terms included in the stiffness evaluation as compared with less rigorous treatment in the literature. An analytical example problem illustrates the automated model generation through complete rotor system dynamic response analysis produced by the current work with special attention to the significance of parametric excitation due to the gear mesh.
Ph. D.

碩士
國立臺灣海洋大學
機械與機電工程學系
94
This study provided an optimum searching method for designing the shafting system. The purpose was to avoid design errors which cause damages to the shafting system. This method utilized Computer-Aided Engineering (CAE) of the Finite Element Method to analyze strengths of the shafting system. It is a precise calculating method which can replace some traditional methods, such as three moment equation method. A simple shafting system model was used to study though three moment method and finite element method. After comparing two results, showed that the maximum deviation of reaction force is 6.84 %, and the minimum is 2.1 %. Computer-Aided Design (CAD) software was utilized to change the curve (offset of bearings) of the shafting system. Then the models were provided for CAE software to analyze individually. Finally, a set of optimum offset bearing positions were found. Comparing the outcome above-mentioned with the shipyard’s original design values, the maximum offset deviation was 0.44 millimeter on the crank shaft, and the minimum was 0.36 millimeter on the intermediate shaft. According to above results, the CAD and CAE optimum searching method has proved that its technical capability as design of shafting system for large merchant ships.

碩士
國立高雄應用科技大學
模具系碩士在職專班
104
This study concentrates on propulsion shafting design and parameters study for MIL-STD-2189 that is a document of design methods for naval shafting. The thesis gets relevant data results and performs case research analysis along with verification for naval propulsion shafting design. Bearing stress and shafting load are designed in the safety range to prevent the shaft and propeller with unnecessary vibration. The study provides reference data for future naval ship propulsion system design and configuration modification. The results for both submarines and surface ships shafting are validated by case studies and proven feasible after the validation. It should be noted that in addition to obtaining the required relevant parameters, boat and environmental conditions in paragraph should be the same as that of the document providing, otherwise the expression will not be validated.

碩士
國立臺灣海洋大學
機械與輪機工程學系
93
Abstract The design of shafting alignment for high speed craft is one of the most important design progresses which related to the successful of ships construction and the safety of life at sea in term of shipbuilding. The purpose of this thesis is mainly to study problems of the propulsion shaft alignment over 100 gross tons high speed crafts built by the local shipyards. Main concerns are driven to adopt two design methodologies, the finite element method (FEM) and the three moment equation method (TMEM), to calculate the static reaction forces at shaft bearings for real case of propulsion shafting system, and then to compare these results with those original design values, such that the accuracy and reliability of currently used design methodologies can be verified and shown. It should be noted that the design target for the analysis to confirm these bearing reaction forces are fully complied with the requirements of High Speed Craft Code of Classification Society, and to meet the original design values in a static shafting alignment analysis. As a result, it shows that the numerical solutions for static shafting bearing load of real cases by using two design methodologies, which match well with the original design values obtained by shipyard. The maximum deviation of bearing load is -9.33%, and the minimum is -2.33% which was less than 15% of maximum acceptable design deviation for bearing load. It also found that the bearing pressure complied with the requirements of 0.55N/mm2 for High Speed Craft Code of Classification Society. Moreover, the maximum design truncation error for evaluation the reliability and accuracy to the real case of shafting is 1.43% which was less than 2.0% - 2.5% of acceptable design range. The conclusion to this study is verified that the two design methodologies can further be applied to the practical design of shafting alignment for high speed craft. It is not only to provide the reliable calculation program and software of static shafting alignment for high speed craft, but also offer more reliable design information of shafting alignment for local shipyard’s designer and the researcher in the future. Besides, it also offer a safer and more reliable guarantee for marine propulsion shafting and reduce the possibility of machinery damage and malfunction and thus, they can promote the safety of life at sea, and the whole running and economical efficiency for the ship owner. Key words: High Speed Craft, Shafting Alignment, Finite Element Method, Three Moment Equation Method.

碩士
國立高雄海洋科技大學
輪機工程研究所
92
This thesis is to research mainly the lateral vibration of ship propulsion shaft system. The investigation on shaft vibration uses the Timoshenko beam theory, which not only considers bending deformation and also adds the effects of shear deformation and rotary inertia, as the foundation to obtain more accurate solutions. And the numerical solutions are obtained by using the finite element method . In this article, taking an actual merchant ship as model for the simulation and the verification, relying on the changes of bearing position for the shaft, and the design changing the solid shafting into the hollow shafting as its key point, are to investigate those effects of its shaft’s natural frequency, the bearing stress distribution as well as the static and dynamic loadings, to avoid the resonance phenomena and obtain the smaller loading on the bearings, also to gain the better setting positions of those bearings as well as the superior inner and outer diameters values of the hollow shafting. Finally, the discussion on considering the different strength of bearing stiffness and the damping effect for the influence of whole shafting is also given.

碩士
國立高雄海洋科技大學
輪機工程研究所
95
The object of this paper is to develop a technique for predicting the deformation of a shaft using its deflection variation information. Because the information concerning the external forces applied on the shaft and its deflection variation cannot be completely obtained, the deformation behavior of the shaft cannot be directly determined. To solve this problem, this paper uses the known deflection variation of the shaft incorporated with the optimization technique to find the unknown forces applied on the shaft and predict its possible deformation behavior. Because the deformation variation of the shaft obtained are very reasonable, the presented technique should be reliable. Keywords: deflection variation of the shaft, optimization

碩士
國立高雄應用科技大學
模具系碩士在職專班
106
Propulsion shafting is used to provide the propelling power for all kinds of ships. In order to coordinate with the inshore combat, Taiwan Navy is now designing and constructing the fast attack cruise shups (AKA FACG) with highiy maneuverability, stealthy function, and better sea keeping. However, Taiwan Navy makes propulsion on FACG with nickel-based alloys, on which the cranks are mainly caused by metal fatigue and engine vibration. The research direction of the paper is focusing on those cranks that are found during regular maintenance then to set up the propulsion shafting lifetime by evaluating the length and depth of the cranks affected by various stress and metal fatigue which provides us the reference of the follow up usage and replacing. This thesis analyzes material fatigue through numerical simulation analysis software ANSYS Workbench 18.1 by evaluating, propulsion shafting stress, strain, deformation, safety factor, damage and life data, The establishment of a big data base with relevants result could offer the Logistics and Support Command of Taiwan Navy in many aspects, such as the decision of maintenance, inspection and replacing propulsion sfafting.

Thesis (M.S.)--University of Wisconsin--Madison, 1994.
Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 171-174).

碩士
國立臺灣海洋大學
輪機工程學系
104
Global trade liberalization pushes forward economical growth and all industries around the globe are even more prosperous. The convenient logistics of bulky and mass goods deeply depends on shipping. A safe, reliable, speedy and punctual shipment rely on navigation safety and high speed. Since main engine and shafting are core of ship's propulsion systems, high efficiency and quality of propulsion have become the main focus of both shipbuilder and owner. To ensure safe and enduring navigation, accurate alignment during installation of main engine (M/E) and shafting system are the most crucial matter. Before installation of M/E and shafting system, the shipbuilder is to mark initial center line of ship hull which is used as the guide line of above mentioned alignment. As a result, the shipbuilder can obtain exact the same initial center line of ship hull conforming with M/E and shafting system. On the voyage, the heated/expanded lubrication oil caused a running M/E to offset in the engine base part. In this regard, the engine base is to be adjusted to a leveling manner simultaneously matching design condition of the tolerance of M/E dropping and crankshaft deflection, then the subsequent components are allowed to install on to the M/E. When propulsion shafting is rotating, it is to undertake loads from propeller bending moment and stress and corresponding bending stress from propeller and shafting. Additionally, when a ship is sailing for a long period of time, the stormy weather caused ship's hull deformity which formed phenomenon of certain number of bearings low-load or unload. Each position load and bending stress when captain is sailing for a long time, the shape of ship is deformed by sea wave to cause unload, because over burden influence, the ship effect the base of main engine double bottom structure deformed by water ballast. The ship ballast to exert influence thruster pad bearing incline to cause extra curve . In accordance with load bearing and the main engine of temperature about cold or hot state, we must check the best position to conform burden's pressure average. When the main engine is non-functioning, we measure the burden of main bearing steady bearing FWD stern bearing to test it comply with a standard or not. However, shaft bending force to vary, use ANSYS to analyze shaft coupling flange of main engine side and intermediate shaft and tail shaft coupling endure of shearing stress and bending moment, we can sure the main engine and shafting propulsion to be reasonable install, the ship will be safe to portage. Keywords: Main Engine Alignment, Shafting Alignment, Propulsion System, Bearing Jack Up Test

碩士
國立高雄海洋科技大學
輪機工程研究所
94
In the existing literature, the conventional Holzer method was usually used for calculating the natural frequencies and mode shapes of a shaft-rotor system with mass moment of inertia of the shaft neglected. In fact, the shaft possesses mass moment of inertia, therefore, the numerical results obtained from the conventional Holzer method will agree with the torsional vibration characteristics of the practical shaft-rotor system only if the mass moment of inertia of the shaft is negligible. To improve the last drawback, this paper presents the enhanced Holzer method such that the mass moment of inertia of the shaft can be considered in the torsional vibration analysis. Firstly, the entire shaft is divided into multiple shaft elements and then the last element is replaced by an equivalent shaft-rotor element with mass moment of inertia of the shaft neglected. Where the torsional spring constant of the shaft element and that of the equivalent shaft-rotor element is exactly the same and the mass moment of inertia of the shaft element is replaced by that of the rotor of the equivalent shaft-rotor element. Assembly of the torsional spring constant and mass moment of inertia of each equivalent shaft-rotor element and the mass moment of inertia of each rotor yields the mathematical model of the entire shaft-rotor system. Finally, the natural frequencies and mode shapes of the shaft-rotor system can be determined by using the procedures similar with those of the conventional Holzer method. For validation, all the numerical results obtained from the enhanced Holzer method are compared with those obtained from the finite element method and good agreement is achieved. Because the expressions for the presented enhanced Holzer method are much easier than those of the finite element method, the presented technique will be meaningful from this point of view.

碩士
國立高雄海洋科技大學
輪機工程研究所
98
This paper presents a tapered shaft element such that the torsional vibration characteristics of a damped shafting system can be easily determined with effect of continuous non-uniformity of the shaft cross-sections being considered. To this end, the shape functions of the tapered shaft element are firstly derived. Then, the stiffness and mass matrices of the last shaft element are determined by means of the Lagrange’s equations. To confirm the reliability of the presented theory, the numerical results obtained from the presented technique are compared with those obtained from a limiting case and good agreement is achieved. Finally, the torsional vibration analysis of a hybrid (tapered) shaft, composed of multiple uniform and tapered shaft segments and carrying multiple disks, is performed to show the applicability of the presented technique. Influence of some relevant parameters, such as damping coefficient, slope of tapered shaft and total number of disks attached to the shaft, on the first five eigenvalues of a torsional shafting system is also investigated. Because the torsional vibration characteristics of a shafting system are important information for the engineers, the presented technique will be significant in practical applications.

Mutual interaction of the two major vibration modes, i.e. torsional and axial, resulting from propeller action in the solid elastic shaft of the merchant ocean going ships is analyzed in this thesis. This type of vibration interaction can be described as torsionally-induced propeller thrust fluctuation. Generated longitudinal vibrations due to the thrust variation, can be the cause of excessive ship hull vibrations in modern merchant ocean going ships. The aim of this study is twofold; i.e. to show how the design of the propulsion line shafting affects the coupling phenomenon between torsional and axial vibrations, and to correlate line shafting design with potential structural problems of the hull. The line shafting design is first addressed using conventional approach which yields information about torsional and axial eigenvalues and stresses. It provides no details regarding propeller coupling. The method used in the analysis is transfer matrix method, which suits well the rotor systems on modern ocean going ships. Vibration coupling computation is then performed using finite element method to demonstrate the importance of obtaining torsionally induced axial force. It is shown that dynamic response of the ship hull will be greatly affected by longitudinal force generated by propeller coupling of torsional and axial vibrations.

博士
國立臺灣海洋大學
系統工程暨造船學系
96
In Taiwan, the material of stainless steel SUS630 is usually used in propulsion shafting system for high-speed crafts. Unfortunately, the pitting corrosion will be a main factor to effect the fatigue life cycle of the stainless alloy SUS630. In this study, the prediction model of the residual fatigue life cycle and the reliability have been established under the pitting corrosion condition for the propulsion shafting system of high-speed crafts. In this study, the growth rate and tendency of pitting corrosion occurred in the stainless steel SUS630 specimen is estimated by the grey system theory through the ferric chloride acceleration corrosion test. Under such pitting corrosions, the prediction model of fatigue life has carried out by the results of the rotation bending tests on a set of specimen. Meanwhile, the constants of fatigue crack growth rate of SUS630 under pitting corrosions have been determined by means of the metallurgical graphs by SEM and the fracture surface analysis techniques. In the consequence of these processes, the residual fatigue life and the reliability of a pitting corroded stainless steel shaft can be assessed. From the results of the pitting corrosion experiment, the tendency of growth rate of pitting corrosion of the SUS630 steel is pertaining to an exponential function with time. Based on the results of fatigue tests on the specimen with pitting corrosions, the residual fatigue life cycle is only 10-20% of that of the uncorroded specimen. By the fracture surface analyses of the SEM graphs, it has shown that the direction of fatigue crack propagation between the stages of crack propagation and abrupt fracture has only a 45° angle of change. In use of the Paris formula, the value of Δk is rated between 26 to 46, the material constants n is determined to be 3 and c is 4.4×10-15 for the stainless steel SUS630 shaft material. The established model in the thesis can be applied to the preliminary design for propulsion shaft under the prescribed reliability index and estimate the allowable limitation of pitting corrosion depth and the residual fatigue life. Meanwhile, in the survey stage, this reliability model can be also applied to ascertain whether the shaft should be repaired or not, once the pitting corrosion depth is measured. Thus, the life cycle reliability and safety of the propulsion shaft system can be envisaged. Key words: propulsion shafting system of high-speed craft, stainless steel SUS630, grey system theory, corrosion fatigue and reliability

碩士
國立高雄科技大學
模具工程系
107
The propulsion shaft systems are utilized on most of the ships' propulsion for patrolling, escorting, anti-subs, mine laying purposes. Taiwan Navy's self-constructing ship projects proposed littoral combat ship designs with abilities of stealth, high maneuvering, and seakeeping. The propulsion shaft is non-hollow one -piece forming nickel based alloy design. However, in actual industrial practice, the shaft might be damaged by impacts, vibrations, metallic fatigue, that produce seams or cracks on the shaft. This study concentrates on establishing shrinkage model and utilize both experimental and numerical methods to analyze material dyamics. The numerical model is established by utilizing ANSYS Workbench 18.0 finite element based software to observe shrinkage model crack generation length, degree of damage and available life cycles. The results can enlarge the Naval shaft mechanics data base for further references on ship’s industrial practices.

碩士
國立高雄第一科技大學
機械與自動化工程所
91
ABSTRACT: In this Thesis, an intelligent hybrid Taguchi-genetic algorithm (IHTGA) approach is proposed to search optimal bearing offsets of shafting alignment for the vessel propulsion system. Its objectives are to minimize the shaft normal stress and shear force. Its constraints include permissible reaction forces and stresses of bearings, and shear forces and bending moments of the shaft thrust flange at operation conditions, which mainly contain cold and hot conditions. As well know, the correct alignment of the shafting system for main propulsion system is important to ensure the safe operation of a vessel. In order to obtain a set of acceptable forces and stresses for bearings and shaft at operation conditions, a set of optimal bearing offsets to be determined. However, instead of usually carried out on a time-consuming trial-and-error procedure in most of shipyard, the IHTGA approach is applied to search for the above bearing offsets. The IHTGA is to combine traditional genetic algorithms (TRGAs) with Taguchi method. Taguchi method is inserted between crossover and mutation operations of TRGAs. Then, the systematic reasoning ability of Taguchi method is incorporated in the crossover operations to intelligently select the better genes to achieve crossover, and consequently enhance the genetic algorithms. Therefore, the IHTGA can be more robust, statistically sound, and quickly convergent. Its fitness function is assigned as a pseudo objective function, which is a linear combination of design objectives and constraints by penalty function method. At the same time, the bearing reaction forces and stresses, and the shaft normal stresses, bending moments and shear forces become determined by using finite element method. The computational experiments show that the proposed IHTGA approach can significant reduce alignment time and improve performance as compared with trial-and-error result for 2200 TEU container vessel.

yes
Traditional rotor dynamics mainly focuses on the steady- state behavior of the rotor and shafting. However, for systems such as hydro turbine generating sets (HTGS) where the control and regulation is frequently applied, the shafting safety and stabilization in transient state is then a key factor. The shafting transient state inevitably involves multiparameter domain, multifield coupling, and coupling dynamics. In this paper, the relative value form of the Lagrange function and its equations have been established by defining the base value system of the shafting. Takingthe rotation angle and the angular speed of the shafting as a link, the shafting lateral vibration and generator equations are integrated into the framework of generalized Hamiltonian system. The generalized Hamiltonian control model is thus established. To make the model more general, additional forces of the shafting are taken as the input excitation in proposed model. The control system of the HTGS can be easily connected with the shafting model to form the whole simulation system of the HTGS. It is expected that this study will build a foundation for the coupling dynamics theory using the generalized Hamiltonian theory to investigate coupling dynamic mechanism among the shafting vibration, transient of hydro turbine generating sets, and additional forces of the shafting.
National Natural Science Foundation of China under Grant Nos. 51179079 and 50839003

博士
國立臺灣海洋大學
機械與機電工程學系
103
ABSTRACT The shipbuilding industry, trial-and-error design method for shafting alignment calculation at the initial design stage of shafting arrangement is mostly carried out by some shipyard designers. But this design method is a design method without basing of engineering knowledge, so it is in general a time-consuming and cost-wasting design procedure in the past. Therefore, the design reliability of theory applied when calculating the high sensitivity of shafting alignment must be determined especially at the initial design stage of shafting arrangement and calculation for the vertical static bearing loads (reaction forces) and pressures in positive uniform values, which complied with the design requirements of High Speed Craft Code of Classification Society. Moreover, adjusting a highly sensitive shaft line within a short period to obtain a reasonable positive design value for each bearing reaction force (load) and bearing pressure for the entire propulsion shafting system is very difficult. Any minor changes in the bearing location and/or off-set design values may cause different analytical results with a large design deviation, such that the finally design result may not comply with the requirements from classification societies and the design criteria from manufacturers. ARPSO algorithm when applied to the design optimization for propulsion shafting alignment calculation and arrangement in the initial design stage of shafting arrangement, searches for the values of global optimal design parameter for each bearing off-set and location in order to create a brand new optimal shafting arrangement. ARPSO-SHAALIN design optimization program, an innovative design program, successfully combines and integrates the design theories of Three Moment Equation Method (TMEM) with Attractive and Repulsive Particle Swarm Optimization (ARPSO) algorithm for automatically calculating and optimizing the design values of each static supporting bearing load, bearing pressure, bearing location and bearing vertical off-set is developed for such a theoretical basis to enable a quick and precise design analysis for propulsion shafting alignment calculation and arrangement. ARPSO-SHAALIN design optimization the results of each vertical static bearing load and pressure on the brand new optimal shafting arrangement are in positive uniform values, which is not only complied with the design requirements of High Speed Craft Code of Classification Society and Maker design standard, but also the ARPSO-SHAALIN design optimization program improves the un-uniform vertical static bearing load and pressure calculated by shipyard original design. Moreover, the design optimization output values of computation experiments verified that the proposed ARPSO-SHAALIN design optimization having the strong capabilities to reduce the design costs for time and promote the design performance for propulsion shafting alignment calculation and arrangement of High Speed Crafts while compared with the trial-and-error design method. Keywords: Design Optimization, Propulsion Shafting Alignment Calculation, High Speed Crafts, ARPSO (Attractive and Repulsive Particle Swarm Optimization) Algorithm, TMEM (Three Moment Equation Method), Static Bearing Load

Rotating machinery is widely used in many industrial fields and is often damaged owing to the breathing of the fatigue crack. The fatigue crack opens and closes once per revolution during shaft rotation. The breathing of the fatigue crack reduces the stiffness of the shaft and hence alters its dynamic response. It changes the vibration characteristics of the shaft. Fatigue cracks are a common occurrence in large rotor systems and can cause catastrophic failure. Detecting faults in rotating machinery before failure is the best way to avoid damage. However, a generalised method of positively identifying a fatigue crack as the cause of anomalous vibrations is not yet available. Vibration diagnostics deliver insights into the mechanical ‘health’ of rotating machinery in real-time when the machine is running. However, studying the vibrations of naturally occurring fatigue cracks is difficult because shafts will often either fail before, or be taken out of service once, the crack is identified. Artificially introduced cracks do not exhibit behaviour identical to that of natural ones owing to the difficulty in cutting into a shaft and leaving a slot with close to zero radius at the crack tip. Therefore, considerable efforts have been devoted to numerically modelling cracked rotors and simulating their operating conditions so that the vibrations can be studied. Numerical modelling techniques are many and varied. In the present thesis, the literature on cracked rotor dynamics is reviewed. Of the crack modelling techniques reviewed, the second area moment method is identified as having potential for improvement. The second area moment method accounts for reduction in bending stiffness of a cracked rotor. Breathing of the fatigue crack is directly related to the second area moment at the crack location. It leads to changes in one of the shaft mechanical properties, stiffness. In a shaft with a crack, the shaft stiffness will change periodically at different rotational angles. Modelling the breathing of the fatigue crack is the key step to analyse the vibration response of a cracked shaft. This breathing phenomenon must be modelled accurately to detect the crack in a rotor. However, it is not yet fully understood how partial crack closure interacts with changes in shaft stiffness, and further, with key variables of the crack detection problem. Unfortunately, almost all existing models are not applicable near the shaft critical speed, because equations of motion developed under the assumption of rotor weight dominance are no longer suitable for analysis near the critical speed. Moreover, localised reduction in stiffness is directly related to crack depth, whereas global reduction in stiffness is directly related to the crack depth and crack location along the shaft. However, researchers opt to either ignore crack location or mitigate its effects. From the literature review, it is evident that accurate modelling, which considers the influence of the crack location and the effect of the unbalance force on the crack breathing behaviour of the fatigue crack to calculate the second area moment of inertia of a cracked shaft to form the stiffness matrix, is still absent. The first topic in this research work is developing a new unbalance model—effectual bending angle—to evaluate the crack breathing response and calculate the second area moment of inertia at any crack location along the shaft length. It is developed considering the effects of unbalance force, rotor weight, rotor physical and dimensional properties and a more realistic fixed-end boundary condition. It governs the opening and closing of a shaft crack that describes the proximity of the shaft bending direction (or shaft deformation direction) relative to the crack direction. The crack breathing behaviours have been studied for every possible crack location and shaft rotation angle. The presented model identifies unique crack breathing behaviours under the influence of unbalance force and rotor physical and dimensional properties, showing the strong dependence of the breathing mechanism on the crack location. Further, the newly developed model is used to obtain the second area moment of inertia of crack cross-section closed area at any crack location along the shaft length under the unbalance force effect about the centroid. The newly developed unbalance model results are validated through 3D FEM results. This thesis finds that this analytical unbalance model captures the main features of crack breathing and is in good agreement with the 3D FEM. However, the approach adopted in this study of using the existing balance model to identify the crack breathing behaviour and the second area moment of inertia needs to be improved. In this research work, a new method is developed to determine crack breathing, which is an improvement in terms of accuracy on adopted methods. The improvement is owing to the removal of two simplifying assumptions used by previous authors, namely, that the cracked shafts will only experience symmetrical bending and the neutral axis would lie perpendicular to the bending direction, that is, always be horizontal. Both assumptions are shown to be invalid on comparison with results from a three-dimensional finite element model. The newly developed method is then used to evaluate nonlinear crack breathing behaviour under different weight–unbalance force ratios at different crack locations by examining the percentage of opening of a crack. The breathing response predicted by the developed method is validated using the three-dimensional finite element model. The results of the algorithm show a significant improvement in accuracy when compared with data from the three-dimensional finite element model of cracked rotors. The mathematical modelling of calculating the cross-section properties, namely, the second area moment and centroid location, is also improved in this research work by considering neutral axis inclination, removing the assumption of collinearity between the bending moment and neutral axis at the crack location. The newly developed equations are used to evaluate the second area moment of inertia as a function of the crack locations and shaft’s angle of rotation about centroid axes. It is found to be highly dependent on crack location, similar to crack breathing behaviours. The work presented in this thesis demonstrates that a common assumption in the literature—that the effects of axial position of a crack can be neglected—is incorrect. The second topic of this research work is analysis of the crack breathing behaviour of an unbalance shaft with a more realistic transverse slant crack and elliptical crack at different crack locations along the shaft length. A three-dimensional finite element model consisting of a two-disk rotor with a crack is simulated with unbalance mass. The finite element model is simulated using Abaqus/standard. It is simulated considering the effects of unbalance force, rotor weight, rotor physical and dimensional properties and a more realistic fixed-end boundary condition. Crack breathing behaviours are visualised by the variation of the crack closed area and represented quantitatively by the percentage of the closing of the crack. Crack breathing behaviour is found to strongly depend on its axial position, angular position and depth ratios as well as unbalance force ratios and angular position of unbalance force. Compared with the balance shaft crack breathing behaviour, two different crack breathing regions along the shaft length are identified, where shaft stiffness is larger or smaller, depending on the unbalance force orientation, magnitude and crack location. However, four specific crack locations along the shaft length are identified where the crack remains fully closed or open or the same as in balance shaft crack breathing during shaft rotation under different loading conditions. The presented research results suggest that a more accurate prediction of the dynamic response of cracked rotors can be expected on considering the effects of unbalance force and individual rotor physical properties on crack breathing. The presented method and results of this research can be used to obtain the stiffness matrix of a cracked shaft element and then to study the vibration response of a cracked rotor where the rotor-weight-dominant assumption on crack breathing no longer holds.

The foremost focus of this thesis is to develop analytical tools that improve society’s collective understanding of the behavioural mechanisms and indicators of fatigue cracks in a rotating shaft. This focus is followed by the desire to improve the likelihood of detecting fatigue cracks in real rotating machinery before failure occurs. Since analytical models of fatigue cracks in rotating shafts are complex and multifaceted, this thesis will narrow the scope by examining the effects of rotating unbalance, vibration, neutral axis orientation and crack-front shape on the breathing behaviour of a fatigue crack in a shaft, and the stiffness changes and vibration of a cracked rotor. The crack type chosen for analysis throughout this thesis is a singular transverse fatigue crack that occurs due to high-cycle fatigue of the rotor shaft as it is occurs quite often in real rotating machinery. A typical precursor for detecting the presence of fatigue cracks in rotating machinery is to develop a robust mathematical or software model that describes the behaviour of fatigue cracks under a variety of conditions. In this thesis, analytical models and three-dimensional finite element software models are the chosen methods for developing new crack breathing models and predicting the vibration of a cracked rotor using the new models.