This thesis investigates the characteristics of static torsional mesh stiffness, load sharing ratio, and transmission errors of gears in mesh with and without a localised tooth crack.Gearing is perhaps one of the most critical components in power transmission systems. The transmission error of gears in mesh is considered to be one of the main causes of gear noise and vibration. Numerous papers have been published on gear transmission error measurement and many investigations have been devoted to gear vibration analysis. There still, however, remains to be developed a general non-linear Finite Element Model capable of predicting the effect of variations of gear torsional mesh stiffness, transmission error, transmitted load and load sharing ratio. The primary purpose of this study was to develop such a model and to study the behaviour of the static torsional mesh stiffness, load sharing ratio, and transmission error over one completed cycle of the tooth mesh.The research outlined in this thesis considers the variations of the whole gear body stiffness arising from the gear body rotation due to tooth bending deflection, shearing displacement, and contact deformation. Many different positions within the meshing cycle were investigated and then compared with the results of a gear mesh having a single cracked tooth.In order to handle contact problems with the finite element method, the stiffness relationship between the two contact areas must be established. Existing Finite Element codes rely on the use of the variational approach to formulate contact problems. This can be achieved by insertion of a contact element placed in between the two contacting areas where contact occurs. For modelling of gear teeth in mesh, the penalty parameter of the contact element is user-defined and it varies through the cyclic mesh. A simple strategy of how to overcome these difficulties is ++ / also presented. Most of the previously published finite element analysis with gears has involved only partial teeth models.In an investigation of gear transmission errors using contact elements, the whole body of the gears in mesh must be modelled, because the penalty parameter of the contact elements must account for the flexibility of the entire body of the gear not just the local stiffness at the contact point.

The investigation of numerical methods for modelling the mechanism properties ofinvolute spur gears in mesh, over the mesh cycle, forms the major part of this thesis.Gearing is perhaps one of the most critical components in power transmission systemsand the transmission error of gears in mesh is considered to be one of the main causes ofgear noise and vibration. Numerous papers have been published on gear transmissionerror measurement and many investigations have been devoted to gear vibration analysis.There still, however, remains to be developed a general Finite Element Model capable ofpredicting the effect of variations in rigid body gear tooth position, in which the criticalstage is the prediction of gear behaviour with profile modifications (including tip-relief).In this thesis, FEA results have been obtained by using various techniques including: (a)adaptive re-mesh with contacts using quad (2D) and brick (3D) elements and (b) theelement birth and death option. Tooth profile modifications can affect the behaviour ofthe gear meshing including the T.E., ratio of local deformation and load-sharing ratioresults, etc, providing an alternative method for gear design. In the high order end, theelastic strains of the gear-shaft system have also been investigated. The results in thisthesis have shown the potential for using strain-vibration relationships to monitor orcontrol the transmission system.The investigations have also included some analysis with non-metallic gears, anapplication area that is rapidly growing. The results achieved here are at a fundamentalstage, and further research would necessitate applying a coupled field analysis (structuraland thermal).

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Optimum design of multistep gearbox, since many high-performance power transmission applications (e.g., automotive, space industry) require compact volume, has become an important interest area. This design application includes more complicated problems that are not taken into account while designing single stage gear drives. Design applications are generally made by trial and error methods depending on the experience and the intuition of the designer. In this study, using Visual Basic 6.0, an interactive program is developed for designing multistep involute standard and nonstandard spur gearbox according to the American Gear Manufacturers Association (AGMA) Standards 218.01 and 2001- B88. All the equations for calculating the pitting resistance geometry factor I, and the bending strength geometry factor J, are valid for external spur gears that are generated by rack-type tools (rack cutters or hobs). The program is made for twostage to six-stage gear drives, which are commonly used in the industry. Compactness of gear pairs and gearbox, and equality of factor of safety against bending failure is taken as the design objective. By considering the total required gear ratio, the number of reduction stages is input by the user. Gear ratios of every stage is distributed to the stages according to the total gear ratio that satisfies the required precision (from &plusmn / 0.1 to &plusmn / 0.00001 on overall gear ratio) depending on the user selected constraints (unequal gear ratio for every stage, noninteger gear ratio e.g.). Dimensional design is determined by considering bending stress, pitting stress, and involute interference constraints. These steps are carried out iteratively until a desirable solution is acquired. The necessary parameters for configuration design such as number of teeth, module, addendum modification coefficient, are selected from previously determined gear pairs that satisfies the constraints by user interaction considering the performance criterion from the developed program. The positions of gears and shafts are determined automatically in order to keep the volume of gearbox as minimum while satisfying the nonlinear spatial constraints (center distance constraint for proper meshing of gear pairs, face distance constraint for proper assembly of pinion and gear having same shaft, gear interference constraint for preventing interferences between gears, shaft interference constraint for preventing interferences between gears and shafts) by using DLL (Dynamic Link Library) technology of Lingo 8.0 optimization software together with Visual Basic 6.0. If shaft interference constraint is removed then cantilevered mounting of gear pairs would also be possible, otherwise the gears should be mounted between bearings. Visual output of assembly is made by using Autodesk Inventor 7.0, automatically by the program.

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