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M. Tech. (Department of Metallurgical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / To meet the ever-increasing demand for maintenance of gear systems, industrial companies have traditionally depended on the shutdown of the machines before processing the fault diagnosis. Nowadays, online monitoring has proven to be effective in terms of machine state analysis and fault prediction. However, the application of such a technique in the analysis of combined multiple nonlinear faults is still a subject of research. The vibration signature of a coexisting nonlinear crack and pit in two-stage gear system is unknown, it can be regarded as one of the most difficult problems to extract and diagnose. Additionally, incorporating both a crack and a pit into numerical models is a time-consuming process that demands a breadth of mechanical understanding. Diagnostics of faulty gears, on the other hand, can be performed in the time and frequency domain or in the Time-Frequency domain, depending on the complexity of the vibration. Non-linear and non-stationary phenomena (Features) occur when repeated pitting and cracking faults occur, reducing the reliability of standard signal processing methods (Gear displacement and Fast Fourier Transform). This thesis solves each of these shortcomings by developing an eight-degree-of-freedom (DOF) gear model with a breathing crack and multiple pitted gear teeth. The identified spur-gear model enabled the investigation of the crack and pitting signatures and their effect on the ensuing vibrations independently of the action of other system components. Additionally, when pitting and cracking coexist, the study was conducted to determine the influence of such a failure on the transmission system. Theoretical results indicated that the presence of pitting and crack in the tooth of the gear resulted in a decrease in mesh stiffness. Additionally, the influence of the breathing pitting and crack results in material fatigue, which results in the generation of a random term in the vibration signal. To corroborate the acquired results, several experimental tests on a spur-gear test rig with a defined pit and crack size range were undertaken under a variety of conditions. In comparison to the presented methodologies, theoretical and experimental results indicate that 3D Frequency-RPM analysis is the most sensitive and resilient method for the early detection and identification of pit and crack faults. Furthermore, when crack or pit faults are studied individually, the STFT analysis yields interesting results. The feature analysis revealed that, when using the Time-Frequency technique, the crack and pit combination in a two-stage gear system is a priori more efficient than the other options.

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Nowadays, increasing pressure from legislation and customer demands in the automotive industry are forcing manufacturers to produce greener vehicles with lower emissions and fuel consumption.As a result, electrified and hybrid vehicles are a growing popular alternative to traditional internal combustion engines (ICE). The noise from an electric vehicle comes mainly from contact between tyres and road, wind resistance and driveline. The noise emitted from the driveline is for the mostpart related to the gearbox. When developing a driveline, it is a factor of importance to estimate the noise radiating from the gearbox to achieve an acceptable design.Gears are used extensively in the driveline of electric vehicles. As the gears are in mesh, a main intrusive concern is known as gear whine noise. Gear whine noise is an undesired vibroacoustic phenomenon and is likely to originate through the gear contacts and be transferred through themechanical components to the housing where the vibrations are converted into airborne and structure-borne noise. The gear whine noise originates primarily from the excitation coming from transmission error (TE). Transmission error is defined as the difference between the ideal smoothtransfer of motion of a gear and what is in practice due to lack of smoothness.The main objective of this study is to simulate the vibrations generated by the gear whine noise in an electric powertrain line developed by AVL Vicura. The electric transmission used in this study provides only a fixed overall gear ratio, i.e. 9.59, under all operation conditions. It is assumed thatthe system is excited only by the transmission error and the mesh stiffness of the gear contacts. In order to perform NVH analysis under different operating conditions, a multibody dynamics model according to the AVL Excite program has been developed. The dynamic simulations are thencompared with previous experimental measurements provided by AVL Vicura.Two validation criteria have been used to analyse the dynamic behaviour of the AVL Excite model: signal processing using the FFT method and comparison with the experimental measurements.The results from the AVL Excite model show that the FFT criterion is quite successful and all excitation frequencies are properly observed in FFT plots. Nevertheless, when it comes to the second criterion, as long as not all dynamic parameters of the system such as damping or stiffnesscoefficients are provided with certainty in the model, it is too difficult to investigate the accuracy of the AVL Excite model. Another investigation is a numerical design study to analyses how the damping coefficients influence the response. After reducing the damping parameters, the results show that the housing and bearings have the highest influence on the response. If more acceptable results are desired,future studies must be concentrated on these to obtain more acceptable damping values. / För närvarande tvingar ökat tryck från lagstiftning och kundkrav inom bilindustrin tillverkarna attproducera grönare fordon med lägre utsläpp och bränsleförbrukning. Som ett resultat ärelektrifierade och hybridfordon ett växande populärt alternativ till traditionellaförbränningsmotorer (ICE). Bullret från ett elfordon kommer främst från kontakten mellan däckoch väg, vindmotstånd och drivlinan. Bullret från drivlinan är i huvudsak relaterat till växellådan.Vid utveckling av en drivlina är det av betydelse att uppskatta bullret från växellådan för att uppnåen acceptabel design.Utväxlingar används i stor utsträckning i elfordons drivlina. Eftersom kugghjulen är i kontaktuppstår ett huvudproblem som är känt som ett vinande ljud från kugghjulskontakten.Kugghjulsljud är ett oönskat vibro-akustiskt fenomen och uppstår sannolikt på grund avkugghjulkontakterna och överförs via de mekaniska komponenterna till växellådshuset därvibrationerna omvandlas till luftburet och strukturburet ljud. Kugghjulsljudet härstammarhuvudsakligen från exciteringen som kommer från transmissionsfel (TE) i kugghjulskontakten.Överföringsfelet definieras som skillnaden mellan den ideala smidiga rörelseöverföringen hoskugghjulen och rörelsen som sker i verkligheten på grund av ojämnheter.Huvudsyftet med denna studie är att simulera vibrationerna som genereras avkugghjulskontakterna i en elektrisk drivlina utvecklad av AVL Vicura. Den elektriska drivlinan somanvänds i denna studie har endast ett fast utväxlingsförhållande, dvs 9,59, för alladriftsförhållanden. Det antas att systemet är exciterat endast av överföringsfelet och kugghjulensstyvhet i kuggkontakterna. För att kunna utföra NVH-analys under olika driftsförhållanden har enstelkroppsdynamikmodell utvecklats med hjälp av programmet AVL Excite. De dynamiskasimuleringarna jämförs sedan med tidigare experimentella mätningar som tillhandahålls av AVLVicura.Två valideringskriterier har använts för att analysera det dynamiska beteendet hos AVL Excitemodellen:signalbehandling med FFT-metoden och jämförelse med experimentella mätningar.Resultaten från AVL Excite-modellen visar att FFT-kriteriet är ganska framgångsrikt och allaexcitationsfrekvenser observeras korrekt i FFT-diagrammen. Men när det gäller det andra kriteriet,så länge som inte alla dynamiska parametrar i systemet, såsom dämpnings- ellerstyvhetskoefficienter, är tillförlitliga i modellen, är det för svårt att undersöka exaktheten hos AVLExcite-modellen.En annan undersökning som utförts är en numerisk designstudie för att analysera hurdämpningskoefficienterna påverkar responsen. Efter minskning av dämpningsparametrarna visarresultaten att växellådshus och lager har störst inflytande på resultatet. Om mer acceptabla resultatär önskvärda måste framtida studier koncentreras på dessa parametrar för att uppnå mer acceptabladämpningsvärden.

ABSTRACT NON-LINEAR MATHEMATICAL MODELING OF GEAR-ROTOR-BEARING SYSTEMS INCLUDING BEARING CLEARANCE G&Uuml / RKAN, Niyazi Ersan M.S. Department of Mechanical Engineering Supervisor: Prof. Dr. H. Nevzat &Ouml / ZG&Uuml / VEN November 2005, 130 pages In this study, a non-linear mathematical model of gear-rotor systems which consists of elastic shafts on elastic bearings with clearance and coupled by a non-linear gear mesh interface is developed. The mathematical model and the software (NLGRD 2.0) developed in a previous study is extended to include the non-linear effects due to bearing clearances by using non-linear bearing models. The model developed combines the versatility of using finite element method and the rigorous treatment of non-linear effect of backlash and bearing clearances on the dynamics of the system. The software uses the output of Load Distribution Program (LDP), which computes loaded static transmission error and mesh compliance for the contact points of a typical mesh cycle, as input. Although non-varying mesh compliance is assumed in the model, the excitation effect of time varying mesh stiffness is indirectly included through the loaded static transmission error, which is taken as a displacement input into the system. Previous computer program which was written in Fortran 77 is rewritten by using MatLAB 7.0 and named as NLGRD (Non-Linear Geared Rotor Dynamics) Version 3.0. The program is highly flexible and open to further developments. The program calculates dynamic to static load ratio, dynamic transmission error, forces and displacements at bearings. The mathematical model suggested and the code (NLGRD version 3.0) are validated by comparing the numerical results obtained from the model suggested with experimental data available in literature. The results are also compared with those of previously developed non-linear models. The effects of different system parameters such as bearing stiffness, bearing clearance and backlash on the gears are investigated. The emphasis is placed on the interaction of clearances in bearings with other system parameters.

Due to their large torque-speed ratio and transmission efficiency, planetary gears are widely used in the automotive industry. However, high amplitude vibrations remain their critical weakness, which limits their usage especially when new strict noise legislations come into action. A new approach to handle the instability problems of planetary gears encountered in real industrial context is presented in this work. First, the dynamic response of a planetary gear failing to pass the noise regulations is theoretically investigated through an analytical model. The equations of motion were solved using the Spectral Iterative Method. The observed experimental results correlated well with those from the developed model. In order to limit the resonance phenomena, impacts of different macro and micro-geometry modifications were analytically investigated: quadratic teeth profile, different planets positioning, different number of teeth and number of planets. Optimum modifications were retrieved and are expected to be tested experimentally on a test bench and on the truck. Finally, the analytical model’s limits and sensitivity to different parameters were investigated in order to certify its reliability, and suggestions for improvements were presented.

Nowadays, increasing pressure from legislation and customer demands in the automotive industryare forcing manufacturers to produce greener vehicles with lower emissions and fuel consumption.As a result, electrified and hybrid vehicles are a growing popular alternative to traditional internalcombustion engines (ICE). The noise from an electric vehicle comes mainly from contact betweentyres and road, wind resistance and driveline. The noise emitted from the driveline is for the mostpart related to the gearbox. When developing a driveline, it is a factor of importance to estimatethe noise radiating from the gearbox to achieve an acceptable design.Gears are used extensively in the driveline of electric vehicles. As the gears are in mesh, a mainintrusive concern is known as gear whine noise. Gear whine noise is an undesired vibroacousticphenomenon and is likely to originate through the gear contacts and be transferred through themechanical components to the housing where the vibrations are converted into airborne andstructure-borne noise. The gear whine noise originates primarily from the excitation coming fromtransmission error (TE). Transmission error is defined as the difference between the ideal smoothtransfer of motion of a gear and what is in practice due to lack of smoothness.The main objective of this study is to simulate the vibrations generated by the gear whine noise inan electric powertrain line developed by AVL Vicura. The electric transmission used in this studyprovides only a fixed overall gear ratio, i.e. 9.59, under all operation conditions. It is assumed thatthe system is excited only by the transmission error and the mesh stiffness of the gear contacts. Inorder to perform NVH analysis under different operating conditions, a multibody dynamics modelaccording to the AVL Excite program has been developed. The dynamic simulations are thencompared with previous experimental measurements provided by AVL Vicura.Two validation criteria have been used to analyse the dynamic behaviour of the AVL Excite model:signal processing using the FFT method and comparison with the experimental measurements.The results from the AVL Excite model show that the FFT criterion is quite successful and allexcitation frequencies are properly observed in FFT plots. Nevertheless, when it comes to thesecond criterion, as long as not all dynamic parameters of the system such as damping or stiffnesscoefficients are provided with certainty in the model, it is too difficult to investigate the accuracy ofthe AVL Excite model.Another investigation is a numerical design study to analyses how the damping coefficientsinfluence the response. After reducing the damping parameters, the results show that the housingand bearings have the highest influence on the response. If more acceptable results are desired,future studies must be concentrated on these to obtain more acceptable damping values. / För närvarande tvingar ökat tryck från lagstiftning och kundkrav inom bilindustrin tillverkarna attproducera grönare fordon med lägre utsläpp och bränsleförbrukning. Som ett resultat ärelektrifierade och hybridfordon ett växande populärt alternativ till traditionellaförbränningsmotorer (ICE). Bullret från ett elfordon kommer främst från kontakten mellan däckoch väg, vindmotstånd och drivlinan. Bullret från drivlinan är i huvudsak relaterat till växellådan.Vid utveckling av en drivlina är det av betydelse att uppskatta bullret från växellådan för att uppnåen acceptabel design.Utväxlingar används i stor utsträckning i elfordons drivlina. Eftersom kugghjulen är i kontaktuppstår ett huvudproblem som är känt som ett vinande ljud från kugghjulskontakten.Kugghjulsljud är ett oönskat vibro-akustiskt fenomen och uppstår sannolikt på grund avkugghjulkontakterna och överförs via de mekaniska komponenterna till växellådshuset därvibrationerna omvandlas till luftburet och strukturburet ljud. Kugghjulsljudet härstammarhuvudsakligen från exciteringen som kommer från transmissionsfel (TE) i kugghjulskontakten.Överföringsfelet definieras som skillnaden mellan den ideala smidiga rörelseöverföringen hoskugghjulen och rörelsen som sker i verkligheten på grund av ojämnheter.Huvudsyftet med denna studie är att simulera vibrationerna som genereras avkugghjulskontakterna i en elektrisk drivlina utvecklad av AVL Vicura. Den elektriska drivlinan somanvänds i denna studie har endast ett fast utväxlingsförhållande, dvs 9,59, för alladriftsförhållanden. Det antas att systemet är exciterat endast av överföringsfelet och kugghjulensstyvhet i kuggkontakterna. För att kunna utföra NVH-analys under olika driftsförhållanden har enstelkroppsdynamikmodell utvecklats med hjälp av programmet AVL Excite. De dynamiskasimuleringarna jämförs sedan med tidigare experimentella mätningar som tillhandahålls av AVLVicura.Två valideringskriterier har använts för att analysera det dynamiska beteendet hos AVL Excitemodellen:signalbehandling med FFT-metoden och jämförelse med experimentella mätningar.Resultaten från AVL Excite-modellen visar att FFT-kriteriet är ganska framgångsrikt och allaexcitationsfrekvenser observeras korrekt i FFT-diagrammen. Men när det gäller det andra kriteriet,så länge som inte alla dynamiska parametrar i systemet, såsom dämpnings- ellerstyvhetskoefficienter, är tillförlitliga i modellen, är det för svårt att undersöka exaktheten hos AVLExcite-modellen.En annan undersökning som utförts är en numerisk designstudie för att analysera hurdämpningskoefficienterna påverkar responsen. Efter minskning av dämpningsparametrarna visarresultaten att växellådshus och lager har störst inflytande på resultatet. Om mer acceptabla resultatär önskvärda måste framtida studier koncentreras på dessa parametrar för att uppnå mer acceptabladämpningsvärden.

This diploma thesis primarily deals with the transmission error issue which is one of the dominant sources of vibration in gear pairs and transmission systems. The vibrations subsequently generate noise which is often subjected to increasingly stricter demands across the industry, including the automotive one. It turns out that reducing the peak-to-peak value of the transmission error has a beneficial effect on the vibro-acoustic properties of gears and gear pairs. This thesis aims to determine the transmission error under static conditions, since a gear pair with a low static transmission error is a good assumption for a low transmission error even under dynamic effects. The resulting values of the transmission error can be influenced already during the design of the gear macro-geometry. It is also suitable to apply micro-geometric adjustments – modifications to the gear teeth. For this reason, the search part of the thesis is dedicated to theoretical knowledge, especially concerning the geometry of gears, modifications of teeth and the overall transmission error and its determination. The transmission error can be determined in several ways, including a technical experiment. However, due to time and financial reasons, this is not always possible, and therefore, the possibility of using numerical simulations is offered. In this thesis, the approach using stress-strain quasi-static contact analysis using the finite element method in Ansys Workbench software is used. The advantage is, among other things, a good comparability of results. The input to the FEM analysis is 3D CAD geometry – in this case, it is specifically a helical gear pair with parallel axes. The model/assembly of this gear pair is created in PTC Creo software fully parametrically, so it is possible to generate arbitrary gear pair configurations by changing the input parameters, which significantly saves time. At the end of this diploma thesis, the stress-strain analysis of various gear configurations is evaluated, with respect to the equivalent stress and contact pressure. Furthermore, the static transmission error – its graphs and peak-to-peak values – is determined from FEM analyses for different gear geometry, including tooth modifications, and for various loading torques. Last but not least, the effects of contact/overlap ratio and centre distance are evaluated.