Face-gear drives: Design, analysis, and testing for helicopter transmission applications

The use of face-gears in helicopter transmissions was explored. A light-weight, split-torque transmission design utilizing face-gears is described. Face-gear design and geometry were investigated. Topics included tooth generation, limiting inner and outer radii, tooth contact analysis, contact ratio, gear eccentricity, grinding, and structural stiffness. Design charts were developed to determine minimum and maximum face-gear inner and outer radii. An analytical study showed that the face-gear drive is relatively insensitive to gear misalignment with respect to transmission errors, but the tooth contact is affected by misalignment. A method of localizing the bearing contact to permit operation with misalignment was explored. Two new methods for grinding of the face-gear tooth surfaces were also investigated. The proper choice of shaft stiffness enabled good load sharing in the split-torque transmission design. Face-gear experimental studies were also conducted. These tests demonstrated the feasibility of face-gears in high-speed, high-load applications such as helicopter transmissions

Comportamiento dinámico de transmisiones de engranajes multietapa. Análisis del desfase en el engrane

RESUMEN Las transmisiones de engranajes son sistemas complejos compuestos por numerosos elementos de geometría complicada. El correcto funcionamiento de una transmisión de engranajes, y más concretamente una transmisión planetaria, necesita de la sinergia de muchos factores y se ve afectado por muchos condicionantes que dificultan la identificación de los problemas. A pesar de su complejidad o quizá consecuencia de ella, las transmisiones de engranajes planetarios han adquirido un papel muy relevante en la industria en las últimas décadas. Nuevas aplicaciones y aplicaciones clásicas han surgido o evolucionado hasta el punto en que las transmisiones de engranajes epicicloidales tienen un papel determinante en su buen funcionamiento. Este desarrollo también ha llevado al planteamiento de nuevas hipótesis y a la aparición de nuevos problemas. En relación con la aparición de nuevos problemas y aplicaciones, esta Tesis trata de analizar en profundidad algunos de ellos, así como, estudiar otros posibles escenarios en busca de dar respuesta a algunos de los interrogantes que surgen tanto a fabricantes como a investigadores sobre el correcto funcionamiento de dichas transmisiones. Principalmente, esta Tesis se centra en el papel que juega la geometría en el comportamiento de las transmisiones planetarias. En lo que se refiere a la geometría, en esta Tesis el interés se centra en el impacto del espaciado angular y la fase de engrane, que son consecuencia directa de los criterios de diseño de la transmisión. En más detalle, esta Tesis analiza el impacto que tienen esos criterios en el reparto de carga en transmisiones planetarias. El reparto de carga se escoge como la magnitud que permite analizar el estado de la transmisión a lo largo de las simulaciones. Una vez que se ha establecido el impacto del espaciado y la fase en el comportamiento de la transmisión, se incluyen nuevos efectos. En este caso, se considera la importancia que tienen los inevitables errores de fabricación en las transmisiones planetarias. Estos errores afectan a la calidad, durabilidad y el comportamiento de las transmisiones planetarias, lo cual da una idea de la importancia que los errores tienen en este campo. En esta Tesis, los errores escogidos se limitan a errores en el espesor de los dientes, así como, errores de montaje de los planetas en el portaplanetas. Además, dadas las características de estos errores, su influencia varía dependiendo de las condiciones de trabajo, por esto, se amplía el estudio a diferentes niveles de carga y sentidos de aplicación de la carga. Después de esto, el interés se centra en el análisis de los procedimientos experimentales de medida y su validez. En esta parte de la Tesis se combinan los estudios anteriores con el uso de la medida de deformaciones en la raíz de los dientes del sol para el cálculo de reparto de carga en transmisiones planetarias. Los resultados demuestran que en configuraciones en fase solo se hace visible la influencia del espaciado de los planetas cuando los apoyos de las ruedas cuentan con flotabilidad. Además, la influencia de la flotabilidad en los apoyos demuestra tener un efecto diferente para transmisiones de 5 planetas que para transmisiones de 3 planetas. Además, el comportamiento de las transmisiones con fase secuencial prueba ser peor, en su reparto de carga, que el de la configuración en fase análoga. Esto, se hace más visible cuando se incluyen errores en las transmisiones simuladas. El desequilibrio creado por un error es mayor y el impacto que tiene en los valores máximos y mínimos de carga es mayor debido a la fase en el engrane. En cuanto a las medidas experimentales, los resultados prueban ser imprecisos en comparación con el reparto de carga real en la transmisión. Además, la inclusión de secuencia en la fase de engrane y errores afecta notablemente la precisión de las medidas de deformaciones como una herramienta de cálculo del reparto de carga en transmisiones planetarias. Finalmente, como conclusiones extraídas de los resultados comentados anteriormente, se demuestra como la secuencia en el engrane afecta notablemente al equilibrio en el reparto de carga en las transmisiones y genera desequilibrios debidos al desfase en el engrane. Esta fase de engrane también incrementa el impacto de los errores en el reparto de carga de la transmisión. Por otra parte, otro factor que incrementa el impacto de los errores es el aumento del número de planetas. El impacto de la rigidez se hace patente con otros cambios como la modificación del número de planetas en la transmisión y el tamaño de los ejes sobre los que se montan las ruedas. En cuanto a las medidas experimentales, prueban ser imprecisas en cualquier configuración diferente de una transmisión equiespaciada y en fase sin errores. Además, esta falta de precisión crece con el tamaño del error y se hace mayor para configuraciones secuenciales. Vistas las conclusiones que se extraen es posible plantear nuevas líneas para continuar con este trabajo. En primer lugar, el modelo se puede extender a un planteamiento tridimensional para tener en cuenta la influencia de esta tercera dimensión en los fenómenos estudiados mediante el análisis de transmisiones planetarias helicoidales. Al mismo tiempo, el número de planetas se puede incrementar por encima de 5, así, nuevos escenarios de estudio aparecen, principalmente en configuraciones con un número par de planetas superior a 5. No obstante, en el modelo plano con el número de planetas ya estudiado, las técnicas de medida experimental estudiadas se pueden extender a otros procedimientos que también se utilizan habitualmente

Friction, Vibration and Dynamic Properties of Transmission System under Wear Progression

This reprint focuses on wear and fatigue analysis, the dynamic properties of coating surfaces in transmission systems, and non-destructive condition monitoring for the health management of transmission systems. Transmission systems play a vital role in various types of industrial structure, including wind turbines, vehicles, mining and material-handling equipment, offshore vessels, and aircrafts. Surface wear is an inevitable phenomenon during the service life of transmission systems (such as on gearboxes, bearings, and shafts), and wear propagation can reduce the durability of the contact coating surface. As a result, the performance of the transmission system can degrade significantly, which can cause sudden shutdown of the whole system and lead to unexpected economic loss and accidents. Therefore, to ensure adequate health management of the transmission system, it is necessary to investigate the friction, vibration, and dynamic properties of its contact coating surface and monitor its operating conditions

Condition Monitoring of Helical Gear Transmissions Based on Vibration Modelling and Signal Processing

Condition monitoring (CM) of gear transmission has attracted extensive research in recent years. In particular, the detection and diagnosis of its faults in their early stages to minimise cost by maximising time available for planned maintenance and giving greater opportunity for avoiding a system breakdown. However, the diagnostic results obtained from monitored signals are often unsatisfactory because mainstream technologies using vibration response do not sufficiently account for the effect of friction and lubrication. To develop a more advanced and accurate diagnosis, this research has focused on investigating the nonlinearities of vibration generation and transmission with the viscoelastic properties of lubrication, to provide an in-depth understanding of vibration generating mechanisms and hence develop more effective signal processing methods for early detection and accurate diagnosis of gear incipient faults. A comprehensive dynamic model has been developed to study the dynamic responses of a multistage helical gear transmission system. It includes not only time-varying stiffness but also tooth friction forces based on an elastohydrodynamic lubrication (EHL) model. In addition, the progression of a light wear process is modelled by reducing stiffness function profile, in which the 2nd and 3rd harmonics of the meshing frequency (and their sidebands) show significant alteration that support fault diagnostic at early stages. Numerical and experimental results show that the friction and progressive wear induced vibration excitations will change slightly the amplitudes of the spectral peaks at both the mesh frequency and its sideband components at different orders, which provides theoretical supports for extracting reliable diagnostic signatures. As such changes in vibrations are extremely small and submerged in noise, it is clear that effective techniques for enhancing the signal-to-noise ratio, such as time synchronous averaging (TSA) and modulation signal bispectrum (MSB) are required to reveal such changes. MSB is preferred as it allows small amplitude sidebands to be accurately characterised in a nonlinear way without information loss and does not impose any addition demands regarding angular displacement measurement as does TSA. With the successful diagnosis of slight wear in helical gears, the research progressed to validate the capability of MSB based methods to diagnose four common gear faults relating to gear tribological conditions; lubrication shortfall, changes in lubrication viscosity, water in oil, and increased bearing clearances. The results show that MSB signatures allows accurate differentiation between these small changes, confirming the model and signal processing proposed in this thesi

Contribution to the study of static and dynamic behaviour of plastic gears

RESUMEN: Inicialmente lleva a cabo un repaso del estado del arte para comprender adecuadamente la literatura sobre engranajes de plástico. A continuación, se propone introducir un modelo dinámico de 14 grados de libertad de un sistema tornillo sinfín – corona sobre el que se encuentran pocas referencias en la bibliografía a pesar de ser uno de los sistemas de engranajes más utilizados en aplicaciones de engranajes de plástico. El siguiente paso es modelar el comportamiento viscoelástico del plástico típicamente utilizado en los engranajes, para lo cual se utiliza un modelo reológico denominado modelo de Maxwell generalizado. Finalmente, se diseña y construye un banco de pruebas que se utiliza para validar el trabajo numérico.ABSTRACT: In the beginning of the PhD research work, a state of the art is made to properly understand the literature on plastic gears. Then, it is proposed to introduce a 14 degrees of freedom dynamic model of a worm drive. The latter is found to be one of the most widely used gearing systems in plastic gearing applications but with minimal mentions in the literature. The next step is to model the viscoelastic behaviour of the plastic typically used in gears. For this purpose, a rheological model called the generalized Maxwell model is used. In the end, a test bench is designed and built. It is therefore used to validate the numerical work

Natural frequency sensitivity and influence analysis of TBM cutterhead system

TBM cutterhead works in complex working conditions, which endures the reverse impact forces of rock breakage, resulting in parts abnormal failure. Hence, the study of the system inherent characteristics is the basis for cutterhead dynamic design. Based on the established vibration model of a TBM split-cutterhead system, the modal method is used in the dynamic model and the natural frequency sensitivity expressions to system parameters are deduced. Then a cutterhead system of a water conservancy project in China is taking as an example, the natural frequency sensitivity with respect to the cutterhead support stiffness and mass parameters is obtained, and the influence of the two parameters on natural characteristics is analyzed. The results show that, the 10th-20th order natural frequencies are mainly affected by the cutterhead support stiffness and mass parameters, and the 9th-11th order frequencies are mainly influenced by cutterhead moment of inertia. Besides, with the change of stiffness and mass parameters, the cutterhead system natural frequency curves cut across each other and there are also many inflection points in the sensitivity curves, then the modal jumping occurs near these points. The parameter sensitive points were obtained from the results, which can provide reference for TBM cutterhead system parameters matching

Development of analytical-numerical methods for dynamic analysis of geared transmission systems

The main objective of the present research activity is the study of geared transmission system dynamics, which is basically represented by a system of nonlinear differential equations. First of all, the different approaches to study the nonlinear dynamics of gears are qualitatively presented. Afterwards, the realization of a lumped parameter model is discussed by analyzing two different modeling strategies linked to two different numerical resolution techniques. The first modeling strategy is based on time integration techniques and enhances the employment of a commercial software to speed-up the modeling set-up phase. The proposed method rely on a block diagram technique and it is developed in Simcenter AMESim, a commercial software widely used in industries. By starting from the single gear pair model, detailed guidelines are given to construct any type of ordinary transmission layout by connecting some pre-programmed devices between them. In order to demonstrate the reliability of the approach, an experimental validation on industrial use case is proposed with excellent outcomes. The second modeling strategy rely on a frequency domain solution technique able to capture unstable solution branches in multi-valued frequency response regions. In particular, it proposes the Asymptotic Numerical Method combined to the Harmonic Balance Method as a valuable approach to solve the nonlinear dynamics of gear pairs. Thanks to a quadratic recast of the equation of motion, the Taylor and Fourier series can be computed in a very efficient way and each step produces a continuous representation of the solution branch making the continuation very robust. Effectiveness and reliability of the method are proved by comparing the numerical outcomes with that obtained from the Runge-Kutta time integration scheme. As a result, this technique provides for excellent computational performance despite additional time is needed for the quadratic recast of the equations system. Once a detailed analysis on the modeling strategy has been conducted, rattle noise and whine noise occurrence are investigated. Regarding the rattle noise, the research activity has conducted to the introduction of a new analytical parameter as a novelty to the current state of the art. A rattle index formulation is retrieved by starting from the classical 6-DOFs equation system defining the nonlinear dynamics of a gear pair. The proposed formulation may be applied to single or multiple branch geartrain, both in idle or loaded condions. The reliability of the analytical formulation is proved by numerical experiments which demonstrate the capability of the proposed index to instantaneously describe the vibro-impacts events related to any gear pair of the driveline. In addition its magnitude may be a measure of the tooth impact severity and it is shown to be a proper indicator of the potential presence of mutual interactions between different gear pairs pertaining to the same driveline. Finally, the investigation of whine noise occurrence addresses to an analytical formulation able to forecast the main overall direction and magnitude of bearing reaction forces on idler gear. By starting from the definition of meshing forces by means of Fourier series development, idler gear bearing forces are obtained under the hypothesis of quasi-static motion. This procedure demonstrates that the alternating component of bearing forces on idler gear describes an elliptical trajectory as the prime mover rotates over a pitch angle. The formulation directly links the bearing forces elliptical trajectory with the gear spatial position, the meshing phase and the amplitude of meshing forces. By properly setting the over-mentioned parameters one may be able to control the magnitude and direction of the overall idler bearing reaction forces. Numerical experiments were performed and the obtained results confirm the author intuitionL’obiettivo principale della presente attività di ricerca riguarda lo studio della dinamica non lineare degli ingranaggi che, di fatto, è rappresentata da un sistema di equazioni differenziali. Prima di tutto, viene presentata un ‘analisi qualitativa finalizzata a valutare i diversi approcci per studiare tale fenomeno. Successivamente, viene descritto lo sviluppo di un modello a parametri concentrati analizzando due diverse strategie di modellazione basate su metodi di risoluzione numerica diversi. Il primo approccio propone l’utilizzo di un software commerciale per velocizzare la fase di set-up del modello ed è basato su tecniche di integrazione temporale. Questa strategia di modellazione è sviluppata in Simcenter AMESim, un software commerciale distribuito da Siemens. Partendo dal modello di una singola coppia di ruote, viene dettagliata una procedura per costruire qualsiasi tipo di treno di ingranaggi grazie alla tecnica dei diagrammi a blocchi. Per dimostrare l’efficacia di tale tecnica, il metodo viene applicato ad un caso industriale ottenendo un’ottima correlazione numerico-sperimentale. Il secondo approccio si basa su tecniche di risoluzione numerica nel dominio della frequenza in grado di calcolare i rami instabili della risposta dinamica. Il metodo propone la combinazione del “Asymptotic Numerical Method” con il “Harmonic Balance Method” utilizzando una formulazione quadratica del sistema di equazioni differenziali. Grazie a tale formulazione, sia la serie di Taylor che quella di Fourier possono essere sviluppate in una maniera molto efficiente rendendo la continuazione della soluzione periodica molto robusta. L’affidabilità di questa tecnica è stata dimostrata confrontando i risultati con quelli ottenuti dal metodo di Runge-Kutta, basato sull’integrazione temporale. In più, tale tecnica garantisce performance computazionali eccellenti, anche se la riformulazione quadratica del sistema iniziale non è sempre facile da ottenere. Una volta analizzate le strategie di modellazione e le tecniche numeriche risolutive, lo studio si concentra su i fenomeni di rattle e whine noise. Riguardo il rattle noise, l’attività di ricerca ha portato all’introduzione di un nuovo parametro analitico come novità rispetto allo stato dell’arte. Partendo dal sistema di equazioni che governa il moto di una coppia di ruote dentate, è stato definito un indice analitico denominato “rattle index”. Tale indice può essere applicato a qualsiasi tipo di treno di ingranaggi, a uno o più rami, sia in condizioni di trasmissione di potenza che in folle. La sua affidabilità è supportata da simulazioni numeriche che dimostrano la capacità del “rattle index” di descrivere istantaneamente la perdita di contatto tra qualsiasi coppia di ruote di una trasmissione. Infine, la sua ampiezza è un indice della severità degli urti e permette di identificare l’esistenza di mutue interazioni tra le ruote della driveline. Infine, lo studio del whine noise ha portato ad una formulazione analitica capace di prevedere la direzione e l’ampiezza delle forze sui cuscinetti delle ruote oziose. Tale formulazione viene ottenuta partendo dalla definizione delle forze di ingranamento tramite lo sviluppo in serie di Fourier e ricavando le forze sui cuscinetti sotto l’ipotesi di moto quasi-statico. Questa procedura dimostra che le componenti alterne delle forze sui cuscinetti seguono una traiettoria ellittica quando il movente ruota di un passo angolare. La formulazione mette in relazione la traiettoria delle forze sui cuscinetti con la posizione delle ruote nel piano, la fase di ingranamento e l’ampiezza delle forze di ingranamento. Agendo sui parametri descritti, è possibile pilotare e controllare la direzione delle forze sui cuscinetti delle ruote oziose. La trattazione analitica è supportata da simulazioni numeriche con un ottimo riscontro

Planetary gearbox condition monitoring based on modulation analysis

The epicycle gearbox or planetary gearbox (PG) is a central power transmission systems of important machines such as helicopters and wind turbines which are mission critical and high cost systems. Condition monitoring (CM) has been explored extensively in recent years to avoid any unexpected interruptions and severe accidences caused by faults PGs. Although, considerable advancements in CM techniques, there still existed significant deficiency such as insensitivity, false diagnosis and high costs in implementing such techniques in industries. To improve CM techniques, therefore, this thesis focuses on an investigation of advanced signal analysis techniques such as higher order spectra (HOS) in order to achieve full characterisation of the nonlinear modulation processes of PG dynamics and thereby develop accurate diagnostic techniques. The lumped mass model is established for modelling the dynamic behaviour of the PG under investigation, which allows the vibration behaviours to be understood for analysing different abnormalities such as tooth breakages and gear errors. This paves the way for subsequent data analytics and fault diagnostics using modulation signal bispectrum (MSB) that allows the vibration data to be examined through HOS, but it is significantly efficient in characterising the multiple and nonlinear modulations of PG dynamics alongside superior noise reduction performance. Different degrees of misalignments in the PG drive system has been investigated and successfully diagnosed using MSB analysis of vibration measurements.. Moreover, the investigation included detection of tooth breakage faults of different severities in both the sun and a planet gear. The tooth faults were diagnosed using the recently developed MSB through accurately representation and estimate of residual sidebands induced by these faults. Consequently, MSB analysis produces an accurate and reliable diagnosis in that it gives correct indication of the fault severity and location for wide operating conditions. Furthermore, these fault diagnosis practices allows the establishment of residual sideband analysis approach. These residual sidebands resulting from the out-of-phase superposition of vibration waves due to asymmetric, multiple meshing sources are much less influenced by gear errors than the in-phase sidebands due to faults or new occurrences of the symmetricity. MSB can provide an accurate characterisation of the residual sidebands and consequently produces consistent diagnosis as confirmed by both simulation and experiment

Transient 3D CFD Simulation of a Stationary Vane, Oil Free, Rotary Compressor

The evaluation of a newly designed oil-free rotary compressor is presented based on transient 3D Computational Fluid Dynamics (CFD) simulations. The simulations are performed at low compression ratios and low pressure ratios and low rotational speeds. To place the results into context, the data presented in related literature was processed and summarized. The methods related to the CFD model of the newly designed compressor were developed, summarized and evaluated. The accessed CFD data are in good agreement with the results of the former rolling piston compressor related investigations. The oil free operation prevents the contamination of the working fluid from lubricant. Since the compressor is planned to work in open cycle within the sensitive environment of thermal heat sources contamination free operation has to be accomplished. However, oil-free operation also results in significantly lower performance based on the modelling results