The thesis reports the results I obtained throughout the PhD course that I have attended for the last three years. My research activity focused on developing mathematical models for predicting gear pump performance, with a particular attention on specific features including helical gears, non-unitary transmission ratio and the need to investigate a wide operating speed range. Such peculiar aspects, usually uncommon in fluid power applications, nowadays constitute standard requirements of high performance automotive auxiliary systems to be matched with classic constraints regarding reliability, NVH behavior and efficiency of the machine itself. Within this framework, robust numerical models represent powerful tools for engineers throughout the entire design process. For this reason, during my research activity I developed methods performance prediction from different perspectives, since modern volumetric pumps must match heterogeneous requirements simultaneously. The pump NVH behavior has been addressed by means of a discrete dynamic model, accounting for backlash nonlinearities and based on a six degrees of freedom system with flexible bearings. Dynamic loads due to the pressure field around the gears are estimated by means of an analytical procedure, as well as speed dependent friction torque. A parametric study has been conducted to evaluate the effects of different outlet pressures, presence of speed dependent high pressure peaks in the trapping volume and various pressurizing zone extensions. The result is a minimal model to study the dynamics of gear pumps based on a limited number of design parameters. These features make it a powerful tool at the early stage of the design process, when the detailed geometry is still to be defined. The originality of the present work stands in the proposed approach itself, which differs from classical methods based on the detailed definition of the pump geometry to reach high accuracy results. Gear pump performances have been evaluated also in terms of volumetric efficiency and pressure phenomena occurring within the gearpair by using a zero-dimensional approach. This model couples the effects of the fluid-dynamic field and the gearpair micromotions on the basis of a novel set of equations. The two phenomena are reciprocally solved, at each time-step, to obtain an accurate estimation of the pump behavior, which is reached by considering multiple load sources. Possibility to study both spur and helical gears and non-unitary transmission ratio gearpairs has been included, in order to ensure the wide applicability of the model in modern design solutions. Results assessment has been achieved by means of a dedicated experimental campaign, involving measurements on 20 nominally identical samples of the same pump design, each one tested at 16 different working conditions. The comparison demonstrated that the proposed approach guarantees high accuracy predictions in terms of volumetric efficiency within the range of working conditions considered. In order to extend the overview of the potential phenomena that may occur in modern design projects, the last part of the thesis introduces an experimental technique for detecting incipient cavitation in external gear pumps by means of vibro-acoustic measurements. The phenomenon has been investigated on four different pump prototypes, where marks of cavitation have been captured with a dedicated post-processing technique applied to signals obtained with a hydrophone, a high frequency accelerometer and two pressure ripple transducers. Comparison between cavitating and not-cavitating pumps has underlined the effective capability of the procedure in detecting the phenomenon and the necessity of further investigations on this subject, which has never been experimentally addressed in the literature, for a deeper understanding of its characteristics.

La tesi riporta i risultati ottenuti durante il corso di dottorato frequentato negli ultimi tre anni. La mia attività di ricerca si è concentrata sullo sviluppo di modelli matematici per la previsione delle prestazioni di pompe ad ingranaggi, focalizzando l’attenzione sull’analisi di caratteristiche specifiche quali l’uso di ingranaggi elicoidali, rapporto di trasmissione non unitario e la necessità di studiare un'ampia gamma di velocità operative. Tali aspetti, solitamente inusuali nelle applicazioni classiche, costituiscono oggi requisiti standard nei sistemi automobilistici ausiliari ad alte prestazioni, in abbinamento ai tipici vincoli di affidabilità, comportamento NVH ed efficienza. In questo contesto, la disponibilità di modelli robusti rappresenta un valore aggiunto durante tutto il processo di progettazione e sviluppo. Per tale motivo, durante la mia attività di ricerca ho affrontato la tematica da diverse prospettive, dal momento che le moderne pompe volumetriche devono soddisfare simultaneamente requisiti eterogenei. Il comportamento NVH della pompa è stato analizzato tramite un modello dinamico discreto a sei gradi di libertà, tenente conto della non linearità legata al backlash e di cuscinetti flessibili. Il modello è stato utilizzato per uno studio parametrico atto a valutare l’effetto di diverse pressioni di mandata, la presenza di picchi di pressione nel volume intrappolato dipendenti dalla velocità e varie estensioni della zona di pressurizzazione. Il risultato è un modello minimale per studiare la dinamica di pompe ad ingranaggi basato su un numero limitato di parametri progettuali, caratteristica che lo rende un valido strumento nella fase iniziale del processo di progettazione, quando la geometria dettagliata deve ancora essere definita. L'originalità del presente lavoro risiede proprio nell'approccio proposto, che differisce dai metodi classici basati sulla completa definizione della geometria per ottenere un’elevata accuratezza dei risultati. Le prestazioni delle pompe a ingranaggi sono state valutate anche in termini di efficienza volumetrica e di distribuzione di pressione all'interno dell’ingranaggio, utilizzando un approccio zero-dimensionale che ha portato alla realizzazione di un modello dove la fluidodinamica è accoppiata ai micro-moti dell’ingranaggio stesso. I due fenomeni fisici sono reciprocamente risolti, ad ogni step di calcolo, ottenendo così una stima accurata del comportamento della pompa. Inoltre, la possibilità di studiare sia ingranaggi a denti dritti che elicoidali e con rapporto di trasmissione non unitario è stata inclusa nel modello, al fine di garantirne l'ampia applicabilità nelle soluzioni progettuali moderne. I risultati sono stati confrontati con dati sperimentali ottenuti da una campagna sperimentale dedicata, eseguita su 20 esemplari di pompa nominalmente identici, ciascuno testato in 16 diverse condizioni di lavoro. L’analisi ha dimostrato che l'approccio proposto garantisce previsioni accurate in termini di efficienza volumetrica nell'ambito delle condizioni di lavoro considerate. Al fine di estendere la panoramica dei potenziali fenomeni che possono verificarsi nei progetti di design moderni, l'ultima parte della tesi descrive una tecnica sperimentale per la rilevazione di cavitazione incipiente in pompe ad ingranaggi esterni mediante misure vibro-acustiche. La problematica è stata studiata su quattro diversi prototipi di pompe, rilevando la presenza di cavitazione con una post-elaborazione dedicata, applicata ai segnali ottenuti da un idrofono, un accelerometro ad alta frequenza e due trasduttori di pressione. Il confronto tra pompe cavitanti e non-cavitanti ha sottolineato l'effettiva capacità della tecnica diagnostica e la necessità di ulteriori approfondimenti su questo argomento, che non è mai stato affrontato sperimentalmente in letteratura, per una più profonda comprensione delle sue caratteristiche.

Performance evaluation in external gear pumps: numerical and experimental methods

BATTARRA, Mattia
2018

Abstract

The thesis reports the results I obtained throughout the PhD course that I have attended for the last three years. My research activity focused on developing mathematical models for predicting gear pump performance, with a particular attention on specific features including helical gears, non-unitary transmission ratio and the need to investigate a wide operating speed range. Such peculiar aspects, usually uncommon in fluid power applications, nowadays constitute standard requirements of high performance automotive auxiliary systems to be matched with classic constraints regarding reliability, NVH behavior and efficiency of the machine itself. Within this framework, robust numerical models represent powerful tools for engineers throughout the entire design process. For this reason, during my research activity I developed methods performance prediction from different perspectives, since modern volumetric pumps must match heterogeneous requirements simultaneously. The pump NVH behavior has been addressed by means of a discrete dynamic model, accounting for backlash nonlinearities and based on a six degrees of freedom system with flexible bearings. Dynamic loads due to the pressure field around the gears are estimated by means of an analytical procedure, as well as speed dependent friction torque. A parametric study has been conducted to evaluate the effects of different outlet pressures, presence of speed dependent high pressure peaks in the trapping volume and various pressurizing zone extensions. The result is a minimal model to study the dynamics of gear pumps based on a limited number of design parameters. These features make it a powerful tool at the early stage of the design process, when the detailed geometry is still to be defined. The originality of the present work stands in the proposed approach itself, which differs from classical methods based on the detailed definition of the pump geometry to reach high accuracy results. Gear pump performances have been evaluated also in terms of volumetric efficiency and pressure phenomena occurring within the gearpair by using a zero-dimensional approach. This model couples the effects of the fluid-dynamic field and the gearpair micromotions on the basis of a novel set of equations. The two phenomena are reciprocally solved, at each time-step, to obtain an accurate estimation of the pump behavior, which is reached by considering multiple load sources. Possibility to study both spur and helical gears and non-unitary transmission ratio gearpairs has been included, in order to ensure the wide applicability of the model in modern design solutions. Results assessment has been achieved by means of a dedicated experimental campaign, involving measurements on 20 nominally identical samples of the same pump design, each one tested at 16 different working conditions. The comparison demonstrated that the proposed approach guarantees high accuracy predictions in terms of volumetric efficiency within the range of working conditions considered. In order to extend the overview of the potential phenomena that may occur in modern design projects, the last part of the thesis introduces an experimental technique for detecting incipient cavitation in external gear pumps by means of vibro-acoustic measurements. The phenomenon has been investigated on four different pump prototypes, where marks of cavitation have been captured with a dedicated post-processing technique applied to signals obtained with a hydrophone, a high frequency accelerometer and two pressure ripple transducers. Comparison between cavitating and not-cavitating pumps has underlined the effective capability of the procedure in detecting the phenomenon and the necessity of further investigations on this subject, which has never been experimentally addressed in the literature, for a deeper understanding of its characteristics.
MUCCHI, Emiliano
TRILLO, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2478774
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