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Lumped parameter modeling is a consolidated technique for analyzing the fluid dynamic behavior of positive displacement machines, owing to their computational swiftness and the ease of integrating other physical domains affecting the operation of the machine. With some very limited exceptions, this modeling technique typically neglects fluid inertia and momentum effects. This paper proposes an approach to study the effects of fluid inertia affecting the pressurization and depressurization of the tooth space volumes of an external gear pump. The approach is based on considering the fluid inertia in the pressurization grooves and inside the control volumes with a peculiar subdivision. Further, frequency-dependent friction is also modeled to provide realistic damping of the fluid inside these channels. Validation of the model has been performed by comparing the lumped parameter model with a full three-dimensional Navier-Stokes solver. The quantities compared, such as tooth space volume pressures and outlet volumetric flow rate, show a good match between the two approaches for varying operating speeds. A comparison with the experiments supports the modeling approach as well. The paper finally, also discusses which operating conditions and geometries play a significant role that governs the necessity to model such fluid inertia effects in the first place. [ABSTRACT FROM AUTHOR]

This paper presents a numerical modeling approach for investigating crescent‐type internal gear pumps (CIGPs) considering radial micromotions of both gears. The modeling approach couples a lumped parameter pressure solver on the bulk fluid domain, with a transient computational fluid dynamics film simulator based on transient gap geometries solved from the gear loading forces. Simulation results on a commercial unit shows that for a wide range of operating conditions, the model gives volumetric efficiency predictions with errors less than 2 % comparing to measurements. To highlight the importance of considering radial micromotions, the paper also provides the results achieved assuming nominal position for both gears. [ABSTRACT FROM AUTHOR]

• An approach for modeling of manufacturing errors in gear machines is presented. • The proposed model incorporates both conicity and concentricity errors. • The model is validated against experiments conducted on six gearsets. • Volumetric efficiency decreases with an increase of the conicity error. • Volumetric efficiency increases with concentricity error in absence of case wear. Manufacturing errors are always unavoidable in actual machines. In external gear machines (EGMs), some of the manufacturing errors are typically on the same scale as the nominal clearances between the internal parts. These clearances are responsible for leakage flows that reduce the volumetric efficiency of EGMs and impact their overall performance. Current approaches of modeling the operation of EGMs neglect the manufacturing errors which limits their accuracy. This paper proposes a technique to study the operation of EGMs accounting for two common gear manufacturing errors: conicity and concentricity. Furthermore, an alternate technique to model these errors is proposed by defining an "effective gap height". This latter technique can be used in any existing lumped parameter model as well as for quick estimations. To validate the approach, experiments are performed with gearsets exhibiting varying amounts of conicity and concentricity errors. The results from both the simulations and the experiments show that the volumetric efficiency decreases with an increase of the conicity error. Instead, by increasing the concentricity error, an increase in the volumetric efficiency is found, at least until the conditions of contact between the gears and the casing's internal surface are avoided. [ABSTRACT FROM AUTHOR]

• A numerical model for the analysis of the compensation mechanism of an aerospace fuel delivery pump is presented. • Coupled fluid and structural effects in lubricating gaps are considered in the analysis. • Effect of frictional forces is shown to create a hysteresis effect on the bearing motion. • Experimental measurements are performed to validate the findings of the numerical model. External gear pumps (EGPs) are one of the most common choices in aerospace engines as a fuel delivery pump. These units usually include a pressure compensation system that defines the lubricating gap at the lateral side of the gears. This lubricating interface is a critical design aspect, which strongly affects the reliability as well as the mechanical and volumetric efficiencies of the pump. Major challenges in designing these lubricating gaps in aero engine fuel pumps, include high operating speeds, delivery pressures and low viscosity of the working fluids. Virtual prototyping methods present a fast and efficient design tool and have the potential to improve the EGP's reliability and efficiency. This paper presents a study on the pressure compensation system of a fuel delivery EGP and shows how the presence of frictional forces opposing the motion of the compensating element significantly affect the lubricating performance of the unit. The presence of these frictional forces produces an effect of hysteresis on the axial balance system, so that the lubricating gaps that develop within the pump at a certain operating condition depend on the previous operating state. This effect was captured in an experimental setup purposely developed for this study at Rolls-Royce. Within this work, this behavior was also reproduced numerically, through a coupled fluid structure interaction – elastohydrodynamic (EHD) model that includes the modeling of these frictional forces. After detailing the implementation of the lateral gap model, this paper presents measurements from carefully conducted experiments which correlate with the simulated predictions of the influence of frictional forces on the performance of a reference EGP design under study. [ABSTRACT FROM AUTHOR]

This paper describes a unique design concept that is capable of electronically controlling the flow delivered by an external gear pump (EGP). The principle used for varying the flow relies on the variable timing concept which has been previously demonstrated by the author's research team for EGP's operating at high pressures (HPs) (p > 100 bar). This principle permits to vary the flow within a certain range, without introducing additional sources of power loss. In this paper, the above concept has been applied to formulate a design for a variable delivery EGP for low pressure (LP) applications (p < 30 bar), suitable for direct electric actuation. Specific design principles for the gear and the flow variation mechanisms are introduced to limit the force required by the electric actuation, and for maximizing the flow variation range. Also, the low target pressure allows the variable timing principle to be realized with an asymmetric solution, with only one variable timing element present at one side of the gears. A detailed analysis concerning the relationship between the electrically commanded position of the flow varying element and the theoretical flow delivered by the pump is also presented. This analysis is used to formulate analytical expressions for the instantaneous flow rate and the flow nonuniformity of the pump. The paper details the design principle of the proposed variable flow pump and describes the multi-objective optimization approach used for sizing the gears and flow variation mechanism. The paper also discusses the experimental activity performed on a prototype of the proposed unit, able to achieve a flow variation of 31%. [ABSTRACT FROM AUTHOR]

External gear pumps are one of the most commonly used types of positive displacement machines in high pressure hydraulic control systems, fuel-injection and fuel transport systems. Despite many merits of the traditional external gear pump design with involute teeth, the significant flow non-uniformity intrinsic of such design is considered to be a detrimental aspect, since it causes undesired noise emissions and mechanical vibrations. A disruptive concept of continuous-contact helical gear pumps (CCHGP) was proposed and successfully commercialized in the recent past. Such concept was proven to have clear advantages in terms of noise emissions. However, a clear interpretation of the displacing action and the transient features of the delivery flow was never addressed in past literature. This paper addresses this gap by first discussing the family of gear profiles suitable for implementing the CCHGP design. Subsequently, an analysis on the kinematic flow ripple is given, showing how such design concept can reduce or even eliminate the kinematic flow pulsations. The paper also presents a numerical approach for modelling the operation of CCHGPs, starting from the modeling of the geometric features necessary for a fluid dynamic analysis based on a lumped parameter approach. For model validation purposes, a commercial CCHGP was tested at the authors’ research center, and the simulation results were compared against the experiments, to show the level of accuracy of the model, as well as it potentials for future design studies. [ABSTRACT FROM AUTHOR]

External Gear Pumps are used in various industries to pump non-Newtonian viscoelastic fluids like plastics, paints, inks, etc. For both design and analysis purposes, it is often a matter of interest to understand the features of the displacing action realized by meshing of the gears and the description of the behavior of the leakages for this kind of pumps. However, very limited work can be found in literature about methodologies suitable to model such phenomena. This article describes the technique of modelling external gear pumps that operate with non-Newtonian fluids. In particular, it explains how the displacing action of the unit can be modelled using a lumped parameter approach which involves dividing fluid domain into several control volumes and internal flow connections. This work is built upon the HYGESim simulation tool, conceived by the authors’ research team in the last decade, which is for the first time extended for the simulation of non-Newtonian fluids. The article also describes several comparisons between simulation results and experimental data obtained from numerous experiments performed for validation of the presented methodology. Finally, operation of external gear pump with fluids having different viscosity characteristics is discussed. [ABSTRACT FROM AUTHOR]

External gear pumps (EGPs) have gained popularity among applications in many fields like fluid power transmissions and systems, automotive, aerospace thanks to their advantage of simplicity, robustness and low cost. Several studies were performed to analyze and innovate the gear profiles of EGPs to achieve better performance, in terms of flow smoothness power to weight ratio. Asymmetric gears represent one of the possible choices. This paper is aimed at developing a methodology of designing asymmetric involute gear, and formulate analytical expression for the instantaneous flowrate and flow non-uniformity given by asymmetric, non-standard involute gear pumps. These analytical expressions are then used within a multi-objective numerical optimization algorithm aimed at minimizing both the flow non-uniformity and the pump size to achieve a specific displacement. The results illustrate the highly constrained nature of the optimization problem, and the relevant impact of certain parameters of the tooth profile. It is shown how gears obtained with the proposed procedure can have significantly higher performance of standard gears, and in particular how the parameters affecting tooth profile asymmetry can further improve the EGP flow irregularity and size. [ABSTRACT FROM AUTHOR]

This article presents a novel mixed-thermoelastohydrodynamic (TEHD) model for the lateral lubricating interfaces which exist between floating lateral bushings and gears in external gear machines (EGMs). The proposed model integrates the influence of surface asperities along with the fluid structure and thermal interaction in the interface, especially in the regions of very low film thicknesses by following a stochastic approach in modelling the mixed lubrication regime. Furthermore, the current work includes validation of the predictions of the mixed-TEHD model against experimentally measured leakages from the lateral gap and compares the performance of this model with a previously developed full film TEHD model for the lateral gaps in EGMs. [ABSTRACT FROM AUTHOR]

A novel fluid–structure interaction–thermal coupled model for the lateral lubricating gaps between gears and lateral bushes in external gear machines (EGM) is presented in this study. The model is the first of the lateral lubricating interface in EGMs capable of considering heat transfer, thermal effects in the fluid film and solid components as well as thermo-elastic deformation of the solids enabling prediction of the film thickness in EGM lateral gaps considering thermoelastohydrodynamic lubrication. Model validation is performed using lateral gap leakage measurement which is dependent on absolute film thickness. A novel relative lubricant film thickness measurement method in gear machines using capacitive sensors is also presented, and used to validate the spatial film thickness predictions from the model. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and numerical modal analysis for an external gear pump considering its mounting on a test rig in a laboratory setting. Most of the previous studies on experimental modal analysis (EMA) of hydraulic pumps focused on the modal frequencies to allow model validation. However, the mode shapes of pump bodies have not extensively been discussed. Furthermore, the nature of the pump components assembly and mounting poses some modeling challenges, such as the uncertain material properties of each component, the behavior of the bolted joints, and some critical modeling boundary conditions related to pump mounting. In this regard, the experimentally obtained vibration modes of a reference pump using the least-square complex exponential (LSCE) method are analyzed with an emphasis on the characteristics of the mode shapes. Then, simple modeling strategies are proposed and validated by performing the analysis from the component level to the full assembly. As a result, the mode shapes are categorized depending on the type of motions that the modes exhibit. It is observed that the pump casing does not show any substantial deformation but is close to the rigid body motion. Moreover, without considerably increasing model complexities, the proposed numerical approach provides reasonable accuracy with average errors in modal frequencies of 6%, as well as good agreement in terms of mode shapes. The vibration reduction strategy is briefly discussed based on the measured mode shapes, and the proposed modeling approaches can be useful to study external gear pumps with minimal model complexities yet allowing reasonable result accuracy. [ABSTRACT FROM AUTHOR]

Highlights: [•] A model to evaluate fluid properties considering the dynamic features of cavitation is presented. [•] The new model for the evaluation of fluid properties is suitable for lumped parameters models. [•] The paper studies the operation of gear pumps under cavitating conditions. [•] Experimental activity on a gear pump was performed to validate the modelling approach. [Copyright &y& Elsevier]

Abstract: In this paper an innovative procedure for determining the optimal design of an external spur gear pump for a particular emission reduction application in automobiles has been proposed. The pump forms the main part of a mechatronic system that controls the flow rate of a mixture of urea in water to catalytically reduce emissions in diesel engines. The proposed research proves to be an advance in gear machine design by using a multi-objective based genetic algorithm, to determine the optimal design of the gears and the casing by maximizing the volumetric efficiency, minimizing pressure overshoots, localized cavitation and noise emissions. The research uses HYGESim (HYdraulic GEar machines Simulator) simulation tool, which is being developed by the authors’ research group, for calculating the important performance features of the machine. The best designs for the machine based on enhancement in performance are presented. Results in terms of simulations and tests which validate the effectiveness of the proposed novel design methodology are also presented. [Copyright &y& Elsevier]

• A fully coupled multi-domain multi-physics dynamic system is presented. • Three components of the loadings are explained and analyzed in detail. • The patterns of 3D transient loadings and dynamics are discussed with simulation results. • A design routine for the axial balancing mechanism of helical gear pumps is provided. • The pattern of wear seen from experiments can be replicated by the wear model. This paper presents a multi-domain dynamic simulation model for continuous-contact helical gear pumps, which is an unconventional hydraulic pump design that is capable of canceling its kinematic flowrate variation. In this model, the fluid dynamics (in its lumped-element representation) are fully coupled in a closed feedback loop with other physical domains, including critical tribological interfaces, 3D dynamic loadings on the solid parts, dynamics, and micro-vibrations of the rotors. The model is compared to the analytical derivation and experimental measurements to prove its validity. The model can be used to provide predictive simulations for existing designs, or as a tool to optimize the design to provide better hydrostatic balancing for future iterations of hydraulic pump designs. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a fluid structure interaction (FSI) model for the simulation of the flow in the lubricating gaps between gears and lateral bushes in external gear machines (EGMs). The proposed model is capable of accounting for elasto-hydrodynamic effects in the lubricant film, and can predict the lubricant film thickness. Three different constraint methods are considered as concerns the structural problem: “ideally supported”, “inertia relief” and a “low pressure” constraint specifically formulated for EGMs. The proposed model is validated against measurements performed on an experimental prototype. Detailed formulation of the FSI model as well as significant simulation results are presented for a wide range of operating conditions along with comparison to experimental results. [Copyright &y& Elsevier]

Abstract: The modelling of positive displacement machines has to deal with the complexity of solving the flow through the unit in presence of simultaneous macro and micro-motions of the moving parts. In this paper, the main phenomena characterizing the operation of the spur external gear units are successfully analyzed by means of a numerical model developed by the authors. The model, here referred as HYdraulic GEar machines Simulator (HYGESim), consists of different modules: a fluid dynamic model, a model for the evaluation of the movements of the gears’ axes of rotation and a geometrical model. When performing a HYGESim simulation, these models are executed in a co-operative simulation. Starting directly from the CAD drawing of the unit as input, the simulation tool permits to describe the main features of the flow though the machine and to evaluate the possible wear of the casing wear accounting for a detailed description of the geometry of the internal components (i.e. teeth’s profile, design of lateral bushes). The paper describes the modelling approach and the main potentials of the simulation tool, pointing out how it can be utilized for design purposes. As a matter of fact, HYGESim permits to analyse the effects of the main design parameters on important aspects like efficiency, internal pressure peaks, local cavitation and fluctuations of flow at unit’s ports (associated with fluid borne noise). The presented tool also allows the evaluation of the radial movements of the gears’ axes of rotation resulting from the forces exerted on both gears, thus permitting to study the balancing feature related to a certain design. The paper also presents several comparisons between simulation results and experimental data coming from an experimental activity specifically performed for validation of the presented tool. [Copyright &y& Elsevier]

• The paper presents a methodology for modeling hydro-mechanical losses in external gear machines. • Friction at the gears' tooth tips, lateral surfaces, shafts and meshing interfaces is considered. • The gear meshing friction is found to be the major contributor to the torque losses. • The simulated hydro-mechanical efficiency trends match the experimental data. During the operation of external gear machines (EGMs), the friction between the internal components results in the loss of hydro-mechanical (or torque) performance of these units. However, current EGM simulation models either do not consider these losses or have significant limitations in their approach. This paper presents a novel methodology for modeling the hydro-mechanical losses in EGMs. The sources of torque losses considered are the friction at the gears' tooth tips, lateral surfaces, shafts, and meshing interfaces. The friction models are developed for each of these sources considering the effects of micromotion of the gears and bushings. Further, the effects of elastohydrodynamic lubrication (EHL) are considered in the modeling of meshing friction. The friction models are integrated in a lumped parameter simulation tool, and the operation of a commercial gear pump is simulated. From the simulation results, the meshing friction is determined to be the dominant source of torque losses. Further, the hydro-mechanical efficiencies predicted by the model are found to match those observed in the experiments indicating the validity of the model developed in this work. [ABSTRACT FROM AUTHOR]

• A novel model for curve-constricted leakage flows in hydraulic gear pumps is presented. • The flow model is applicable over a wide range of flow regimes including localized cavitation. • The model is developed in dimensionless form based on sets of CFD simulations. • Model validation is achieved through experiments conducted on a custom test apparatus. The internal leakage flows in external gear and gerotor pumps are often represented by flow through curved constrictions. The nature of this flow can vary from laminar to turbulent and the flow can experience localized cavitation too. In the current literature, there is a scarcity of techniques for accurately modelling such curve-constricted flows which limits the accuracy of the current simulation tools for gear pumps. This paper presents a novel flow model for curve-constricted geometries that is applicable over a wide range of flow regimes including localized cavitation. Using a dimensionless form, the proposed model characterizes the constriction flow velocity as the function of the constriction shape, the pressure difference, and a properly defined cavitation indicator. The functional relationships between these dimensionless parameters are developed based on CFD simulations. The flow model is validated by the means of several experiments conducted on a custom test apparatus. The model presented in this paper can be incorporated in the lumped parameter simulation tools widely used for modelling gear pumps, improving their accuracy in predicting the internal leakages. Consequently, this model will also aid the development of novel energy efficient gear pump designs, where such leakages are kept to a minimum. [ABSTRACT FROM AUTHOR]

This paper presents the experimental characterization of the vibroacoustic fields and the evaluation of noise performances of hydraulic pumps. Research on hydraulic pump noise has traditionally focused on the fluid-borne noise sources, and very often the analyses of vibration and noise have been performed focusing on a few local points. This trend results in the lack of investigation on the overall behaviors of vibroacoustic fields of hydraulic pumps, and it has been one of the obstacles to understand the complete mechanisms of noise generation. Moreover, despite the existence of the ISO standards for the determination of noise levels, diverse metrics have been used for the evaluation of noise performances of the pumps, but the adequacy of these metrics has not been carefully examined. In this respect, this paper aims at introducing a way to characterize and interpret the measured vibroacoustic field and providing proper methods which are also capable of applying the ISO standards for the fair assessment of pump noise performances. For the characterization of the vibroacoustic field, operational deflection shapes (ODS) and corresponding radiated sound fields are visualized at harmonics of the pumping frequency by using a spectral analysis. Observations are made regarding the motions of the pump and its mounting plate and the resultant radiated noise, depending on the frequency, as well as their correlation. A numerical analysis using the Rayleigh integral equation is also performed to further investigate the contribution of the mounting plate motion on the noise radiation. For the evaluation of noise performance, two different units are tested at multiple operating conditions, and comparisons are made based on their measured sound power levels (SWLs) and sound pressure levels (SPLs). The results emphasize the importance of SWL measurement for the fair noise performance evaluation, and the two methods are proposed as practices to determine the minimum number of measurement points for practicability and to have reliable sound power determination for hydraulic pumps. [ABSTRACT FROM AUTHOR]

In this paper, External Gear Machine (EGM) torque losses arising from friction at lubricating interfaces are modeled by considering mixed lubrication conditions. A novel contribution of this paper is to consider mixed elastohydrodynamic lubrication contact conditions along with the effect of gear flank surface roughness to determine the meshing losses, which are also the major contributors towards the EGM torque loss. These hydromechanical loss models are integrated in a multibody, multi-physics simulation tool Multics-HYGESim developed at the authors' research center. Experimental activity is performed on two EGM units using different surface finish for gears. Simulated hydromechanical efficiencies match the experimental trends with average deviation of 2.5%. Most importantly, the results capture effects of different gear flank roughness on the torque efficiency. An average increase of 0.9% in the efficiency value is predicted by the simulation model for the EGM with lower teeth roughness, as compared to 1.1% rise obtained via experiments. The proposed torque loss evaluation methodology shows high potential in assisting designers and manufacturers of EGMs to choose the suitable surface finishing for achieving desired hydromechanical performance. • Torque efficiency of external gear machines has been determined via simulation. • Mixed Elasto hydrodynamic lubrication model is used to evaluate meshing frictional loss. • Experimental tests show rise in torque efficiency for lower gear surface roughness. • Computational analysis of lubricating interfaces predicts leakage and friction loss. • Proposed model exhibits potential for virtual prototyping of new gear pump designs. [ABSTRACT FROM AUTHOR]

The flow of energy within external gear machines (EGMs) leads to the variation of fluid temperature in the EGMs, which affects their performance. However, the common approaches for the simulation of EGMs assume isothermal conditions. This isothermal assumption negatively impacts their modelling accuracy in terms of the internal flows which are dependent on the fluid temperature (via fluid properties). This paper presents a lumped parameter based thermal model of EGMs where the fluid temperature in the EGM is evaluated considering the effects of compression/expansion, internal flows, and power losses. Further, numerical techniques are developed to model each of these three aspects. The thermal model is validated via the outlet temperature and volumetric efficiency measurements obtained from experiments conducted on six units of an EGM taken as a reference with different internal clearances. The results from the model show that the fluid temperature increases as it is carried from the inlet side to the outlet side during the pumping operation. However, the fluid at the ends of the shafts has the highest temperature. By comparing the isothermal simulation results with the proposed thermal model, the results also point out how the isothermal assumption becomes inaccurate, particularly in conditions of low volumetric efficiency. [ABSTRACT FROM AUTHOR]

External gear pumps are among the most popular fluid power positive displacement pumps, however they often suffer of excessive flow pulsation transmitted to the downstream circuit. To meet the increasing demand of quiet operation for modern fluid power system, a better understanding of the ripple source of gear pumps is desirable. This paper presents a novel approach for the analysis of the ripple source of gear pumps based on decomposition into a kinematic component and a pressurization component. The pump ripple can be regarded as the superposition of the displacement solution and the pressurization solution. The displacement solution is driven by the kinematic flow, and it can be derived from the kinematic flow theory; instead, the pressurization solution can be approximated by overlapping the pressurization flow for a single displacement chamber. Furthermore, in this way the changes of these two components with modification of the delivery circuit are determined in both analytical and numerical ways. The result of this analysis provides a good interpretation of the pulsation simulated by a detailed lumped-parameter simulation model, thus showing its validity. The result also indicates that the response of two ripple sources to the change of the loading in the downstream hydraulic circuit is very different. These findings reveal the limitation of the traditional experimental method for determining the pump ripple, that new experimental methods which are more physics-based can be potentially formulated based on this work. [ABSTRACT FROM AUTHOR]

• A design parameterization of a helical/spur external gear machine was developed. • An optimization procedure was developed for design of helical and spur gear pumps. • Helical gears have more potential for better meshing stress ripple than spur. • Helical gears also have more potential for compactness and efficiency. • Spur gears offer more potential for flow ripple reduction than helical. This paper addresses the problem of determining the relative performance of spur and helical external gear pumps (EGPs) for fluid power applications. Helical EGPs are commonly considered as quieter units than spur ones; however, there is no specific study reported in literature that proves such claim. Similarly, it is hard to find data indicating which design is better in terms of compactness or energy performance. To tackle this problem, a procedure is developed for virtual design optimization of both helical and spur gear EGPs. This includes addressing the two fundamental challenges of the work, parameterizing a generic EGP design and quantifying its performance. By applying this procedure, a genetic algorithm can continue improving from generation to generation, until the pareto optimal set of designs is identified for both helical and spur units. In the comparison of these, the differences between the two configurations will be identified and the fundamental question of this work can be answered; are helical gears 'better' than spur gears? [ABSTRACT FROM AUTHOR]