Modeling Noise Sources and Propagation in External Gear ... - MDPI

energies Article

Modeling Noise Sources and Propagation in External Gear Pumps Sangbeom Woo 1, *, Timothy Opperwall 1 , Andrea Vacca 1 and Manuel Rigosi 2 1 2

*

Maha Fluid Power Research Center, Purdue University, 1500 Kepner dr., Lafayette, IN 47905, USA; [email protected] (T.O.); [email protected] (A.V.) Casappa SpA, Via Balestrieri 1, Lemignano di Collecchio, 43044 Parma, Italy; [email protected] Correspondence: [email protected]

Received: 21 June 2017; Accepted: 20 July 2017; Published: 22 July 2017

Abstract: As a key component in power transfer, positive displacement machines often represent the major source of noise in hydraulic systems. Thus, investigation into the sources of noise and discovering strategies to reduce noise is a key part of improving the performance of current hydraulic systems, as well as applying fluid power systems to a wider range of applications. The present work aims at developing modeling techniques on the topic of noise generation caused by external gear pumps for high pressure applications, which can be useful and effective in investigating the interaction between noise sources and radiated noise and establishing the design guide for a quiet pump. In particular, this study classifies the internal noise sources into four types of effective load functions and, in the proposed model, these load functions are applied to the corresponding areas of the pump case in a realistic way. Vibration and sound radiation can then be predicted using a combined finite element and boundary element vibro-acoustic model. The radiated sound power and sound pressure for the different operating conditions are presented as the main outcomes of the acoustic model. The noise prediction was validated through comparison with the experimentally measured sound power levels. Keywords: fluid-borne noise; structure-borne noise; air-borne noise; external gear pumps; vibro-acoustic modeling

1. Introduction Oil hydraulics is the best technology for transmitting mechanical power in many engineering applications due to its advantages in power density, ease of control, layout flexibility, and efficiency. Due to these advantages, hydraulic systems are present in many different applications from aerospace to construction and agriculture. Particularly for applications in close proximity to humans, noise is one of the main constraints to the acceptance and spread of the fluid power technology. In order to increase the range of applications where fluid power is advantageous, the noise generation must be better understood and ultimately reduced. Besides environmental concerns, decreasing the noise generation of hydraulic components has potential additional benefits of smoothing control and increasing machine life and reliability. As the key component in mechanical to fluid power transfer, positive displacement machines often represent the major sources of noise in hydraulic systems. In many cases, the limiting factor in the implementation of hydraulic systems is the amount of noise and vibration introduced into the environment by the displacement machines, as opposed to the noise from valves, loads, and other hydraulic sources. Thus, investigation into the sources of noise is focused on the displacement machines and discovering strategies to reduce noise is a key part of applying fluid power systems to a wider area of applications. The present work focuses on noise generation from displacement machines through simulation techniques. Energies 2017, 10, 1068; doi:10.3390/en10071068

www.mdpi.com/journal/energies

Energies 2017, 10, 1068 Energies 2017, 10, 1068

2 of 20 2 of 20

The mechanics of noise generation are very similar between all types of positive displacement The mechanics of noise generation are very similar between all types of positive displacement machines due to the physics behind the displacing action realized by the machine and the nature machines due to the physics behind the displacing action realized by the machine and the nature of of the oscillatory loads acting on the internal parts. A widely used type of displacement machine, the oscillatory loads acting on the internal parts. A widely used type of displacement machine, the the external gear machine machine(EGM) (EGM)isistaken takenasasa areference reference this study with particular of the external gear forfor this study with thethe particular casecase of the external gear pump (EGP), as shown in Figure 1. The displacing action in an EGM is achieved by external gear pump (EGP), as shown in Figure 1. The displacing action in an EGM is achieved by the the meshing of two gears, which causes thevolume volumeinside inside every tooth space volume (TSV) meshing of two gears, which causesthe thechanges changes of the every tooth space volume (TSV) in each gear. TheThe fluid is brought inletside; side;ititisisthen then carried around sides in each gear. fluid is broughtinto intothe theTSVs TSVs on on the inlet carried around the the sides of of the gears by the teeth. displacing actionoccurs occursin inthe themeshing meshing zone, zone, where the gears by the teeth. TheThe displacing action wherethe thefluid fluidininthe theTSV TSV is is delivered the output fluid is drawn fromthe theinlet inletport. port. delivered to thetooutput port,port, thenthen the the newnew fluid is drawn from

Figure 1. External gear pumps TSV pressure pressuredistribution distribution EGP Figure 1. External gear pumps(EGP), (EGP), and and typical typical TSV forfor an an EGP for for highhigh pressure applications. pressure applications.

Study of the physical phenomena of noise is typically separated into three categories: fluid, Study of the physical phenomena of noise is typically separated into three categories: fluid, structure, and air-borne noise [1]. The fluid-borne noise (FBN) can be composed of a variety of structure, and air-borne noise [1]. The fluid-borne noise (FBN) can be composed of a variety of different phenomena. Primarily, there are large scale pressure fluctuations caused by the displacing different phenomena. Primarily, there are large scale pressure fluctuations caused by the displacing action and the resulting loading forces. Additional point sources of noise can be localized cavitation, action and the resulting loading pressure forces. Additional point the sources can be localized cavitation, pressure peaks, and dynamic gradients within TSVs.ofAsnoise the loads applied by the unit pressure peaks, and dynamic pressure gradients within the TSVs. As the loads applied by the unit operation interact with the solid body of the pump, the structure-borne noise (SBN) can be separated operation interact with theThe solid body of the pump, the structure-borne noise (SBN) be separated into two main aspects. structure is typically considered both as impedance for thecan transmission into of two main aspects. The structure is transmits typically its considered both impedance for the transmission FBN to the environment, and also own sources ofas noise in the forms of forces and of FBN to thecarried environment, andcomponents. also transmits its approaches own sources noise intothe forms forces and moments by the solid Many areofavailable study theof air-borne noise (ABN) forby general acoustic applications,Many while approaches it is difficult to simulate the mechanisms noise moments carried the solid components. are available to study theofair-borne ingeneral hydrostatic units applications, to predict the fluid-borne noise and noise sources. noisegeneration (ABN) for acoustic while it is difficult tostructure-borne simulate the mechanisms of noise There have been many studies aimed at reducing the noise in positive displacement machines. generation in hydrostatic units to predict the fluid-borne noise and structure-borne noise sources. While reducing internal sources ofthe SBN [2], the main focus in most research on Theresome haveworks been focus manyonstudies aimed at reducing noise in positive displacement machines. noise in hydraulic pumps is on reducing the magnitude of the pressure ripple oscillations at the outlet While some works focus on reducing internal sources of SBN [2], the main focus in most research on port [3–8]. For EGMs, this effort has resulted in the formulation of design solutions that involve tooth noise in hydraulic pumps is on reducing the magnitude of the pressure ripple oscillations at the outlet profile modifications able to reduce the kinematic flow oscillations: Manring and Huang formulated portcriteria [3–8]. For EGMs, this effort has resulted in the formulation of design solutions that involve tooth suitable for standard involute designs [6,9]; Negrini introduced the so-called dual-flank profile modifications able to reduce thecurrently kinematic flow oscillations: Manring and Huang formulated principle, a zero-backlash solution adopted by several manufacturers that permits to criteria suitable for standard involute designs [6,9]; Negrini introduced the so-called increase the number of displacement chambers [4] to reduce the flow oscillations. Most recentdual-flank efforts principle, a zero-backlash currently by several manufacturers that permits to increase involved the research ofsolution non-standard gearadopted profiles—such as asymmetric [10,11], cycloidal-involute the number of displacement chambers to reduce the associated flow oscillations. recent efforts [12–15] able to minimize the kinematic[4] flow oscillations with theMost meshing of the gears.involved The effects ofoffluid compressibility on the outlet flow oscillations in EGMscycloidal-involute was considered by[12–15] severalable the research non-standard gear profiles—such as asymmetric [10,11], researchers, as Mucchi Casoli et associated al. [16], Borghi al.meshing [17], and of criteria for minimizing to minimize the such kinematic flow [5], oscillations withetthe the gears. The effectstheir of fluid impact on the flow oscillations through design optimization of recesses facing the gear in the meshing compressibility on the outlet flow oscillations in EGMs was considered by several researchers, such as area [5], wereCasoli provided in [16], several studies, as [18–20]. The source impedance method to characterize Mucchi et al. Borghi et such al. [17], and criteria for minimizing their impact on the flow FBN through outlet flow oscillations, introduced by Edge et al. [21], was also recently used for EGMs oscillations through design optimization of recesses facing the gear in the meshing area were provided [22]. Despite these efforts, the interaction between pressure ripples and ABN has yet to be clearly in several studies, such as [18–20]. The source impedance method to characterize FBN through outlet investigated [23]. Thus, from the perspective of a quiet pump design, a comprehensive modeling flow oscillations, introduced by Edge et al. [21], was also recently used for EGMs [22]. Despite these approach is needed in order to investigate the relationship between all the internal sources of FBN efforts, the interaction between pressure ripples andresultant ABN hasABN. yet to be clearly investigated [23]. Thus, including outlet pressure ripples and the SBN and

from the perspective of a quiet pump design, a comprehensive modeling approach is needed in order to investigate the relationship between all the internal sources of FBN including outlet pressure ripples and the SBN and resultant ABN.

Energies 2017, 10, 1068

3 of 20

In this regard, several authors have addressed different approaches to comprehensively model Energies 2017, 10, 1068 3 of 20 the acoustic behaviors of EGP. Tang et al. predicted the pump noise based on the combined computational dynamics (CFD) method and the different Lighthill’s acoustic analogy (LAA) algorithm, In thisfluid regard, several authors have addressed approaches to comprehensively model but they only considered low delivery pressure cases barbased [24]. onThere has been the acoustic behaviors the of EGP. Tang et al. predicted thebelow pump 3.3 noise the combined also the numerical-experimental approach receives the experimentally measured computational fluid dynamics integrated (CFD) method and the that Lighthill’s acoustic analogy (LAA) algorithm, but theyasonly considered the low delivery pressure 3.3 barfinite [24]. element There hasmethod been also the acceleration an input and calculates the sound fieldcases usingbelow combined (FEM) numerical-experimental integrated that receives theapproach experimentally measured acceleration and boundary element method (BEM)approach [25,26]. Although their is simple and useful at the as anlevel, inputpreliminary and calculates the sound measurements field using combined finiterequired element to method (FEM) and industrial experimental are always predict the noise boundary element method (BEM) [25,26]. Although their approach is simple and useful at thea emissions of the pump. A significant contribution was also made by Mucchi et al. who implemented industrial level, preliminary experimental measurements are always required to predict the noise lumped-parameter model to compute FBN and FEM/BEM model to investigate SBN and ABN [27,28]. emissions of the pump. A significant contribution was also made by Mucchi et al., who implemented Although based on different modeling assumptions particularly related to the determination of the FBN, a lumped-parameter model to compute FBN and FEM/BEM model to investigate SBN and ABN this latter work is similar to the approach used in this paper. This work also contributes to identifying [27,28]. Although based on different modeling assumptions particularly related to the determination the different FBN sources and determining their contribution to the overall ABN. This evaluation of the FBN, this latter work is similar to the approach used in this paper. This work also contributes of FBN noise sources is expected to be useful and effective in seeking the interaction between noise to identifying the different FBN sources and determining their contribution to the overall ABN. This sources and actual noisenoise in the future. this study, the noise measurements for the evaluation of FBN sources is Furthermore, expected to be in useful and effective in seeking the interaction model validation were takenand inside the semi-anechoic chamber, which canin provide more the strict and between noise sources actual noise in the future. Furthermore, this study, noise precise determination of sound power levels. measurements for the model validation were taken inside the semi-anechoic chamber, which can The proposed model takes advantage of a simulation forlevels. EGM specifically developed by the provide more strict and precise determination of sound tool power authors’ research team: model HYdraulic machine This simulator provides The proposed takesGEar advantage of a Simulator simulation (HYGESim) tool for EGM[29]. specifically developed by the the accurate pressure and force in the fluid (FBN) [29]. acting onsimulator the pump casing. authors’dynamic research team: HYdraulic GEarinformation machine Simulator (HYGESim) This provides accuratenoise dynamic pressure andclassified force information the fluid (FBN) acting (pressures on the pump casing. Thesethe predicted sources are then into four in types of load functions at (1) inlet, These(3) predicted noise sources classified into four types and of load functions at (1) (2) outlet, TSV pressure regions,are andthen (4) journal bearing regions) applied to the(pressures corresponding inlet,of(2) TSV pressure regions,way. and (4) journal regions) to the surfaces theoutlet, pump(3)structure in a realistic After that, bearing the analyses of and SBNapplied and ABN are corresponding surfaces of the pump structure in a realistic way. After that, the analyses of SBN and performed by combining a modal analysis performed in ANSYS and an acoustic simulation in LMS ABN areNormalized performed by combining analysis in ANSYS acoustic simulation Virtual.Lab. sound powera modal spectra, soundperformed power level (SWL), and andan sound pressure level in LMS Virtual.Lab. Normalized sound power spectra, sound power level (SWL), and sound pressure (SPL) distributions for the four different operating conditions will be presented as the main outcomes of level (SPL) distributions for the four different operating conditions will be presented as the main the acoustic model. The model is validated by showing fairly good agreements with the experimentally outcomes of the acoustic model. The model is validated by showing fairly good agreements with the measured SWLs. The past work done by the authors’ research team [30] focused on the outlet pressure experimentally measured SWLs. The past work done by the authors’ research team [30] focused on ripple among all possible noise sources, and partially confirmed the common assumption that outlet the outlet pressure ripple among all possible noise sources, and partially confirmed the common pressure ripple is the primary noise source is valid at some shaft speeds. However, the predicted assumption that outlet pressure ripple is the primary noise source is valid at some shaft speeds. ABN However, showed a large differenceABN withshowed the measured The current numerical model is improved by the predicted a largeABN. difference with the measured ABN. The current mapping noise model sourcesis to the structures in a more the predicted results showed the numerical improved by mapping noiserealistic sources way, to theand structures in a more realistic way, and acceptable difference with the experimental results. the predicted results showed the acceptable difference with the experimental results. 2. Vibro-Acoustic Model of External Gear Pump 2. Vibro-Acoustic Model of External Gear Pump The reference pumppump considered for thisfor research is a 22 cc/rev commercial no-backlash dual-flank The reference considered this research is a 22 cc/rev commercial no-backlash contact gear pump produced by Casappa (model PLP20QW, Parma, Italy). Details this 12 teethof pump dual-flank contact gear pump produced by Casappa (model PLP20QW, Parma,of Italy). Details this are shown in Figure 2. The pump body is typically composed of three pieces which enclose the gears 12 teeth pump are shown in Figure 2. The pump body is typically composed of three pieces which enclose the gears andfor have machined ports fortoconnecting thesystem. pump to a pressure hydrauliccompensated system. The and have machined ports connecting the pump a hydraulic The compensated bushings arebalance. used for The sealing and reference axial balance. Theischosen lateralpressure bushings are used forlateral sealing and axial chosen pump amongreference the most pump is among the most successful designs in mobile hydraulic applications, within pressure ranges successful designs in mobile hydraulic applications, within pressure ranges up to 300 bar. up to 300 bar.

Figure 2. Reference external gear pump.

Figure 2. Reference external gear pump.

Energies 2017, 2017, 10, 10, 1068 1068 Energies Energies 2017, 10, 1068

of 20 20 44 of 4 of 20

2.1. Modeling Approach 2.1. Modeling 2.1. Modeling Approach Approach The modeling approach follows the three categories of noise generation: fluid-borne noise (FBN), The modeling approach follows follows the the three three categories categories of noise noise generation: generation: fluid-borne fluid-borne noise (FBN), (FBN), The modeling approach structure-borne noise (SBN), and air-borne noise (ABN), of according to the basic idea of thenoise left side of structure-borne noise and noise (ABN), according totothe idea of(SBN), thethe leftleft side of structure-borne noise (SBN), andair-borne air-borne noise (ABN), according thebasic basic idea of side Figure 3. In order to (SBN), fully model the loading forces (FBN), the structure response and the Figure 3. In order to fully model the loading forces (FBN), the structure response (SBN), and the of Figure 3. Intoorder to(ABN), fully model theisloading (FBN), the structure response (SBN), and the transmission the air a model neededforces for each domain. transmission to to the the air air (ABN), (ABN), aa model model is is needed needed for for each each domain. domain. transmission

Figure 3. Transmission of sound from working fluid to field points. Figure 3. 3. Transmission Transmission of sound from Figure of sound from working working fluid fluid to to field field points. points.

The HYGESim model provides the pressure fluctuations in the fluid (FBN). The predicted The HYGESim model provides the pressure fluctuations in the fluid The predicted dynamic model pressure fluctuations the(FBN). fluid (FBN). The predicted dynamic HYGESim pressure forces in provides the form the of frequency function areinused as loading functions to the pressure in the formin of the frequency are used as loading functions to thefunctions structure.to Then, dynamic forces pressure forces form offunction frequency function are used as loading the structure. Then, combined finite element method (FEM) and boundary element method (BEM) combined finite element method (FEM) and boundary element (BEM) approach are used to structure. Then, element (FEM) andmethod boundary element (BEM) approach are usedcombined to predict finite SBN and ABN. method The FEM/BEM approach was chosen duemethod to its efficiency predict SBN The FEM/BEM approach was chosen due towas its efficiency accuracy in approach areand usedABN. to predict SBN and ABN. The FEM/BEM approach chosen dueand to its efficiency and accuracy in predicting the ABN radiated from noise sources; FEM models are widely accepted predicting thein ABN radiated from noise sources; FEM models are widely accepted for the structural and accuracy predicting ABN radiated from noise models widely accepted for the structural vibration,the and BEM is accepted as the sources; best for FEM modeling theare near-field acoustic vibration, and BEMvibration, is accepted as the best for modeling the near-field acoustic effects in modelsacoustic that are for the structural and BEM is accepted as best for modeling the near-field effects in models that are placed in unbounded environments. The model type considers the placed environments. The model typeenvironments. considers the interaction of type the load conditions effects in inunbounded models that are placed in unbounded The model considers the interaction of the load conditions with the mode shapes to investigate the structural vibration of the with the mode shapes to investigate the structural vibration of the pump (SBN). Processing the fluid interaction of Processing the load conditions the mode to investigate theand structural vibration of the pump (SBN). the fluid with dynamic resultsshapes involves selecting load surfaces and mapping dynamic results involvesthe selecting load and surfaces and mapping ontosurfaces the correct of a pump (SBN). Processing fluid dynamic results involves selectingloads load and and areas mapping loads onto the correct areas of a structural FEM mesh, made in ANSYS. Then, the BEM wrapper mesh structural FEM mesh, made in aANSYS. Then, themesh, BEM made wrapper mesh technique isBEM used wrapper for calculation loads onto the correct areas of structural FEM in ANSYS. Then, the mesh technique is used for calculation of the transmission of sound from the pump surface mesh out to the of the transmission of calculation sound fromofthe pump surface mesh out to the field (ABN). The main structure of technique is used for the transmission of sound from the pump surface mesh out to the field (ABN). The main structure of the model is adapted from the BEM acoustics methodology for the model is adapted from the BEM acoustics methodology for LMS Virtual.Lab Acoustics. A scheme field (ABN). The main structure of the model is adapted from the BEM acoustics methodology for LMS Virtual.Lab Acoustics. A scheme of the sound transmission is represented on the right side of of theVirtual.Lab sound transmission is represented the right transmission side of Figureis3,represented and an overview of the acoustic LMS Acoustics. scheme ofon the sound onofthe sidewill of Figure 3, and an overview ofAthe acoustic model is shown in Figure 4. The details theright model model Figure 4.ofThe of the model will beindescribed thedetails following sections. Figure is 3, shown and anin overview thedetails acoustic model is shown Figure 4.in The of the model will be described in the following sections. be described in the following sections.

Figure Figure 4. 4. Overview Overview of of the the vibro-acoustic vibro-acoustic model. model. Figure 4. Overview of the vibro-acoustic model.

Energies 2017, 10, 1068 Energies 2017, 10, 1068

5 of 20 5 of 20

2.2. Model Model of of Internal Internal Fluid-Borne Fluid-Borne Noise Noise Sources Sources 2.2. This section section provides provides aa simplified simplified description description of of the the fluid fluid dynamic dynamic model model of of HYGESim, HYGESim, used used in in This this research research for for the the evaluation evaluation of of the the FBN FBN sources. sources. this HYGESim is a simulation tool to study HYGESim is a simulation tool to study for for EGMs EGMs developed developed over over the the last last decade decade at at the the authors’ authors’ research center [31]. As represented in Figure 5, the model can simulate a unit starting from the CAD CAD research center [31]. As represented in Figure 5, the model can simulate a unit starting from the drawings of of the the machine. machine. With different modules, modules, HYGESim HYGESim solves solves the the main main flow flow through through the the unit unit drawings With different considering the radial micro-motions of the gears caused by the pressure forces and contact forces considering the radial micro-motions of the gears caused by the pressure forces and contact forces and the the behavior behavior of of the the journal journal bearings. bearings. This This is is performed performed through through aa lumped lumped parameter parameter approach approach and for the the solution solution of of the the flow flow displacing displacing action action realized realized by by the the gears gears [29], [29], coupled coupled with with aa numerical numerical for solution of the journal bearings [32]. The geometrical model and the control volume schematization, solution of the journal bearings [32]. The geometrical model and the control volume schematization, suitable for for aa large large variety variety of of gear gear profiles, profiles, are are documented documented in in [33]. [33]. For suitable For aa complete complete pump pump simulation, simulation, the lubricating gap flow at gear lateral surfaces along that results from the instantaneous position of of the lubricating gap flow at gear lateral surfaces along that results from the instantaneous position the floating lateral bushings (Figure 2), a fluid-structure interaction model was developed to run in the floating lateral bushings (Figure 2), a fluid-structure interaction model was developed to run in co-simulation with with the the solution solution of of the the main main flow flow through through the the EGM EGM [31,34]. [31,34]. Except Except for for the the acoustic acoustic co-simulation FEM/BEM module, which will be described in the next sections, all the HYGESim modules are FEM/BEM module, which will be described in the next sections, all the HYGESim modules are written written in C++ language, taking advantage of O-Foam libraries. Only a simplified formulation of the in C++ language, taking advantage of O-Foam libraries. Only a simplified formulation of the main main dynamic fluid dynamic model foranalysis the analysis of displacing the displacing action is detailed in the following, since fluid model for the of the action is detailed in the following, since it it provides the instantaneous pressure used for the loading function of the acoustic simulation of this provides the instantaneous pressure used for the loading function of the acoustic simulation of this paper. However, However,more more details HYGESim canfound be found the above-mentioned papers. The paper. details on on HYGESim can be in the in above-mentioned papers. The acoustic acoustic simulation module—represented by the bottom right box in Figure 5—complements the simulation module—represented by the bottom right box in Figure 5—complements the other modules other modules to obtain an omni-comprehensive model capable of predicting the acoustic noise of an to obtain an omni-comprehensive model capable of predicting the acoustic noise of an EGM. EGM.

Figure 5. 5. HYGESim HYGESim model. model. Figure

The main fluid dynamic model involves four main control volume groups (as shown in The main fluid dynamic model involves four main control volume groups (as shown in Figure 6). Figure 6). They are the inlet port volume (𝑉LP ), the outlet port volume (𝑉HP ), the set of control volumes They are the inlet port volume (VLP ), the outlet port volume (VHP ), the set of control volumes for the for the TSVs in the drive gear (𝑉1,𝑖 ), and the set of volumes for the TSVs in the slave gear (𝑉2,𝑖 ). The TSVs in the drive gear (V1,i ), and the set of volumes for the TSVs in the slave gear (V2,i ). The pressure pressure inside the control volumes as a function of fluid properties, geometric volume variation and inside the control volumes as a function of fluid properties, geometric volume variation and the net the net mass transfer with the adjacent control volumes can be given by the pressure build up mass transfer with the adjacent control volumes can be given by the pressure build up equation [29]: equation [29]:    dpd𝑝 dV dV𝑣𝑎𝑟,𝑗 . . d𝑉𝑗j d𝑉 d𝑝 j 𝑗 11dp var,j × [∑ == (1) | p𝑝=𝑝 | ̇ in,j− −∑ ∑m𝑚 ̇ out,j−−ρ𝜌| )] out,j ∑ m𝑚in,j = p j 𝑗 ( dt − (1) dtd𝑡 V𝑉 dt d𝜌 p𝑝=𝑝 𝑑𝑡 𝑑𝑡 j 𝑗dρ = pj 𝑗

thepressure, pressure, t 𝑡isisthe thetime, time,V𝑉isisthe thevolume, volume,Vvar 𝑉𝑣𝑎𝑟is is thevariation variationofofthe thevolume volumewith with shaft where p𝑝isisthe the . . 𝑚̇out are the the mass rotation during the the meshing meshing process, process, 𝜌ρ is the density density of of the the fluid, fluid, and and 𝑚 ṁ inin and and m out are flow rates entering and leaving the control volume, respectively. In particular, the symbols with the subscript j represent the corresponding quantities inside the j-th control volume. Proper lumped

Energies 2017, 10, 1068

6 of 20

flow rates entering and leaving the control volume, respectively. In particular, the symbols with the 6 of 20 subscript j represent the corresponding quantities inside the j-th control volume. Proper lumped parameterflow flowequations equations(orifice (orifice flow flow equation, internal leakages) areare used parameter equation, laminar laminarflow flowequations equationsfor for internal leakages) to determine the mass flow rate terms entering or leaving each control volume [29]. used to determine the mass flow rate terms entering or leaving each control volume [29]. The fluid dynamic results HYGESim, terms pressures, used evaluate sources The fluid dynamic results of of HYGESim, in in terms of of pressures, areare used to to evaluate thethe sources FBN. better understand noise sources propagate and what the dominant noise sources of of FBN. To To better understand howhow noise sources propagate and what the dominant noise sources are, are, the key physical phenomena for noise sources need to be understood. As far as the authors the key physical phenomena for noise sources need to be understood. As far as the authors areare concerned, previous research acoustic modeling external gear pump clearly define concerned, previous research onon acoustic modeling of of external gear pump diddid notnot clearly define or or classify the internal noise sources. Thus, this section describes all possible internal noise sources classify the internal noise sources. Thus, this section describes all possible internal noise sources in in external gearpump pumpthat thatcan canbe beobserved observed from from the the hydrodynamic thethe external gear hydrodynamic results resultsof ofthe theHYGESim HYGESimand andthe inin the current acoustic model. thenoise noisesources sourcesthat thatare areconcerned concerned the current acoustic model. Energies 2017, 10, 1068

Figure 6. Instantaneous volume of a tooth space chamber (TSV) (blue) and TSV pressure (red) obtained Figure 6. Instantaneous volume of a tooth space chamber (TSV) (blue) and TSV pressure (red) from HYGESim. On the left, the angular convention, where θ defines the TSV position with respect to obtained from HYGESim. On the left, the angular convention, where θ defines the TSV position with the start of the internal casing. respect to the start of the internal casing

Figure 6 shows working volume and pressure inside a particular tooth space volume (TSV) Figure 6 shows thethe working volume and pressure inside a particular tooth space volume (TSV) calculated by HYGESim, according to the angular convention shown on the left side of the same figure. calculated by HYGESim, according angular convention shown on the left side of the same ◦ of the gear rotation, and decreases down to A single TSV TSV is atisfull volume for for approximately 270270° figure. A single at full volume approximately of the gear rotation, and decreases down minima at the center of the meshing zone. The resulting pressure thatTSV TSV (normalized with to minima center of the meshing zone. The resulting pressure ininthat (normalized with thethe delivery pressure order magnitude 100 bar) shown Figure 6 (red line). pressure delivery pressure in in thethe order of of magnitude of of 100 bar) is is shown in in Figure 6 (red line). AA pressure peak results from compression TSV, and value mitigated the internal connections peak results from thethe compression of of thethe TSV, and itsits value is is mitigated byby the internal connections realized lateral bushings Figure This is consistent with what already observed previous realized in in thethe lateral bushings of of Figure 2. 2. This is consistent with what already observed in in previous ◦ fluid dynamic simulations done authors’ team [16,17,29]. Likewise, from 305through through 320◦ , fluid dynamic simulations done byby thethe authors’ team [16,17,29]. Likewise, from 305° 320°, when theTSV TSVvolume volumeincreases, increases, the pressure below atmospheric, causing a little onset when the pressure in inthe theTSV TSVfalls falls below atmospheric, causing a little of localized aeration [35].[35]. TheThe figure also highlights steep pressure gradients that occur when onset of localized aeration figure also highlights steep pressure gradients that occur whenthe high pressure pressure(HP) (HP)and andlow lowpressure pressure (LP) values theTSV TSVpressurizes pressurizesand anddecompresses decompresses between between the high (LP) values respectively at the inlet and at the outlet ports. The TSV pressurization can occur through leakages respectively at the inlet and at the outlet ports. The TSV pressurization can occur through leakages and/or through proper connections with outlet port purposely realized floating elements, and/or through proper connections with thethe outlet port purposely realized onon thethe floating elements, visible Figure This latter case reference unit considered this work. The whole as as visible in in Figure 7. 7. This latter is is thethe case of of thethe reference unit considered in in this work. The whole course of the TSV pressure in Figure 6 is considered as FBN source, applied to a proper region course of the TSV pressure in Figure 6 is considered as FBN source, applied to a proper region of of thethe casing shown Figure casing to to bebe shown in in Figure 7. 7.

Energies 2017, 10, 1068 Energies 2017, 10, 1068

7 of 20 7 of 20

Figure 7. Regions exposed to the pressure in external gear pumps. Figure 7. Regions exposed to the pressure in external gear pumps.

Another sources in inthe thefigure figureisisgiven givenby bythe theoutlet outletpressure pressure fluctuations. It can Another point of noise sources fluctuations. It can be be noted that reference pump TSV pressure almost coincides with outlet pressure due noted that forfor thethe reference pump thethe TSV pressure almost coincides with thethe outlet pressure due to to the internal connection to the outlet HP previously mentioned port via the pressurization groove the internal connection to the outlet HP previously mentioned port pressurization groove along along the the edge edge of of the the lateral lateralplate plate(see (seeright rightside sideof ofFigure Figure7). 7). Among Among the the mentioned mentioned noise noise sources, sources, the the contribution contribution of of possible possible localized localized cavitation cavitation inside inside the the ◦ TSV ) isisnot ABN evaluation, although pressure fluctuations at TSV(around (around310 310°) notconsidered consideredininthe thecurrent current ABN evaluation, although pressure fluctuations the inletinlet portport are considered. This simplification reduces implementation complexity, and it is partially at the are considered. This simplification reduces implementation complexity, and it is justified the factbythat sources not directly on the act pump case. partiallyby justified thethese fact that thesedosources do notact directly on the pump case. Other Other noise noise sources sources that that do do not not appear appear in in Figure Figure 6, 6, but but which which are arecalculated calculated by by HYGESim HYGESim and and applied appliedto to the the structure, structure, are arethe the inlet inlet pressure pressureripple rippleand andthe the total total net net radial radial forces forcesacting acting on on the the gears gears that that are are carried carried by bythe thejournal journalbearing bearingregions. regions. All All these these noise noise sources sources were were applied applied to to the the structure structure in in order order to to model model the the acoustic acoustic noise noise of of the the EGM. basic assumption assumptionthat thatall allforces forcesmust mustpass passthrough throughthe thepump pump casing order EGM. First First of all, the basic casing in in order to to radiate to the surroundings is made. advantage ofassumption this assumption if the forces radiate outout to the surroundings is made. The The advantage of this is thatisifthat the forces on the on the interior of the separating casing separating the interior parts the casing can be accurately interior of the casing the interior moving moving parts from thefrom casing can be accurately modeled, modeled, the moving parts be removed acoustic simulation. Thus,the theinternal internal pump then the then moving parts can becan removed fromfrom the the acoustic simulation. Thus, pump components components such such as as the the gears gears are are included included only only in in the the generation generation of of the the loading loading conditions, conditions, but but not not in in the the current current acoustic acoustic propagation propagation model. model. This This simplification simplification also also neglects neglects the the influence influence of of forces forces transmitting transmitting through throughthe thedrive drivegear gearand andcoupling couplinginto intothe theelectric electricmotor motoror orother otherprime primemovers. movers. Figure Figure 77 shows shows the the regions regions exposed exposed to to the the dynamic dynamic pressure in the EGMs, and in this study, these these regions regions are are subdivided subdivided into into 44 areas. areas. First, First, the the case case contact contact with with outlet outlet pressure pressure in in red red occurs occurs at at the the outlet outlet port port and and the the high-pressure high-pressure balance balance area areaon onthe thelateral lateralbushing. bushing. Likewise, Likewise, the the case case contact contact with with inlet inlet pressure pressure in in blue blue occurs occurs at at the the inlet inlet port port and and the the low-pressure low-pressure balance balance area area on on the the lateral lateral bushing. In addition, the journal bearing regions in black carry the gear loads. That is, the journal bushing. journal bearing regions in black carry the gear loads. That is, the journal bearing bearing must must react react all all the the forces forces put put on on the the gears gears by fluid pressures and gear contact forces. Finally, there there is is aa region region in inpurple purple which which is is the the portion portion of of the the case case in in contact contact with with fluctuating fluctuating pressure pressure at at the the whole TSV. whole TSV. The The load load area area selection selection on on the the mesh mesh of of the the pump pump geometry geometry corresponding corresponding to to these these areas areas in in the the model model is is shown shown in in Figure Figure 8. 8. All All the the regions regions exposed exposed to to fluid fluid fluctuations fluctuations are are concerned; concerned; the the outlet outlet pressure pressureregion regionof ofthe thepump pumpisisshown shownin inred redon onthe theright, right,the the inlet inlet in in blue blue on on the the left, left, the the TSV TSV pressure pressure regions regions in in aa purple purple arc, arc, and and the the bearing bearing load load areas areas in in black. black. Specifically, Specifically,in in order orderto to properly properlymap map the the whole TSV pressure, the circumferential parts of the case are discretized with 7.5 degrees of the angular whole TSV pressure, the circumferential parts of the case are discretized with 7.5 degrees of the interval as shown on shown the right Figure This angular interval was interval determined on the angular(ϕ) interval (φ) as onside theof right side8. of Figure 8. This angular wasbased determined sensitivity study which will be which discussed 2.5.in Section 2.6. based on the sensitivity study willin beSection discussed

Energies 2017, 10, 1068 Energies2017, 2017,10, 10,1068 1068 Energies

8 of 20 8 8ofof2020

Figure8.8.Load Load areasconsidered considered in themodel model (left)and and discretizationofofTSV TSV pressureregion region (right). Figure Figure 8. Loadareas areas consideredininthe the model(left) (left) anddiscretization discretization of TSVpressure pressure region(right). (right).

Themethodology methodologyfor forload loadcreation creationisiscompleted completedininMatlab. Matlab.The Thesimulated simulatedloads loadsthat thatoccur occuratat The Thesurfaces methodology for load for creation is completed in Matlab. The simulated loads100 that occur at specific on the model the operating condition of 1500 rpm shaft speed bar outlet specific surfaces on the model for the operating condition of 1500 rpm shaft speed 100 bar outlet specific surfaces onin the for the operating of 1500 shaft speed 100 outlet pressureare areshown shown themodel following figures (Figurecondition inlet,Figure Figure 10:rpm outlet, Figure 11:TSV TSVbar pressure pressure in the following figures (Figure 9:9:inlet, 10: outlet, Figure 11: pressure pressure are shown in the following figures (Figure 9: inlet, Figure 10: outlet, Figure 11: TSV pressure regions,and andFigure Figure12: 12:journal journalbearing bearingregions). regions).The Theleft leftside sideofofthese thesefigures figuresshows showsthe thenormalized normalized regions, regions, and Figure 12: journal bearing regions). The left side of these figures shows the normalized pressurefluctuation fluctuationdepending dependingon ontime, time,and andthe theright rightside sideofofthe thefigures figuresshows showsFourier Fouriertransform transformofof pressure pressure fluctuation depending on time, the right sidemany of thediscrete figures shows Fourier transform of thenormalized normalized pressure fluctuation. Forand brevity, among pointsin inthe theTSV TSV pressure the pressure fluctuation. For brevity, among many discrete points pressure the normalized pressure fluctuation. For brevity, among many discrete points in the TSV pressure regions,only onlythe theload loadon onthe thesignificant significantpoint pointassociated associatedwith withthe thepressurization pressurizationisispresented presentedinin regions, regions, only the load on the significant point associated with the pressurization is presented in Figure11. 11.Note Notethat thatall allthe thepressure pressurefunctions functionsininthese thesefigures figuresare arenormalized normalizedwith withthe themaximum maximum Figure Figure 11. Note that all the pressure functions in these figures are normalized with the maximum pressureofofinterest interestininthis thisstudy. study.The Theloads loadswere wereapplied appliedtotothe thecorresponding correspondingareas areasofofFigure Figure88asas pressure pressure of interest in this study. The loads were applied todynamic the corresponding areas on of Figure 8 as functions of frequency. From the figures, it appears that the pressures acting thejournal journal functions of frequency. From the figures, it appears that the dynamic pressures acting on the functions of frequency. From the of figures, it appears the dynamic pressures acting on thepressure journal bearingsand and oncertain certainlocations locations theTSV TSV pressurethat arelarger larger magnitude than theoutlet outlet bearings on of the pressure are ininmagnitude than the pressure bearings and on certain locations of the TSV pressure are larger in magnitude than the outlet pressure ripple,although althoughthey theyare areapplied appliedtotolimited limitedarea arearegions. regions.Furthermore, Furthermore,these theseregions regionsshow showlarger larger ripple, ripple, although they are applied to limited area regions. Furthermore, these regions show larger high-frequencycomponents components that thatcan can be be responsible responsible for forthe thehigh-frequency high-frequencycomponents componentsofofthe the high-frequency high-frequency components thatpressure can be responsible forto the high-frequency components of the resultant resultantnoise noisewhile while theoutlet outlet rippleseems seems only excitethe thelow-frequency low-frequency noise. Thiscan can resultant the pressure ripple to only excite noise. This noise while the outlet pressure ripple to only research excite thework low-frequency noise. This can be besupported supported bythe theexperimental experimental resultsseems previous publishedby by theauthors’ authors’ team be by results ofofaaprevious research work published the team supported by thework, experimental results of a previous research work published byas the authors’ team [36]. [36].InInthis thispast past theauthors authors considered onlyoutlet outlet pressure oscillations FBN source, surface [36]. work, the considered only pressure oscillations as FBN source, surface In this past work, the authors considered only outlet pressure oscillations as FBN source, surface vibrationsasasSBN, SBN,and andthe theradiated radiatedairborne airbornenoise noiseasasABN. ABN.These Thesequantities quantitieswere weremeasured measuredfor forshaft shaft vibrations vibrations as SBN,from and the radiated airborne noisecross-correlations as ABN. These quantities were measured for shaft speeds ranging 500 to 2100 rpm, and of FBN-SBN, FBN-ABN, and speeds ranging from 500 to 2100 rpm, and cross-correlations of FBN-SBN, FBN-ABN, and speeds ranging from 500 to 2100 rpm, and cross-correlations of FBN-SBN, FBN-ABN, and SBN-ABN SBN-ABNwere wereconsidered. considered.The Theresults resultsshowed showedthat thatthere thereisisaavery veryweak weakcorrelation correlationbetween between SBN-ABN were considered. The results showed that there is a very weakwhile correlation betweenof FBN-SBN and FBN-SBN and FBN-ABN especially at high-frequency regions the correlation SBN-ABN FBN-SBN and FBN-ABN especially at high-frequency regions while the correlation of SBN-ABN isis FBN-ABN especially at range high-frequency regions while the numerical correlationand of SBN-ABN is strong through strongthrough through wide frequencies. Thus, both experimental results imply strong aawide range ofoffrequencies. Thus, both numerical and experimental results imply athat wide range of frequencies. Thus, both numerical and experimental results imply that the theoutlet outletpressure pressureripple ripplealone alonecan canhardly hardlycontribute contributetotothe thehigh-frequency high-frequencycomponents componentsofoutlet ofthe the that the pressure ripple alone can hardly contribute to the high-frequency components of the radiated noise. radiated noise. radiated noise.

(a) (a)

(b) (b)

Figure9.9.Inlet Inlet pressureripple ripple dependingon on time(a) (a) andfrequency frequency (b). Figure Figure 9. Inletpressure pressure rippledepending depending ontime time (a)and and frequency(b). (b).

Energies Energies2017, 2017,10, 10,1068 1068 Energies2017, 2017,10, 10,1068 1068 Energies

99of of20 20 9 9ofof2020

Energies 2017, 10, 1068

9 of 20

(a) (b) (a) (b) (a) (b) Figure 10. Outlet pressure ripple depending on time (a) and (a) (b) frequency (b). Figure10. 10.Outlet Outletpressure pressureripple rippledepending dependingon ontime time(a) (a)and andfrequency frequency(b). (b). Figure Figure 10. Outlet pressure ripple depending on time (a) and frequency (b). Figure 10. Outlet pressure ripple depending on time (a) and frequency (b).

(a) (b) (a) (b) (a) (b) Figure 11. Pressure ripples at the (a)TSV pressure regions at θ = 51° for the drive (b) gear depending on time (a) Figure11. 11.Pressure Pressureripples ripplesatatthe theTSV TSVpressure pressureregions regionsatatθθ= =51° 51°for forthe thedrive drivegear geardepending dependingon ontime time(a) (a) Figure ◦ and frequency (b). Figure 11. Pressure ripples at the TSV pressure regions at θ = 51 for the drive gear depending on time and frequency (b). Figure 11. Pressure and frequency (b). ripples at the TSV pressure regions at θ = 51° for the drive gear depending on time (a) (a) and frequency (b). and frequency (b).

Figure 12. Pressure ripples at the bearing region for the (a) drive gear and (b) driven gear depending Figure 12.Pressure Pressureripples ripplesatatthe thebearing bearingregion regionfor forthe the(a) (a)drive drivegear gearand and(b) (b)driven drivengear geardepending depending Figure on time12. (left) and frequency (right). on time (left) and frequency (right). Figure 12. Pressure ripples at the bearing region for the (a) drive gear and (b) driven gear depending Figure 12. Pressure ripples at the bearing region for the (a) drive gear and (b) driven gear depending on time (left) and frequency (right). on time time (left) (left) and and frequency frequency (right). (right). on

2.3. Structural Model of Pump Body Response 2.3.Structural StructuralModel ModelofofPump PumpBody BodyResponse Response 2.3. The structural model the Response pump is required for determining the potential resonant behavior 2.3. Model 2.3. Structural Structural Model of of Pump PumpofBody Body Response Thestructural structuralmodel modelofofthe thepump pump isrequired requiredfor for determiningthe the potentialresonant resonantbehavior behavior and The the vibrations at the surface of the ispumps under determining operating loads. potential The modeling approach for and the vibrations at the surface of the pumps under operating loads. The modeling approach for The structural of is required for the resonant behavior Thevibrations structural model model of the the pump pump ispumps required for determining determining the potential potential resonant behavior and the at the surface of the under Thefrom modeling approach predicting SBN is structured in three steps as shown inoperating Figure 13.loads. Starting the 3 D CAD of for the predicting SBNisisstructured structured inthree three steps shown inFigure Figure13. 13. Starting from the33D DCAD CADofoffor the and the at the of pumps underinoperating loads. The modeling approach and the vibrations vibrations at the surface surface of the pumps Thefrom modeling approach for predicting SBN steps asasshown the the component, the FEM mesh isingenerated. Next, the modal analysisStarting is performed with a preliminary component, the FEM mesh is generated. Next, the modal analysis is performed with a preliminary predicting SBN is structured in three steps as shown in Figure 13. Starting from the 3 D CAD of the predicting SBN is structured in three steps as shown in Figure 13. Starting from the 3 D CAD of the component, the FEMThe mesh is step generated. Next,model, the modal is performed with a preliminary pump constraining. final is the BEM with analysis the introduction of a wrapper mesh. pumpconstraining. constraining. The final stepisisthe theBEM BEM model, withanalysis theintroduction introduction wrapper mesh. component, the mesh is generated. Next, the is with component, the FEM FEMThe mesh is step generated. Next, the modal modal analysis is performed performed with aa preliminary preliminary pump final model, with the ofofaawrapper mesh. pump pump constraining. constraining. The The final final step step is is the the BEM BEM model, model, with with the the introduction introduction of a wrapper mesh.

Figure 13. Structural model path.

Figure 13. Structural model path.

Figure Structuralmodel modelpath. path.for finding approximate solutions The finite element method (FEM) is 13. a13. numerical technique Figure Structural Figure 13. Structural model path. to boundary value problems for(FEM) partialis differential Thefinding goals for the FEM mesh are to The finite element method a numericalequations. technique for approximate solutions to Thefinite finiteelement elementmethod method(FEM) (FEM)isisaanumerical numericaltechnique techniquefor forfinding findingapproximate approximatesolutions solutionstoto The boundary value problems for partial differential equations. The goals for the FEM mesh are to boundary value problems for(FEM) partial equations. Thefinding goalsfor forthe theFEM FEMmesh meshare areto The finite element method isdifferential adifferential numericalequations. technique The for approximate solutions boundary value problems for partial goals toto boundary value problems for partial differential equations. The goals for the FEM mesh are to

Energies 2017, 10, 1068 Energies 2017, 10, 1068

10 of 20 10 of 20

accurately model the modal harmonics and the surface vibration of the pump body. Before generating FEM mesh,model the internal pump components suchsurface as the vibration gears andofshafts were removed because of the accurately the modal harmonics and the the pump body. Before generating assumption thatinternal all forces must pass through pump in order radiate because out to the FEM mesh, the pump components such the as the gearscasing and shafts weretoremoved of surroundings as described in Section 2.2. Furthermore, the structural model for the reference pump the assumption that all forces must pass through the pump casing in order to radiate out to the was simplifiedasby eliminating small 2.2. structural details the suchstructural as the fillets, and plaques as surroundings described in Section Furthermore, modelgrooves, for the reference pump shown in Figure 14a. This was because small structural details have and littleplaques impacts the was simplified by eliminating smalldone structural details such as the fillets, grooves, as on shown interaction between the low-frequency loading functions and the structure. Furthermore, the quality in Figure 14a. This was done because small structural details have little impacts on the interaction of FEM mesh can be increased because it prevents of the nodesthe andquality elements near between the low-frequency loading functions andthe theconcentration structure. Furthermore, of FEM small features on the pump. After the simplification of the pump geometry, the structural meshes mesh can be increased because it prevents the concentration of the nodes and elements near small were created inpump. ANSYSAfter usingthe a patch-independent tetrahedral mesh asthe shown in Figure 14b.were This features on the simplification of the pump geometry, structural meshes mesh allows for the accurate definition of small features while givinginanFigure efficient created in ANSYS using a patch-independent tetrahedral mesh also as shown 14b.mesh Thisacross mesh large areas. The meshing parameters were determined thean mesh sensitivity study large until allows for the accurate definition of small features while through also giving efficient mesh across convergence in theparameters modal frequencies was reached. Thethe detailed information about mesh is areas. The meshing were determined through mesh sensitivity study untilFEM convergence given in Table 1. Particularly, the “mapped faceinformation meshing” about method was applied to inthe area in the modal frequencies was reached. The detailed FEM mesh is given Table 1. corresponding to the TSV pressure regions to obtain an even discretization when the meshes were Particularly, the “mapped face meshing” method was applied to the area corresponding to the TSV generated. pressure regions to obtain an even discretization when the meshes were generated.

Figure 14. (a) the geometry geometry of of the the reference reference pump pump and and (b) (b) FEM FEM mesh. mesh. Figure 14. (a) Simplification Simplification of of the Table 1. 1. FEM FEM ANSYS ANSYS meshing meshing parameters. parameters. Table Parameter Parameter Method Method Algorithm Algorithm Midside nodes Midside nodes Minimum edge length Minimum edge length Number of elements Number of of nodes elements Number

Number of nodes

Value Value Tetrahedral mesh Tetrahedral mesh Patch PatchIndependent Independent No No 0.0005 m 0.0005 m 17,942 17942 29,966 29966

After that, a modal analysis was performed because it determines the vibration characteristics After that, a modal analysis was performed because it determines the vibration characteristics (natural frequencies and mode shapes) of a structure or a machine component. It can also serve as (natural frequencies and mode shapes) of a structure or a machine component. It can also serve as a a starting point for another, more detailed, dynamic analysis, such as a transient dynamic analysis, starting point for another, more detailed, dynamic analysis, such as a transient dynamic analysis, a a harmonic analysis, or a spectrum analysis. The natural frequencies and mode shapes are important harmonic analysis, or a spectrum analysis. The natural frequencies and mode shapes are important parameters in the design of a structure for dynamic loading conditions. Modal frequencies are parameters in the design of a structure for dynamic loading conditions. Modal frequencies are the the frequencies that structural components will react at most strongly if the structure is excited frequencies that structural components will react at most strongly if the structure is excited periodically. Mode shapes are the forms the structure will take when it vibrates at a modal frequency. periodically. Mode shapes are the forms the structure will take when it vibrates at a modal frequency. The geometry was tested with constraints, following the real mounting of the pump on a test-rig or The geometry was tested with constraints, following the real mounting of the pump on a test-rig or commercial/industrial application as shown in the middle of Figure 13: the holes on the flange and commercial/industrial application as shown in the middle of Figure 13: the holes on the flange and the mounting area are fixed and the structures are bounded along the axial direction. The natural the mounting area are fixed and the structures are bounded along the axial direction. The natural frequencies (normalized with respect to the first mode) are shown in Table 2. All these 16 modes are in frequencies (normalized with respect to the first mode) are shown in Table 2. All these 16 modes are the audible frequency range and considered in the acoustic model. in the audible frequency range and considered in the acoustic model.

Energies 2017, 10, 1068 Energies 2017, 10, 1068

11 of 20 11 of 20

Table 2. Numerical normalized modal frequencies. Mode Normalized Modalmodal Frequencies Table 2. Numerical normalized frequencies. 1 1.00 2 1.02 Mode Normalized Modal Frequencies 3 1.95 1 1.00 4 2.751.02 2 3.711.95 35 3.892.75 46 5.183.71 57 5.433.89 68 79 5.605.18 810 5.725.43 911 5.855.60 10 5.72 12 6.27 11 5.85 13 6.36 12 6.27 6.606.36 1314 6.946.60 1415 7.046.94 1516 16 7.04

The final step to the structural model is to generate the boundary element surface mesh made in LMS Virtual.Lab Acoustics as shownmodel in Figure The BEM size was chosen to 5mm maximum The final step to the structural is to15. generate themesh boundary element surface mesh made in element size in order to achieve a material maximum frequency up to 10 kHz (the maximum element LMS Virtual.Lab Acoustics as shown in Figure 15. The BEM mesh size was chosen to 5 mm maximum size was determined that the number of elements per the wavelength is 6). The size element size in ordertotosatisfy achieve a material maximum frequency upshortest to 10 kHz (the maximum element of the boundary elements is regularly distributed across the whole mesh. The number of quadrilateral size was determined to satisfy that the number of elements per the shortest wavelength is 6). The size elements and nodes of BEM were 2453 and 2451 of the boundary elements is mesh regularly distributed acrossrespectively. the whole mesh. The number of quadrilateral

elements and nodes of BEM mesh were 2453 and 2451 respectively.

Figure 15. Boundary element surface mesh. Figure 15. Boundary element surface mesh.

2.4.Acoustic AcousticModel Model 2.4. Thenext nextstep stepfor forpredicting predictingthe theacoustic acousticnoise noiseof ofthe thepumps pumpsisistotomodel modelthe theacoustic acousticenvironment environment The for the exterior domain. To do this, the field point mesh (FPM) and two reflecting planes were were for the exterior domain. To do this, the field point mesh (FPM) and two reflecting planes introducedas asshown shownin inFigure Figure16 16in inorder orderto tomimic mimicthe theenvironments environmentsof ofthe thesemi-anechoic semi-anechoicchamber chamber introduced where noise measurements were conducted for the model validation (as it will be seen in Section 3.2). where noise measurements were conducted for the model validation (as it will be seen in Section 3.2). Two reflecting reflecting planes planes represent represent the the floor floor and and wall wall inside inside the the sound soundchamber. chamber. Because Becausethe thefloor floorand and Two wall are assumed to be rigid, the so-called image method is used in the software; two symmetry planes wall are assumed to be rigid, the so-called image method is used in the software; two symmetry generate the mirror noise sources against the planes boundaries are boundaries removed, which planes generate theimages mirrorofimages of noise sources againstand thethe planes and the are are acoustically equivalent to the presence of the rigid planes. This method can make the problems removed, which are acoustically equivalent to the presence of the rigid planes. This method can make simpler and allow more computation. In addition, the is a visualization which is the problems simpler andefficient allow more efficient computation. InFPM addition, the FPM is amesh, visualization used to compute and represent the acoustic results in space around the vibrating pumps. This mesh mesh, which is used to compute and represent the acoustic results in space around the vibrating does notThis influence acoustical solution simply limits the number of environmental solution pumps. mesh the does not influence thebut acoustical solution but simply limits the number of

Energies 2017, 10, 1068

12 of 20

Energies 2017, 10, 1068

12 of 20

points (each point of FPMpoints can be(each regarded asof theFPM microphone). To get the mesh geometry in To Figure 16, environmental solution point can be regarded as the microphone). get the amesh spherical mesh of 1-meter radius from the center of the pump was first generated and then, mesh geometry in Figure 16, a spherical mesh of 1-meter radius from the center of the pump was first elements below theelements floor andlocated behind below the wall generatedlocated and then, mesh thewere floorremoved. and behind the wall were removed.

Figure16. 16. Field FieldPoint PointMesh Meshand andreflecting reflectingplanes. planes. Figure

After creating FPM and reflecting planes, a modal superposition vibro-acoustic response After creating FPM and reflecting planes, a modal superposition vibro-acoustic response simulation type is run in LMS Virtual.Lab. This type sets up and solves the coupled FEM/BEM simulation type is run in LMS Virtual.Lab. This type sets up and solves the coupled FEM/BEM equation involving both the structural displacements (𝑤 ) and the acoustic pressure (𝑝̂𝑖1 : pressure at equation involving both the structural displacements (wi𝑖) and the acoustic pressure ( pˆ i1 : pressure at the nodes of coupling interface, 𝑝̂ : pressure at the remaining nodes) as unknowns: the nodes of coupling interface, pˆ i2 :𝑖2pressure at the remaining nodes) as unknowns: 𝐾𝑠 + 𝑗𝜔𝐶𝑠 − 𝜔2 𝑀𝑠 𝐿𝐶 0 𝑤𝑖  𝐹 𝑠    Ks + [jωCs𝜌− ω22𝐵M 0 𝐴12 (2) 𝑎1 } Fs  ] {w𝑝̂i𝑖1 } = {𝐹   0𝜔 11s𝑇𝑠 LC 𝐴11   2 2 𝑝̂ 𝐹 (2) ρ0 ω B𝜌11 Ts 𝐵21 𝑇𝑠 A11 𝐴A2112  𝐴22 pˆ i1𝑖2 = 𝑎2 Fa1  0𝜔   pˆ     F   2B T ρ ω A A s 0 22 matrix, a2 mass matrix, [𝐿 ] is the 21[𝐶 ] is the 21 i2 [𝑀 ] is the where [𝐾𝑠 ] is the stiffness matrix, damping 𝑠 𝑠 𝐶 coupling matrix, [𝑇𝑠 ] is the transformation matrix that relates the normal velocity to the where [Ks ] is the stiffness matrix, [Cs ] is the damping matrix, [ Ms ] is the mass matrix, [ LC ] is the displacement, [𝐴] and [𝐵] are the matrices that relate nodal pressure values to the nodal normal coupling matrix, [ Ts ] is the transformation matrix that relates the normal velocity to the displacement, velocity, {𝐹𝑠 } and {𝐹𝑎 } are the vectors that contain the prescribed structural and acoustical the the matrices that relate nodal pressure values to the nodal normal velocity, { Fs } and [ A] and [ B] are boundary conditions set, 𝜔 is the angular frequency, and 𝜌 is the density of the air. The details of { Fa } are the vectors that contain the prescribed structural and0acoustical the boundary conditions set, the equations put into practice in the model can be found in the works done by Desmet et al [37]. This ω is the angular frequency, and ρ0 is the density of the air. The details of the equations put into practice model form allows to compute the response of the system using a modal model and a given load data in the model can be found in the works done by Desmet et al. [37]. This model form allows to compute set. This case assumes the modal damping matrix to be purely diagonal, and does not make an actual the response of the system using a modal model and a given load data set. This case assumes the projection of the system of equations onto the modal basis. modal damping matrix to be purely diagonal, and does not make an actual projection of the system of equations onto the modal basis. 2.5. Sensitivity Study on the Angular Interval for Discretization of the TSV Pressure Region

2.5. Sensitivity Study the Angular Interval Discretization of the TSV Pressure Region In this work, theonarea of the EGM casefor next to the TSV pressure region (Figure 7) was discretized to properly map the pressure of the moving TSV to the stationary pump case. If is not In this work, the area of the EGM case next to the TSV pressure region (Figure 7)this wasregion discretized divided into enough number of sections, high spatial discontinuity of the loads brings the acoustic to properly map the pressure of the moving TSV to the stationary pump case. If this region is not model far from realistic. Whileofthe larger number of split sections in of thethe TSV pressure region enables divided into enough number sections, high spatial discontinuity loads brings the acoustic the gentler and more realistic spatial variation of the loads, it increases computing time and efforts. model far from realistic. While the larger number of split sections in the TSV pressure region enables Thus, a sensitivity study was performed determine reasonable angular for the gentler and more realistic spatial variation to of the loads, it the increases computing time interval and efforts. discretization of the TSV pressure region. (Smaller angular interval means larger number of split Thus, a sensitivity study was performed to determine the reasonable angular interval for discretization sections inpressure the TSV region. pressure region)angular interval means larger number of split sections in the TSV of the TSV (Smaller Figure 17 shows the overview of the sensitivity study cases. First, the angular interval of a TSV pressure region). (30°,Figure for a 12 was chosen largest angular interval for the discretization of the of TSV 17 teeth showsunit) the overview of as thethe sensitivity study cases. First, angular interval a pressure region. Then, finer angular intervals were considered by progressively reducing by half, ◦ TSV (30 , for a 12 teeth unit) was chosen as the largest angular interval for discretization of the TSV until it reached 1.875 degree. Consequently, 5 cases were considered with the following angular intervals: 30, 15, 7.5, 3.75, and 1.875 degrees, which means that the numbers of split sections in one

Energies 2017, 10, 1068

13 of 20

pressure region. Then, finer angular intervals were considered by progressively reducing by half, until it Energies reached2017, 1.875 degree. Consequently, 5 cases were considered with the following angular intervals: 10, 1068 13 of 20 Energies 2017, 10, 1068 13 angle of 20 30, 15, 7.5, 3.75, and 1.875 degrees, which means that the numbers of split sections in one TSV areTSV 1, 2,angle 4, 8, and results of 5 cases for theofoperating condition of 1500condition rpm shaftof are 16. 1, 2,Then, 4, 8, the andacoustic 16. Then, the acoustic results 5 cases for the operating TSV angle are bar 1, 2,outlet 4, 8, and 16. Then, the acoustic results of 5 cases for the operating condition of speed and 100 pressure were compared. 1500 rpm shaft speed and 100 bar outlet pressure were compared. 1500 rpm shaft speed and 100 bar outlet pressure were compared.

Figure Overview the sensitivity study for the determination ofthe the angular interval Figure 17. Overview the sensitivity study for the determination angular interval Figure 17.17.Overview ofofof the sensitivity study for the determination ofofthe angular interval forforfor discretization of TSV pressure region. discretization of TSV pressure region. discretization of TSV pressure region.

Figure shows the normalized SWLs for the considered cases reference set toto the Figure 18 shows the normalized SWLs forfor thethe fivefive considered cases (the(the reference waswas set the Figure 1818 shows the normalized SWLs five considered cases (the reference wasto set SWL the case 1.875 degree the angular interval). figure shows how the simulated SWL SWL forfor the case of of 1.875 degree of of theof angular interval). TheThe figure shows how the simulated SWL the SWL for the case of 1.875 degree the angular interval). The figure shows how the simulated decreases as the number of sections in the TSV pressure region is increased. The spatially gentle decreases as the number of sections in the TSV pressure region is increased. The spatially gentle SWL decreases as the number of sections in the TSV pressure region is increased. The spatially gentle variation the loads in this region caused number seems to bring lower SWL. More variation of the loads inin this region caused by by increasing thethe number seems to bring SWL. More variation ofof the loads this region caused byincreasing increasing the number seems tolower bring lower SWL. notable the amount change over number of split sections. While SWL greatly notable is isthe of of change in in SWL over thethe number of of split sections. While SWL greatly More notable isamount the amount of change inSWL SWL over the number split sections. While SWL greatly decreases as the number of split sections in one TSV angle increases up to 4, the SWL variations decreases as the number of split sections in one TSV angle increases up to 4, the SWL variations decreases as the number of split sections in one TSV angle increases up to 4, the SWL variations become become almost negligible than 1 number dB) is larger than 4. This to the conclusion become almost negligible (less than dB) as as thethe number larger than 4. This to the conclusion almost negligible (less than 1(less dB) as 1the is number largeristhan 4. This leads toleads theleads conclusion that 7.5◦ that 7.5° (corresponding angle to 4 split sections in one TSV angle) is small enough for the angular that 7.5° (corresponding angle to 4 split sections in one TSV angle) is small enough for the angular (corresponding angle to 4 split sections in one TSV angle) is small enough for the angular interval for interval for discretization of TSV pressure region. interval for discretization of TSV pressure region. discretization of TSV pressure region.

Figure 18.18. Normalized SWLs depending on on thethe number of split sections in one TSVTSV angle within the the Figure Normalized SWLs depending number of split sections in one angle within Figure 18. Normalized SWLs depending on the number of split sections in one TSV angle within the TSV pressure region. TSV pressure region. TSV pressure region.

3.3. Acoustic Results Acoustic Results 3.1. Numerical Results 3.1. Numerical Results SWL and SPL are considered for four different operating conditions as the main output of the SWL and SPL are considered for four different operating conditions as the main output of the acoustic model. These were calculated every 15 Hz (for 1500 rpm shaft speed) and 20 Hz (for acoustic model. These were calculated every 15 Hz (for 1500 rpm shaft speed) and 20 Hz (for 2000 rpm shaft speed) between 0 and 10 kHz. 2000 rpm shaft speed) between 0 and 10 kHz. The resulting normalized sound power spectra are shown in Figure 19. Note that the normalized The resulting normalized sound power spectra are shown in Figure 19. Note that the normalized SWL was referenced to the sound power of the experimentally measured mean noise floor inside the SWL was referenced to the sound power of the experimentally measured mean noise floor inside the

Energies 2017, 10, 1068

14 of 20

3. Acoustic Results 3.1. Numerical Results SWL and SPL are considered for four different operating conditions as the main output of the acoustic model. These were calculated every 15 Hz (for 1500 rpm shaft speed) and 20 Hz (for 2000 rpm Energies 2017, 10, 1068 14 of 20 shaft speed) between 0 and 10 kHz. The resulting normalized sound power spectra are shown in Figure 19. Note that the normalized semi-anechoic chamber (experimental measurements for validation were taken as will be described SWL was referenced to the sound power of the experimentally measured mean noise floor inside the in Section 3.2). It means that the noise level corresponding to the measured mean noise floor was semi-anechoic chamber (experimental measurements for validation taken as will be described designated as 0 dB. Because coupling with the electric motor orwere other prime mover was not in considered Section 3.2).inItthe means that the noise level corresponding to the measured mean noise floorand was model, harmonics of the shaft rotational frequency (fundamentals of 1500 designated as 0 dB. Because coupling with the electric motor or other prime mover was not considered 2000 rpm are 25 and 33.3 Hz, respectively) are not effective. Taking into account that the number of in gear the model, of fundamentals the shaft rotational frequency (fundamentals 2000 rpm are teeth isharmonics 12 and so the of meshing frequency are 300 and of 4001500 Hz, and harmonics of the 25 meshing and 33.3frequency Hz, respectively) are not effective. Taking into account that the number of gear teeth are dominant in the sound power spectra. The fundamental of meshing frequencyis 12 (𝑓 and so the fundamentals of meshing frequency are 300 and 400 Hz, harmonics of the meshing 0 ) was calculated by Equation (3): frequency are dominant in the sound power spectra. The∙ 𝜔 fundamental of meshing frequency ( f 0 ) was 𝑛teeth 𝑓0 = (3) calculated by Equation (3): 60 nteeth · ω f 0 = 𝜔 is the shaft speed in rpm. Another observation one (3) where 𝑛teeth is the number of gear teeth and 60 can make is that the noise level at the second harmonic is higher than the level at the first harmonic. where nteeth is the number of gear teeth and ω is the shaft speed in rpm. Another observation one can This can be explained by the zero backlash (dual flank) nature of the displacing action of the make is that the noise level at the second harmonic is higher than the level at the first harmonic. This can considered EGM. be explained by the zero backlash (dual flank) nature of the displacing action of the considered EGM.

Figure 19.19. Normalized operating conditions. conditions. Figure Normalizedsound soundpower powerlevel levelspectra spectra for for the the four operating

integrating each frequencycomponent, component,ititisispossible possible to to obtain obtain aa value ByBy integrating each frequency valueidentifying identifyingthe theoverall overall sound power level. Table 3 shows the normalized overall sound power levels for the four operating sound power level. Table 3 shows the normalized overall sound power levels for the four operating conditions. Note that the overall SWLs were also referenced to the same value used for the calculation conditions. Note that the overall SWLs were also referenced to the same value used for the calculation of sound power spectra in Figure 19. of sound power spectra in Figure 19. Increasing the outlet pressure from 100 to 200 bar at the shaft speed of 1500 rpm, the SWL rises by Table 3. Normalized overall sound power levels for the four different operating conditions. 5.1 dB. Keeping the same outlet pressure of 100 bar, and increasing the shaft speed to 2000 rpm results Operating Conditions Normalized SWLoutlet pressure at the same in 2.6 dB increase in the noise level. Finally, increasing shaft Overall speed and 1500 rpm, 100 bar 40.0 dB time, the SWL enhances by 8.1 dB compared to the initial condition of 1500 rpm, 200 bar. 1500 rpm, 200 bar

45.1 dB

2000 rpm, 100 bar

42.6 dB

2000 rpm, 200 bar

48.1 dB

Increasing the outlet pressure from 100 to 200 bar at the shaft speed of 1500 rpm, the SWL rises

Energies 2017, 10, 1068

15 of 20

Table 3. Normalized overall sound power levels for the four different operating conditions.

Energies 2017, 10, 1068

Operating Conditions

Normalized Overall SWL

1500 rpm, 100 bar

40.0 dB

15 of 20

1500 rpm, 200 bar 45.1 dBshaft speed and outlet pressure at the results in 2.6 dB increase in the noise level. Finally, increasing 2000 rpm, 100 bar 42.6 dB same time, the SWL enhances by2000 8.1rpm, dB 200 compared to the initial bar 48.1 dB condition of 1500 rpm, 200 bar. Energies 2017, 10, 1068 15 of 20 Next, consider the SPL distribution. Figure 20 shows the coordinate system for the SPL Next, consider the SPL distribution. Figure 20represent shows the coordinate system the SPL distribution. results in 2.6 dB increase in the noise level. Finally, increasing shaftinlet speed andfor outlet pressure at the distribution. Positive and negative x directions the and outlet side, respectively. The Positive and x directions the inlet andinitial outletcondition side, respectively. The200 back side and same time, thenegative SWL enhances by 8.1represent dB compared to the of 1500 rpm, bar. back side and the flange side are set to the positive and negative y directions.

the flange are setthe to the and negative directions. Next, side consider SPLpositive distribution. Figure y20 shows the coordinate system for the SPL distribution. Positive and negative x directions represent the inlet and outlet side, respectively. The back side and the flange side are set to the positive and negative y directions.

FigureFigure 20. Coordinate system for the SPL distribution in21. Figure 21. Figure 20.Coordinate Coordinate systemfor forthe the SPL distribution Figure 21. 20. system SPL distribution ininFigure 21 showsthe theSPL SPLdistribution distribution at the offrom 1 m the pump for 4 different Figure 21 shows at the distance of 1 m for 4 different operating Figure 21Figure shows the SPL distribution at thedistance distance of from 1 pump m the from the pump for 4 different operating conditions. The pump is located at the origin. The blue arrow indicates the inlet side the conditions. The pump is located at the origin. The blue arrow indicates the inlet side of the pumpofwhile operating conditions. The is located at reflecting the origin. The blue arrow indicates the inlet pump the red pump arrow theTwo outlet side. Two reflecting for floor the wall and floor arein side of the the redwhile arrow indicates theindicates outlet side. planes for theplanes wall and are represented represented in gray. that SPLsthe arewith normalized with the global minimum SPL results. of for the entire results. pump while theNote redthat arrow indicates outlet side. Two reflecting the wall and floor are gray. SPLsNote are normalized the global minimum SPL of the planes entire In each case, In each case, there are crucial red areas on the inlet and outlet sides (positive and negative are crucial redthat areasSPLs on the are inletnormalized and outlet sideswith (positive negative x-direction). Furthermore, representedthere in gray. Note theand global minimum SPL of the entire results. x-direction). the shaft effectand of increasing speedisshaft outlet is from quitethe similar, as the effect of Furthermore, increasing speed outlet pressure quiteand similar, as pressure confirmed analysis In each case, therefrom are crucial red areas onboth thetheinlet and and outlet sides (positive and negative confirmed the analysis of SWL; changing shaft speed outlet pressure, it is possible of SWL; changing both the shaft speed and outlet pressure, it is possible to observe an increase and an x-direction). Furthermore, the effect of speed shaft outlet pressure is quite similar, as to observe an increase andred anzone enlargement of the dark red zone on and the mesh. enlargement of the dark onincreasing the mesh. confirmed from the analysis of SWL; changing both the shaft speed and outlet pressure, it is possible to observe an increase and an enlargement of the dark red zone on the mesh.

Figure Figure21. 21.Normalized NormalizedSPL SPLdistribution distributionfor forthe thefour fourdifferent differentoperating operatingconditions. conditions.

3.2. Experimental Validation To validate the presented acoustic model, experimental noise measurements were taken using the semi-anechoic chamber available at the Maha Fluid Power Research Center of Purdue University as shown in Figure 22a. The open hydraulic circuit used for the experiments is shown in Figure 22b,

Energies 2017, 10, 1068

16 of 20

3.2. Experimental Validation To validate the presented acoustic model, experimental noise measurements were taken using the semi-anechoic chamber available at the Maha Fluid Power Research Center of Purdue University as shown in Figure 22a. The open hydraulic circuit used for the experiments is shown in Figure 22b, Energies 2017, 10, 1068 reported in Table 4. The pump under testing and short connecting lines 16 of 20 with further details were inside of the sound chamber, while the driving electric motor and other hydraulic components were pump outlet is reflecting graduallywalls. closedThe until the desired outlet pressure reached. After the cooling isolated behind measurement procedure usedwas for the tests can be that, summarized as circuit was adjusted to maintain the inlet temperature constant follows. The electric motor was started at the desired shaft speed and the variable orifice at the pumpat 50 °Cis(under an accuracy of 1the °C). Then,outlet noisepressure measurements were taken as soon as steady state outlet gradually closed until desired was reached. After that, the cooling circuit conditions ofto inlet temperature were achieved. constant at 50 ◦ C (under an accuracy of 1 ◦ C). Then, was adjusted maintain the inlet temperature noise measurements were taken as soon as steady state conditions of inlet temperature were achieved.

Figure 22. (a) Picture of semi-anechoic chamber and (b) hydraulic schematic. Figure 22. (a) Picture of semi-anechoic chamber and (b) hydraulic schematic. Table 4. Details of test rig components. Table 4. Details of test rig components. No. No. 1 12 3 24 5

3

6

47 58 9

6

10

7

Description Description

Details Details

Wika TR33, Temperature range 30–120 ◦ C SSB, Temperature 500 Nm, speedrange ±300030–120 rpm °C Wika TR33, Casappa PLP20QW, 22 cc/rev Hydac SSB, 4745—Strain type—Range: 500 Nm,gauge speed ±3000 rpm 0–400 bar Kracht VC5 24V—Fixed displacement volume (gear type) —Range: 1–191 `/min Test pump Casappa PLP20QW, 22100 cc/rev Sun Hydraulics RPICKCN, Capacity: gpm (378.5 `/min), Pressure relief valve Maximum operating pressure: 5000 psi (344.7 bar) Outlet pressure Sun Hydraulics NFECKEN, Capacity: 30 gpm 0–400bar (113.6 `/min), Hydac 4745—Strain gauge type—Range: Needle valve sensor Maximum operating pressure: 5000 psi (344.7 bar) Heat exchanger OAW 46-60, Cooling Capacity: 23–142type) hp (17.2–105.9 Outlet flow meter Kracht VC5Parker 24V—Fixed displacement volume (gear —Range:kW) 1–191 ℓ/min Parker 50AT, Nominal Filter Rating: 10 micron, Nominal Flow Rating: 40 gpm Filter Pressure relief Sun Hydraulics RPICKCN, Capacity: 100 gpm (378.5 ℓ/min), Maximum (151.4 `/min) Reservoir Buyers UR 70S, pressure: Capacity: 70 gallon ), ISO 46 oil valve operating 5000 psi (265.0 (344.7`bar) Inlet temperature temperature sensor Inlet Electric motor sensor Test pump Outlet pressure Electric motor sensor Outlet flow meter

Needle valve

ISO:Sun International Organization for Capacity: Standardization. Hydraulics NFECKEN, 30 gpm (113.6 ℓ/min), Maximum

operating pressure: 5000 psi (344.7 bar)

The sound power levels of pump noise at 4 different operating conditions were determined 8 Heat exchanger 46-60, Cooling Capacity: 23–142 hp (17.2–105.9 kW) closely following ISO 9614-1: 1993Parker [38]. OAW The measurement surface was chosen the same with the Parker 50AT, Nominal Filter Rating: 10 micron, Nominal Flow Rating: gpm geometry of field point mesh in Figure 16, which was the remaining parts of the sphere of 40 1-meter 9 Filter (151.4 radius from the pump excluding the areas behind the wall andℓ/min) below the floor. The measurement 10 were evenly Reservoir Buyers of UR107 70S,over Capacity: 70 gallon (265.0 ℓ),the ISOsound 46 oil source. The points distributed by the number the surface enclosing ISO: International Organization for Standardization

The sound power levels of pump noise at 4 different operating conditions were determined closely following ISO 9614-1: 1993 [38]. The measurement surface was chosen the same with the geometry of field point mesh in Figure 16, which was the remaining parts of the sphere of 1-meter

Energies 2017, 10, 1068 Energies 2017, 10, 1068

17 of 20 17 of 20

The number 107 points was determined by grid the grid study with a different number measurement number of 107ofpoints was determined by the study with a different number of of measurement points, which showed the reasonable accuracy and measuring time. points, which showed the reasonable accuracy and measuring time. The soundintensities intensitiesatatdiscrete discretepoints pointswere weremeasured measuredover overthe theselected selectedsurface. surface.Theoretically, Theoretically, The sound it is ideal for the sound intensity to be measured at multiple points at the same time using multiple it is ideal for the sound intensity to be measured at multiple points at the same time using multiple intensityprobes. probes.Due Duetotothe thecost cost constraint,however, however,one one sound intensity probe composedofof three intensity constraint, sound intensity probe composed three microphones (GRAS, three microphones Type 40A0—Sensitivity 0.2 dB ref 20 μPa, ½“ diameter) was 1 microphones (GRAS, three microphones Type 40A0—Sensitivity 0.2 dB ref 20 µPa, /2“ diameter) was moved to the corresponding measurement points using the robot arm under the assumption that the moved to the corresponding measurement points using the robot arm under the assumption that the noise emission remains unchanged during the steady-state operating condition.The Thesound soundintensity intensity noise emission remains unchanged during the steady-state operating condition. was calculated based on the cross-spectral density of the sound pressure signals measured two was calculated based on the cross-spectral density of the sound pressure signals measured atattwo microphones using the following equation: microphones using the following equation: 1  𝑝 𝑝 (𝜔)} 𝐼𝑟 (𝜔) = 1 𝐼𝑚{𝐺 (4) 𝜌 Ir (ω ) = 0 𝜔𝑑 Im G1p1 2p2 (ω ) (4) ρ0 ωd where 𝐼𝑟 is the sound intensity in r direction, 𝜌0 is the density of air, 𝜔 is the angular frequency of where Ir is𝑑the sound intensity in r direction, ρ0 is theand density is the angular frequency of interest, is the distance between two microphones, 𝐺𝑝1𝑝of isair, theωcross-spectral density of sound 2 interest, d is the distance between two microphones, and G is the cross-spectral density of sound p1 p2 pressures measured at microphone 1 (𝑝1 ) and 2 (𝑝2 ). The details of sound intensity calculation can be pressures at microphone 1 (p 2 (p2 ).by The details of sound intensitysound calculation can over be 1 ) and found inmeasured [39]. Lastly, sound power was obtained integrating the measured intensity found in [39]. Lastly, sound power was obtained by integrating the measured sound intensity over the the measurement surface. measurement surface. overall SWLs of experimental results for 4 different operating conditions The normalized The normalized overall SWLs of experimental results for 4 different conditions obtained by the procedure mentioned above were compared with theoperating numerical results asobtained shown in byFigure the procedure mentioned above were compared with the numerical results as shown in Figure 23 23 and Table 5. Note that the reference of SWL is the same value used in Section 3.1. Similar and Table 5. Note that the reference of SWL is the same value used in Section 3.1. Similar trends trends of numerical results can be seen in the experimental results; as the delivery pressure and of the numerical results can be seenoverall in the experimental as the delivery pressure andisthe shaftnot speed shaft speed are increased, SWL tends to results; be increased. However, this trend found to be are increased, SWL tends toSWL be increased. However, this trendof is 1500 found not200 to be always true. always true. overall In the experiments, for the operating conditions rpm bar showed the Inhigher the experiments, the200 operating conditions 1500 rpm 200 bar showed the higher value value thanSWL 2000for rpm bar. This may be of because resonant behaviors of the pump and than 2000 rpm 200 bar. This may be because resonant pump anddetermines attached structures attached structures can be changed by different shaftbehaviors speeds as of thethe shaft speed the system can be changed by different shaft speeds as the shaft speed determines the system excitation frequency. excitation frequency. Furthermore, it can be seen that numerical and experimental results are very Furthermore, it can be seen thatthe numerical andranges experimental results very close while to eachthe other within close to each other within acceptable of noise levelare differences; noise level the acceptable ranges of noise level differences; while the noise level difference of 3.4 dB for 2000 rpm, difference of 3.4 dB for 2000 rpm, 200 bar is a little high, the difference for other 3 operating conditions 200 is than a little high,This the result difference for otherthe 3 operating conditions are less than 2 dB. This result can arebar less 2 dB. can support validity of our acoustic model. support the validity of our acoustic model.

Figure 23.23.Comparison (yellow) with withthe thenumerical numericalSWLs SWLs(dark (dark blue) Figure Comparisonof of measured measured SWLs SWLs (yellow) blue) forfor thethe four four different operating conditions. different operating conditions.

Energies 2017, 10, 1068

18 of 20

Table 5. Comparison of measured SWLs with numerical SWLs for four different operating conditions. Operating Conditions

Numerical Normalized SWL

Measured Normalized SWL

SWL Difference

1500 rpm, 100 bar 1500 rpm, 200 bar 2000 rpm, 100 bar 2000 rpm, 200 bar

40.0 dB 45.1 dB 42.6 dB 48.1 dB

40.5 dB 46.9 dB 42.5 dB 45.7 dB

−0.5 dB −1.8 dB +0.1 dB +3.4 dB

In terms of SPL distributions, trends similar to the numerical results of Figure 21 were observed in the experimental results. In particular, noisy areas are present near the inlet and outlet sides. Furthermore, an increase of the delivery pressure does not greatly change the overall shapes of the SPL distributions, but it results in an increment of the overall noise level. However, the agreement between the experimental and numerical results that pertains to the SPL distributions is not as close as the one related to the SWL comparison. There are multiple reasons for a possible mismatch related to the experimental environment. For instance, the coupling with the electric motor, the presence of the robot, and the properties of the walls in the anechoic room were neglected or approximated by the model. However, the main discrepancies between numerical and experimental results seem to come from the absence of the structures attached to the pump in the acoustic model. While the standalone pump was considered in the acoustic model, the actual noise can come from the vibration of structures attached to the pump such as lines and plates as well as the vibrations of the pump itself. Including the attached structures can change the resonant behavior of the whole system. Thus, by further developing the current acoustic model, the effects of different mounting situations on noise emissions can be studied in the future. These considerations will also allow for a better accuracy of the results pertaining the SPL distributions representative of noise directionality. However, the current model can predict the “total” sound energy radiated by the pump per unit time (overall SWL) with a fairly good accuracy. Thus, the current acoustic model shows the potentials to investigate the dominant noise sources in a deeper level and serve for future studies aimed at designing quieter pumps. 4. Conclusions This paper presented a numerical model for the evaluation of the noise emitted by EGMs along with its experimental validation. The sources of fluid-borne noise (FBN) were evaluated taking advantage of the results provided by the authors’ HYGESim (HYdraulic GEar machine Simulator) model. In particular, a procedure to evaluate the dynamic pressure forces acting on the pump case was defined for the outlet pressure region, the inlet pressure region, the tooth space volume (TSV) pressure region and the region of the journal bearings. Vibration and sound radiation were then predicted using a combined finite element and boundary element vibro-acoustic model. Considering a commercial pump as reference unit, normalized sound power spectra, sound power level (SWL), and the sound pressure level (SPL) distributions for the different operating conditions were discussed. The results showed the general trends that both SWL and SPL increase with both the shaft speed and the outlet pressure. An experimental activity was performed using a semi-anechoic room at the Maha Fluid Power Research Center, and the numerical results were compared with the experimentally measured SWL to validate the acoustic model. The numerically predicted SWL showed similar values than the experimental results conducted in the semi-anechoic chamber. The proposed model shows how an accurate prediction of the noise emitted by an EGM is possible with a good accuracy on the base on an acoustic model that considers all the most important FBM noise sources. In future, the presented model can serve studies related to the design of quieter EGMs. For this purpose, it is worthwhile to observe that alternative simulation packages could be used to implement a similar simulation workflow for the analysis of FBN, SBN and ABN. Additionally, the authors believe that the software interfacing presented in this work might also be useful to advance the development of commercial software towards the simulation of noise emissions in positive displacement machines.

Energies 2017, 10, 1068

19 of 20

Acknowledgments: The authors would like to express their gratitude to Siemens for the use of AMESim and LMS Virtual.Lab. Author Contributions: Sangbeom Woo, Timothy Opperwall, and Andrea Vacca conceived the simulation model, designed and performed the validation experiments performed at the Maha Fluid Power Research Center of Purdue University. Manuel Rigosi provided all technical data of the reference pump, and he also provided technical assistance in all activities of the project. All the authors analyzed the data and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 11. 12. 13. 14. 15. 16.

17.

18. 19.

Fiebig, W. Location of noise sources in fluid power machines. Int. J. Occup. Saf. Ergon. 2007, 13, 441–450. [CrossRef] [PubMed] Bonanno, A.; Pedrielli, F. A study of the structure borne noise of hydraulic gear pumps. In Proceedings of the 7th JFPS International Symposium on Fluid Power, Toyama, Japan, 15–18 September 2008; pp. 641–646. Edge, K.A. Designing quieter hydraulic systems—Some recent developments and contributions. In Proceedings of the Fourth JHPS International Symposium on Fluid Power, Tokyo, Japan, 15–17 November 1999; pp. 3–27. Negrini, S. A gear pump designed for noise abatement and flow ripple reduction. In Proceedings of the International Fluid Power Exposition and Technical Conference, Chicago, IL, USA, 23–25 April 1996. Mucchi, E.; Dalpiaz, G.; Del Rincon, A.F. Elastodynamic analysis of a gear pump. Part I: Pressure distribution and gear eccentricity. Mech. Syst. Signal Proc. 2010, 24, 2160–2179. [CrossRef] Manring, N.D.; Kasaragadda, S.B. The theoretical flow ripple of an external gear pump. ASME J. Dyn. Syst. Meas. Control 2003, 125, 396–404. [CrossRef] Harrison, K.A.; Edge, K.A. Reduction of axial piston pump pressure ripple. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 2000, 214, 53–64. [CrossRef] Opperwall, T.; Vacca, A. Modeling noise sources and propagation in displacement machines and hydraulic lines. In Proceedings of the 9th JFPS International Symposium on Fluid Power, Matsue, Japan, 28–31 October 2014. Huang, K.J.; Chen, C.C. Kinematic displacement optimization of external helical gear pumps. Chung Hua J. Sci. Eng. 2008, 6, 23–28. Morselli, M.A. Geared Hydraulic Machine and Relative Gear Wheel. U.S. Patent 20150330387 A1, 19 November 2015. Devendran, R.S.; Vacca, A. Design potentials of external gear machines with asymmetric tooth profile. In Proceedings of the ASME/Bath Symposium on FPMC 2013, Sarasota, FL, USA, 8–11 October 2013; p. 12. Nagamura, K.; Ikejo, K.; Tutulan, F.G. Design and performance of gear pumps with a non-involute tooth profile. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 2004, 218, 699–711. [CrossRef] Zhou, Y.; Hao, S.; Hao, M. Design and performance analysis of a circular-arc gear pump operating at high pressure and high speed. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2016, 230, 189–205. [CrossRef] Morselli, M.A. A Positive-Displacement Rotary Pump with Helical Rotors. EP Patent 1132618 B1, 30 April 2008. Lätzel, M.; Schwuchow, D. An innovative external gear pump for low noise applications. In Proceedings of the 8th International Fluid Power Conference (IFK), Dresden, Germany, 26–28 March 2012. Casoli, P.; Vacca, A.; Franzoni, G.; Guidetti, M. Effects of some relevant design parameters on external gear pumps operating: Numerical predictions and experimental investigations. In Proceedings of the 6IFK Internationales Fluidtechnisches Kolloquium, Dreden, Germany, 31 March–2 April 2008. Borghi, M.; Milani, M.; Zardin, B.; Patrinieri, F. The influence of cavitation and aeration on gear pump and motors meshing volume pressures. In Proceedings of the ASME International Mechanical Engineering Congress & Exposition, Chicago, IL, USA, 5–10 November 2006; pp. 47–56. Wang, S.; Sakurai, H.; Kasarekar, A. The optimal design in external gear pumps and motors. IEEE/ASME Trans. Mechatron. 2011, 16, 945–952. [CrossRef] Mucchi, E.; Tosi, G.; D’Ippolito, R.; Dalpiaz, G. A robust design optimization methodology for external gear pumps. In Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis ESDA 2010, Istanbul, Turkey, 12–14 July 2010; pp. 1–10.

Energies 2017, 10, 1068

20. 21.

22.

23.

24.

25. 26.

27.

28. 29. 30.

31. 32.

33. 34. 35. 36. 37. 38. 39.

20 of 20

Devendran, R.S.; Vacca, A. Optimal design of gear pumps for exhaust gas aftertreatment applications. Simul. Model. Pract. Theory 2013, 38, 1–19. [CrossRef] Edge, K.A.; Johnston, D.N. The “secondary source” method for the measurement of pump pressure ripple characteristics Part 1: Description of method. Proc. Inst. Mech. Eng. Part A J. Power Energy 1990, 204, 33–40. [CrossRef] Nakagawa, S.; Ichiyanagi, T.; Nishiumi, T. Experimental investigation on effective bulk modulus and effective volume in an external gear pump. In Proceedings of the BATH/ASME 2016 Symposium on Fluid Power and Motion Control, Bath, UK, 7–9 September 2016. Hartmann, K.; Harms, H.H.; Lang, T. A model based approach to optimize the noise harmonics of internal gear pumps by reducing the pressure pulsation. In Proceedings of the 8th International Fluid Power Conference (IFK) 2012, Dresden, Germany, 26–28 March 2012. Tang, C.; Wang, Y.S.; Gao, J.H.; Guo, H. Fluid-sound coupling simulation and experimental validation for noise characteristics of a variable displacement external gear pump. Noise Control Eng. J. 2014, 62, 123–131. [CrossRef] Carletti, E.; Miccoli, G.; Pedrielli, F.; Parise, G. Vibroacoustic measurements and simulations applied to external gear pumps: An integrated simplified approach. Arch. Acoust. 2016, 41, 285–296. [CrossRef] Miccoli, G.; Carletti, E.; Pedrielli, F.; Parise, G. Simplified methodology for pump acoustic field analysis: The effect of different excitation boundary conditions. In Proceedings of the Inter-Noise 2016, Hamburg, Germany, 27–30 August 2016; pp. 3984–3992. Mucchi, E.; Dalpiaz, G. Numerical vibro-acoustic analysis of gear pumps for automotive applications. In Proceedings of the International Conference on Noise and Vibration Engineering ISMA 2012, Leuven, Belgium, 17–19 September 2012; pp. 3951–3961. Mucchi, E.; Rivola, A.; Dalpiaz, G. Modelling dynamic behaviour and noise generation in gear pumps: Procedure and validation. Appl. Acoust. 2014, 77, 99–111. [CrossRef] Vacca, A.; Guidetti, M. Modelling and experimental validation of external spur gear machines for fluid power applications. Simul. Model. Pract. Theory 2011, 19, 2007–2031. [CrossRef] Opperwall, T.; Vacca, A. A combined FEM/BEM model and experimental investigation into the effects of fluid-borne noise sources on the air-borne noise generated by hydraulic pumps and motors. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2014, 228, 457–471. [CrossRef] Dhar, S.; Vacca, A. A fluid structure interaction-EHD model of the lubricating gaps in external gear machines: Formulation and validation. Tribol. Int. 2013, 62, 78–90. [CrossRef] Pellegri, M.; Vacca, A. A CFD-radial motion coupled model for the evaluation of the features of journal bearings in external gear machines. In Proceedings of the ASME/BATH 2015 Symposium on Fluid Power and Motion Control, Chicago, IL, USA, 12–14 October 2015. Zhao, X.; Vacca, A. Numerical analysis of theoretical flow in external gear machines. Mech. Mach. Theory 2017, 108, 41–56. [CrossRef] Thiagarajan, D.; Vacca, A. Mixed lubrication effects in the lateral lubricating interfaces of external gear machines: Modelling and experimental validation. Energies 2017, 10, 111. [CrossRef] Zhou, J.; Vacca, A.; Casoli, P. A novel approach for predicting the operation of external gear pumps under cavitating conditions. Simul. Model. Pract. Theory 2014, 45, 35–49. [CrossRef] Opperwall, T.; Vacca, A. A transfer path approach for experimentally determining the noise impact of hydraulic components. In Proceedings of the SAE Commercial VEC 2015, Rosemont, IL, USA, 6–8 October 2015. Desmet, W.; Sas, P.; Vandepitte, D. Numerical Acoustics Theoretical Manual; LMS International: Lueven, Belgium, 2012. Acoustics—Determination of Sound Power Levels of Noise Sources using Sound Intensity. Part 1: Measurement at Discrete Points; International Standardization Organization (ISO): Geneva, Switzerland, 1993. Fahy, F.J. Sound Intensity, 2nd ed.; E & FN Spon: London, UK, 1995. © 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).