Utafiti huu unachunguza dynamic stiffness na damping behavior ya oil film yenye unene wa micrometers chache tu kati ya side face ya gear na moving lateral bushing katika external gear pumps kwa kutumia three-dimensional computational fluid dynamics (CFD). Eneo ambalo study inalenga hasa ni suction side ya pump; kwa sababu inachukuliwa kwamba minimum axial clearance hutokea katika eneo hili kutokana na tilt ya bushing na oil film huwa sensitive zaidi kwa changes za operating conditions.

External gear pump inapofanya kazi, rotation ya gear huunda sliding (sliding/Couette) flow katika oil film. Wakati huo huo, micrometric movement ya floating bushing kuelekea gear hupunguza clearance na kuunda squeeze-film effect. Study inachunguza kama hydrodynamic pressure inayoundwa na mechanisms hizi mbili kwa pamoja hutenda kama spring na damper, na jinsi micro-dimples zilizoongezwa kwenye surface zinavyobadilisha behavior hii.

Three-dimensional CFD model inawakilisha tooth moja na corresponding bushing sector. Tooth inaposonga karibu 90° kutoka meshing region kuelekea suction side, gear–bushing clearance hupungua karibu 6 µm. Katika simulation, ISO VG46 oil ilitumika; density ilichukuliwa kuwa 850 kg/m³ na dynamic viscosity 0,039 Pa·s katika 50 °C.

Surface textures mbili tofauti zililinganishwa: mpangilio wa 3-row micro-dimples wenye lower texture density na mpangilio wa 5-row micro-dimples wenye higher textured area. Results zinaonyesha kwamba kadiri clearance inavyopungua, oil huzidi kunaswa, hydrodynamic pressure huongezeka, na effective stiffness na damping ya oil film huongezeka kwa nguvu.

Hata hivyo, micro-dimples nyingi zaidi hazikutoa automatically better dynamic performance. 5-row texture iliongeza effective mean clearance kidogo, ikapunguza peak hydrodynamic pressure na load-carrying capacity; kwa hiyo stiffness na damping values kwa ujumla zilibaki lower kuliko 3-row structure. Kwa sababu hii, watafiti wanasisitiza kwamba kuongeza surface texture kiasi cha kuboresha friction au lubrication pekee haitoshi; oil-film support inayohakikisha axial stability lazima pia ihifadhiwe.

Result nyingine muhimu ya study ni kwamba oil film haitendi kama simple viscous damper yenye constant coefficient. Damping inategemea clearance height, squeezing speed, pump speed na hasa kama squeezing motion inaaccelerate au inadecelerate. Kwa hiyo, source inaelezea oil film kwenye suction side kama nonlinear na acceleration-dependent damper.

Katika condition ya 2500 rpm, mean squeezing speed ya 0,9 mm/s na micromotion frequency ya 1000 Hz zilitumika; katika condition ya 4500 rpm, 1,6 mm/s na 1800 Hz zilitumika. Katika cases zote mbili, total applied clearance change ilikuwa 5,4 µm.

Findings zinategemea CFD calculations pekee. Direct experimental validation katika film level haikufanywa. Pia, katika modeli clearance hufunga continuously na kwa kuwa surfaces hazitengani, cavitation haitokei. Kwa hiyo, stiffness na damping maps zilizopatikana zinawakilisha tu full-film, cavitation-free hydrodynamic operating regime iliyofafanuliwa katika study.

Kwa mtazamo wa Uturuki: Study haikufanywa kwenye specific pump manufacturer, hydraulic system au field application nchini Uturuki. Hata hivyo, method inatoa important engineering approach kwa research na design teams zinazotengeneza external gear pumps, hydraulic power units na precision-lubricated machine elements nchini Uturuki. Hasa, microtexture itakayotumika kwenye bushing surface inaweza kuchunguzwa katika design work si kwa static friction pekee bali pia kwa axial stiffness na damping characteristics za oil film. Lakini kwa transfer kwenda real pump design, temperature-dependent properties za oil, real bushing deformation, surface tolerances, cavitation, pressure distribution, wear na pump-level experimental performance lazima zithibitishwe kando.

Kwa nini clearance ya micrometers chache ni muhimu sana katika external gear pump?

Katika external gear pumps, kuna very thin oil film kati ya side faces za gears na lateral bushings. Clearance hii ina roles mbili zinazokinzana: kutoa lubrication ya kutosha kuzuia metal-metal contact ya rotating parts na wakati huo huo kupunguza internal leakage ndani ya pump.

Clearance inapokuwa kubwa kupita kiasi, hydrodynamic support ya oil film inaweza kupungua. Ikipungua sana, surfaces zinaweza kukaribiana na kuongeza risk ya mixed lubrication na surface damage.

Kwa hiyo, focus ya study si tu swali “clearance ni kiasi gani?”. Swali muhimu zaidi ni force inayotolewa na oil film inabadilika kiasi gani wakati clearance inabadilika kwa micrometers chache, na damping kiasi gani inatengenezwa wakati wa motion.

Kwa nini suction side ilichaguliwa?

Kulingana na source model, floating bushing husogea kuelekea gear kutokana na hydrostatic force imbalance ndani ya pump na bending moment inayoundwa na pressure differences kati ya surfaces.

Kutokana na tilt ya bushing, minimum clearance hutokea kwenye suction side. Kwa kuwa region hii pia ni low-pressure, oil film huwa sensitive zaidi kwa changes za operating conditions.

Tooth inaposonga karibu 90° kutoka meshing region kuelekea suction side, axial clearance hupungua kutoka maximum value \(h_{max}\) hadi minimum value \(h_{min}\). Source inatoa clearance change ya karibu 6 µm wakati wa transition hii.

Sliding na squeezing hutokea kwa wakati mmoja

Rotation ya gear husababisha surface moja ya oil film kusogea relative kwa surface nyingine. Hii huunda Couette-type sliding flow.

Wakati huo huo, bushing inapokaribia gear katika axial direction, oil layer hukandamizwa. Oil inapojaribu kutoka kwenye narrowing region huunda additional hydrodynamic pressure. Mechanism hii ya pili ndiyo squeeze-film effect.

Total dynamic support hutokana na combination ya mechanisms hizi mbili:

• stiffness component: hydrodynamic force inabadilika kiasi gani wakati clearance height inabadilika,
• damping component: resistance inayotolewa na oil dhidi ya speed ya squeezing motion.

3B CFD model ilijengwaje?

Ili kusolve micrometric flow structure huku computational cost ikidhibitiwa, tooth moja na corresponding lateral-bushing region vilimodeliwa badala ya pump nzima.

Computational domain ina sehemu tatu kuu:

• rotating gear surface,
• textured au smooth bushing surface ambayo ni stationary lakini axial boundary motion inatumika,
• oil volume kati ya surfaces mbili.

Oil iliyotumiwa katika modeli ni ISO VG46:

Reynolds equation

Pressure generation katika thin oil film inawakilishwa na Reynolds equation. General three-dimensional form iliyotolewa katika source ni:

\[ \frac{\partial}{\partial x} \left( \frac{\rho h^3}{12\mu} \frac{\partial p}{\partial x} \right) + \frac{\partial}{\partial y} \left( \frac{\rho h^3}{12\mu} \frac{\partial p}{\partial y} \right) = \frac{\partial}{\partial x} \left( \frac{\rho h u}{2} \right) + \frac{\partial}{\partial y} \left( \frac{\rho h v}{2} \right) + \rho\frac{\partial h}{\partial t} \]

.

Kwa kuwa density change ilibaki chini ya %0,5 katika conditions zilizochunguzwa kwenye suction side, oil ilichukuliwa kuwa incompressible. Kwa rigid-surface assumption, equation inapunguzwa kuwa:

\[ \frac{\partial}{\partial x} \left( \frac{h^3}{12\mu} \frac{\partial p}{\partial x} \right) + \frac{\partial}{\partial y} \left( \frac{h^3}{12\mu} \frac{\partial p}{\partial y} \right) = \frac{u}{2}\frac{\partial h}{\partial x} + \frac{v}{2}\frac{\partial h}{\partial y} + \frac{\partial h}{\partial t} \]

.

Squeezing speed imefafanuliwa kama:

\[ w=\frac{\partial h}{\partial t} \]

.

Kwa nini oil film hutenda kama spring?

Hydrodynamic stiffness inaonyesha oil-film force inabadilika kiasi gani kwa small change ya clearance height:

\[ k(h)=\frac{\partial W}{\partial h} \]

Katika numerical calculation, successive force values zilitumiwa kupitia relation:

\[ K(\bar{h})= \frac{W_{d1}(h_1)-W_{d2}(h_2)} {h_1-h_2} \]

.

Katika stiffness calculation, clearance height ilibadilishwa kwa increments za 0,5 µm na sliding motion ya gear pekee ilizingatiwa.

Kwa nini oil film hutenda kama damper?

Damping coefficient inaelezea sensitivity ya hydrodynamic force kwa approach/squeezing speed:

\[ D(h,v)=\frac{\partial W_d}{\partial v} \]

Numerically:

\[ D(\bar{h},\bar{v})= \frac{W_{d1}(h_1,v_1)-W_{d2}(h_1,v_2)} {v_1-v_2} \]

relation ilitumika.

Ili kuwakilisha micromotion ambayo bushing inaweza kufanya kutokana na pressure fluctuations wakati wa real operation, harmonic disturbance iliongezwa juu ya nominal approach motion:

\[ h(t)=h_0(t)-a\sin(\omega t) \]

Operating conditions mbili

Katika transient analysis, clearance hufunga continuously kutoka karibu 8,5 µm hadi 3,1 µm. Ingawa speed inaoscillate, inabaki positive, kwa hiyo bushing haisogei mbali na gear katika stage yoyote.

Kwa nini cavitation haikutokea?

Katika source model, squeezing speed iko katika direction ileile throughout simulation na hakuna separation phase kati ya surfaces. Katika conditions hizi, local pressure haikushuka chini ya vapor pressure, kwa hiyo cavitation haikutriggeriwa.

Kwa hiyo, study hii haichunguzi cavitating pump regime. Stiffness na damping coefficients katika results ni za full-film hydrodynamic regime.

Kwa nini filtering ilitumika katika damping calculation?

Instantaneous damping ilihesabiwa kwa finite difference kama:

\[ D(t_i)\approx \frac{W_{i+1}-W_{i-1}} {v_{i+1}-v_{i-1}} \]

.

Change ya squeezing speed inapokaribia zero, denominator huwa very small na calculation huwa extremely sensitive kwa numerical noise. Kwa hiyo, watafiti:

• waliondoa samples zenye \(|a|<2\ \mathrm{m/s^2}\),
• waliainisha \(a>2\ \mathrm{m/s^2}\) kama accelerating compression,
• waliainisha \(a<-2\ \mathrm{m/s^2}\) kama decelerating compression

katika groups mbili tofauti.

Pia, wakati wa kutengeneza damping maps, only positive instantaneous damping coefficients zilihifadhiwa. Data-processing decision hii inapaswa kuzingatiwa wakati wa interpretation ya results; maps haziwakilishi complete sign-preserved distribution ya all raw finite-difference results.

Kwa nini mesh independence ni critical?

Kwa kuwa oil film ina unene wa micrometers chache tu, number ya elements zinazotumiwa across clearance inaweza kuwa na effect kubwa kwenye calculated pressure na force.

Study ililinganisha meshes nne zenye 4, 7, 9 na 11 layers.

Four-layer mesh ilitoa only %75 ya reference force, huku seven-layer mesh ikifikia %95. Nine layers zilikubaliwa kama reference, na transition kwenda 11 layers ilibadilisha normalized force kutoka 1,00 hadi 1,02 tu.

Kwa hiyo, ili kuweka balance kati ya computational cost na solution sensitivity, watafiti walitumia mesh yenye 1.113.346 elements na nine layers across clearance katika subsequent CFD analyses.

Time resolution

Katika transient simulations, second-order implicit time integration na adaptive time stepping zilitumika. Courant number ilihifadhiwa katika range ya 0,9–0,95.

Kwa nini flow ilichukuliwa kuwa laminar?

Katika highest examined speed ya 4500 rpm, upper velocity limit ilipochukuliwa kuwa karibu 18 m/s, Reynolds number ilihesabiwa kuwa karibu 1,96 kwa 5 µm clearance na karibu 1,17 kwa 3 µm clearance.

Kwa kuwa values hizi ziko well below transition region, RANS au LES turbulence model haikutumika na flow ilichukuliwa kuwa laminar.

Micro-dimples zinafanya nini katika pressure field?

Katika comparisons za 3,5 µm clearance, highest pressures zilitokea karibu na central region ya gear ambako fluid escape ni difficult zaidi. Oil iliyokuwa locally trapped kati ya micro-dimples pia ilichangia load support.

Hata hivyo, peak pressure ya 5-row micro-dimple arrangement ilikuwa lower kuliko 3-row design. Watafiti wanaeleza hii kwa dense texture kuongeza effective mean clearance.

Pump speed ilipoongezeka kutoka 2500 rpm hadi 4500 rpm, shear-generated pressure production iliimarika na general pressure level katika oil film ikaongezeka.

Vortices huunda ndani ya micro-dimples

Katika velocity field iliyowasilishwa kwa 2500 rpm na 3,5 µm clearance, expected Couette profile inaonekana across oil film: highest velocity iko kwenye rotating gear surface na speed hushuka kuelekea zero karibu na stationary bushing.

Ndani ya micro-dimple cavities, interaction ya main shear flow na geometry huunda small local recirculation/vortex regions. Structures hizi hubadilisha local pressure distribution na kuchangia hydrodynamic behavior ya textured surface.

Kwa nini force huongezeka haraka clearance inapopungua?

Katika source Figure 11, absolute force values hazikutolewa kwa sababu ya commercial confidentiality na force ilinormalized relative kwa maximum value.

Clearance ikiwa juu ya karibu 6,5 µm, hydrodynamic force hujibu more slowly kwa clearance change. Inaposhuka chini ya karibu 5 µm, hata small reduction ya clearance huongeza hydrodynamic load kwa kiasi kikubwa.

Change hii inaonyesha kwamba oil inanaswa kwa nguvu katika narrow region na film behavior ni tofauti na linear spring.

Stiffness result

Katika Figure 12, hydrodynamic stiffness huongezeka sharply kadiri clearance inavyopungua kutoka maximum kwenda minimum.

Behavior hii ina pande mbili kwa design. Kukaribia minimum clearance kunaweza kutoa stronger restoring hydrodynamic force kwa floating bushing; lakini operating region hiyo hiyo ndiyo yenye highest risk ya mixed lubrication na surface damage.

Kwa hiyo, target si kupata maximum stiffness pekee, bali kuhifadhi required dynamic support pamoja na sufficient film thickness.

Phase lag katika transient force

Katika transient analysis, squeezing speed inapobadilika harmonically, force signal haijibu immediately kwa change hiyo hiyo. Source inaonyesha clear phase lag kati ya speed na force.

Hasa katika baadhi ya points ambapo squeezing speed inakaribia zero, hydrodynamic force haishuki hadi zero. Hii inaonyesha kwamba oil film ina finite hydrodynamic stiffness hata bila instantaneous squeezing motion.

Phase lag ni direct indicator ya viscous/damping component inayodissipate energy katika system.

Kwa nini damping inategemea sign ya acceleration?

Accelerating compression na decelerating compression hazina force history ileile hata kwa clearance na speed value zilezile.

Squeezing speed inapoanza kupungua, oil pressure haiwezi kuadapt instantly kwa change. Delayed response ya pressure field huleta different hydrodynamic resistance katika deceleration regime.

Kwa hiyo, study haitathmini damping kama:

\[ D=D(h,v) \]

pekee, bali kwa practical interpretation kama quantity inayotegemea pia acceleration/deceleration history ya motion.

3-row au 5-row?

Kwa clearance ileile, three-row texture arrangement kwa ujumla hutoa higher hydrodynamic support kuliko five-row arrangement.

Katika mean damping curves za source, 3-row texture pia consistently hutoa higher damping kuliko corresponding 5-row structure kwa given clearance height.

Sababu ni kwamba denser 5-row texture huongeza mean effective clearance kidogo, hupunguza pressure generation na hivyo kupunguza load-carrying capacity ya oil film.

Result hii inaonyesha kwamba simple design assumption ya “micro-dimples nyingi zaidi zinatoa better lubrication performance” si valid kwa dynamic support.

Mbinu na Matokeo ya Utafiti

Research design

Study ni fully numerical CFD research na ina main analysis stages mbili:

1. steady-state analyses: hydrodynamic force ilihesabiwa kwa different fixed clearance heights ili kupata force–clearance relation na stiffness;
2. transient analyses: harmonic micromotion iliongezwa kwenye nominal closing motion ya bushing ili kukokotoa speed–force relation na damping coefficients.

CFD software na physical assumptions

Numerical validation

Katika mesh-independence study, transition kutoka 4 layers hadi 9 layers iliongeza normalized gear force kutoka 0,75 hadi 1,00. Kutoka nine layers kwenda 11 layers, result iliongezeka only %2 hadi 1,02.

Kwa hiyo, mesh yenye nine layers na 1.113.346 elements ilichaguliwa kama base solution.

Global mass conservation ilimonitoriwa katika simulations zote na conservation target ya 0,01 ilitumika kwa ANSYS CFX.

Main pressure findings

• Clearance inapopungua, oil huzidi kunaswa na hydrodynamic pressure huongezeka.
• Kuongeza rotational speed kutoka 2500 rpm hadi 4500 rpm huongeza shear-generated pressure production.
• Highest pressures hutokea mainly katika central region ambako fluid escape ni limited zaidi.
• 5-row texture hutoa lower peak pressure kuliko 3-row texture kwa sababu ina larger effective clearance.
• Local recirculation structures ndani ya micro-dimples hubadilisha pressure distribution.

Main force na stiffness findings

• Hydrodynamic load hupungua monotonically kadiri clearance inavyoongezeka.
• Katika clearances above karibu 6,5 µm, force sensitivity kwa clearance change ni relatively low.
• Katika region below karibu 5 µm, very small clearance changes husababisha large force changes.
• Stiffness huongezeka strongly kadiri clearance inavyopungua.
• Kwa hiyo, oil film haitendi kama constant-coefficient linear spring.
• Higher textured area hupunguza hydrodynamic pressure na hivyo effective stiffness.

Main transient findings

Katika transient CFD analysis, squeezing speed ilionyesha six distinct oscillations wakati clearance ilifunga kutoka 8,5 µm hadi 3,1 µm.

Force kwa ujumla ilifuata static force–clearance trend; lakini harmonic speed change iliunda local peaks kwenye force.

Phase difference kati ya speed na force inaonyesha dissipative behavior ya oil film. Kadiri clearance inavyopungua, amplitude ya force oscillation na dynamic effect ya oil film huongezeka.

Main damping findings

• Damping coefficient huongezeka clearly kadiri clearance inavyopungua.
• 3-row texture hutoa higher average damping kuliko 5-row texture kwa clearance ileile.
• Damping inategemea si clearance na squeezing speed pekee bali pia kama acceleration ni positive au negative.
• Katika decelerating compression, delayed oil-pressure response huunda different dynamic resistance.
• Highest damping values hutokea katika strong squeeze-film region yenye smallest clearances.

Matokeo yanayoungwa mkono na utafiti

• Gear–bushing oil film kwenye suction side inaweza kuonyesha nonlinear hydrodynamic spring behavior.
• Oil film pia hutenda kama nonlinear damper inayotegemea motion history na acceleration regime.
• Pump rotational speed huathiri pressure generation na hydrodynamic force.
• Stiffness na damping huongezeka clearly kadiri minimum clearance inavyokaribiwa.
• Higher texture density katika examined designs iliongeza effective clearance na kupunguza dynamic load support.
• 3-row texture ilionyesha higher average damping kuliko 5-row texture kwa clearance ileile.
• Stiffness na damping maps zilizopatikana zinaweza kutoa numerical input kwa development ya simpler lumped-parameter dynamic models za external gear pump.

Matokeo ambayo utafiti haujathibitisha

• Haijathibitishwa kwamba 3-row texture ndiyo best surface design kwa external gear pumps zote.
• Film-level stiffness na damping coefficients zilizopatikana na CFD hazijapimwa directly experimentally.
• Haijaonyeshwa kwamba coefficients zilezile ni valid katika operating conditions zenye cavitation.
• Effect ya surface na housing deformation kwenye results haijasolved katika rigid-surface model hii.
• Temperature-dependent viscosity change ya oil haijachunguzwa pamoja na detailed thermal model.
• Study haipimi directly total volumetric au hydro-mechanical efficiency ya pump experimentally.
• Long-term wear life au real-field durability haijathibitishwa na modeli hii.
• Common optimum ya effects zote za texture kwenye friction, leakage, wear na dynamic stability haijabainishwa.

Main limitations

Limitation muhimu zaidi ni kutokuwepo kwa direct experimental validation katika film level. Watafiti wanaeleza kwamba kufanya hivyo moja kwa moja ni difficult kutokana na micrometric clearance na results zilitathminiwa kwa physical consistency na pump trends zilizoonekana katika previous experiments.

Limitation ya pili muhimu ni absence ya cavitation ndani ya current model. Source inaacha effect ya multiphase cavitation modeling kwenye dynamic coefficients kwa future research.

Tatu, static hydrodynamic force haikuchapishwa katika absolute units na ilinormalized kwa maximum force kwa sababu ya confidentiality. Kwa hiyo, actual absolute load-carrying force ya pump haiwezi kutolewa kutoka Figure 11.

Nne, low-acceleration points na negative instantaneous damping values zilifilteriwa katika instantaneous damping calculations. Selection hii ilifanywa kupunguza numerical instability, lakini inapaswa kukumbukwa kwamba displayed damping maps zinategemea filtering procedure iliyotumiwa.

Maelezo ya Chanzo na Mbinu

Jina kamili asilia la utafiti: Dynamic Tribological Behavior of Surface-Textured Bushings in External Gear Pumps: A CFD Investigation

Waandishi: Masoud Hatami Garousi; Paolo Casoli; Massimo Rundo; Seyed Mojtaba Hejazi.

Corresponding author: Paolo Casoli.

Taasisi: Department of Engineering for Industrial Systems and Technologies, University of Parma, Parma, Italy; Department of Energy, Politecnico di Torino, Torino, Italy.

Aina ya chanzo: Research article.

Peer-review status: Actuators ni peer-reviewed scientific journal.

Jarida: Actuators.

Mchapishaji: MDPI.

Publication: 2026, Volume 15, Article 168.

Submission date: 12 February 2026.

Revision date: 5 March 2026.

Acceptance date: 12 March 2026.

Publication date: 16 March 2026.

DOI: 10.3390/act15030168.

Official link:https://doi.org/10.3390/act15030168

Leseni: Creative Commons Attribution (CC BY).

Funding: Waandishi waliripoti kwamba research haikupokea external funding.

Support/acknowledgment: Waandishi walitaja katika acknowledgments active support iliyotolewa na Casappa S.p.A., Parma, Italy kwa research.

Ethics committee: Iliripotiwa kuwa not applicable.

Informed consent: Iliripotiwa kuwa not applicable.

Data availability: Imeelezwa kwamba original contributions za study ziko ndani ya article na additional questions zinaweza kuelekezwa kwa corresponding author.

Conflict of interest: Waandishi waliripoti kwamba hakuna conflict of interest.

Critical note kuhusu evidence level

Study hii haitoi new experimental stiffness au damping measurement kwenye physical external gear pump. Main evidence ya research ni 3B CFD calculations.

Waandishi wanaeleza kwamba direct film-level experimental validation si practical kutokana na micrometric clearance; na numerical results zinaendana na previous experimental pump-performance trends. Kwa hiyo, results zinapaswa kutathminiwa si kama dynamic coefficients zilizopimwa directly kwenye real device, bali kama numerically na physically consistent CFD characterizations kwa examined operating range.

Source-internal boundary-condition inconsistency

Katika method section, pressure outlet condition ya side openings imeandikwa kama “1 bar absolute pressure”. Table 1 kwenye page ileile inatoa value `1` kwa variable “Opening pressure (MPa)”.

1 bar absolute pressure na 1 MPa si physical value ileile. Source text haielezi sababu ya inconsistency hii. Kwa hiyo, katika Verianla text hii haijakisiwa ni value gani sahihi na boundary condition haijabadilishwa kuwa single definitive value.

Confidentiality ya force data

Source inaeleza wazi katika Figure 11 kwamba static hydrodynamic force values zilinormalized kwa maximum value kwa sababu ya confidentiality. Kwa hiyo, absolute load-carrying force katika Newton haiwezi kutolewa kutoka \(F/F_{ref}\) values kwenye graph.

Filtering ya damping data

Damping coefficient inapohesabiwa kwa finite-difference method, speed difference ikikaribia zero numerical instability hutokea. Kwa hiyo, samples za \(|a|<2\ \mathrm{m/s^2}\) ziliondolewa kwenye analysis, remaining points zikagawanywa katika positive na negative acceleration groups, na only positive instantaneous damping values zikahifadhiwa wakati wa kutengeneza damping maps.

Kwa hiyo, published damping maps si direct na unfiltered transformation ya raw CFD force-time series; ni result ya data-selection na filtering procedure iliyofafanuliwa na source.

Cavitation limit

Kwa kuwa lubrication clearance hupungua continuously katika examined kinematics, separation motion haikutokea na cavitation haikutriggeriwa. Source imeacha effect ya multiphase cavitation model kwenye stiffness na damping coefficients kwa future work.

Kwa hiyo, results zinazowasilishwa hapa hazipaswi kugeneralized directly kwa cavitating, surface-separating au mixed-lubrication regimes.

Technical equations, parameters, result trends na limitations katika Verianla explanation hii zinategemea solely source study iliyochunguzwa. Absolute force values ambazo source haikuchapisha hazijakisiwa kutoka graphs; pressure boundary-condition inconsistency ndani ya source haijasahihishwa kimya kimya kwa external information.