Uaminifu na ufanisi wa nishati wa high-speed air compressors zinazotumiwa katika magari ya hydrogen fuel cell hutegemea gas foil bearings zinazoruhusu rotor kuzunguka bila mafuta ya kulainisha. Wakati compressor inaanzishwa na kusimamishwa mara kwa mara, gas film ya kutosha huwa bado haijaundwa, hivyo contact na wear vinaweza kutokea kati ya rotor na top foil. Utafiti huu unalenga kutabiri kwa usahihi wa juu jinsi wear inavyobadilisha rotor vibration, gas-film thickness, pressure distribution na power loss inayotokana na friction.

Watafiti waliunda physics-based dynamic model inayojumuisha wear-dependent gas-film geometry, transient Reynolds equation, foil stiffness na damping, hydrodynamic bearing forces na rigid-rotor motion yenye degrees of freedom nne. Athari ambazo haziwezi kuwakilishwa katika theoretical model zilifidiwa kwa learnable four-dimensional model-discrepancy term iliyoongezwa kwenye rotor equation of motion. Term hii huzalishwa na neural network yenye hidden layer moja inayopokea displacement, velocity na acceleration components kutoka previous time step pamoja na current rotor speed.

Model ilicalibrate kwa experimental vibration data kutoka healthy gas foil bearing katika speeds tano kati ya 20.000 na 40.000 rpm, kisha ikajaribiwa kwa bearing group tofauti yenye artificial wear ya kina cha 30 µm na katika eneo la 140°-220°. Traditional physics model ilitoa average synchronous-vibration error ya %9,11 katika healthy condition na %25,22 katika worn condition, wakati proposed high-fidelity model ilipunguza averages hizo hadi %2,02 na %2,48 mtawalia. Highest relative error katika speed na direction conditions zote ilikuwa %5,73.

Matokeo ya parametric model yanaonyesha kwamba kadiri wear depth na worn circumferential region vinavyoongezeka, minimum gas-film thickness hupungua, maximum pressure huongezeka na pressure field hubadilika kutoka single-peak distribution kwenda kwenye maeneo mawili tofauti ya high pressure. Deterioration ya haraka ilionekana hadi wear depth ya takribani 15 µm, huku katika depths kubwa zaidi changes za gas film na pressure zikikaribia saturation kwa kiasi.

Katika wear scenario ya kina cha 30 µm na upana wa 80°, calculated bearing friction power iliongezeka kwa kiwango cha juu cha %44,5 katika 20.000 rpm na %28,1 katika 40.000 rpm ukilinganisha na healthy condition. Viwango hivi vinaonyesha tu calculated viscous-friction loss katika gas-foil-bearing–rotor system; havionyeshi kwamba total energy consumption ya air compressor au gari imeongezeka kwa viwango hivyo hivyo.

Utafiti unatoa matokeo yenye nguvu kwa vibration-based high-fidelity modelling na quantitative analysis ya wear effects. Hata hivyo, bearing geometry moja tu, artificial wear profile moja na rotational speeds tano zilijaribiwa. Gas-film pressure, minimum film thickness na friction power hazikupimwa moja kwa moja kwa majaribio; quantities hizi zilikokotolewa kupitia model iliyocalibrate kwa vibration data. Model pia haitabiri moja kwa moja jinsi wear inavyoendelea kwa muda au remaining useful life ya bearing.

Tatizo kuu la utafiti ni nini?

Katika proton-exchange-membrane fuel cells, air compressor hutoa hewa kwa cathode side kwa pressure na flow rate zinazohitajika. Katika utangulizi wa utafiti, kwa kutegemea tafiti za awali, inaelezwa kwamba air-compression process inaweza kuwakilisha zaidi ya %80 ya auxiliary power consumption katika fuel-cell system. Kiwango hiki hakikupimwa katika jaribio la utafiti wenyewe; kilichukuliwa kutoka fasihi ili kueleza kwa nini air-supply system ni muhimu.

Rotor ya air compressor lazima ifanye kazi kwa rotational speeds za juu sana bila kutumia mafuta ya kulainisha. Gas foil bearing huinua shaft kutoka kwenye surface kwa hydrodynamic gas film inayoundwa rotor inapozunguka. Hivyo hitaji la liquid lubricant huondolewa na high-speed operation huwezeshwa.

Gas film hufikia thickness ya kutosha tu rotor inapofikia speed fulani. Wakati wa start na stop periods, gas film huwa dhaifu; rotor inaweza kugusa top foil ya bearing. Repeated start-stop cycles zinazotumika kuendana na power demand ya gari zinaweza kusababisha gradual surface wear katika load-carrying region.

Wear si geometric surface loss pekee. Local shape ya top foil inapobadilika:

• Gas-film thickness kati ya rotor na foil hubadilika.
• Hydrodynamic pressure field husambazwa upya.
• Bearing forces zinazobeba rotor hubadilika.
• Rotor orbit na vibration amplitude vinaweza kuharibika.
• Viscous shear na friction power katika gas layer vinaweza kuongezeka.
• Local load concentration inaweza kuharakisha wear mpya au loss of lubrication.

Swali kuu la utafiti ni hili: Kwa calibrating physics-based bearing-rotor model pamoja na experimental data, vibrations za healthy na worn gas foil bearings pamoja na wear-related lubrication na friction changes zinaweza kutabiriwa kwa usahihi gani?

Ni pengo gani la fasihi linalolengwa?

Tafiti za awali zimechunguza load capacity, power consumption, foil stiffness, damping, preload na nonlinear rotor behaviour za gas foil bearings. Models zinazojumuisha wear pia zimeendelezwa, zikishughulikia transient lubrication, wear topography, foil deformation na rotor motion kwa pamoja.

Hata hivyo, kwa mujibu wa watafiti, matatizo mawili makuu bado yapo:

1. Models nyingi za rotor huwakilisha bearing kwa initial perfect geometry na hazizingatii progressive surface wear.
2. Kwa sababu ya idealizations katika multiphysics models, unknown parameters na dynamic effects ambazo ni vigumu kupima, theoretical vibrations hazilingani vya kutosha na real experimental signals.

Utafiti hauondoi physical model na kutoa prediction ya data-driven pekee. Badala yake, Reynolds equation, foil dynamics na rotor motion zinabaki kuwa msingi, huku unexplained dynamic difference ikifidiwa kwa small neural network.

Gas foil bearing-rotor system imeundwaje?

Kielelezo 1 katika ukurasa wa 6 wa utafiti kinaonyesha system katika scales tatu. Sehemu ya kwanza ina cross-section ya air compressor, sehemu ya pili ina rotor assembly yenye turbine, rotor na radial gas foil bearings mbili, na sehemu ya tatu ina cross-section ya gas foil bearing moja.

Vipengele vikuu vya gas foil bearing ni:

• Bearing housing: Hutoa fixed mechanical support kwa nje.
• Bump foil: Hutoa elastic stiffness na damping kwa top foil.
• Top foil: Ni smooth surface inayozunguka rotor na kuingiliana moja kwa moja na gas film.
• Gas film: Ni thin gas layer inayopressurize kwa rotor motion na kubeba shaft bila contact.

Katika model, gas film na foil structure si independent. Pressure hudeform foil; foil deformation hubadilisha gas-film thickness; thickness iliyobadilika huamua pressure field mpya katika Reynolds equation. Iterative solution hufanywa hadi quantities hizi mbili ziconverge.

Muundo wa jumla wa proposed high-fidelity model

Modelling framework katika Kielelezo 1 inaunganisha components tatu kuu:

1. Physics-based model yenye wear: Hutatua gas film, foil structure, bearing forces na rotor dynamics.
2. Learnable model-discrepancy term: Huwakilisha dynamic effects ambazo hazipo katika theoretical model kwa neural network.
3. Parameter identification yenye physical bounds: Hutambua hard-to-measure model parameters kutoka experimental signals huku ikizuia values kutoka nje ya physical ranges.

Katika forward calculation, model hutoa rotor vibrations, gas-film pressure na film thickness. Katika inverse calculation, frequency spectra za experiment na simulation hulinganishwa; physical model parameters na neural-network weights husasishwa kwa error backpropagation.

Wear imeongezwaje kwenye gas-film thickness equation?

Top-foil wear inapozingatiwa, local gas-film thickness imeelezwa kama:

\[ h(\theta,z)=C+e\cos(\theta-\theta_0)+\delta(\theta,z)+\delta_w(\theta) \]

• h(θ,z): Gas-film thickness inayotegemea circumferential angle na axial position,
• C: Nominal bearing clearance,
• e: Rotor eccentricity,
• θ₀: Rotor attitude angle,
• δ(θ,z): Foil deformation chini ya pressure,
• δ_w(θ): Local geometric change inayotokana na wear.

Wear ilimodeliwa katika lower load-carrying region kama piecewise function yenye constant depth na sharp boundaries:

\[ \delta_w(\theta)= \begin{cases} d_m, & \theta_s<\theta<\theta_f \\ 0, & \text{diğer açılarda} \end{cases} \]

• d_m: Wear depth,
• θ_s: Starting angle ya worn region,
• θ_f: Ending angle ya worn region.

Kielelezo 3 kinaonyesha wear kama rectangular-profile surface loss katika lower load-carrying region ya bearing. Simplification hii hurahisisha kutenganisha parametric effects; hata hivyo, katika real bearings wear depth inaweza kutokuwa uniform circumferentially au axially, edges zinaweza kutokuwa sharp na surface roughness inaweza kubadilika kwa muda.

Gas-film pressure ilikokotolewaje?

Chini ya assumption ya ideal gas, dimensionless transient Reynolds equation iliyotumika imeandikwa kwa ujumla kama:

\[ \frac{\partial}{\partial\theta} \left(PH^3\frac{\partial P}{\partial\theta}\right) + \frac{\partial}{\partial Z} \left(PH^3\frac{\partial P}{\partial Z}\right) = \Lambda\frac{\partial(PH)}{\partial\theta} + 2\Lambda\nu\frac{\partial(PH)}{\partial T} \]

Dimensionless variables na bearing number zinategemea definitions zifuatazo:

\[ P=\frac{p}{p_0},\qquad H=\frac{h}{C},\qquad Z=\frac{z}{R},\qquad \Lambda=\frac{6\mu\omega R^2}{p_0C^2} \]

• P: Dimensionless gas-film pressure,
• p: Local absolute pressure,
• p₀: Ambient pressure,
• H: Dimensionless gas-film thickness,
• R: Bearing radius,
• μ: Dynamic viscosity ya gas,
• ω: Rotor angular speed,
• Λ: Bearing number inayounganisha effects za rotational speed, viscosity, radius na clearance.

Upande wa kushoto wa equation unawakilisha circumferential na axial pressure diffusion; upande wa kulia unawakilisha rotor motion na compression effect ya time-varying film geometry.

Foil structure imewakilishwaje?

Top foil na bump support structure zilimodeliwa kama local dynamic support yenye equivalent stiffness na damping:

\[ P=K_v\delta+C_v\frac{d\delta}{dt} \]

• K_v: Dimensionless foil structural stiffness,
• C_v: Dimensionless structural damping,
• δ: Foil deformation.

Gas-film pressure na foil deformation hutatuliwa mara kwa mara kwa single-step time-domain difference method. Pressure inapoconverge, horizontal na vertical hydrodynamic forces hupatikana kwa integration juu ya bearing surface:

\[ F_x=-\int_0^L\int_0^{2\pi}(p-p_0)R\sin\theta\,d\theta\,dz \]

\[ F_y=-\int_0^L\int_0^{2\pi}(p-p_0)R\cos\theta\,d\theta\,dz \]

Simpson 1/3 rule ilitumika kwa numerical integration.

Friction-related power loss ilikokotolewaje?

Viscous shear ndani ya gas film ilikokotolewa kutokana na combination ya Couette flow inayotokana na rotor surface velocity na flow inayotokana na circumferential pressure gradient. Integration ya shear stress hii juu ya bearing surface ilitoa friction torque.

Viscous power consumption ilikokotolewa kutoka friction torque iliyooneshwa kwa symbol F_c katika utafiti kwa relation ifuatayo:

\[ P_c=\omega F_c \]

• P_c: Calculated viscous-friction power ya gas foil bearing-rotor system,
• ω: Rotor angular speed,
• F_c: Friction torque kwa notation ya makala.

Quantity hii si total electrical consumption ya compressor. Turbine losses, aerodynamic compression work, motor losses au power-electronics losses hazipo katika equation hii.

Rotor dynamic model

Rotor ilimodeliwa kama rigid body yenye degrees of freedom nne relative na centre of mass:

• Horizontal linear displacement x_G,
• Vertical linear displacement y_G,
• Angular displacement kuhusu X axis φ_xG,
• Angular displacement kuhusu Y axis φ_yG.

Positions za bearings mbili hupatikana kutoka centre-of-mass motion kupitia relations za aina hii:

\[ x_A=x_G-d_{AG}\varphi_{yG},\qquad y_A=y_G+d_{AG}\varphi_{xG} \]

\[ x_B=x_G+d_{BG}\varphi_{yG},\qquad y_B=y_G-d_{BG}\varphi_{xG} \]

Basic rotor equation of motion ni:

\[ \mathbf{M}\ddot{\mathbf{u}}+\omega\mathbf{G}\dot{\mathbf{u}} =\mathbf{F} \]

Hapa:

• M: Mass matrix inayojumuisha rotor mass na moments of inertia,
• G: Gyroscopic matrix,
• u: Four-component vector ya linear na angular displacements,
• F: Total force vector yenye gas-film forces kutoka bearings mbili, moments zake na rotor unbalance forces.

Wilson-θ method ilitumika kwa time integration kama unconditionally stable algorithm. Appendix A inatoa kwa kina acceleration, velocity na displacement update equations za method hiyo.

Neural network imeongezwaje kwenye physical model?

Kwa kuwa theoretical rotor equation haiwakilishi real system kikamilifu, learnable model-discrepancy term iliongezwa kwenye equation of motion:

\[ \mathbf{M}\ddot{\mathbf{u}}_t+ \omega\mathbf{G}\dot{\mathbf{u}}_t = \mathbf{F}_t+\mathbf{E}_t \]

E_t ni four-component neural-network output. Inputs za network ni:

• Horizontal na vertical displacements katika previous time step,
• Previous horizontal na vertical velocities,
• Previous horizontal na vertical accelerations,
• Current rotor rotational speed.

Network haichukui nafasi ya Reynolds equation au rotor equation. Physical model inaendelea kukokotoa msingi wa dynamics, huku neural network ikiwakilisha residual dynamic effects zinazofanana na forces na moments ambazo hazijamodeliwa.

Unknown physical parameters zimewekewaje mipaka?

Scaled sigmoid transformation ilitumika kuzuia learnable parameters kwenda kwenye non-physical values:

\[ w_i= \frac{1}{1+e^{-\theta_i}} \left(w_{i,\max}-w_{i,\min}\right)+w_{i,\min} \]

• θ_i: Raw variable inayosasishwa kwa uhuru wakati wa optimization,
• w_i,min na w_i,max: Predefined physical bounds za parameter,
• w_i: Bounded physical parameter inayoingia kwenye model.

Mbinu hii huzuia identified parameters kutoka nje ya ranges zilizobainishwa. Hata hivyo, haithibitishi peke yake kwamba parameters zimetambuliwa uniquely ndani ya ranges hizi au kwamba parameter combinations tofauti haziwezi kutoa vibration ileile.

Forward calculation loop

Kielelezo 2 katika ukurasa wa 8 wa utafiti kinaonyesha columns mbili zilizounganishwa za forward calculation:

1. Initial displacement, velocity na acceleration hufafanuliwa.
2. Gas-film thickness hukokotolewa kwa kutumia rotor position na wear profile.
3. Pressure field hutatuliwa kwa Reynolds equation.
4. Foil deformation husasishwa na loop hurudiwa hadi pressure iconverge.
5. Bearing forces hukokotolewa kwa integration ya pressure field.
6. Mass, gyroscopic na force matrices huundwa.
7. Neural network huzalisha model-discrepancy term.
8. Wilson-θ method hukokotoa new rotor displacement, velocity na acceleration.
9. New rotor state hurudishwa kwenye gas-film model.
10. Loop huendelea hadi termination time.

Model outputs ni rotor vibrations, gas-film pressure na gas-film thickness.

Model ilifundishwa kwa loss function gani?

Experiment na simulation hazikulinganishwa moja kwa moja kwenye entire time signal, bali kwenye frequency spectrum iliyopatikana kwa discrete Fourier transform:

\[ D_k=\sum_{j=0}^{n-1}d_j e^{-i2\pi jk/n} \]

Total training loss ina components mbili:

\[ L_{\mathrm{total}}=\lambda_A L_A+\lambda_E L_E \]

Vibration-spectrum matching loss ni:

\[ L_A= \frac{1}{2n} \sum_{i=1}^{n} \left[ (A_{xi}-\hat A_{xi})^2+ (A_{yi}-\hat A_{yi})^2 \right] \]

Regularization component inayozuia neural network unexplained force kuwa kubwa bila sababu imeandikwa kwa ujumla kama:

\[ L_E= \frac{1}{n_t}\sum_{t} \|\mathbf{E}_t\|^2 \]

imeandikwa.

• A_xi, A_yi: Experimental horizontal na vertical spectrum amplitudes,
• Â_xi, Â_yi: Model spectrum amplitudes,
• L_E: Term inayozuia neural-network model-discrepancy output.

Spectrum-matching weight ilitolewa kuwa 100, na model-discrepancy regularization weight kuwa 1. Katika PDF, Equation 17 inaonyesha coefficient hii ya pili kama λ_E, lakini Table 2 inaandika λ_B. Kulingana na maelezo ya maandishi, zote mbili zinaelekea kuashiria weight ya model-discrepancy loss; hata hivyo, symbol inconsistency hii inapaswa kufafanuliwa wakati method inarudiwa.

Experimental setup

Kielelezo 5 katika ukurasa wa 14 wa utafiti kinaonyesha laboratory test setup na disassembled rotor assembly. Rotor huzungushwa kutoka upande mmoja na turbine inayotumia high-pressure gas na kuungwa mkono na radial gas foil bearings mbili. Thrust disk na thrust foil bearings mbili upande wa pili hutoa axial stability.

Measurement system ilitumia:

• Laser tachometer inayosoma reflective tape kwenye turbine end,
• Eddy-current displacement sensors mbili zilizowekwa perpendicular katika horizontal na vertical directions,
• 20 kHz data-acquisition system

kurekodi rotor speed na radial vibrations.

Healthy na worn bearings

Bearing conditions mbili ziliandaliwa:

Sifa kuu za bearings zilizotumika:

• Bearing diameter: 30 mm,
• Axial bearing length: 30 mm,
• Top foil thickness: 0,1 mm,
• Bump foil thickness: 0,1 mm,
• Foil material: X-750,
• Bump height: 0,55 mm,
• Number of bump strips: 26.

Kielelezo 6 katika ukurasa wa 15 wa utafiti kinaonyesha T0 na T1 bearings kando kwa kando. Worn region katika T1 ime-machined wazi katika lower load-carrying surface. Hali hii hutoa repeatable validation sample; hata hivyo, haiwakilishi kikamilifu irregular topography ya real start-stop wear.

Experimental data iligawanywaje?

Katika rotor run-down experiments, speed ilipunguzwa kutoka 40.000 rpm hadi 20.000 rpm. Kwa kila bearing condition:

• 20.000 rpm,
• 25.000 rpm,
• 30.000 rpm,
• 35.000 rpm,
• 40.000 rpm

signal segments za sekunde 0,05 zilitolewa katika speeds tano.

Data za healthy T0 bearing katika speeds tano zilitengwa kwa training, na data za worn T1 bearing katika speeds zilezile kwa independent validation. Hivyo model ilijaribiwa si kwa randomly split data kutoka bearing ileile, bali kwa bearing yenye tofauti ya surface condition.

Hata hivyo, training set haina worn example. Mafanikio ya T1 yanategemea physical wear geometry kutolewa kwa usahihi kwenye model na error compensation iliyojifunza kutoka healthy condition kuweza kuhamishwa kwenda worn condition. Real wears za depths na shapes tofauti hazikuingizwa katika experimental validation set.

Neural-network architecture na training settings

Hidden layer moja yenye neurons 20 inaonyesha kwamba network imeundwa kama limited error-compensation component badala ya black box kubwa ya kuchukua nafasi ya physical equations. Hata hivyo, utafiti hauwasilishi comparative architecture-sensitivity analysis kwa network widths, layer counts au activations tofauti.

Physical parameters zilizotambuliwa

Utafiti unaripoti single optimal value set. Confidence intervals, posterior distributions au variability across multiple random initializations hazijatolewa kwa values hizi. Kwa hiyo experimental uncertainty na identifiability ya parameters haziwezi kubainishwa kando.

Validation results katika healthy bearing

Kielelezo 8 katika ukurasa wa 18 wa utafiti kinaonyesha grafu tatu kwa kila speed:

• Orbit ya rotor centre katika X-Y plane,
• Vertical vibration frequency spectrum,
• Horizontal vibration frequency spectrum.

Blue curves zinaonyesha experiment, yellow curves original physics model, na red curves high-fidelity model iliyosahihishwa na neural network. Red curves ziko karibu zaidi na experimental signal kuliko yellow curves kwa orbit size na synchronous-spectrum peak.

Katika healthy T0 group:

• Original model error range: %2,49-%14,00,
• Original model average error: %9,11,
• High-fidelity model error range: %0,14-%4,74,
• High-fidelity model average error: %2,02.

Validation results katika worn bearing

Kielelezo 9 katika ukurasa wa 19 wa utafiti kinaonyesha kwamba rotor orbits za worn T1 bearing zimekuwa kubwa na irregular zaidi ikilinganishwa na healthy condition. Katika speeds zilezile, synchronous vibration amplitudes kwa ujumla pia ni kubwa kuliko katika T0 group.

Watafiti wanaeleza mabadiliko haya kwa wear kuvuruga gas-film thickness na pressure distribution, hivyo kuunda additional nonlinear forces kwenye rotor.

Katika worn T1 group:

• Original model error range: %17,49-%38,23,
• Original model average error: %25,22,
• High-fidelity model error range: %0,25-%5,73,
• High-fidelity model average error: %2,48.

Original model kuwa mbaya zaidi wazi katika worn condition kunaonyesha kwamba simulation inayotegemea initial geometry na theoretical parameters pekee haiwezi kuwakilisha surface degradation kwa usahihi. Wear geometry na learned error compensation zinapotumiwa pamoja, synchronous amplitudes zinalingana kwa karibu zaidi na experiment.

Athari ya wear depth kwenye minimum gas-film thickness

Kielelezo 10(a) kinabadilisha wear depth kutoka 0-30 µm huku worn region ikiwa fixed kati ya 140°-220°. Katika speeds zote, minimum film thickness hupungua kwa kasi katika hatua za mwanzo.

Baada ya critical depth ya takribani 15 µm, kupungua kwa curves hupungua sana, na small fluctuations huonekana katika baadhi ya speeds. Watafiti wanaeleza hali hii kwa pressure na film geometry ndani ya worn clearance kukaribia saturation.

Matokeo haya hayamaanishi kwamba 15 µm ni universal failure threshold kwa gas foil bearings zote. Value hii ni ya 30 mm-diameter bearing, clearance, foil structure, loading na speed conditions za utafiti huu.

Athari ya width ya worn region

Kielelezo 10(b) kinapanua worn circumferential region kutoka 0°-80° huku depth ikiwa fixed katika 30 µm. Minimum gas-film thickness hupungua kwa utaratibu katika speeds zote.

Kulingana na approximate graph reading, katika 20.000 rpm minimum film thickness ni takribani 15 µm katika healthy geometry na hushuka hadi takribani 10 µm katika 80° worn region. Katika 40.000 rpm, corresponding values ni takribani 19 µm na 14 µm. Hizi ni approximate values zilizosomwa kutoka grafu.

Wear depth huamua magnitude ya local film collapse, huku width ya worn region ikiamua circumferential spread ya degradation.

Gas-film thickness distribution

Kielelezo 11 kinaonyesha film thickness katika bearing mid-plane katika 40.000 rpm kulingana na circumferential angle.

Wear depth inapoongezeka, high step-like geometric region hutokea kati ya boundaries za 140° na 220°, huku film thickness ikibadilika kwa ghafla katika entry na exit ya region hii. Worn region ikipanuliwa, step area hii hupanuka na boundary gradients huhamia kwenye angles tofauti.

Grafu zinaonyesha kwamba ingawa total bearing clearance ndani ya worn recess inaweza kuwa geometrically larger, kwa sababu rotor position na hydrodynamic load distribution hujirekebisha, minimum operating gas film katika sehemu nyingine ya system huwa nyembamba. Hivyo jibu la swali “wear inaongeza clearance, kwa nini film inakuwa nyembamba?” ni kwamba rotor huhama chini ya load na hydrodynamic wedge effect huvurugika.

Mabadiliko ya maximum gas-film pressure

Kielelezo 12(a) kinaonyesha kwamba wear depth inapoongezeka katika 80°-wide worn region, dimensionless maximum pressure huongezeka kutoka takribani 1,23 hadi 1,5-1,6. Ongezeko ni la haraka katika first 10-15 µm na kisha linakuwa limited.

Kielelezo 12(b) kinaonyesha kwamba maximum pressure kwa ujumla huongezeka worn region inapopanuka. Hata hivyo, baadhi ya speed curves zinafikia peak karibu 60° na kisha kushuka kidogo katika 80°. Ingawa main text inafupisha trend kama general increase, grafu inaonyesha small speed-dependent nonlinearity katika widest worn region.

Kupungua kwa minimum film thickness pamoja na kuongezeka kwa maximum pressure kunaonyesha kwamba load inaconcentrate katika local regions ndogo zaidi.

Kwa nini pressure field hubadilika kutoka single peak kwenda double peak?

Kielelezo 13 kinaonyesha circumferential pressure distribution katika 40.000 rpm. Katika healthy condition kuna single broad pressure peak katika load-carrying region.

Wear depth inapoongezeka, abrupt change ya gas-film geometry katika boundaries mbili za worn region huunda separate hydrodynamic wedge effects. Pressure field hugawanyika na kuunda:

• Peak ya kwanza karibu na entrance ya worn region,
• Peak ya pili na ya juu zaidi karibu na exit boundary

.

Depth inapozidi 15 µm, peak magnitudes huwa largely stable. Worn-region width inapobadilishwa, circumferential positions za peaks huhama pamoja na wear boundaries.

Kulingana na mechanistic interpretation ya utafiti, wear depth huamua magnitude ya pressure peak, huku worn region ikiamua positions za peaks. Double-peak structure imewasilishwa kama potential indicator ya nonuniform local loading na loss of lubrication.

Kwa nini friction power huongezeka?

Wear huunda mechanisms mbili zenye athari kwa wakati mmoja:

1. Minimum gas film inapokuwa nyembamba, velocity gradient na viscous shear kati ya rotor na foil huongezeka.
2. Local gas-film pressure inapoongezeka, pressure-driven shear na load concentration huimarika.

Kielelezo 14(a) kinaonyesha kwamba friction power huongezeka nonlinearly wear depth inapoongezeka katika fixed 80° worn region. Baada ya takribani 15 µm, rate ya increase hupungua kwa namna inayoendana na saturation ya film na pressure.

Kielelezo 14(b) kinaonyesha kwamba friction power huongezeka worn region inapopanuka katika fixed depth ya 30 µm.

Kulingana na approximate graph reading, absolute friction power huongezeka kutoka karibu 7 W hadi takribani 10 W katika 20.000 rpm, na kutoka karibu 23 W hadi takribani 29 W katika 40.000 rpm. Ingawa absolute power ni kubwa zaidi katika high speed, percentage increase ni kubwa zaidi katika 20.000 rpm kwa sababu baseline value katika low speed ni ndogo.

Nguvu za utafiti

• Wear, gas film, flexible foil na four-degree-of-freedom rotor dynamics zimeunganishwa katika model moja.
• Neural network imetumika si kuchukua nafasi ya physical model, bali kama limited term inayofidia model discrepancy.
• Unknown physical parameters zimehifadhiwa ndani ya plausible ranges kwa sigmoid functions.
• Physical parameters na network weights zimecalibrate kwa pamoja kwa experimental vibration data.
• Healthy bearing ilitumika kwa training, na worn bearing tofauti ikatumika kwa independent validation.
• Horizontal na vertical directions zilitathminiwa kando katika rotational speeds tano tofauti.
• Mchango wa neural-network compensation ulionyeshwa kwa direct comparison dhidi ya original physics model.
• Average synchronous-vibration errors katika healthy na worn conditions zilipunguzwa hadi karibu %2.
• Majukumu ya wear depth na circumferential width kwenye film thickness, pressure na friction yalichunguzwa kando.
• Mabadiliko ya pressure field kutoka single peak kwenda double peak yaliunganishwa mechanistically na wear boundaries.
• Makala inaeleza wazi katika conclusion kwamba model haipaswi kuhamishwa moja kwa moja nje ya validated range.

Mapungufu ya utafiti

• Utafiti ni preprint ambayo haijapitia peer review.
• Bearing geometry moja, X-750 foil material na rotor setup moja tu zilitumika.
• Validation imewekewa mipaka ya speeds tano katika 20.000-40.000 rpm.
• Model ilifundishwa kwa healthy T0 data na kujaribiwa kwa artificial worn condition moja tu, T1.
• T1 wear ni uniform profile ya depth 30 µm na width 80°; haiwakilishi real two-dimensional na irregular wear topography.
• Uundaji wa wear kwa muda wakati wa start-stop haukumodeliwa. Wear profile ilitolewa kwenye model mapema.
• Model haitabiri moja kwa moja wear rate, total cycle life au remaining useful life.
• Gas-film pressure na film thickness ni model outputs katika parametric analysis; utafiti haukuzithibitisha moja kwa moja kwa sensor.
• Friction power pia haikuthibitishwa kwa direct torque au electrical-power measurement.
• Model validation inategemea zaidi synchronous vibration amplitudes; hakuna single aggregate metric iliyotolewa kwa entire broadband spectrum, phase na time-domain error.
• Signal segments za sekunde 0,05 pekee zilitumika katika kila speed.
• Idadi ya experimental repeats, measurement uncertainty na sensor confidence intervals hazikuripotiwa.
• Uncertainty intervals za calibrated physical parameters hazikutolewa.
• Identifiability analysis ya kama parameter sets tofauti zinaweza kutoa vibrations zinazofanana haikufanywa.
• Hakuna systematic sensitivity au ablation analysis kwa neural-network architecture, learning rate na loss weights.
• Hakuna comparison na hybrid physics-data methods nyingine.
• Temperature, thermal expansion, temperature dependence ya gas viscosity na wear-thermal-dynamic interaction havikujumuishwa katika model.
• Leakage, foil-coating degradation, evolution ya surface roughness na material temperature havikumodeliwa kama separate state variables.
• Kuna λ_E/λ_B inconsistency katika symbol ya second loss weight kati ya Equation 17 na Table 2.
• Ongezeko la %44,5 ni calculated bearing-friction loss pekee; haliwakilishi efficiency ya entire air compressor au fuel-cell system.
• Real-time online condition monitoring, failure alarm threshold au maintenance decision havikutekelezwa katika utafiti huu.

Utafiti unaunga mkono nini?

• Physics-based gas foil bearing-rotor model inaweza kuletwa karibu zaidi na experimental vibrations kwa learnable model-discrepancy term.
• Hybrid model iliyocalibrate katika healthy bearing iliweza kutabiri synchronous vibrations katika worn bearing tofauti kwa error ndogo wakati known wear geometry ilipotolewa.
• Worn bearing ilizalisha rotor orbits kubwa na complex zaidi kuliko healthy bearing.
• Wear depth na worn circumferential area hupunguza minimum gas-film thickness.
• Wear huongeza maximum gas-film pressure na kusababisha load kuconcentrate katika local areas.
• Baada ya takribani 15 µm, film na pressure changes katika model iliyochunguzwa hukaribia saturation kwa kiasi.
• Wear inaweza kubadilisha pressure field kutoka single-peak structure kwenda double-peak structure.
• Film thinning na pressure increase kwa pamoja huongeza calculated viscous-friction power.
• Minimum film thickness na maximum pressure zinaweza kutumika kama wear-sensitive condition indicators katika system iliyochunguzwa.

Utafiti haujathibitisha nini?

• Haijathibitishwa kwamba model itatoa accuracy ileile katika hydrogen fuel-cell air compressors zote.
• Haijaonyeshwa kwamba error chini ya %5,73 itadumishwa katika speeds nje ya validation range.
• Haijaonyeshwa kwamba wear depth ya 15 µm ni universal maintenance au failure threshold kwa gas foil bearings zote.
• Model haitabiri real wear progression au remaining life ya bearing.
• Calculated pressure na film-thickness fields hazijathibitishwa kwa direct experimental measurement.
• Haiwezi kusemwa kwamba %44,5 increase ya friction power itaongeza vehicle energy consumption kwa %44,5.
• Haijaonyeshwa kwamba total auxiliary power ya air compressor imekokotolewa moja kwa moja na model hii.
• Haijathibitishwa kwamba discrepancy term iliyojifunza na neural network inalingana na single physical fault.
• Haijaonyeshwa kwamba proposed method kwa ujumla ni bora kuliko hybrid au fully data-driven models nyingine.
• Utafiti haujaanzisha real-time maintenance system kwa online field data.
• Artificial wear profile haiwakilishi topographies zote zinazotokea katika real vehicle operation.

Maana inayowezekana kwa magari ya hydrogen fuel cell

Hasara ndogo katika air-compressor efficiency zinaweza kubadilika kuwa significant auxiliary-power consumption katika fuel-cell system. Kutabiri kwa usahihi wear condition ya gas foil bearing kunaweza kuwa muhimu katika:

• Kupanga maintenance time kulingana na vibration data,
• Kutambua lubrication degradation kabla wear haijaendelea,
• Kuepuka compressor operation katika low-efficiency region,
• Design optimization ya bearing geometry na foil structure,
• Kuendeleza digital twin au condition-monitoring systems.

Hata hivyo, kwa applications hizi, model inahitaji recalibration katika bearings tofauti, temperatures tofauti, real start-stop cycles na long-term field data.

Utafiti wa baadaye

Waandishi wanapendekeza expansions mbili kuu kwa studies zijazo:

1. Thermally coupled model inayojumuisha interaction kati ya wear, temperature na rotor dynamics,
2. Two-dimensional wear topography inayokua axially na circumferentially badala ya uniform piecewise profile.

Zaidi ya hayo, direct pressure au film-thickness measurement, multiple wear levels, repeated experiments, parameter uncertainty na real-time prediction validation vinahitajika ili model ibadilike kuwa maintenance application.

Mbinu na Matokeo ya Utafiti

Muhtasari wa experimental na numerical design

Matokeo yote ya synchronous-vibration validation

Muhtasari wa accuracy results

Katika worn group, original model average error ilipungua kwa takribani mara 10 kutoka %25,22 hadi %2,48. Comparison hii inaonyesha mchango wazi wa neural-network compensation na calibrated parameters. Hata hivyo, performance ilipimwa katika single validation bearing yenye known wear geometry ndani ya test setup ileile.

Muhtasari wa kiufundi wa parametric findings

Tafsiri ya kiufundi ya vielelezo

Kielelezo 1: High-fidelity modelling framework

Upper row ina compressor, rotor na gas foil bearing cross-section; lower row ina physical GFB model, neural-network discrepancy term, bounded parameter identification na experiment-model loss minimization. Kielelezo kinaeleza kwamba physics na data zimeunganishwa katika single closed optimization loop.

Kielelezo 2: Forward calculation flow

Left column inaonyesha convergence ya Reynolds equation na foil deformation, huku right column ikionyesha time integration kutoka bearing forces hadi rotor dynamics na neural-network correction. Columns hizi mbili hulishana kila mara kwa rotor states na bearing forces.

Vielelezo 5 na 6: Experimental setup na bearing conditions

Kielelezo 5 kinaonyesha sensor placement, turbine, radial bearings mbili, rotor na thrust disk. Kielelezo 6 kinalinganisha kwa macho healthy T0 surface na T1 wear iliyotengenezwa katika lower load region.

Kielelezo 7: Run-down signals

Horizontal na vertical time signals za takribani sekunde 7-11 kwa healthy na worn bearings zimeonyeshwa. Worn group ina vibration band pana na irregular zaidi. Model training inategemea segments za sekunde 0,05 zilizochaguliwa kutoka long signals hizi.

Vielelezo 8 na 9: Rotor orbits na spectra

Katika healthy group, orbits ni regular na limited zaidi; katika worn group zinapanuka na shape kuharibika. Red curves za high-fidelity model ziko karibu zaidi na experimental blue curves kuliko original yellow model. Numerical validation ilifanywa kwa amplitudes katika synchronous-frequency peak.

Vielelezo 10 na 11: Film thickness

Kielelezo 10 kinalinganisha minimum-film values katika speeds, huku Kielelezo 11 kikionyesha circumferential distribution katika 40.000 rpm. Depth hudhibiti intensity ya local collapse, na region width hudhibiti spread ya degradation.

Vielelezo 12 na 13: Pressure field

Kielelezo 12 kinaonyesha maximum pressure kuongezeka na wear; Kielelezo 13 kinaonyesha single pressure peak kugawanyika kuwa peaks mbili kwenye wear boundaries. Depth hubadilisha peak magnitude, na boundaries za worn region hubadilisha peak positions.

Kielelezo 14: Friction power

Absolute friction power huongezeka na rotor speed. Wear-related relative increase ni kubwa zaidi katika 20.000 rpm. Depth effect hukaribia saturation baada ya takribani 15 µm, huku width effect ikiendelea kuongezeka ndani ya studied range.

Dokezo la statistics na uncertainty

Utafiti hauripoti classical hypothesis tests, p-values au confidence intervals zinazotegemea measurement repeats. Model accuracy ilitathminiwa kupitia relative error katika synchronous vibration amplitude.

Kauli “error chini ya %5,73 katika conditions zote” inatumika tu kwa:

• Measurement directions mbili,
• Rotor speeds tano,
• Healthy bearing condition moja na worn bearing condition moja,
• Laboratory setup hii

. Statistical confidence interval ya result katika population pana zaidi haijaripotiwa.

Maelezo ya Chanzo na Mbinu

Kichwa kamili cha asili: High-fidelity wear simulation of gas foil bearing-rotor systems in hydrogen fuel cell air compressors using a physics-informed neural network

Waandishi na mpangilio wao: Yongliang Zhou; Xingkai Yang; Pengcheng Zhu; Junyang Shang; Xulong Hu; Wenjun Li; Kai Feng.

Equal contribution au co-first authorship: PDF haina tamko la equal contribution au co-first authorship.

Corresponding authors waliotajwa katika PDF: Xingkai Yang na Kai Feng.

Barua pepe za corresponding authors: xkyang1992@163.com na jkai.feng@gmail.com.

SSRN contact-author record: Official SSRN page inamwonyesha Kai Feng kama “Contact Author”. Kwa kuwa PDF ina corresponding authors wawili, tamko la PDF limetumiwa kama msingi wa maelezo ya scientific identity.

Taasisi: College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China.

Aina ya chanzo: Makala ya preprint yenye experimental validation, multiphysics rotor-bearing modelling na physics-informed neural-network calibration.

Maeneo ya utafiti: Gas foil bearings, rotor dynamics, tribology, hydrogen fuel-cell air compressors, physics-informed machine learning na condition monitoring.

Idadi ya kurasa: 29.

Jukwaa la uchapishaji: SSRN.

Tarehe ya kupakia SSRN: 15 Juni 2026.

DOI: 10.2139/ssrn.6945898

Kiungo rasmi:https://ssrn.com/abstract=6945898

Kiungo cha DOI:https://doi.org/10.2139/ssrn.6945898

Hali ya peer review: Haijapitia peer review. Kila ukurasa wa PDF una onyo la “Preprint not peer reviewed”.

Peer-reviewed journal: Kufikia 27 Julai 2026, peer-reviewed journal version iliyothibitishwa haikupatikana.

Mchapishaji wa asili wa jarida: Kwa kuwa peer-reviewed journal publication haijathibitishwa, haipo. Current scientific publication platform ni SSRN.

Michango ya waandishi

PDF iliyopakiwa haina CRediT authorship contribution au author-specific task distribution. Kwa hiyo haijakisiwa ni mwandishi gani alifanya conceptualization, experiment, model development, software au writing.

Ufadhili

Utafiti uliungwa mkono na miradi ifuatayo:

• National Science and Technology Major Project, project number 2026ZD0719001,
• National Natural Science Foundation of China, grant number 52505181,
• Hunan Provincial Natural Science Foundation of China, grant number 2025JJ60319.

Mgongano wa maslahi

Waandishi walitangaza kwamba hakuna known financial interest au personal relationship inayoweza kuathiri utafiti.

Upatikanaji wa data

Imeelezwa kwamba data zitatolewa kwa ombi. PDF haina open data repository, training-code au model-weight link.

Mbinu ya kuandaa makala

Makala hii ya Kituruki ya Verianla imeandaliwa kwa kuchunguza title na author information ya preprint ya kurasa 29 iliyopakiwa na mtumiaji, main text, equations 17 za msingi, Wilson-θ appendix, tables nne, main figures 14, experimental images, vibration orbits, spectra, gas-film thickness na pressure graphs, friction-power results, funding statement na references.

Maelezo ya kisayansi yanategemea tu utafiti, mbinu na matokeo yaliyowasilishwa katika PDF iliyopakiwa. Vyanzo vya nje vilitumika tu kwa bibliographic verification ya title, authors, institution, DOI, upload date, platform na current publication status. Hakuna experimental finding mpya kutoka nje ya PDF iliyoongezwa.

Kikomo kikuu cha kimethodolojia

Validation yenye nguvu zaidi ya utafiti ni kwamba model iliyocalibrate katika healthy condition ilitabiri synchronous vibrations katika separate artificially worn bearing kwa maximum relative error ya %5,73. Kwa upande mwingine, film thickness, pressure na friction results zinazohusiana na lubrication na energy ni model outputs ambazo hazikupimwa moja kwa moja.

Model inapaswa kutafsiriwa ndani ya bearing geometry, material properties, wear profile na 20.000-40.000 rpm speed range ambamo ilivalidate. Kwa direct transfer kwenda compressors nyingine, physical parameters zinahitaji recalibration, model equations kupanuliwa inapohitajika na new experimental validation kufanywa.

Preprint hii inatoa strong physics-data hybrid framework ya kueleza effects za gas foil bearing wear kwenye rotor vibration na calculated lubrication losses. Hata hivyo, method bado haijavalidate kama field-scale remaining-life prediction, automatic maintenance alarm au energy optimization ya entire fuel-cell air system.