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October 13th, 2016
Implementation of a Thermo- Hydrodynamic Model
to Predict “Morton Effect”
Antonini, Fausti, Mor
Polibrixia srl - via A. Tadini 49 - 25125 Brescia
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
www.polibrixia.it
1. Morton effects and its explenations
2. Physiscs behind the effect
3. Approximation and methodology
4. Comsol implementation
5. Conclusion
Contents
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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• Shaft sustained with fluid film bearings
• Every journal has a residual unbalance
• The journal exhibits a synchronous orbit
1.A - Morton effect and its explenations
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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• Inside fluid film bearing a small part of the journal is HOT, while the opposite side is COLD
• Non uniform temperature distributioninside oil
• Thermal bending
1.B - Morton effect and its explenations
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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Now consider an overhung mass…
• Thermal bending causes a certain unbalance
• Thermal unbalance can:
✦ reinforce the effect reducing againminimum film thickness (UNSTABLE)
✦ reduce the effect counter-balancing themechanical unbalance (STABLE)
1.C - Morton effect and its explenations
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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CFD physics: Reynolds equation
2.A - Physics behind the effect
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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Thermal physics
2.B - Physics behind the effect
Energy generation rate + Influx energy rate = energy accumulation rate
𝑞 + 𝛻 ∙ 𝑘𝛻𝑢 = 𝑢𝑡
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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Mechanical physics and multibody dynamics
2.C - Physics behind the effect
𝑴 𝑿 + 𝑪 𝑿 + 𝑲𝑿 = 𝑴𝒖𝜔2 𝑠𝑖𝑛 𝜔𝑡𝑐𝑜𝑠 𝜔𝑡
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
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3.A - Approximation and methodology
Static equilibrium position(short bearing approximation)
A. C. Balbahadur, R. G. Kirk, Part I—Theoretical Model for a Synchronous Thermal Instability Operating in Overhung Rotors, International Journal of Rotating Machinery, 10(6): 469–475, 2004
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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Orbit and motion (short bearing approximation)
3.B - Approximation and methodology
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Headquarter: Via Branze 45, 25123 Brescia (IT)
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Temperature distribution(short bearing approximation)
3.C - Approximation and methodology
𝐸𝑣𝑖𝑠𝑐 = 𝐸𝑓𝑙𝑢𝑖𝑑 𝜗 + 𝑑𝜗 − 𝐸𝑓𝑙𝑢𝑖𝑑 𝜗 + 𝐸𝑗𝑜𝑢𝑟𝑛𝑎𝑙+ 𝐸𝑏𝑒𝑎𝑟𝑖𝑛𝑔
𝑑𝑇
𝑑𝜉+
2𝐻
𝜌𝑐𝜔ℎ−
2𝐻𝑇𝑎𝑚𝑏
𝜌𝑐𝜔ℎ+2𝜇𝜔𝑅𝑗
2
𝜌𝑐ℎ2= 0
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
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Unbalance (mechanical, total, limit)
3.D - Approximation and methodology
𝑈𝑡ℎ𝑟 =0.15 𝑊
𝜔2
𝑈𝑡 = 𝑚𝑜𝑦𝑜 = 𝑚𝑜
𝛼Δ𝑇
𝑅𝑗𝐿𝐿𝑜
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
www.polibrixia.it
4 – Comsol implementation
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
www.polibrixia.it
4 – Comsol implementation
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
www.polibrixia.it
4 – Comsol implementation
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
www.polibrixia.it
4 – Comsol implementation
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
www.polibrixia.it
Implementation of a model to predict Morton effect (suggested by the literature)
• Hard numerical computation made by COMSOL
• A dedicated algorithm uses result computed with COMSOL
FUTURE WORKS
Eliminate approximation introduced to compute
• temperature distribution
• static equilibrium position
Conclusion & future works
Polibrixia s.r.l.
Headquarter: Via Branze 45, 25123 Brescia (IT)
Tel. +39.030.6595051-52
www.polibrixia.it
Thank you for
your kind attention
