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# Understanding dynamic response

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Understanding Dynamic Response of a simple structure. This applies to conventional turbo-machinery diagnostics and understanding the sychronous vibration response through the full speed range.

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### Understanding dynamic response

1. 1. GE Oil & Gas Understanding Dynamic Response Extract from Bently Nevada Machinery Diagnostics Training
2. 2. Transient Vibration Data Formats • Amplitude and Phase displayed together • Slow roll runout vector • Heavy/high spot location • Rotor and structural resonances • Rotor mode shape “1st critical” Bode’ and Polar Plots
3. 3. Bode' Plot
4. 4. Polar Plot •Typical “synchronous rotor response”. Phase lag angle increases with machine speed. Amplitude increases to a max. at “critical” speed, then reduces
5. 5. Dynamic Stiffness – Simple Model K D M Dynamic Unbalance Force F(t) = m.r. W2 = U. W2 DampingSpring Mass Displacement From rest d (t) Equation of Motion: dMdDdKFt  )( ti t ed W )(let: dieid ti WW W deid ti WW W 222 then: and: dMdDidKF WW 2    DiMK d F WW 2 Simple Dynamic Stiffness: Direct displacement accelerationvelocity Quadrature
6. 6. Dynamic Stiffness at Low Speed K Synchronous Dynamic Stiffness f = 20 D.W M.W2 At low speeds, dominant factor is “Spring Stiffness”
7. 7. Dynamic Stiffness at Resonance K Synchronou s Dynamic Stiffness f = 90 D.W M.W2 At resonance, dominant factor is “Damping Stiffness” This is also known as “Quadrature Stiffness” 2 W MK At Resonance: M K res W Resonant Frequency:
8. 8. Dynamic Stiffness at High Speed K Synchronous Dynamic Stiffness f = 150 D.W M.W2 At high speeds, dominant factor is “Mass Stiffness” – i.e: Inertial effect
9. 9. Synchronous Vibration Response – Low Speed M.W2 K D.W At low speeds, displacement is in same direction as unbalance force Unbalance Unbalance Force = U.W2 Dynamic response (displacement) = Force / Dynamic Stiffness Displacement
10. 10. M.W2 K D.W At resonance, displacement has a 90 degree phase lag from unbalance force Unbalance Force = U.W2 Dynamic response (displacement) = Force / Dynamic Stiffness Displacement f = 90 Synchronous Vibration Response – Resonance Unbalance
11. 11. M.W2 K D.W At high speeds, displacement vector is almost opposite the unbalance force Unbalance Force = U.W2 Locus of displacement vectors through the whole speed range Dynamic response (displacement) = Force / Dynamic Stiffness Displacement Synchronous Vibn Response – High Speed Unbalance
12. 12. 1X (Synchronous) Response 0° 90° 180° 270° Probe Heavy Spot WR = System Resonance Frequency W WWR High Spot Angle of Heavy Spot fu f 0 90° 180° PhaseLag 1XAmplitude|A| A
13. 13. Transient Vibration Analysis • Reveals information on whether Dynamic stiffness has changed from run to run. Confirms integrity of the rotor. • Shows symptoms caused by increased system stiffness – like seal rubs • Indicates where we should add our trial balance weights • Gives clues about why the machine behaves this way – ie: might be running near a natural resonance…
14. 14. Questions?