An Experimental Comparison Between Rotor Balancing Methods XIII Researchers Meeting, Universidad del Turabo Jorge L. Santiago
[email protected] Héctor M. Rodríguez, Ph.D., P.E.
[email protected] José Santiváñez, Ph.D.
[email protected] March 6, 2015
Outline Introduction/Objective Basic Concepts in Balancing Balancing Methods Experimental Set up Numerical Results Conclusions and Recommendations
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Introduction/Objective Rotor balancing is critical for operation of industrial machinery. Influence Coefficients (IC) and the Four Run (4R) are common methods for balancing. Interest in experimental comparison between methods in terms of
vibration reduction and time.
Comparison of effectiveness and efficiency between IC and 4R Santiago, Rodríguez and Santiváñez
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Basic Concepts in Balancing Rotor unbalance due to difference in center of mass and rotating axis Key objective is to determine “heavy spot” (HS) Simple cases can be corrected with a single mass 180° from HS Some methods require vibration amplitude and phase information
Axis of Rotation z HS
Balancing requires adding or removing mass to reduce vibration Santiago, Rodríguez and Santiváñez
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Balancing Methods Influence Coefficients (IC) Method Tachometer + Key phasor
Accelerometer
The magnitude and phase of the vibration is measured. “Heavy spot”
Trial Mass
A correction mass is placed to determine how the system responds to added mass.
Requires vibration amplitude and phase sensors Santiago, Rodríguez and Santiváñez
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Balancing Methods Influence Coefficients (IC) Method Tachometer + Key phasor
Accelerometer
The magnitude and phase of the vibration is measured and the influence coefficient is determined.
Correction Mass A correction mass and its position are determined and the vibration magnitude is measured to determine if additional correction is needed.
Balance correction from sensitivity or rotor to mass changes Santiago, Rodríguez and Santiváñez
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Balancing Methods Four-Run (4R) Method Accelerometer The magnitude of the vibration is measured. “Heavy spot”
Trial Mass
Accelerometer
A trial mass is placed in an arbitrary position of the rotor and the magnitude of the vibration is measured.
Requires only vibration amplitude measurements Santiago, Rodríguez and Santiváñez
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Balancing Methods Four-Run (4R) Method Accelerometer The same trial mass is placed in a position 120° away from the 1st position and the magnitude of the vibration is measured.
Accelerometer The same trial mass is placed a 2nd time placed in a position 120° away from the latter position and the magnitude of the vibration is measured.
Balance correction after 4 sequential trial runs Santiago, Rodríguez and Santiváñez
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Balancing Methods Four-Run (4R) Method Accelerometer The same trial mass is placed a 3rd time placed in a position 120° away from the 2nd position and the magnitude of the vibration is measured.
Correction Mass
Accelerometer
A correction mass and its position are determined and the vibration magnitude is measured to determine if additional correction is needed.
Balance correction after 4 sequential trial runs Santiago, Rodríguez and Santiváñez
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Experimental Set Up
4 1
3
2
1 – Accelerometer 2 – Rotor 3 – Tachometer 4 - Driving Motor
Realistic rotor environment Santiago, Rodríguez and Santiváñez
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Results: Initial Unbalance Response Vibration level (acceleration in g) As Is Condition 0.065
Data
0.060
0.055
0.050
0.045 4R it 0
IC it 0
Negligible difference in initial conditions (p-value=0.541) Santiago, Rodríguez and Santiváñez
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Results: IC Method Relative vibration level to initial (as-is) condition 100% 1st attempt
90%
2nd attempt 3rd attempt
80%
4th attempt 5th attempt
Relative Response
70%
6th attempt
7th attempt
60%
8th attempt 9th attempt 10th attempt
50% 40% 30% 20% 10%
0% 0
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2
3
4
8 7 6 5 Number of Iterations
~95% reduction in first trial
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10
11
12
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Results: 4R Relative vibration level to initial (as-is) condition 100% 90%
1st attempt 2nd attempt
80%
3rd attempt
Reponse Reduction [%]
4th attempt
70%
5th attempt 6th attempt
60%
7th attempt 8th attempt 9th attempt
50%
10th attempt
40% 30% 20% 10% 0% 0
1
2
3
4 5 6 Number of iterations
~80% reduction in first trial Santiago, Rodríguez and Santiváñez
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8
9
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Results: Response After 1st Balance Shot Vibration level (acceleration in g) First Balance Shot 0.025
0.020
Data
0.015
0.010
0.005
0.000 4R it 1
IC it 1
Significant difference in results: greater vibration reduction and less variability for IC Method (p-value=0.004) Santiago, Rodríguez and Santiváñez
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Results: Response After 2nd Balance Shot Vibration level (acceleration in g) Second Shot 0.008 0.007 0.006
Data
0.005 0.004 0.003 0.002 0.001 0.000 4R it 2
IC it 2
Negligible difference in results: both methods lead to comparable vibration reduction after second iteration (p-value=0.139) Santiago, Rodríguez and Santiváñez
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Time (min.) per Balance Shot (First) 8
4R 7
7
7 6
Time (min)
6 5
5
7
6
6
5
5 4
4 3
3
I.C.
3
3
3
4
3
3 2
2
3
2
1 0 1
2
3
4
5
6
7
8
9
10
Balancing Attempt
4R takes ~1.9X IC (average 5.7 min vs. 3 min) Santiago, Rodríguez and Santiváñez
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Conclusions and Recommendations IC provides greater vibration reduction during 1st balancing shot (with reduced variability). Negligible difference in vibration reduction for second iteration (i.e., 2nd balance shot), both methods are equally effective in reducing vibration (4R requires more iterations).
IC method is more efficient, each balance shot requires ~ ½ time. IC requires more instrumentation (i.e., amplitude and phase), its implementation will be more expensive. Greater efficiency of IC method must be contrasted against potential higher costs during implementation.
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Back Ups
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Basic Concepts in Balancing A rotor is an assembly of rotating elements in a mechanical system Mass unbalance is represented by a “heavy spot”
Centrifugal forces created by “the heavy spot” can cause fatigue of rotor elements.
Rotor unbalance due to difference in center of mass and rotating axis Santiago, Rodríguez and Santiváñez
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Influence Coefficients Method •
Consists of finding a vector that describes how the vibration of a machine will be influenced by adding mass to the rotor. • Procedure: 1. An initial run is performed to find the “as is” condition of the rotor. 2. A trial mass is placed on the rotor, and the new unbalance condition is measured. 3. The influence coefficient is described by 𝑇−0 𝐻 = 𝑚𝑐𝑎𝑙 Where: 𝑇 = trial response 0 = original response 𝑚𝑐𝑎𝑙 = trial mass 4. The correction mass and its position are calculated as −0 𝑚𝑐𝑜𝑟 = 𝑁 ∠𝑚𝑐𝑜𝑟 = ∠ −O − ∠H 5. The correction mass is placed on the rotor and the new condition of the machine is measured. If necessary, the procedure is repeated by using the new condition of the rotor as the “as is” condition. Santiago, Rodríguez and Santiváñez
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Four-Run Method •
Provides a balancing alternative that does not require phase measurement instruments. • Procedure: 1. An initial run is performed to find the “as is” condition of the rotor. 2. The rotor is stopped and a trial mass is placed arbitrarily in the rotor. This position is designated 0°. 3. Two additional runs are made placing the trial mass 120° apart the correction mass is found by using Wc
where:
X
2 P1 2 P2 2 P3 2
Y
6O 2
P2 2 P3 2 3.4641O 2
Wt X Y 2
2
arctan (
Y ) 180 X
Wc = correction mass Wt = the trial mass O = original vibration amplitude P1, P2 & P3 = vibration amplitudes of each run
4. The condition of the rotor is measured and if deemed necessary, steps 2&3 are repeated by replacing the new condition of the rotor as the “as is” condition.
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