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EXPERIMENTAL VALIDATION AND DYNAMIC SIMULATION
OF ROTOR FAULTS IN INDUCTION MOTORS
Ariunbolor PURVEE
Professor of Power Engineering and Automation
German Mongolian Institute for Resources and Technology, Mongolia
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Outlines
2
• The Problem
• Background
• Research Approach and Results
• Conclusion
• Acknowledgements
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The Problem
Motors are the beating heart of
industrial mining
About 50% of industrial mining
expenses are due to faults
In geographically remote and
landlocked locations such as
Mongolia, this problem is a
significant one
26/11/20193
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Background: Online condition monitoring of motors
• Used to better understand the
current health and performance
of equipment
• Measures vibration to record
changes in the operation of the
equipment
426/11/2019
https://vibralign.com/wp-content/uploads/2015/09/loop-eagle.gif
https://windrock.com/blog/why-condition-monitoring-is-important/
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Background: The Squirrel-Cage Induction Motor
5
https://vibralign.com/wp-content/uploads/2015/09/loop-mvx.gif
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Research Approach: Objectives
The objectives of this research then,
are:
- to determine whether
characteristic frequencies in
spectrum analysis to determine
rotor faults is based on dynamic
simulation and
- to validate results in the
laboratory and test in the field.
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𝑉𝑠 3𝑥1 = а𝑠 , 𝑏
𝑠 , 𝑐𝑠 3𝑥1
𝑇
𝐼𝑠 3𝑥1 = 𝑖а𝑠 𝑖𝑏
𝑠 𝑖𝑐𝑠 3𝑥1
𝑇
𝑉𝑟 𝑛𝑥1𝑇 = 1
𝑟 2𝑟 … 𝑛
𝑟 𝑛𝑥1𝑇
𝐼𝑟 𝑛𝑥1 = 𝑖1
𝑟 𝑖2𝑟 … 𝑖𝑛
𝑟 𝑛𝑥1𝑇
𝑠 3𝑥1 = а𝑠,𝑏
𝑠,𝑐
𝑠 3𝑥1𝑇
𝑟 𝑛𝑥1 = 1
𝑟 2
𝑟…𝑛
𝑟 𝑛𝑥1𝑇
𝑀 =𝑅𝑠
𝑑𝐿𝑠𝑟
𝑑𝑡𝜔
𝑑𝐿𝑟𝑠
𝑑𝑡𝜔 𝑅𝑟
; 𝜔 =𝑑𝜃
𝑑𝑡
𝑁 =𝐿𝑠𝑠 𝐿𝑠𝑟
𝐿𝑟𝑠 𝐿𝑟𝑟
𝑇𝑒 = 𝐼𝑠𝑇𝑑𝐿𝑠𝑟
𝑑𝜃𝐼𝑟
𝑇𝑒 = 𝐽𝑑2𝜃
𝑑𝑡2+ 𝐵𝑚
𝑑𝜃
𝑑𝑡+ 𝑇𝐿
Equations of dynamic simulation
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Research Approach: Motor Simulation and Dynamics
Stator
Stator resistance (get_M)
Calculate inductances
Stator inductance matrix (get_LSSd_nd)
Rotor loop inductance matrix (get_LRRd_nd)
Rotor loop inductance matrix
Winding Function
(get_wdgfn18)
Mutual inductances of rotor
loop (get_L)
Self-inductance matrix of rotor bars of
healthy motor (get_se_rl)
Stator inductance matrix
Mutual inductance between rotor and stator
Mutual Inductance of stator phases (get_LCC_del)
Mutual Inductance of
stator coils
(get_L_del)
Winding Function
(get_wdgfn_de)l
Mutual
inductance
(get_se_del)
Self- inductance matrix of rotor end-rings of healthy motors (get_LRR_LU_er)
Mutual inductance between faulty rotor loop and stator
phases ([temp_2,temp1_2] = get_LSR_LU_brb1_2nd)
Mutual inductance between faulty rotor loop and a stator
phase (mishra_LSR_414_1brb2nd)
close_table*Mutual inductance between a rotor loop and stator
phases of healthy motor (get_LSR_LU)
Mutual inductance between a rotor loop and a
stator phase (mishra_LSR_414)
get_psi*
get_se_rl*
get_se_del*
get_LSC_rl_del*
Ls, Lb,Le,Rs,Rb,Re (get_spec1) r,L,g0,wsi,nss,nrb,wri,CC,const (get_spec)
Give data
f, J, Bm, V, P
get_wdgfn_del
Broken rotor bar Healthy motor
Self-inductance matrix of broken rotor bars (get_LRR_LU_brb1_2nd)
Calculate resistance
Resistance of rotor bar of healthy motor
(get_Rr)
Resistance of rotor end-rings of healthy
motor (get_Rr) (get_matrix_reduce)
Rotor
Resistance of broken rotor bar
(get_Rr_nrb)
𝑅𝑠 3𝑥3 =
𝑅𝑎𝑠 0 0
0 𝑅𝑏𝑠 0
0 0 𝑅𝑏𝑠
3𝑥3
𝑅𝑟 𝑛𝑥𝑛 =
ሻ2(𝑅𝑏 + 𝑅𝑒 −𝑅𝑏 0
−𝑅𝑏 ሻ2(𝑅𝑏 + 𝑅𝑒 −𝑅𝑏⋯
0 0 −𝑅𝑏
0 0 0⋮ ⋮ ⋮ ⋱ ⋮ ⋮ ⋮0 0 0
−𝑅𝑏 0 0⋯
−𝑅𝑏 ሻ2(𝑅𝑏 + 𝑅𝑒 −𝑅𝑏
0 −𝑅𝑏 ሻ2(𝑅𝑏 + 𝑅𝑒 𝑛𝑥𝑛
𝐿𝑠𝑠 3𝑥3 =
𝐿𝑚𝑚𝑠 + 𝐿𝑙
𝑠 𝐿𝑎𝑏𝑠 𝐿𝑎𝑐
𝑠
𝐿𝑏𝑎𝑠 𝐿𝑚𝑚
𝑠 + 𝐿𝑙𝑠 𝐿𝑏𝑐
𝑠
𝐿𝑐𝑎𝑠 𝐿𝑐𝑏
𝑠 𝐿𝑚𝑚𝑠 + 𝐿𝑙
𝑠3𝑥3
𝐿𝑅𝑅 𝑛𝑥𝑛 =
𝐿𝑟𝑚𝑚 + 2 𝐿𝑏 + 𝐿𝑒 ሻ−(𝐿𝑟2𝑟1 + 𝐿𝑏
ሻ−(𝐿𝑟2𝑟1 + 𝐿𝑏 𝐿𝑟𝑚𝑚 + 2 𝐿𝑏 + 𝐿𝑒
⋯−𝐿𝑟1𝑟𝑛−1 ሻ−(𝐿𝑟1𝑟𝑛 + 𝐿𝑏
−𝐿𝑟2𝑟𝑛−1 −𝐿𝑟2𝑟𝑛
⋮ ⋱ ⋮−𝐿𝑟𝑛−1𝑟1 −𝐿𝑟𝑛−1𝑟2
ሻ−(𝐿𝑟𝑛𝑟1 + 𝐿𝑏 −𝐿𝑟𝑛𝑟2⋯
𝐿𝑟𝑚𝑚 + 2 𝐿𝑏 + 𝐿𝑒 ሻ−(𝐿𝑟𝑛−1𝑟𝑛 + 𝐿𝑏
ሻ−(𝐿𝑟𝑛𝑟𝑛−1 + 𝐿𝑏 𝐿𝑟𝑚𝑚 + 2 𝐿𝑏 + 𝐿𝑒 𝑛𝑥𝑛
𝑁𝑖 𝜃 =
𝑤𝑖
2𝜋𝛿2𝜋 𝜃 − 𝜃𝑖1 + 𝛿 𝜋 − 𝛼𝑖 ,
𝑤𝑖 1 −𝛼𝑖
2𝜋
𝑤𝑖 1 −𝛼𝑖
2𝜋+
𝜃𝑖2 − 𝜃
𝛿−
1
2
−𝑤𝑖𝛼𝑖
2𝜋,
𝜃𝑖1 −𝛿
2≤ 𝜃 ≤ 𝜃𝑖1 +
𝛿
2
𝜃𝑖1 +𝛿
2≤ 𝜃 ≤ 𝜃𝑖2 −
𝛿
2
𝜃𝑖2 −𝛿
2≤ 𝜃 ≤ 𝜃𝑖2 +
𝛿
2𝜃 − ийн бусад утга
Flowchart of dynamic simulation
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Inductances of motors
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Results of dynamic simulation
26/11/[email protected]
Stator Current
Torques
Healthy Broken Rotor bar
Steady State
Transient
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fr = 24.2Гц − RPM;fs = 50Гц − Supply;
fr = fr ∗ nbr − frequency from rotor bars
Spectrum analysis of steady state of torque
𝒇𝒔𝒎 = 𝟑. 𝟐Гц Гулсалт
Broken Rotor bar
Healthy
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Spectrum analysis of steady state of torque
26/11/2019 [email protected]
-2 -1 0 1 2
-2 527.84 551.98 576.1 600.28 624.43
-1 577.84 601.98 626.1 650.28 674.43
0 627.84 651.98 676.1 700.28 724.43
1 677.84 701.98 726.1 750.28 774.43
2 727.84 751.98 776.1 800.28 824.43
Роторын давтамжийн гармоник, fr
Сүл
жээ
ни
й д
ав
там
жи
йн
га
рм
он
ик,
fs 11 fr
fs -2 -1 0 +1 +2
-2
frs-2fs-2fr frs-2fs-fr frs-2fs frs-2fs+fr frs-2fs+2fr
frs-2fs-2fr frs-2fs-fr frs-2fs frs-2fs+fr frs-2fs+2fr
frs-2fs-2fr frs-2fs-fr frs-2fs frs-2fs+fr frs-2fs+2fr
-1
frs-fs-2fr frs-fs-fr frs-fs frs-fs+fr frs-fs+2fr
frs-fs-2fr frs-fs-fr frs-fs frs-fs+fr frs-fs+2fr
frs-fs-2fr frs-fs-fr frs-fs frs-fs+fr frs-fs+2fr
+0
frs-2fr frs-fr frs frs+fr frs+2fr
frs-2fr frs-fr frs frs+fr frs+2fr
frs-2fr frs-fr frs frs+fr frs+2fr
+1
frs+fs-2fr frs+fs-fr frs+fs frs+fs+fr frs+fs+2fr
frs+fs-2fr frs+fs-fr frs+fs frs+fs+fr frs+fs+2fr
frs+fs-2fr frs+fs-fr frs+fs frs+fs+fr frs+fs+2fr
+2
frs+2fs-2fr frs+2fs-fr frs+2fs frs+2fs+fr frs+2fs+2fr
frs+2fs-2fr frs+2fs-fr frs+2fs frs+2fs+fr frs+2fs+2fr
frs+2fs-2fr frs+2fs-fr frs+2fs frs+2fs+fr frs+2fs+2fr
Healthy
𝒇𝒏 = 𝜶𝒇𝒓𝒔 ∓ 𝜷𝒇𝒔 ∓ 𝜸𝒇𝒓
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Spectrum analysis of steady state of torque
26/11/2019 [email protected]
Broken Rotor bars
fs fsm -2 -1 0 1 2
-1 531.2 555.4 579.5 603.7 627.8
0 527.8 552.0 576.1 600.3 624.4
1 524.4 548.6 572.7 596.9 621.0
-1 581.2 605.4 629.5 653.7 677.8
0 577.8 602.0 626.1 650.3 674.4
1 574.4 598.6 622.7 646.9 671.0
-1 631.2 655.4 679.5 703.7 727.8
0 627.8 652.0 676.1 700.3 724.4
1 624.4 648.6 672.7 696.9 721.0
-1 681.2 705.4 729.5 753.7 777.8
0 677.8 702.0 726.1 750.3 774.4
1 674.4 698.6 722.7 746.9 771.0
-1 731.2 755.4 779.5 803.7 827.8
0 727.8 752.0 776.1 800.3 824.4
1 724.4 748.6 772.7 796.9 821.0
1 fr
-2
-1
0
1
2
fsm -2 -1 0 +1 +2
-1 frs-2fs-2fr-fsm frs-2fs-fr-fsm frs-2fs-fsm frs-2fs+fr-fsm frs-2fs+2fr-fsm
0 frs-2fs-2fr frs-2fs-fr frs-2fs frs-2fs+fr frs-2fs+2fr
+1 frs-2fs-2fr+fsm frs-2fs-fr+fsm frs-2fs+fsm frs-2fs+fr+fsm frs-2fs+2fr+fsm
-1 frs-fs-2fr-fsm frs-fs-fr-fsm frs-fs-fsm frs-fs+fr-fsm frs-fs+2fr-fsm
0 frs-fs-2fr frs-fs-fr frs-fs frs-fs+fr frs-fs+2fr
+1 frs-fs-2fr+fsm frs-fs-fr+fsm frs-fs+fsm frs-fs+fr+fsm frs-fs+2fr+fsm
-1 frs-2fr-fsm frs-fr-fsm frs-fsm frs+fr-fsm frs+2fr-fsm
0 frs-2fr frs-fr frs frs+fr frs+2fr
+1 frs-2fr+fsm frs-fr+fsm frs+fsm frs+fr+fsm frs+2fr+fsm
-1 frs+fs-2fr-fsm frs+fs-fr-fsm frs+fs-fsm frs+fs+fr-fsm frs+fs+2fr-fsm
0 frs+fs-2fr frs+fs-fr frs+fs frs+fs+fr frs+fs+2fr
+1 frs+fs-2fr+fsm frs+fs-fr+fsm frs+fs+fsm frs+fs+fr+fsm frs+fs+2fr+fsm
-1 frs+2fs-2fr-fsm frs+2fs-fr-fsm frs+2fs-fsm frs+2fs+fr-fsm frs+2fs+2fr-fsm
0 frs+2fs-2fr frs+2fs-fr frs+2fs frs+2fs+fr frs+2fs+2fr
+1 frs+2fs-2fr+fsm frs+2fs-fr+fsm frs+2fs+fsm frs+2fs+fr+fsm frs+2fs+2fr+fsm
fr
-2
-1
+0
+1
+2
Сүл
жээний д
авта
мж
ийн г
арм
оник,
fs
fs
1
𝒇𝒏 = 𝜶𝒇𝒓𝒔 ∓ 𝜷𝒇𝒔 ∓ 𝜸𝒇𝑟 ∓ 𝑓𝑠𝑚
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Laboratory-Based Validation of Results
Laboratory for validating torque’s spectrumLaboratory for validating vibration spectrum
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Laboratory-Based Test: Vibration Analysis
4-р бүлэг
Healthy
Broken rotor bar𝒇𝒔𝒎 = 𝟑. 𝟐Гц Гулсалт
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4-р бүлэг
Healthy
Laboratory-Based Test: Torque Analysis
Broken rotor bar
𝒇𝒔𝒎 = 𝟎,𝟔 𝐻𝑧 𝑆𝑙𝑖𝑝
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Conclusions
• The characteristic frequencies of a broken rotor
appear as harmonics of the slip frequency on both
sides of the peak magnitude at the rotation per
second, and at the frequency of rotor bar, in the
torque spectrum and the vibration spectrum,
respectively.
26/11/2019 [email protected]
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Conclusions
• To determine if a broken rotor bar exists, the
characteristic frequencies in the vibration analysis
are the same as those in the torque analysis.
Therefore, either a vibration data acquisition
device or a torque data acquisition device can be
used.
26/11/2019 [email protected]
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ACKNOWLEDGMENTS
This project was funded by the German Mongolian
Institute for Resources and Technology and The Deutsche
Gesellschaft für Internationale Zusammenarbeit (GIZ) and
I would like to thank my colleagues at Baganuur coal mine
and my postdoctoral student, who provided ready access
to on-site resources and contributed significantly to data
collection, respectively.
26/11/2019 [email protected]
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