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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

ariunbolor@gmit.edu.mn

Outlines

2

• The Problem

• Background

• Research Approach and Results

• Conclusion

• Acknowledgements

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

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/

Background: The Squirrel-Cage Induction Motor

5

https://vibralign.com/wp-content/uploads/2015/09/loop-mvx.gif

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.

ariunbolor@gmit.edu.mn

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

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

Inductances of motors

Dynamic simulation design

26/11/2019 ariunbolor@gmit.edu.mn10

Results of dynamic simulation

26/11/2019ariunbolor@gmit.edu.mn11

Stator Current

Torques

Healthy Broken Rotor bar

Steady State

Transient

Spectrum analysis of steady state

26/11/2019 ariunbolor@gmit.edu.mn12

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

Spectrum analysis of steady state of torque

26/11/2019 ariunbolor@gmit.edu.mn14

-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

Spectrum analysis of steady state of torque

26/11/2019 ariunbolor@gmit.edu.mn15

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

Laboratory-Based Validation of Results

Laboratory for validating torque’s spectrumLaboratory for validating vibration spectrum

Laboratory-Based Test: Vibration Analysis

4-р бүлэг

Healthy

Broken rotor bar𝒇𝒔𝒎 = 𝟑. 𝟐Гц Гулсалт

4-р бүлэг

Healthy

Laboratory-Based Test: Torque Analysis

Broken rotor bar

𝒇𝒔𝒎 = 𝟎,𝟔 𝐻𝑧 𝑆𝑙𝑖𝑝

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 ariunbolor@gmit.edu.mn19

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 ariunbolor@gmit.edu.mn20

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 ariunbolor@gmit.edu.mn21

ACKNOWLEDGMENTS

26/11/2019 ariunbolor@gmit.edu.mn22