From the 2D to the 3D Finite Element Analysis of the Broken Bar - - PowerPoint PPT Presentation

From the 2D to the 3D Finite Element Analysis of the Broken Bar Fault in Squirrel-Cage Induction Motors

Virgiliu FIRETEANU, Alexandru-Ionel CONSTANTIN

ICATE 2016, October 6 - 8, Craiova, Romania

Summary

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Introduction

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Important Results of an Induction Motor 2D Finite Element Analysis

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Scalar 3D Model of the Quasi-static Electromagnetic Field in an Induction Motor

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Effects of the Broken bar Fault on the Motor Torque and Unbalanced Rotor Force

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Signatures of the Broken Bar Fault in the Stator Currents and in the Magnetic Field Outside

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Fault Diagnosis through Harmonics and Diagnosis Efficiency

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Conclusions

Dedicated Finite Element 2D Model of a Squirrel- cage Induction Motor with a Broken Rotor Bar

B [Bx(x,y), By(x,y), 0] J [0, 0, J(x,y,t)] A [0, 0, A(x,y,t)] curl[(1/)curlA] +  [A/t ] = J1 2D assumptions, mathematical model, regions (a) nonlinear & nonconductive magnetic cores,  = 0, J1 = 0 (b) stator winding,  = 0, J1  0, unknown - coil conductor type (c) rotor bars, motor frame,   0, J1 = 0 - solid conductor type regions (d) nonmagnetic & nonconductive magnetic cores, 0 ,  = 0, J1 = 0 7.5 kW 2880 rpm 3 x 380 V 50 Hz

Current Density in the Rotor Bars

Coupled Electromagnetic Field – Electric Circuit – Rotor Motion IM 2D model

J = 0 Healthy Motor Motor with one Broken Bar, J = 0

Magnetic Field Inside and Outside the Motor

Maps of the Magnetic Flux Density Inside the Motor Outside the Motor

Magnetic Field Inside and Outside the Motor

Lines of the Magnetic Flux Density Healthy Motor Motor with one Broken Bar

Scalar 3D Model of the Quasi-static Electromagnetic Field Motor in a Squirrel-cage Induction Motor

Scalar Formulation of the Electromagnetic field (a) Solid conductor type regions: electric vector potential T and magnetic scalar potential  curl [ (1/) curl T] + [(T - grad)]/t = 0 div[(T - grad)] = 0, and divT = 0 The current density and the magnetic field intensity: J = curl T, H = T – grad (b) Magnetic and nonconductive regions: magnetic scalar potential  div[grad)] = 0 The magnetic field intensity is H = – grad (c) Nonconductive and nonmagnetic regions: reduced magnetic scalar potential r div[0(H0 - gradr )] = 0 , where H0 - the source magnetic field in the infinitely extended free space, associated to the current density J1 in the volume V is given by Biot-Savart formula:





V 3 1

dV r x J 4π 1 H r

The magnetic field intensity is H = H0 – gradr

3D Geometry of a Squirrel-cage Induction Motor

Magnetic Field Inside and Outside the Motor in the Symmetry Plane z = 0

Inside the Motor Outside the Motor

Current Density in the Squirrel-cage of the Rotor

Healthy Motor Faulty Motor broken bar

Effects of the One Broken bar Fault on the Motor Torque and Unbalanced Rotor Force

• A. Time variation and Harmonics of

MOTOR TORQUE

• B. Time variation and Harmonics of

ROTOR UNBALANCED ELECTROMAGNETIC FORCE

Time Variation and Harmonics of the Motor Torque

Healthy Motor Faulty Motor

Time Variation and Harmonics of the Rotor Unbalanced Force

Healthy Motor Faulty Motor

Signatures of the Rotor Broken Bar Fault. Fault Diagnosis through Harmonics

• A. Signature in the Stator Currents

A1/B1. Harmonics under 50 Hz A2/B2. Harmonics over 50 Hz

• B. Signature in the Magnetic Field Outside the Motor

Signature in the Stator Currents, Harmonics under 50 Hz

Healthy Motor Faulty Motor

Signature in the Stator Currents, Harmonics over 50 Hz

Healthy Motor Faulty Motor

Efficiency FA/HE of Fault Diagnosis Based on Fault Signature in the Stator Currents

f[Hz] 10 18 30 42 46 HE [mA] 8.707 3.355 17.41 25.98 40.93 FA [mA] 31.12 10.25 36.18 108.1 525.7 FA/HE 3.586 3.054 2.079 4.160 12.84

Harmonics under 50 Hz of the IU current Harmonics over 50 Hz of the IU current

f[Hz] 125 150 225 250 275 HE [mA] 5.707 3.584 20.37 37.74 4.907 FA [mA] 23.46 22.67 70.97 156.3 28.74 FA/HE 4.110 6.325 3.484 4.142 5.857

Signature in the Magnetic Field Outside the Motor, Harmonics under 50 Hz

Point1 [116, 0, 0] Point2 [-116, 0, 0] Components Bx , By Healthy Motor Faulty Motor

Efficiency FA/HE of Fault Diagnosis Based on Fault Signature in the Magnetic Field in the Plane z = 0

f[Hz] 2 6 18 22 46 HE [T] 19.54 8.996 1.693 0.859 6.797 FA [T] 1385 47.42 9.433 3.952 68.14 FA/HE 70.90 5.271 5.573 4.603 10.02 f[Hz] 2 26 34 42 46 HE [T] 0.894 1.769 2.133 2.602 9.297 FA [T] 50.68 6.189 17.85 14.34 134.1 FA/HE 56.69 3.498 8.369 5.509 14.43

Harmonics of Bx1 – Bx2 Harmonics of By1 – By2

Efficiency FA/HE of Fault Diagnosis Based on Fault Signature in the Magnetic Field in Plane z = 90 mm

Point3 [116, 0, 90] Point4 [-116, 0, 9] Components Bx , By, Bz

f[Hz] 2 6 22 42 46 HE [T] 6.760 0.682 0.175 2.133 4.970 FA [T] 98.16 6.621 1.409 6.092 28.85 FA/HE 14.52 9.716 8.067 2.857 5.804 f[Hz] 2 6 30 34 46 HE [T] 2.245 1.954 0.328 0.353 2.372 FA [T] 197.8 6.824 1.742 6.250 30.05 FA/HE 88.11 3.492 5.311 17.73 12.67 f[Hz] 1 2 3 4 5 HE [T] 0.0129 19.30 0.0369 0.0265 0.0225 FA [T] 1.332 2059 2.239 1.342 1.100 FA/HE 102.8 106.7 60.73 50.63 48.96

Harmonics of Bx3 – Bx4 Harmonics of By3 – By4 Harmonics of Bz3 + Bz4

Conclusions

The comparison of the 3D results related the efficiency of the rotor bar breakage detection through harmonics of the stator currents, respectively through harmonics of the magnetic field

• utside the motor, shows that the last method represents a better
• ption..

In comparison with previous investigations using 2D models, the 3D finite element analysis of a squirrel-cage induction motor requires important computer resources and computation time. Very useful information for the diagnosis of faulty operation state requires 3D analyses. As example, the last results related a better efficiency in the broken bar fault detection through the magnetic field in a plane z = 90 mm, far from the symmetry plane z = 0 of the motor can be obtained only with 3D models.

THANKS

ICATE 2016, October 6 - 8, Craiova, Romania