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 Introduction  Important Results of an Induction Motor  2D Finite Element Analysis Scalar 3D Model of the Quasi-static  Electromagnetic Field in an Induction Motor Effects of the Broken bar Fault on the Motor  Torque and Unbalanced Rotor Force Signatures of the Broken Bar Fault in the Stator  Currents and in the Magnetic Field Outside Fault Diagnosis through Harmonics and  Diagnosis Efficiency Conclusions 

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

Coupled Electromagnetic Field – Electric Circuit – Rotor Motion IM 2D model Current Density in the Rotor Bars 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 Motor with one Broken Bar Healthy Motor

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 ( H 0 - grad  r )] = 0 , where H 0 - the source magnetic field in the infinitely extended free space, associated to the current density J 1 in the volume V is given by Biot-Savart formula: 1 J x r   1 H dV 0 4 π 3 r V The magnetic field intensity is H = H 0 – 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 broken bar Healthy Motor Faulty Motor

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 Faulty Motor Healthy Motor

Time Variation and Harmonics of the Rotor Unbalanced Force Faulty Motor Healthy Motor

Signatures of the Rotor Broken Bar Fault. Fault Diagnosis through Harmonics A. Signature in the Stator Currents B. Signature in the Magnetic Field Outside the Motor A1/B1. Harmonics under 50 Hz A2/B2. Harmonics over 50 Hz

Signature in the Stator Currents, Harmonics under 50 Hz Faulty Motor Healthy 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 Harmonics under 50 Hz of the I U current 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 over 50 Hz of the I U 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 Faulty Motor Healthy Motor

Efficiency FA/HE of Fault Diagnosis Based on Fault Signature in the Magnetic Field in the Plane z = 0 Harmonics of Bx1 – Bx2 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 Harmonics of By1 – By2 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

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

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 outside the motor, shows that the last method represents a better option.. 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