• No results found

Based on the results obtained from finite element analysis as well as statistical analysis (ANOVA) it is recommended that electrical machines designers take into account the rotor bars breakage fault when designing squirrel cage induction machines. From both methods, it is evident that the rotor bar breakage fault has an influence on the performance of squirrel cage induction machines. It has also been established through the statistical analysis that the two design parameters (rotor bar shape and stator slot opening) have a great influence on the performance of these induction machine types particularly the efficiency and power factor. A proper selection of these parameters can yield a better performing induction machine, even when its rotor bars are broken, this is an ideal situation as the rotor bar breakage fault is known to negatively affect the overall performance of squirrel cage induction machines. Another important aspect is the combination of number of rotor bars and stator slots of a squirrel cage induction machine; as rotor bars break, this combination is altered therefore changing the overall behavior of the SCIM.

88

For future work, it is important to look into the effect that different magnetic wedge sizes as well as different magnetic wedge marerials have on performance of three phase squirrel cage induction machines with broken rotor bars. We can further look into combining all three parameters (rotor bar shape, stator slot opening width and magnetic wedges) and studying how an optimal selection thereof can lead to better performing three-phase SCIMs with broken rotor bars. It will also be interesting to investigate a total number of broken rotor bars under which a SCIM will continue to operate.

89

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APPENDIX A

Table A 1: Ratings of three-phase SCIM

Parameter Value

Rated Output Power 5.5 kW

Number of Phases 3 Rated Voltage 400 V Rated Current 11.59 A Rated Speed 1360 Number of poles 4 Frequency 50Hz

Table A 2: SCIM Dimensions

Parameter Value (mm)

Stator Outer Radius _Rso 105

Stator Inner Radius _Rsi 73.5

Rotor Outer Radius _Rro 73.15

Airgap Length (g) 0.35

Shaft Radius _Rsh 18

Table A 3: Rotor bar Dimensions (T1)

Parameter Value (mm)

Slot opening height_Hs0 1

Slot body height _Hs2 16.38

Slot opening width_Bs0 1.5

Slot wedge maximum width_Bs1 6.16

Slot maximum width_Bs2 2.12

Table A 4: bar Dimensions (T2)

Parameter Value (mm)

Slot opening height_Hs0 1

Slot body height _Hs2 19.2

Slot opening width_Bs0 1.5

Slot wedge maximum width_Bs1 7.08

Slot maximum width_Bs2 2

Table A 5: Rotor bar Dimensions (T3)

Parameter Value (mm)

95

Slot body height _Hs2 16.2

Slot opening width_Bs0 1.5

Slot wedge maximum width_Bs1 6.7

Slot maximum width_Bs2 2.08

Table A 6: Rotor bar Dimensions (T4)

Parameter Value (mm)

Slot opening height_Hs0 1

Slot body height _Hs2 13

Slot opening width_Bs0 1.5

Slot wedge maximum width_Bs1 3

Slot maximum width_Bs2 7.16

Table A 7: Rotor bar Dimensions (T5)

Parameter Value (mm)

Slot opening height_Hs0 1

Slot body height _Hs2 19.405

Slot opening width_Bs0 1.5

Slot wedge maximum width_Bs1 4.49

Slot maximum width_Bs2 4.49

Table A 8: Stator slot Dimensions Parameter Value (mm) Rs 1 B0 Varies B1 6.5 B2 8.7 H0 1 H1 1 H2 16

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APPENDIX B

Torque and Torque Ripple for different rotor bar types and different slot width opening

Table B 1: Average Torque (Nm) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 37.711 37.727 37.754 34.575 36.774 1 34.479 37.543 37.632 34.167 35.359 1.5 40.911 34.239 34.403 32.147 33.751 2 34.292 37.3827 37.387 38.364 35.303 2.5 34.289 37.3387 37.425 34.799 36.677

Table B 2: Average Torque (Nm) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 38.245 38.336 38.254 35.033 37.346 1 32.480 38.180 38.039 34.601 37.261 1.5 38.576 32.538 32.714 30.658 32.026 2 32.311 38.047 37.936 38.426 36.731 2.5 32.307 38.013 38.013 34.956 37.304

Table B 3: Average Torque (Nm) 3 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 38.229 38.344 38.242 35.109 37.340 1 35.494 38.209 38.139 34.593 37.291 1.5 38.062 32.031 32.281 29.569 31.277 2 35.363 38.048 38.008 37.874 36.963 2.5 35.382 38.069 38.038 35.434 43.114

Table B 4: Torque Ripple (%) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 16.426 10.957 15.421 21.711 13.608 1 12.539 9.653 13.723 18.775 12.797 1.5 10.829 9.866 12.670 13.467 10.622 2 9.440 7.186 9.923 13.146 6.331 2.5 11.289 8.037 9.331 13.873 10.956

Table B 5: Torque Ripple (%) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 19.036 12.568 17.798 24.688 15.885 1 22.915 11.597 16.398 22.387 15.248 1.5 21.182 19.968 22.140 21.254 18.877 2 18.320 8.547 12.038 16.507 8.757 2.5 19.115 10.500 11.259 15.688 13.407

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Table B 6: Torque Ripple (%) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 20.937 13.668 17.352 27.254 17.193 1 17.769 12.149 17.609 23.965 16.063 1.5 32.028 24.033 28.444 31.085 29.594 2 12.646 8.547 12.971 18.894 13.559 2.5 12.145 11.707 12.897 18.642 13.396

Efficiency and power factor for different rotor bar types and different slot width openings.

Table B 7: Efficiency (%) Healthy

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.212 75.678 77.975 78.641 77.470 1 76.926 75.357 77.197 78.374 77.177 1.5 76.189 75.054 76.923 78.129 77.003 2 76.393 74.749 76.652 77.893 76.674 2.5 76.135 74.464 76.535 77.221 76.556

Table B 8: Efficiency (%) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.713 76.040 77.978 79.090 77.427 1 77.331 75.738 77.705 78.835 77.196 1.5 72.511 75.484 77.331 78.441 79.668 2 76.376 75.343 76.062 78.369 76.675 2.5 76.555 75.068 76.947 78.194 76.969

Table B 9: Efficiency (%) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.675 76.539 78.209 78.731 78.233 1 77.575 76.258 75.157 79.075 77.440 1.5 74.917 75.752 77.534 78.668 79.752 2 77.057 75.701 75.661 78.622 77.509 2.5 76.819 75.435 77.261 74.349 74.103

Table B 10: Efficiency (%) 3 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.944 76.500 78.197 79.436 78.196 1 77.829 76.231 77.946 79.039 77.958 1.5 74.732 75.644 77.424 78.609 77.556 2 77.342 75.703 77.813 78.592 77.488 2.5 77.116 75.429 77.231 78.384 77.266

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Table B 61: Power Factor (pu) Healthy

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.871 0.888 0.862 0.854 0.868 1 0.874 0.892 0.871 0.858 0.871 1.5 0.882 0.895 0.874 0.860 0.873 2 0.879 0.899 0.877 0.863 0.877 2.5 0.883 0.903 0.878 0.870 0.878

Table B 12: Power Factor (pu) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.865 0.884 0.862 0.850 0.868 1 0.869 0.888 0.865 0.853 0.871 1.5 0.927 0.891 0.869 0.857 0.844 2 0.880 0.892 0.884 0.858 0.877 2.5 0.878 0.892 0.874 0.860 0.873

Table B 13: Power Factor (pu) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.865 0.878 0.860 0.854 0.859 1 0.867 0.881 0.894 0.850 0.868 1.5 0.897 0.887 0.867 0.854 0.842 2 0.872 0.888 0.888 0.855 0.867 2.5 0.875 0.891 0.870 0.904 0.907

Table B 14: Power Factor (pu) 3 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.862 0.879 0.859 0.846 0.859 1 0.864 0.882 0.862 0.850 0.862 1.5 0.899 0.889 0.868 0.855 0.867 2 0.869 0.888 0.864 0.855 0.867 2.5 0.872 0.891 0.870 0.858 0.869

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APPENDIX C

Summary of single factor ANOVA for different number of broken rotor bars with average torque, torque, efficiency and power factor as response variable

Table C 1: (a) Average Torque for conventional IM (with rotor bar type 1)

Tavg (Nm)

Healthy Faulty

1 Bar 2 Bars 3 Bars

36.23 40.91 38.57 38.06

Table C 1: (b) Summary of single factor ANOVA for different number of broken rotor bars with average torque as response variable

Source of Variation SS df MS F P-value F crit

Between Groups 2073.529 1 2073.529 1253.001 3.8E-06 7.708647 Within Groups 6.6194 4 1.65485

Total 2080.148 5 Table C 2: (a) Torque Ripple for conventional IM (with rotor bar type 1)

Tripple (%)

Healthy Faulty

1 Bar 2 Bars 3 Bars

10.903 10.829 21.182 32.028

Table C 2: (b) Summary of single factor ANOVA for different number of broken rotor bars with torque ripple as response variable

Source of Variation SS df MS F P-value F crit

Between Groups 4.78757 1 4.78757 9.46874 0.037035 7.708647 Within Groups 2.022474 4 0.505618

Total 6.810044 5 Table C 3: (a) Power Factor for conventional IM (with rotor bar type 1)

Power Factor (pu)

Healthy Faulty

1 Bar 2 Bars 3 Bars

0.882 0.927 0.897 0.899

Table C 3: (b) Summary of single factor ANOVA for different number of broken rotor bars with power factor as response variable

Source of Variation SS df MS F P-value F crit

Between Groups 2.511028 3 0.837009 1.043968 0.464171 6.591382 Within Groups 3.207032 4 0.801758

100

Table C 4: (a) Efficiency for conventional IM (with rotor bar type 1)

Efficiency (%)

Healthy Faulty

1 Bar 2 Bars 3 Bars

76.189 72.511 74.917 74.732

Table C 4: (b) Summary of single factor ANOVA for different number of broken rotor bars with efficiency as response variable

Source of Variation SS df MS F P-value F crit

Between Groups 2.490525 3 0.830175 0.910382 0.511165 6.591382 Within Groups 3.647592 4 0.911898

Total 6.138117 7

Summary of two-way ANOVA for different number of broken rotor bars with average torque, torque, efficiency and power factor as response variable

Table C 5: (a) Average Torque

Rotor Bar Type Healthy 1 Broken Bar 2 Broken Bars 3 Broken Bars

Type 1 36.239 Nm 40.911 Nm 38.576 Nm 38.062 Nm

Type 2 35.986 Nm 34.239 Nm 32.538 Nm 32.031 Nm

Type 3 37.965 Nm 34.403 Nm 32.714 Nm 32.281 Nm

Type 4 33.606 Nm 32.147 Nm 30.658 Nm 29.569 Nm

Type 5 35.432 Nm 33.751 Nm 32.026 Nm 31.277 Nm

Table C 5: (b) Summary of two-way ANOVA with average torque as response variable

Source of Variation SS df MS F P-value F crit

Rows 107.1456 4 26.7864 11.99749 0.000372 3.259167 Columns 33.62794 3 11.20931 5.020594 0.017537 3.490295 Error 26.792 12 2.232667

Total 167.5655 19

Table C 2: (a) Torque Ripple

Rotor Bar Type Healthy 1 Broken Bar 2 Broken Bars 3 Broken Bars

Type 1 10.903 % 10.829 % 21.182 % 32.028 %

Type 2 7.389 % 9.866% 19.968 % 24.033%

Type 3 10.518 % 12.670 % 22.140 % 28.444 %

Type 4 10.257 % 13.467 % 21.254 % 31.085 %

Type 5 7.124 % 10.622 % 18.897 % 29.594 %

Table C 6: (b) Summary of two-way ANOVA with torque ripple as response variable

Source of Variation SS df MS F P-value F crit

Rows 0.004125 4 0.001031 4.677376 0.016573 3.259167 Columns 0.123789 3 0.041263 187.1563 2.44E-10 3.490295 Error 0.002646 12 0.00022

101

Table C 7: (a) Efficiency

Rotor Bar Type Healthy 1 Broken Bar 2 Broken Bars 3 Broken Bars

η (%) η (%) η (%) η (%) Type 1 76.189 72.511 74.917 74.732 Type 2 75.054 75.484 75.752 75.644 Type 3 76.923 77.331 77.534 77.424 Type 4 78.129 78.441 78.668 78.609 Type 5 77.003 79.668 79.752 77.556

Table C 7: (b) Summary of two-way ANOVA with efficiency as response variable

Source of Variation SS df MS F P-value F crit

Rows 49.97689 4 12.49422 12.20007 0.000344 3.259167 Columns 1.451425 3 0.483808 0.472418 0.707163 3.490295 Error 12.28933 12 1.024111

Total 63.71764 19

Table C 8: (a) Power Factor

Rotor Bar Type Healthy 1 Broken Bar 2 Broken Bars 3 Broken Bars

PF (pu) PF (pu) PF (pu) PF (pu)

Type 1 0.882 0.927 0.897 0.899

Type 2 0.895 0.891 0.887 0.889

Type 3 0.874 0.869 0.867 0.868

Type 4 0.860 0.857 0.854 0.855

Type 5 0.873 0.844 0.842 0.867

Table C 8: (b) Summary of two-way ANOVA with power factor as response variable

Source of Variation SS df MS F P-value F crit

Rows 0.006576 4 0.001644 11.72436 0.000413 3.259167 Columns 0.000208 3 6.94E-05 0.494829 0.692599 3.490295 Error 0.001683 12 0.00014

Total 0.008467 19 Table C 9: (a) Average Torque (Nm) Healthy

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 36.405 38.317 36.453 33.368 35.485 1 36.264 36.119 36.306 33.124 35.363 1.5 36.239 35.986 37.965 33.606 35.432 2 36.055 35.942 36.074 33.476 35.303 2.5 36.053 35.889 36.088 33.539 35.316

Table C 9: (b) Summary of two-way ANOVA with average torque as response variable (healthy IMs)

Source of Variation SS df MS F P-value F crit

Rows 1.771978 4 0.442995 1.318611 0.305355 3.006917 Columns 34.15813 4 8.539533 25.41864 9.24E-07 3.006917 Error 5.375289 16 0.335956

102

Table C 10: (a) Average Torque (Nm) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 37.711 37.727 37.754 34.575 36.774 1 34.479 37.543 37.632 34.167 35.359 1.5 40.911 34.239 34.403 32.147 33.751 2 34.292 37.3827 37.387 38.364 35.303 2.5 34.289 37.3387 37.425 34.799 36.677

Table C 10: (b) Summary of two-way ANOVA with average torque as response variable (IMs with 1 broken bar)

Source of Variation SS df MS F P-value F crit

Rows 9.706283 4 2.426571 0.572452 0.686526 3.006917 Columns 16.13108 4 4.032771 0.95137 0.46028 3.006917 Error 67.82256 16 4.23891

Total 93.65992 24 Table C 3: (a) Average Torque (Nm) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 38.245 38.336 38.254 35.033 37.346 1 32.480 38.180 38.039 34.601 37.261 1.5 38.576 32.538 32.714 30.658 32.026 2 32.311 38.047 37.936 38.426 36.731 2.5 32.307 38.013 38.013 34.956 37.304

Table C 4: (b) Summary of two-way ANOVA with average torque as response variable (IMs with 2 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 49.19732 4 12.29933 2.080414 0.131088 3.006917 Columns 25.52018 4 6.380044 1.079175 0.399448 3.006917 Error 94.59142 16 5.911964

Total 169.3089 24 Table C 12: (a) Average Torque (Nm) 3 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 38.229 38.344 38.242 35.109 37.340 1 35.494 38.209 38.139 34.593 37.291 1.5 38.062 32.031 32.281 29.569 31.277 2 35.363 38.048 38.008 37.874 36.963 2.5 35.382 38.069 38.038 35.434 43.114

Table C 12: (b) Summary of two-way ANOVA with average torque as response variable (IMs with 3 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 93.2067 4 23.30167 4.646673 0.011115 3.006917 Columns 23.89889 4 5.974721 1.191441 0.352277 3.006917 Error 80.23521 16 5.0147

103

Table C 13: (a) Torque Ripple (%) Healthy

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 12.785 9.455 11.416 17.962 10.874 1 10.607 9.666 12.099 14.942 9.507 1.5 10.903 7.389 10.518 10.257 7.124 2 6.832 6.527 6.692 9.710 5.932 2.5 7.722 7.479 8.133 9.060 8.491

Table C 13: (b) Summary of two-way ANOVA with torque ripple as response variable (healthy IMs)

Source of Variation SS df MS F P-value F crit

Rows 98.46382 4 24.61596 13.40058 5.58E-05 3.006917 Columns 57.50844 4 14.37711 7.8267 0.001078 3.006917 Error 29.3909 16 1.836931

Total 185.3632 24 Table C 14: (a) Torque Ripple (%) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 16.426 10.957 15.421 21.711 13.608 1 12.539 9.653 13.723 18.775 12.797 1.5 10.829 9.866 12.670 13.467 10.622 2 9.440 7.186 9.923 13.146 6.331 2.5 11.289 8.037 9.331 13.873 10.956

Table C 14: (b) Summary of two-way ANOVA with torque ripple as response variable (IMs with 1 broken bar)

Source of Variation SS df MS F P-value F crit

Rows 125.4716 4 31.36791 17.10904 1.24E-05 3.006917 Columns 135.3522 4 33.83805 18.45633 7.68E-06 3.006917 Error 29.33458 16 1.833411

Total 290.1584 24 Table C 15: (a) Torque Ripple (%) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 19.036 12.568 17.798 24.688 15.885 1 22.915 11.597 16.398 22.387 15.248 1.5 21.182 19.968 22.140 21.254 18.877 2 18.320 8.547 12.038 16.507 8.757 2.5 19.115 10.500 11.259 15.688 13.407

Table C 15: (b) Summary of two-way ANOVA with torque ripple as response variable (IMs with 2 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 204.1191 4 51.02978 10.032 0.000293 3.006917 Columns 227.3727 4 56.84319 11.17486 0.000161 3.006917 Error 81.38722 16 5.086701

104

Table C 16: (a) Torque Ripple (%) 3 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 20.937 13.668 17.352 27.254 17.193 1 17.769 12.149 17.609 23.965 16.063 1.5 32.028 24.033 28.444 31.085 29.594 2 12.646 8.547 12.971 18.894 13.559 2.5 12.145 11.707 12.897 18.642 13.396

Table C 16: (b) Summary of two-way ANOVA with torque ripple as response variable (IMs with 3 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 809.3392 4 202.3348 66.98834 8.69E-10 3.006917 Columns 255.0091 4 63.75228 21.10689 3.21E-06 3.006917 Error 48.32717 16 3.020448

Total 1112.676 24

Table C 17: (a) Efficiency (%) Healthy

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.212 75.678 77.975 78.641 77.470 1 76.926 75.357 77.197 78.374 77.177 1.5 76.189 75.054 76.923 78.129 77.003 2 76.393 74.749 76.652 77.893 76.674 2.5 76.135 74.464 76.535 77.221 76.556

Table C 17: (b) Summary of two-way ANOVA with efficiency as response variable (healthy IMs)

Source of Variation SS df MS F P-value F crit

Rows 4.447119 4 1.11178 42.19997 2.62E-08 3.006917 Columns 23.62835 4 5.907087 224.2161 7.89E-14 3.006917 Error 0.421528 16 0.026346

Total 28.49699 24 Table C 18: (a) Efficiency (%) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.713 76.040 77.978 79.090 77.427 1 77.331 75.738 77.705 78.835 77.196 1.5 72.511 75.484 77.331 78.441 79.668 2 76.376 75.343 76.062 78.369 76.675 2.5 76.555 75.068 76.947 78.194 76.969

Table C 5: (b) Summary of two-way ANOVA with efficiency as response variable (IMs with 1 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 4.518449 4 1.129612 0.828561 0.526251 3.006917 Columns 29.3181 4 7.329525 5.376145 0.00613 3.006917 Error 21.81347 16 1.363342

105

Table C 19: (a) Efficiency (%) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.675 76.539 78.209 78.731 78.233 1 77.575 76.258 75.157 79.075 77.440 1.5 74.917 75.752 77.534 78.668 79.752 2 77.057 75.701 75.661 78.622 77.509 2.5 76.819 75.435 77.261 74.349 74.103

Table C 19: (b) Summary of two-way ANOVA with efficiency as response variable (IMs with 2 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 14.32262 4 3.580655 1.842717 0.170014 3.006917 Columns 10.85455 4 2.713637 1.396523 0.279732 3.006917 Error 31.09022 16 1.943139

Total 56.26739 24 Table C 20: (a) Efficiency (%) 3 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 77.944 76.500 78.197 79.436 78.196 1 77.829 76.231 77.946 79.039 77.958 1.5 74.732 75.644 77.424 78.609 77.556 2 77.342 75.703 77.813 78.592 77.488 2.5 77.116 75.429 77.231 78.384 77.266

Table C 20: (b) Summary of two-way ANOVA with efficiency as response variable (IMs with 3 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 5.268776 4 1.317194 4.931775 0.008765 3.006917 Columns 22.96069 4 5.740172 21.49208 2.85E-06 3.006917 Error 4.27333 16 0.267083

Total 32.50279 24 Table C 21: (a) Power Factor (pu) Healthy

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.871 0.888 0.862 0.854 0.868 1 0.874 0.892 0.871 0.858 0.871 1.5 0.882 0.895 0.874 0.860 0.873 2 0.879 0.899 0.877 0.863 0.877 2.5 0.883 0.903 0.878 0.870 0.878

Table C 21: (b) Summary of two-way ANOVA with power factor as response variable (healthy IMs)

Source of Variation SS df MS F P-value F crit

Rows 0.000566 4 0.000142 40.14184 3.76E-08 3.006917 Columns 0.003122 4 0.00078 221.3901 8.72E-14 3.006917 Error 5.64E-05 16 3.52E-06

106

Table C 30: (a) Power Factor (pu) 1 Broken Bar

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.865 0.884 0.862 0.850 0.868 1 0.869 0.888 0.865 0.853 0.871 1.5 0.927 0.891 0.869 0.857 0.844 2 0.880 0.892 0.884 0.858 0.877 2.5 0.878 0.892 0.874 0.860 0.873

Table C 30: (b) Summary of two-way ANOVA with power factor as response variable (IMs with 1 broken bars (%)

Source of Variation SS df MS F P-value F crit

Rows 0.0006 4 0.00015 0.805198 0.539643 3.006917 Columns 0.003669 4 0.000917 4.926241 0.008805 3.006917 Error 0.002979 16 0.000186

Total 0.007249 24 Table C 31: (a) Power Factor (pu) 2 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.865 0.878 0.860 0.854 0.859 1 0.867 0.881 0.894 0.850 0.868 1.5 0.897 0.887 0.867 0.854 0.842 2 0.872 0.888 0.888 0.855 0.867 2.5 0.875 0.891 0.870 0.904 0.907

Table C 31: (b) Summary of two-way ANOVA with power factor as response variable (IMs with 2 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 0.001891 4 0.000473 1.85682 0.167391 3.006917 Columns 0.001332 4 0.000333 1.308062 0.309 3.006917 Error 0.004073 16 0.000255

Total 0.007296 24 Table C 32: (a) Power Factor (pu) 3 Broken Bars

Stator Slot Opening (mm)

Rotor Bar Type

T1 T2 T3 T4 T5 0.5 0.862 0.879 0.859 0.846 0.859 1 0.864 0.882 0.862 0.850 0.862 1.5 0.899 0.889 0.868 0.855 0.867 2 0.869 0.888 0.864 0.855 0.867 2.5 0.872 0.891 0.870 0.858 0.869

Table C 32: (b) Summary of two-way ANOVA with power factor as response variable (IMs with 3 broken bars)

Source of Variation SS df MS F P-value F crit

Rows 0.000694 4 0.000174 5.120685 0.007515 3.006917 Columns 0.002982 4 0.000746 21.99882 2.44E-06 3.006917

Error 0.000542 16 3.39E-05

107

APPENDIX D

Table D 1: Quietest slot combinations for test motor (in increasing noise level order)

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