Effect of rotor bar shape and stator slot opening on a three phase induction motor with broken bars

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(1)COPYRIGHT AND CITATION CONSIDERATIONS FOR THIS THESIS/ DISSERTATION. o Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. o NonCommercial — You may not use the material for commercial purposes.. o ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.. How to cite this thesis Surname, Initial(s). (2012). Title of the thesis or dissertation (Doctoral Thesis / Master’s Dissertation). Johannesburg: University of Johannesburg. Available from: http://hdl.handle.net/102000/0002 (Accessed: 22 August 2017)..

(2) EFFECT OF ROTOR BAR SHAPE AND STATOR SLOT OPENING ON A THREE PHASE INDUCTION MOTOR WITH BROKEN BARS. By. Mamakhetha Eveline Makhetha. Submitted in Partial Fulfilment of the Requirement for the Degree. MAGISTER TECHNOLOGIAE Electrical Engineering. In the Department of Electrical Engineering. FACULTY OF ENGINEERING AND BUILT ENVIRONMENT. UNIVERSITY OF JOHANNESBURG. Supervisor: Dr. M. Muteba Co-Supervisor: Prof. D. Nicolae. January 2019.

(3) DECLARATION I declare that this research work is entirely my own work and has not been submitted at any other institution of higher learning. It is submitted as a partial fulfilment for Magister Technologiae in Electrical and Electronic Engineering at the University of Johannesburg. A list of references and citations have been provided for any text taken from various articles, and any other external assistance has been acknowledged.. Mamakhetha Eveline Makhetha. i.

(4) ACKNOWLEDGEMENT I would like to thank my main supervisor, Dr. MC Muteba for his guidance and never ending support from the beginning to the end of this research work. Thank you for sharing your knowledge and for always pushing me to go an extra mile. Most of all I would like to thank you for helping me realise my full potential. To my co-supervisor, Prof. D Nicolae, thank you for your patience with me, thank you for always keeping your office door open for me and my fellow colleagues. I am gratefully indebted to your very valuable input to this research work. I would also like to thank my line manager at Tshwane University of Technology, Prof. JL Munda for his continued support and encouragement throughout the process of completing this work. A special thanks to my friends and colleagues at Tshwane University of Technology (Mrs Hlungulu and Ms Memane) for their never ending support and encouragement, thank you for being there in good and bad times, I highly appreciate the support you showed me at all times. To my fellow colleagues at the University of Johannesburg, thank you for being such a great team to work with, thanks for always willing to share ideas as well as offering support in challenging times. A special thanks to Mr. Aguba and Ms. Muremi for always making time to assist whenever I called for help. Finally, I would like to offer my profound gratitude to my friends and family, your support throughout this program is immeasurable. I will always be grateful for the support you have shown me.. ii.

(5) ABSTRACT This work analyses the effect of different rotor bar shapes and stator slot opening of a three phase induction motor operating under healthy and broken rotor bar fault conditions. Due to symmetrical nature of the machine, and the omission of end winding flux leakages in this work, the three phase squirrel cage induction motor (SCIM) is designed and modelled using the two dimension (2D) finite element method (FEM). The magnetostatic solver is used to obtain the flux density distribution under different operating conditions, while the instantaneous torque, torque ripple, power factor, efficiency etc., are computed using the AC magnetic transient solver. For qualitative and quantitative evaluation of the effect of rotor bar shape and stator slot opening width on the performance of three phase SCIMs, the Analysis of Variance (ANOVA) assisted by Finite Element Analysis (FEA) is used, for single and multi-factor analysis. In both single and multi-factor analysis, a two-way ANOVA is used together with FEA to assist analysing the level of significance that the design parameters have on the performance responses of the three-phase SCIM under healthy and broken rotor bars. From the FEA results, it is evident that the rotor bar shapes and stator slot openings have a significant influence on the airgap conductance and flux density distribution of the three-phase squirrel cage induction motor (SCIM). A change in rotor bar shape results in varying the rotor bar parameters, and this has a significant impact on certain performance indexes of the SCIM, such as the torque, efficiency and power factor. Furthermore, the FEA results also evidenced that the electromagnetic torque profile is affected when there is occurrence of a broken rotor bar, therefore introducing a number of unwanted torque harmonics. The latter contribute to torque ripple production in the three-phase SCIM.. iii.

(6) From FEA alone, it is quite difficult for design engineers to decide on the type of rotor bar shape and stator slot opening width that would mitigate the effect of rotor bar breakages on the torque profile and other performance indexes. Therefore, this work has made use of a statistical approach to complement the FEA in order to study the inference that the rotor bar shape and the stator slot opening width has on the electromagnetic parameters of interests, when the three-phase SCIM operates under healthy and broken bar conditions. The method utilizes the single and multi-factor ANOVA, which are experimental designs. From ANOVA results, it is evident that the SCIM designed with a specific rotor bar shape and operating with a certain number of broken rotor bars has a significant impact on the average torque and torque ripple. The same has been noticed for the efficiency and power factor responses. On other hand, the results proved that the stator slot opening width has a significant impact on the torque ripple than the average torque and the efficiency.. iv.

(7) TABLE OF CONTENTS DECLARATION ........................................................................................................................ i ACKNOWLEDGEMENT .........................................................................................................ii ABSTRACT ............................................................................................................................. iii INTRODUCTION ..................................................................................................................... 1 1.1. Background ................................................................................................................. 1. 1.2. Problem Statement ...................................................................................................... 3. 1.3. Research Questions ..................................................................................................... 4. 1.4. Research Objectives .................................................................................................... 5. 1.5. Hypothesis ................................................................................................................... 5. 1.6. Delimitations of the study ........................................................................................... 5. 1.7. Contributions ............................................................................................................... 6. 1.8. Dissertation Outline..................................................................................................... 7. REVIEW OF THREE PHASE SQUIRREL CAGE INDUCTION MACHINES WITH BROKEN ROTOR BARS ......................................................................................................... 9 2.1 Introduction ...................................................................................................................... 9 2.2 Induction Machines with Broken Rotor Bars ................................................................... 9 2.3 Three Phase Squirrel Cage Induction Machine Construction ........................................ 10 2.4 Broken Rotor Bar Fault .................................................................................................. 11 2.5 Causes of Rotor Bar Breakage in Squirrel Cage Induction Machines ........................... 13 2.5.1 Frequently starting a squirrel cage induction motor .............................................. 14 2.5.2 Manufacturing defects ............................................................................................. 15 2.5.3 Interbar currents...................................................................................................... 16 2.6 Effects of Stator Slot Opening and Magnetic Wedges on performance of IMs ............. 16 2.7 Different Rotor Bars ....................................................................................................... 18 2.8 Summary ........................................................................................................................ 21 ANALYSIS OF THREE PHASE SQUIRREL CAGE INDUCTION MACHINES WITH BROKEN ROTOR BARS. ...................................................................................................... 23 3.1 Introduction .................................................................................................................... 23 3.2 Finite Element Method (FEM) ....................................................................................... 24 3.2.1 Background .............................................................................................................. 24 3.2.2 Induction machine simulation parameters .............................................................. 26 3.3 Airgap Flux Density Distribution................................................................................... 27. v.

(8) 3.4 Effect of Broken Rotor Bar Fault on Stator current ....................................................... 30 3.5 Flux Linkage Analysis of IM with Broken Rotor Bars .................................................. 32 3.6 Torque and Torque Ripple Analysis .............................................................................. 34 3.7 Performance Evaluation ................................................................................................. 37 3.8 Summary ........................................................................................................................ 38 INFLUENCE OF ROTOR BAR SHAPE AND STATOR SLOT OPENING ON THE PERFORMANCE OF SQUIRREL CAGE INDUCTION MACHINE .................................. 40 4.1 Introduction .................................................................................................................... 40 4.2 Influence of rotor bar shape on the performance of squirrel cage induction machine ... 41 4.3 Airgap Flux Density Distribution................................................................................... 44 4.4 Dynamic Analysis of rotor bar types in healthy condition............................................. 46 4.5 Dynamic Analysis of rotor bar types in both healthy and faulty condition ................... 48 4.6 Performance Evaluation (Efficiency and Power factor) ................................................ 53 4.7 Influence of stator slot opening on the performance of squirrel cage induction machine .............................................................................................................................................. 54 4.8 Dynamic analysis of slot opening .................................................................................. 57 4.9 Efficiency and Power Factor .......................................................................................... 62 4.10 Summary ...................................................................................................................... 63 ANALYSIS OF VARIANCES THROUGH PARAMETER INFERENCE METHOD ......... 64 5.1 Introduction .................................................................................................................... 64 5.2 Single factor ANOVA .................................................................................................... 64 5.2.1 Single-factor Method Overview ............................................................................... 65 5.3 Multi factor ANOVA (two-way ANOVA) .................................................................... 69 5.3.1 Multi-factor (two-way) method Overview ............................................................... 70 5.4 Summary ........................................................................................................................ 81 CONCLUSION AND RECOMMENDATIONS .................................................................... 83 6.1 Introduction .................................................................................................................... 83 6.2 Review of Three Phase Squirrel Cage Induction Machines with Broken Rotor Bars ... 83 6.3 Analysis of Three Phase Squirrel Cage Induction Machines with Broken Rotor Bars.. 84 6.4 Influence of Rotor Bar Shape and Stator Slot Opening on the Performance of Squirrel Cage Induction Machine ...................................................................................................... 84 6.5 Analysis of variances through Parameter Inference Method ......................................... 86 6.6 Recommendation and Future work ................................................................................ 87 REFERENCES ........................................................................................................................ 89 vi.

(9) APPENDIX A .......................................................................................................................... 94 APPENDIX B .......................................................................................................................... 96 APPENDIX C .......................................................................................................................... 99 APPENDIX D ........................................................................................................................ 107. vii.

(10) LIST OF FIGURES Figure 2.1:Typical Rotor Bar Types (a) Rectangular, (b) Double cage, (c) Conventional (semi closed), (d) Trapezoidal, (e) Conventional (fully closed) and (f) Round ................................ 19. Figure 3.1: Motor Specification ............................................................................................... 26 Figure 3.2: Magnetic Flux density distribution: (a) healthy, (b) one broken bar, (c) two broken bars and (d) three broken bars. ................................................................................................. 29 Figure 3.3:Comparisons of flux density distribution: (a) flux density profile and (b) FFT of flux density profile for conventional machine under healthy and faulty (broken rotor bars) conditions ................................................................................................................................. 30 Figure 3.4: Comparison of induced current under healthy and broken rotor bar; (a) transient and (b) Zoomed transient. ........................................................................................................ 32 Figure 3.5: FFTs of the stator current for healthy and faulty IM ............................................. 32 Figure 3.6: Comparison of the simulated flux linkages SCIM both in healthy and fault conditions (a) Flux Linkage and (b) Flux Linkage zoomed .................................................... 33 Figure 3.7: Flux linkage profile Comparison between healthy and faulty (broken rotor bars) IM. ............................................................................................................................................ 34 Figure 3.8: Dynamic Torque for rotor bar under healthy and faulty (broken rotor bars) conditions. ................................................................................................................................ 36 Figure 3.9: Steady state Torque for healthy and faulty motor conditions; (a) average torque and (b) FFT profile. ........................................................................................................................ 37. Figure 4.1: Model of the rotor cage (only three bars are shown); (a) Equivalent model, (b) Rotor current phasor representation ................................................................................................... 41 Figure 4.2: Representation of different rotor bar shapes; (a) T2, (b) T3 (c) T4 and (d) T5. ...... 43 Figure 4.3: Magnetic flux density distribution comparisons for healthy different rotor types. .................................................................................................................................................. 45 Figure 4.4: Magnetic flux density distribution comparison (a) airgap flux density profile and (b) FFT profile ......................................................................................................................... 46 Figure 4.5: Starting Torque for Type 1, 2, 3, 4 and 5 of rotor bar shape under healthy conditions. .................................................................................................................................................. 47 Figure 4.6: Dynamic torque for healthy different rotor bar types (a) average torque and (b) FFT profile. ...................................................................................................................................... 48 Figure 4.7: Instantaneous Torque for (a) Type 2, (b) Type 3, (c) Type 4 and (d)Type 5 rotor bars under healthy and faulty (adjacent broken rotor bars) conditions .................................... 50 Figure 4.8: Type 2 rotor bar under healthy and faulty conditions (a) steady-state and (b) FFT Profile. ...................................................................................................................................... 50 Figure 4.9: Steady state Torque for (a) Type 3, (b) Type 4 and (c) Type 5 rotor bar under healthy and faulty (adjacent broken rotor bars) conditions .................................................................. 52 Figure 4.10: Flux density distribution comparisons for machine with different slot opening under healthy condition (a) 0.5 mm, (b) 1 mm, (c) 1.5 mm, (d) 2mm and (e) 2.5mm. ........... 55 viii.

(11) Figure 4.11: Flux density distribution comparisons for different slot opening under healthy condition: (a) airgap flux density profile (b) FFT profile. ....................................................... 57 Figure 4.12: Instantaneous torque for rotor bar T2 with different stator slot opening widths under healthy condition............................................................................................................ 58 Figure 4.13: Average torque for rotor bar T2 with different stator slot opening widths under healthy condition (a) steady-state and (b) FFTs profile. .......................................................... 59 Figure 4.14: Instantaneous torque for different rotor bar types with stator slot opening widths of 0.5 mm when the IM is healthy. .......................................................................................... 60 Figure 4.15: Instantaneous torque for different rotor bar types with stator slot opening widths of 1 mm when the IM has 1 broken rotor bar. ......................................................................... 60 Figure 4.16: Average torque with different rotor bar types at stator slot opening widths of 0.5 mm under healthy condition. ................................................................................................... 61 Figure 4.17: Average torque with different rotor bar types at stator slot opening widths of 1mm under 1 broken rotor bar. ......................................................................................................... 61. Figure 5.1: Single-factor evaluation method overview............................................................ 66 Figure 5.2: Response for different number of broken rotor bars, (a) Average torque (b) Torque ripple ........................................................................................................................................ 67 Figure 5.3: Response for different number of broken rotor bars, (a) Power factor (b) Efficiency .................................................................................................................................................. 68 Figure 5.4: Two-way evaluation method overview ................................................................. 70 Figure 5.5: (a) Torque response, (b) torque ripple response, (c) efficiency response and (d) power factor response for different rotor bar types and different number of broken bars ....... 72 Figure 5.6: Torque response for (a) healthy IM, (b) IM with 1 broken bar, (c) IM with 2 broken bars and (d) IM with 3 broken rotor bars for various rotor bar types and stator slot openings75 Figure 5.7: Torque ripple response for (a) healthy IM, (b) IM with 1 broken bar, (c) IM with 2 broken bars and (d) IM with 3 broken rotor bars for various rotor bar types and stator slot openings ................................................................................................................................... 76 Figure 5.8: Efficiency response for (a) healthy IM, (b) IM with 1 broken bar, (c) IM with 2 broken bars and (d) IM with 3 broken rotor bars for various rotor bar types and stator slot openings ................................................................................................................................... 78 Figure 5.9: Power factor response for (a) healthy IM, (b) IM with 1 broken bar, (c) IM with 2 broken bars and (d) IM with 3 broken rotor bars for various rotor bar types and stator slot openings ................................................................................................................................... 80. ix.

(12) LIST OF TABLES Table 2. 1: Stresses Found in Rotor Assembly ........................................................................ 12. Table 3. 2: Motor dimension .................................................................................................... 27 Table 3. 3: Average Torque for conventional IM .................................................................... 37 Table 3. 4: Torque Ripple for conventional IM ....................................................................... 37 Table 3. 5: Table 3.5 Power Factor for conventional IM ......................................................... 38 Table 3. 6: Efficiency for conventional IM ............................................................................. 38. Table 4. 1: Rotor bar dimensions (T1) ..................................................................................... 43 Table 4. 2: Average Torque ..................................................................................................... 52 Table 4. 3: Torque Ripple ........................................................................................................ 52 Table 4. 4: Efficiency (η) ......................................................................................................... 53 Table 4. 5: Power Factor (pu) .................................................................................................. 53 Table 4. 6: Stator Slot Dimension ............................................................................................ 55 Table 4. 7: Average Torque (Nm) Healthy .............................................................................. 62 Table 4. 8: Torque Ripple (%) Healthy ................................................................................... 62. Table 5. 1: Summary of single-factor ANOVA model ............................................................ 64 Table 5.2: Summary of ANOVA for different number of broken rotor bars with average output torque as response variable ...................................................................................................... 67 Table 5.3: Summary of ANOVA for different number of broken rotor bars with torque ripple as response variable ................................................................................................................. 67 Table 5. 4: Summary of ANOVA for different number of broken rotor bars with power factor as response variable ................................................................................................................. 68 Table 5. 5: Summary of ANOVA for different number of broken rotor bars with efficiency as response variable ...................................................................................................................... 69 Table 5. 6: Summary of two-way ANOVA model .................................................................. 69 Table 5. 7: Summary of ANOVA for Torque response for different rotor bar types and different number of broken bars ............................................................................................................. 72 Table 5. 8: Summary of ANOVA for Torque ripple response for different rotor bar types and different number of broken bars .............................................................................................. 73 Table 5. 9: Summary of ANOVA for Efficiency response for different rotor bar types and different number of broken bars .............................................................................................. 73 Table 5. 10: Summary of ANOVA for Power factor response for different rotor bar types and different number of broken bars .............................................................................................. 73 Table 5. 11: Summary of ANOVA for Torque response for healthy IM for various rotor bar types and stator slot openings .................................................................................................. 75 Table 5. 12: Summary of ANOVA for Torque response for IM with 1 broken bar for various rotor bar types and stator slot openings ................................................................................... 75. x.

(13) Table 5. 13: Summary of ANOVA for Torque response for IM with 2 broken bars for various rotor bar types and stator slot openings ................................................................................... 75 Table 5.14: Summary of ANOVA for Torque response for IM with 3 broken rotor bars for various rotor bar types and stator slot openings....................................................................... 76 Table 5. 15: Summary of ANOVA for Torque ripple response for healthy IM for various rotor bar types and stator slot openings ............................................................................................ 77 Table 5. 16: Summary of ANOVA for Torque ripple response for IM with 1 broken bar for various rotor bar types and stator slot openings....................................................................... 77 Table 5. 17: Summary of ANOVA for Torque ripple response for IM with 2 broken bars for various rotor bar types and stator slot openings....................................................................... 77 Table 5. 18: Summary of ANOVA for Torque ripple response for IM with 3 broken bars for various rotor bar types and stator slot openings....................................................................... 77 Table 5. 19: Summary of ANOVA for Efficiency response for healthy IM for various rotor bar types and stator slot openings .................................................................................................. 79 Table 5.20: Summary of ANOVA for Efficiency response for IM with 1 broken bar for various rotor bar types and stator slot openings ................................................................................... 79 Table 5.21: Summary of ANOVA for Efficiency response for IM with 2 broken bars for various rotor bar types and stator slot openings ................................................................................... 79 Table 5.22: Summary of ANOVA for Efficiency response for IM with 3 broken bars for various rotor bar types and stator slot openings ................................................................................... 79 Table 5.23: Summary of ANOVA for Power factor response for healthy IM for various rotor bar types and stator slot openings ............................................................................................ 80 Table 5.24: Summary of ANOVA for Power factor response for IM with 1 broken bar for various rotor bar types and stator slot openings....................................................................... 81 Table 5.25: Summary of ANOVA for Power factor response for IM with 2 broken bars for various rotor bar types and stator slot openings....................................................................... 81 Table 5.26 Summary of ANOVA for Power factor response for IM with 3 broken bars for various rotor bar types and stator slot openings....................................................................... 81. Table A 1: Ratings of three-phase SCIM ................................................................................. 94 Table A 2: SCIM Dimensions.................................................................................................. 94 Table A 3: Rotor bar Dimensions (T1) .................................................................................... 94 Table A 4: bar Dimensions (T2) .............................................................................................. 94 Table A 5: Rotor bar Dimensions (T3) .................................................................................... 94 Table A 6: Rotor bar Dimensions (T4) .................................................................................... 95 Table A 7: Rotor bar Dimensions (T5) .................................................................................... 95 Table A 8: Stator slot Dimensions ........................................................................................... 95. Table B 1: Average Torque (Nm) 1 Broken Bar ..................................................................... 96 Table B 2: Average Torque (Nm) 2 Broken Bars .................................................................... 96 Table B 3: Average Torque (Nm) 3 Broken Bars .................................................................... 96 Table B 4: Torque Ripple (%) 1 Broken Bar ........................................................................... 96 xi.

(14) Table B 5: Torque Ripple (%) 2 Broken Bars ......................................................................... 96 Table B 6: Torque Ripple (%) 2 Broken Bars ......................................................................... 97 Table B 7: Efficiency (%) Healthy .......................................................................................... 97 Table B 8: Efficiency (%) 1 Broken Bar ................................................................................. 97 Table B 9: Efficiency (%) 2 Broken Bars ................................................................................ 97 Table B 10: Efficiency (%) 3 Broken Bars .............................................................................. 97 Table B 61: Power Factor (pu) Healthy ................................................................................... 98 Table B 12: Power Factor (pu) 1 Broken Bar .......................................................................... 98 Table B 13: Power Factor (pu) 2 Broken Bars ........................................................................ 98 Table B 14: Power Factor (pu) 3 Broken Bars ........................................................................ 98. Table C 1: (a) Average Torque for conventional IM (with rotor bar type 1) .......................... 99 Table C 1: (b) Summary of single factor ANOVA for different number of broken rotor bars with average torque as response variable................................................................................. 99 Table C 2: (a) Torque Ripple for conventional IM (with rotor bar type 1) ............................. 99 Table C 2: (b) Summary of single factor ANOVA for different number of broken rotor bars with torque ripple as response variable .................................................................................... 99 Table C 3: (a) Power Factor for conventional IM (with rotor bar type 1) ............................... 99 Table C 3: (b) Summary of single factor ANOVA for different number of broken rotor bars with power factor as response variable .................................................................................... 99 Table C 4: (a) Efficiency for conventional IM (with rotor bar type 1) .................................. 100 Table C 4: (b) Summary of single factor ANOVA for different number of broken rotor bars with efficiency as response variable ...................................................................................... 100 Table C 5: (a) Average Torque .............................................................................................. 100 Table C 5: (b) Summary of two-way ANOVA with average torque as response variable .... 100 Table C 6: (a) Torque Ripple ................................................................................................. 100 Table C 6: (b) Summary of two-way ANOVA with torque ripple as response variable ....... 100 Table C 7: (a) Efficiency........................................................................................................ 101 Table C 7: (b) Summary of two-way ANOVA with efficiency as response variable .......... 101 Table C 8: (a) Power Factor ................................................................................................... 101 Table C 8: (b) Summary of two-way ANOVA with power factor as response variable ....... 101 Table C 9: (a) Average Torque (Nm) Healthy ....................................................................... 101 Table C 9: (b) Summary of two-way ANOVA with average torque as response variable (healthy IMs) .......................................................................................................................... 101 Table C 10: (a) Average Torque (Nm) 1 Broken Bar ............................................................ 102 Table C 10: (b) Summary of two-way ANOVA with average torque as response variable (IMs with 1 broken bar) .................................................................................................................. 102 Table C 11: (a) Average Torque (Nm) 2 Broken Bars .......................................................... 102 Table C 11: (b) Summary of two-way ANOVA with average torque as response variable (IMs with 2 broken bars) ................................................................................................................ 102 Table C 12: (a) Average Torque (Nm) 3 Broken Bars .......................................................... 102 Table C 12: (b) Summary of two-way ANOVA with average torque as response variable (IMs with 3 broken bars) ................................................................................................................ 102 xii.

(15) Table C 13: (b) Summary of two-way ANOVA with torque ripple as response variable (healthy IMs) ........................................................................................................................................ 103 Table C 14: (a) Torque Ripple (%) 1 Broken Bar ................................................................. 103 Table C 14: (b) Summary of two-way ANOVA with torque ripple as response variable (IMs with 1 broken bar) .................................................................................................................. 103 Table C 15: (a) Torque Ripple (%) 2 Broken Bars ................................................................ 103 Table C 15: (b) Summary of two-way ANOVA with torque ripple as response variable (IMs with 2 broken bars) ................................................................................................................ 103 Table C 16: (a) Torque Ripple (%) 3 Broken Bars ................................................................ 104 Table C 16: (b) Summary of two-way ANOVA with torque ripple as response variable (IMs with 3 broken bars) ................................................................................................................ 104 Table C 17: (a) Efficiency (%) Healthy ................................................................................. 104 Table C 17: (b) Summary of two-way ANOVA with efficiency as response variable (healthy IMs) ........................................................................................................................................ 104 Table C 18: (a) Efficiency (%) 1 Broken Bar ........................................................................ 104 Table C 18: (b) Summary of two-way ANOVA with efficiency as response variable (IMs with 1 broken bars) ........................................................................................................................ 104 Table C 19: (a) Efficiency (%) 2 Broken Bars ...................................................................... 105 Table C 19: (b) Summary of two-way ANOVA with efficiency as response variable (IMs with 2 broken bars) ........................................................................................................................ 105 Table C 20: (a) Efficiency (%) 3 Broken Bars ...................................................................... 105 Table C 20: (b) Summary of two-way ANOVA with efficiency as response variable (IMs with 3 broken bars) ........................................................................................................................ 105 Table C 21: (a) Power Factor (pu) Healthy ........................................................................... 105 Table C 21: (b) Summary of two-way ANOVA with power factor as response variable (healthy IMs) ........................................................................................................................................ 105 Table C 30: (a) Power Factor (pu) 1 Broken Bar................................................................... 106 Table C 30: (b) Summary of two-way ANOVA with power factor as response variable (IMs with 1 broken bars (%) ........................................................................................................... 106 Table C 31: (a) Power Factor (pu) 2 Broken Bars ................................................................. 106 Table C 31: (b) Summary of two-way ANOVA with power factor as response variable (IMs with 2 broken bars) ................................................................................................................ 106 Table C 32: (a) Power Factor (pu) 3 Broken Bars ................................................................. 106 Table C 32: (b) Summary of two-way ANOVA with power factor as response variable (IMs with 3 broken bars) ................................................................................................................ 106. Table D 1: Quietest slot combinations for test motor (in increasing noise level order) ........ 107 Table D 2: Number of rotor slot and stator slot combination (skewed rotor slots) ............... 107. xiii.

(16) LIST OF SYMBOLS AND ABBRIVIATIONS Greek Letters ∇. Gradient operator. ∇×. Divergence operator. ∇.. Curl operator. 𝜌. Magnetic field strength (T). Roman Alphabets A. Magnetic vector potential (V.s/m). B. Magnetic field density (T). D. Magnetic field strength (T). J. Current density (A/m^2). B. Magnetic flux density (T). H. Magnetic field strength (T). I. Current (A). R. Resistance (Ω). T. Time (s). E. Electric field intensity (V/m). xiv.

(17) ABRIVIATIONS FEM. Finite element method. FEA. Finite element analysis. RMxprt. Rotating machine expert. 2D. Two dimensional. 3D. Three dimensional. IM. Induction machine. SCIM. Squirrel cage induction machine. AC. Alternating current. DC. Direct current. OD. Outer stator diameter. ID. Inner stator diameter. SD. Slot depth. LCD. Liquid crystal display. ANOVA. Analysis of variance. CAD. Computer aided design. MMF. Magneto-motive force. EMF. Electro-motive force. Tmax. Maximum torque. Tmin. Minimum torque. Tavg. Average torque. SS. Sum of squares. df. Degree of freedom. MS. Mean squares. F. Ratio of between-group and within-group variance. F-crit. Critical value of F-distribution. P-value. Probability of obtaining F-value (or more extreme) under the null hypothesis xv.

(18) g = number of groups ni = number of observations in a group i 𝑥̅ = average across all groups 𝑥̅𝑖𝑗 = jth observation in group i. xvi.

(19) CHAPTER 1 INTRODUCTION 1.1. Background. Induction machines are the most encountered in industry, especially the squirrel cage type. Over 80% of electrical motors used in industry are induction machines with squirrel cage type as the most popular. They are simple, robust, reliable and low in cost (Faiz & Ebrahimi, 2008, Thusi, 2009, Mehran, et al., 2012, Saied & Ali, 2013, Praveen & Isha, 2016 and Ouacktouk, et al., 2017) it is therefore not surprising to find them so popular in modern industrial applications. However, despite these advantages, three phase squirrel cage induction machines have this problem of rotor bar breakage. This fault may result from a wide range of causes (Ouacktouk, et al., 2017). Several theories have advanced for the root cause of this problem. However, none has gained worldwide acceptance. With the problem continuing to occur, it is best to identify a geometric design of rotor and stator that will give better performance during the occurrence of the fault. According to Petrovic (Petrovic, et al., 2010) and Vaimann (Vaimann, et al., 2014) efficiency, reliability, safety and low cost are some of the major characteristic of system applications with squirrel cage induction motor. It is because of these attributes that squirrel cage induction motors have gained so much popularity in industrial applications. However, despite these advantages, there is still room to improve the performance of three phase SCIMs, and this can be achieved through better design. The purpose of this research project is therefore to investigate the most optimal geometric design of SCIMs when rotor bars are broken. This work investigates the best rotor bar shape and stator slot opening with the view to find the best design or combination of designs that will improve the performance of squirrel cage induction machines under rotor bar breakage fault. The work will commence with a critical indepth literature review. The behavioural performance of the induction machine with different 1.

(20) geometric changes is studied through parameters like torque, toque ripple, airgap flux density, power factor and efficiency. Changes in the geometry of the machine’s rotor bar shape and stator slot opening is made in order to analyse the performance of the machine in order to realise the impact that these geometrical changes have on the performance of SCIMs. Changing the shape of the rotor bar results in changed rotor resistance and reactance; this in turn yields improved or decreased performance indexes such as starting torque and efficiency. It is a well-known fact deep rotor bars results in increased starting torque, unfortunately this rotor slot types increase the leakage flux which reduces the efficiency of the induction motor. It is therefore important to strike a balance when designing rotor bar shapes to ensure that high starting torque and efficiency are maintained (Lee, et al., 2017). Several researchers have studied the effect that rotor bars shape has on the performance of SCIMs, from this studies, it is evident that the shape of the rotor bars has an effect on the starting behaviour of the induction machine, particularly the starting torque and starting time (Young, 2015). The shape of the rotor is also reported to have a significant impact on the average torque as well as the efficiency of SCIMs, with focus being on the trapezoidal shape, pear shape and rounded rotor slots (Iqbal & Singh, 2014). Work has also been done on the effects that the geometry of the rotor slots have on the vibration in three-phase SCIM. In this instant the two (rectangular and round) rotor bar shapes with equal cross-sectional areas are compared and is realised that the rectangular shape experiences more vibration as a result of increased radial forces as compared to the round bar shape (Pao-Laor, et al., 2007). Stator slot opening also plays a significant role in the overall performance of SCIMs. The slotting effect is said to generate harmonic components in the airgap, this is why it is important to take into consideration the stator slot opening when designing three-phase induction machine (Jelassi, 2.

(21) et al., 2013). As reported by (Jelassi, et al., 2013), a good choice of the stator slot opening of a three-phase induction machine resulted in reduction of dynamic iron losses caused by flux density harmonics which will in turn yield a more efficient induction machine. Work on the influence that stator slot opening width has on the magnetic noise in three-phase induction machines has also been conducted, it is realised from this work that a wider stator slot opening can result in reduced magnetic noise if chosen properly (Le Besnerais, et al., 2009) which is a practice that is contrary to the common design rule of reducing rotor and stator slot opening width in order to reduce magnetic noise in three-phase IMs. Although the work done by these researchers is significant and adds value to the electrical machines design environment, it is worthwhile to investigate how the two design parameters (rotor bar shape and stator slot opening width) when selected properly can impact the performance of three-phase squirrel cage induction machines. This research work therefore investigates how these two specific design parameters will affect the overall performance of three-phase SCIMs under both healthy and broken rotor bar operating conditions. 1.2. Problem Statement. Squirrel cage induction machines are simple, robust, reliable and low in cost; it is therefore not surprising to find them so popular in today’s industrial applications. However, despite these listed advantages, three-phase squirrel cage induction machines have this problem of rotor bar breakage. This is one of the catastrophic failures in induction machines and its occurrence is more popular in large expensive induction machines driving high inertia loads taking them longer to start up (Panday, et al., 2012). The problem of rotor bar breakage in squirrel cage induction machines has been of interest to various researchers in the past and in recent years. However, previous work was aimed at. 3.

(22) developing detection methods, fault diagnosis and general performance analysis of SCIM with broken rotor bars (Thusi, 2009) and (Menacer, et al., 2009). Several literature studies have been published on improving induction machine performance through geometry re-design, with much focus on stator slot opening, stator and rotor bar shape and use of magnetic and non-magnetic wedges (Galido, et al., 2002, Salon, et al., 2002, Kappatou, et al., 2008, Madescu, et al., 2012 Appiah, et al., 2013 & Jelassi, et al., 2013). No work was dedicated to re-designing the geometry of the induction machine (particularly the rotor bar shape and stator slot opening) in view of enhancing the performance of SCIMs with the broken rotor bar fault. Therefore, this work is set to investigate how modification of rotor bar shape and stator slot opening width can better the performance of squirrel cage induction machines with broken rotor bars. The problem statement is therefore as follows: Due to a continuous occurrence of rotor bar breakage in three phase squirrel cage induction machines, there is a need to investigate the impact that rotor bar shape and stator slot opening have on the performance these induction machine types taking into account the rotor bar breakage fault. 1.3. Research Questions . What effect does the rotor bar shape and stator slot opening width have on the performance of three phase squirrel cage induction machine.. . How to develop a 2D Finite Element Model to analyse the performance of the three-phase SCIMs with different rotor bar shapes and stator slot opening width for both healthy and broken rotor bar operating conditions.. . How to qualify and quantify the effect that geometry modification has on the performance of a three phase SCIMs. 4.

(23) 1.4. Research Objectives . To analyse the effect of rotor bar shapes and stator slot opening widths on the performance of three phase squirrel cage induction machine.. . To analyse the performance of the SCIM using 2D Finite Element Analysis for both healthy and faulty operating conditions.. . To evaluate both qualitative and quantitative, the effect of geometry modification on the performance of a three phase SCIM using Analysis of Variance (ANOVA).. 1.5. Hypothesis. The geometric parameters of the rotor and stator have an impact on the performance of three phase squirrel cage induction machines (SCIMs). It is because of the interaction in the airgap of the magnetic fields of the two components (rotor and stator) that a torque that drives the load is produced. With geometric parameters altered, the magnetic field distribution will change therefore affecting the torque developed. Broken rotor bar fault also results in change in the rotor resistance, the rotor resistance is also changed as the rotor bar shape changes as a result of skin effect, resulting in variation of the electromagnetic torque and the starting performance of the motor. The stator slot opening width has an effect on the magnetic flux distribution in the airgap which therefore influences the performance of induction machines. Increasing or reducing the stator slot opening width will affect the magnetizing current which produces flux and electromagnetic torque, the correct choice of this geometric parameter is therefore important. 1.6. Delimitations of the study. This work deals with analysing the performance of three-phase squirrel cage induction machines taking into account changes in rotor bar shapes and stator slot opening widths. This analysis is done under both healthy and broken rotor bar operating conditions. The electromagnetic torque, torque ripple, efficiency and power factor are performance indexes that are analysed in this work.. 5.

(24) Both the static and dynamic analysis of the squirrel cage induction machines are carried out with Ansys Maxwell 2D FEM software under both healthy and faulty conditions. For broken rotor bar fault modelling, all broken rotor bars are adjacent. It is important to note that the following in relation to this study: . This work does not attempt to create an optimal design of this squirrel cage induction machine.. . Although FEM takes saturation effects into consideration, it is neglected in both static and dynamic analysis.. . The effects of space harmonics originating from the stator winding is neglected in the analysis.. 1.7. . Skewing is also neglected in this study.. . With regards to the analysis of variance (ANOVA), the tests are done without replication. Contributions. This work offers a significant contribution by analysing the impact that both the rotor bar shape as well as the stator slot opening width have on the performance of three phase SCIMs under healthy and broken rotor bar operation condition. The first contribution of this work is found in chapter 3 where the effect that different rotor bar shapes have on the performance of three-phase SCIMs is looked into, taking into account the broken rotor bar fault. The next contribution is found chapter 4, which addresses how both the rotor bar shape and stator slot opening widths affect the performance of three-phase SCIMs. With both research outputs, the torque and its torque ripple, efficiency and power factor were analysed. It is evident that changing the rotor bar shape as well as the stator slot opening width has a significant impact on the overall performance of three-phase SCIMs taking into account the. 6.

(25) broken rotor bar fault. The research outputs of this work are reported in the following conference proceeding. [1] E. Maloma, M. Muteba, D.V. Nicolae, "Effect of rotor bar shape on the performance of three phase induction motors with broken rotor bars", 2017 International Conference on Optimization of Electrical and Electronic Equipment (OPTIM) & 2017 Intl Aegean Conference on Electrical Machines and Power Electronics (ACEMP), pp. 364-369, Jul. 2017. [2] E. Makhetha, M. Muteba, D.V. Nicolae, " Effect of Rotor Bar Shape and Stator Slot Opening on the Performance of Three Phase Squirrel Cage Induction Motors with Broken Rotor Bars", 2019 South African Universities Power Engineering Conference (SAUPEC), Jan. 2019 1.8. Dissertation Outline. Chapter 2: In this chapter a detailed review of literature on three phase squirrel cage induction machines is presented. In-depth overview of rotor bar breakage fault in three phase squirrel cage induction machines is presented, supported by studies performed by other researchers. Also the effect of stator slot opening, magnetic wedges and rotor bar shapes on the performance of squirrel cage induction machines is studied. Chapter 3: In this chapter parameters and quantities used in simulating the three-phase induction machine are presented. The transient and steady state analysis of a three-phase SCIM before geometry modification is presented. This study is based on 36 stator slots and 33 rotor slots three phase, low voltage SCIM for both healthy and faulty conditions. Chapter 4: In this chapter the focus is improving the performance of the three phase induction machine by changing the rotor bar shapes as well as stator slot opening under both healthy and broken rotor bar conditions. The impact that these changes have on the overall performance of. 7.

(26) the machine are studied by looking at the following performance parameters; torque, torque ripple, power factor and efficiency. Chapter 5: This chapter deals with a method for evaluating both qualitative and quantitative, the effect of the rotor bar shape and stator slot opening on the performance of a three phase SCIMs. A two factor Analysis of Variance (ANOVA) is used to analyse the significance of the results obtained from the FEA. Chapter 6: In this chapter a conclusion on how different rotor bar shapes and stator slot opening widths impact the performance of three-phase SCIMs under healthy and faulty conditions is drawn based on the results presented in the previous three chapters. Recommendations that will be of benefit to electrical machines designers will also be highlighted as well as future work.. 8.

(27) CHAPTER 2 REVIEW OF THREE PHASE SQUIRREL CAGE INDUCTION MACHINES WITH BROKEN ROTOR BARS 2.1 Introduction Three phase Squirrel Cage Induction Machines are widely used induction machine types as modern industrial drives as a result of their reliability, efficiency and eased maintenance. Among widespread failures of induction machines, rotor bar breakage fault is one of the popular shortcomings of these three phase induction machines. This issue of broken rotor bar fault is not new and continues to occur, this is why many researchers have shown so much interest in this fault and are trying to find ways to address it. It will therefore be a great benefit to industry to find ways that SCIMs can be designed with the broken rotor bar fault in mind, such that the motor continues to operate efficiently even under broken rotor bar fault conditions. In this chapter a detailed review of literature on three phase squirrel cage induction machines is presented. In-depth overview of rotor bar breakage fault in three phase squirrel cage induction machines is presented, supported by studies performed by other researchers. Also the effect of stator slot opening, rotor bar shapes on the performance of squirrel cage induction machines is looked into. 2.2 Induction Machines with Broken Rotor Bars In the past various researchers have shown interest in squirrel cage induction machine faults especially rotor bar breakage. Some have used finite element method to analyse different aspects of a three phase squirrel cage induction machine with broken rotor bars, some chose to use less accurate methods as compared to finite element method, in fear of its long computational time due to its complexity.. 9.

(28) Interest has also been shown in improving the performance of squirrel cage induction machines through redesigning of the rotor and stator geometry. It therefore makes sense to combine the two and find how performance can be improved through rotor and stator redesign during the occurrence of the inevitable rotor bar breakage. In order to address this problem, it is necessary to understand the construction of these IM types as well as their principle of operation. 2.3 Three Phase Squirrel Cage Induction Machine Construction To understand the fault occurrence in squirrel cage induction motors, one has to fully understand the construction of this induction machine types. Induction machines are categorised into two types which are defined by their rotor types, these are the squirrel cage induction motors and the wound rotor induction motors. Like other induction machines, squirrel cage induction motor has two main components which are the stator and the rotor. Its stator is similar to that of other induction machines. It is the rotor of this machine that separates it from the rest and this part of the machine is of interest to us. The rotor consists of longitudinal bars that are usually made of aluminium or copper. These conductive bars are short-circuited on both ends with rings forming a cage-like shape. The bars are therefore electrically connected by the two short-circuit rings, also known as end-rings. The name ‘Squirrel Cage’ is derived from the appearance similarity of these end-rings and bars to a rodent exercising wheel from over a century ago. The rotor core is built by stacking thin insulated steel laminations sheets through which rotor slots are punched to place the rotor bars. The bars go through the slots and are welded or brazed onto the end-rings. The rotor is then placed in the middle of a stator whose supply will is connected to the three phases of the grid (Keljik, 2009, Bishop, 2003, Karmakar, et al., 2016). The squirrel cage rotor can be described as the secondary winding because there is no direct connection between the cage and the supply. Its electrical power is obtained through induction 10.

(29) like a secondary winding of a transformer from the flux produced by the stator winding, which in this case is similar to the primary winding of a transformer. The electromotive force (EMF) is induced into each rotor bar because of current induced in these bars (Bonnet, 2008). The principle of operation of induction machines is based on the fact that , when placing a current carrying conductor in a magnetic field , that conductor will have a force exerted on it and that force is propotional to the current flowing in the conductor and the strength of the magnetic field. With induction machines three single phase windings in stator slots carry three currents that are electrically placed 120 degrees apart from each other. Because of these currents, a rotating magnetic field results. This field moves around the stator at a speed (synchronous speed) dependent of the number of poles of the machine and the fundamental frequency. The rotating magnetic field will cut through the rotor bars, inducing a voltage in these bars resulting in the generation of a magnetic field in the rotor core. The reaction between the stator magnetic field and rotor magnetic field results in a torque that causes rotation of the rotor and the shaft, upon which different loads can be coupled and driven (Keljik, 2009). 2.4 Broken Rotor Bar Fault Among other squirrel cage induction machine parts, its rotor is the most stressed component (Leon, 2007). This stress is associated with a summary of forces found in a rotor assembly. It is reported that rotor structure (rotor bars and end-ring) failure accounts for about 5-10% of induction machine failures (Alexandru-Ionel & Virgiliu, 2017, Praveen & Isha, 2016, Karmakar, et al., 2016, Thusi, 2009, Faiz, et al., 2007 and Haji & Toliyat, 2001). The structure of a squirrel cage induction machine is subjected to undesirable electrical and mechanical conditions. These conditions include thermal and electrical overload, excessive vibration caused by the imbalance in the supply voltage, load variation and frequent starts and. 11.

(30) stops of the induction motor which extremely stresses the motor because of the excessive startup current (Faiz, et al., 2007 and Praveen & Isha, 2016). As reported by (Hammadi, 2000) and (Bonnett, 2000), a major part of rotor failures is caused by different forces acting on the rotor assembly. Table 2.1 below shows a summary of stresses found in the rotor assembly. Table 2. 1: Stresses Found in Rotor Assembly.  Thermal Overload Thermal Unbalance Excessive Rotor Losses Hot Spots Sparking  Magnetic Rotor Pullover Noise Vibration Off Magnetic Centre Saturation of Lamination Circulating Currents  Residual Stress Concentrations Uneven Bar Stress  Dynamic Vibration Rotor Rub Over-speeding Cyclic Stresses Centrifugal Stresses.  Contamination Abrasion Foreign Particles Restricted Ventilation Excessive Ambient Temperature  Mechanical Casting Variations Loose Laminations Incorrect Shaft/Core fit Fatigue or Part Breakage Poor Rotor to Stator Geometry Material Deviations  Other Misapplications Poor Design Practices Manufacturing Variation Loose Bars, Core Transient Torques Wrong Direction of Rotation. The squirrel cage induction machine is said to have broken rotor bar fault when one or more of its bars are completely broken or partially broken (Karmakar, et al., 2016). According to (Karmakar, et al., 2016), when one of the rotor bars breaks, the nearby bars will carry more current than usual which will lead to thermal and mechanical stress in these neighbouring bars leading to further propagation of the fault. Partial or complete rotor bar breakage is likely to occur on different positions of the bar, either along the length of the bar or at the joint of the rotor bar and the end-ring. The breakage at the 12.

(31) joint is mainly because of the poor brazing of the bar on to the end-ring, another reason for bar breakage at this point is that this is regarded the weakest point of the rotor cage or the weakest mechanical point on the rotor cage that is more prone to failure (Thusi, 2009). According to (Haji & Toliyat, 2001) the joint between rotor bars and end ring are the critical locations where the cracks are most likely to occur. This is because the accelerating and braking forces that the rotor bars provide on the end ring when the speed of the induction motor changes. When rotor bars break, they do not immediately cause the induction machine to fail but instead they affect the overall performance of the induction machine. The rotor bar breakage fault results in the following problems; reduced starting torque, stressed neighbouring bars and increased rotor temperature to name a few. If operation of the machine is continued without repairing the machine, more bars are likely to break and eventually the machine will completely fail (Leon, 2007). (Juneghani, et al., 2012) State that the important reason behind the breakage of rotor bars is the rotor slot linkage flux caused by rotor current; this current generates electrodynamic force. This force tends to reposition the bars in a radial direction between the top and bottom of the slot. The forces also causes the bar to vibrate at twice the rotor current frequency, causing a bending stress in the bars leading to eventual breakage of the bar. 2.5 Causes of Rotor Bar Breakage in Squirrel Cage Induction Machines As mentioned earlier, there are several factors responsible for rotor bar breakage in squirrel cage induction machines. These factors include mechanical forces, electromagnetic forces, centrifugal forces, environmental stresses, frequent motor starts and many more. Below some of these factors are discussed (Juneghani, et al., 2012) :. 13.

(32) 2.5.1 Frequently starting a squirrel cage induction motor A squirrel cage induction motor with multiple starts and stops or one that is operated under various load conditions is likely to experience the problem of broken rotor bars (Maruthi & Hegde, 2013) and (Thusi, 2009). When starting a motor, it experiences significantly high values of current flowing through its rotor cage. These high currents generate a massive amount of temperature in the bars and endrings which may results in minor deformations in the rotor bars and end-rings. According to (Thusi, 2009), “frequently starting the motor places the heavy stress on the rotor bars because the bars tend to carry the highest current as the motor is running at a speed lower than its synchronous speed.” Each time a squirrel cage induction machine is started, the current in the rotor bars shoots ‘sky high’, this generates a tremendous amount of heat that is absorbed by both the rotor bars and the rotor core. The longer the machine takes to come to speed, this heat measured in watts is further generated. If the rotor bars become too hot, they become more brittle hence are easily broken (Thusi, 2009) and (Penrose, 2006). For this reason, manufacturers have specified a limited number of starts for each induction machine depending on their different sizes. With squirrel cage induction machines, the ends of the bars and the end-ring are separated from the core and are therefore exposed to various stresses and mechanical forces during every direct on line starting. If the driven load has high inertia (centrifugal fans, grinders, refiners, etc.), the thermal stresses will increase significantly because of high starting current that is present in the bars for longer. With high inertia loads, a long acceleration period is required before the motor reaches the required operating speed resulting in extended presence of high starting current present in rotor. 14.

(33) bars. This will lead to breakage of the brazed or welded joints of the bars and the end-rings (Stone, et al., 2009). 2.5.2 Manufacturing defects Induction machines are constantly faced with unavoidable manufacturing defects; poor brazing or welding of the bar onto the end ring results in a weak joint. A weak joint along with the heating of the bar and large centrifugal forces can result in a cracked bar. Another cause of broken rotor bars due to manufacturing defects is loose rotor bars; rotor bars that are loose in the rotor core also place excessive stress on the end-ring joint. All these issues combined lead to cracking in the bars, these cracks usually propagate leading to complete rotor bar breakage. It is therefore not surprising to find the occurrence of this fault in squirrel cage induction motors (Thusi, 2009). During rotor manufacturing process, specifically the pressure die-casting of the squirrel cage, in cases where grease and oil are used as lubricants for the casting moulds, use of too much or wrong type of lubricant will produce a gas that will in turn produce holes in both the bars and the short-circuit rings. This is called a ‘Swiss Cheese’ effect. This effect results in high rotor resistance, hot spots in the rotor, unbalanced rotors and other possible defects. Another manufacturing process concern is the temperature of the molten aluminium or copper. A very high temperature will lead to excessive shrinking during the cooling process; and this will result in high stresses in the bar. These stresses will lead to possible bar breakage during motor operation. On the other hand, a very low molten temperature will result in molten material that solidifies before the die-casting process is complete (Toliyat & Klimanv, 2004).. 15.

(34) 2.5.3 Interbar currents Another issue that is worth noting with rotor bar breakage is the inter-laminar currents, often referred to as inter-bar currents (Sizov, et al., 2009). This inter-bar current phenomenon occurs when the current continues to flow in a broken rotor bar. The current enters the bar from the end that is intact and flows along the bar length, leaving the bar through the core into the adjacent healthy bars. This usually results in lamination burning due to high resistance particularly where the current enters the lamination. It is therefore concluded that there is a relationship between these current and overheating, with thermal stress considered one of the major contributors to rotor bar breakage (du Preez, 2006, Penrose, 2006 and Thusi, 2009). It is reported by (Thusi, 2009) that a crack in a rotor bar results in increase resistance which will cause the bar to overheat therefore worsening the crack. The neighbouring bars will have increased current as a result of reduced current in the faulty rotor bar. With rotor bars broken, inter-bar currents will flow in the laminated core, this is very common in large squirrel cage induction machines. 2.6 Effects of Stator Slot Opening and Magnetic Wedges on performance of IMs The presence of the stator slot opening in an induction machine stator is to allow windings to be inserted in the slots, it is therefore necessary to ensure that the size of this openings allows easy insertion of windings while not compromising the performance of the machine (Appiah, et al., 2013). It is because of their effect on magnetic flux distribution that the slot opening have an influence on the performance of the machine. In (Appiah, et al., 2013) the authors used the field analysis method as well as finite element method to analyse the effect that stator slot opening has on the performance of a six phase, two pole induction machine. For the finite element analysis, both the no-load and loaded conditions were analysed. The analysis was also backed up with an experimental study on a 1.5kW with the. 16.

(35) conventional stator slot opening with the aim of validating the computational method. From the results it was evident that reducing the stator slot opening resulted in a better performance of the machine. As reported by (Jelassi, et al., 2013) harmonic components that exist in the airgap are as a result of the slotting effect. In their work, they determine ways to calculate dynamic iron loss taking into consideration the slotting effect. The purpose of their work is to find an optimal design of IM slots, particularly the best slot opening choice in order to improve the efficiency of the machine by reducing dynamic iron losses. From their study, they concluded that the effect that rotor and stator opening have on iron losses cannot be ignored especially during the design of induction machines with the aim of reducing flux density harmonics and overall iron losses. In (Le Besnerais & Souron, 2016), the effect of stator magnetic wedges in vibration and noise of squirrel cage induction machines is studied. According to the authors, it is essential to make use of magnetic wedges that reduce the slotting effect in induction machines, it is this effect that results in increased noise and vibration in squirrel cage induction machines. The authors also concluded based on the review of the effect of magnetic wedges in induction machines that the use of the stator slot wedges will result in a better performance on the motor due to the following reasons: . Reduced magnitude of the airgap stator slotting harmonic.. . Reduced induction machine harmonic torques.. . Reduced rotor magnetic losses and stator eddy currents.. . Reduced losses on the stator tooth that are caused by low flux pulsations.. . Reduced stator current slotting harmonics.. . Increased motor efficiency as a result of loss reduction.. . Increased leakage inductance in the stator slot. 17.

(36) Use of stator slot magnetic wedges is an effective way of reducing magnetic field slot ripple harmonics, these harmonic components are of interest because they play a role in increasing losses, vibration and noise in induction machines which in turn reduces the efficiency of the machine (Mikami, et al., 1997). In their work (Mikami, et al., 1997) made use on 2D finite element method to study the effect magnetic wedges in a three phase squirrel cage induction machine in terms of slot ripple harmonics. From the results, it is evident that using stator magnetic wedges results in a reduction of the amplitude of the stator slot ripple harmonic components, reduced no-load current and increased motor efficiency. 2.7 Different Rotor Bars There are various rotor slot shapes available and these depend upon the starting and rated load specifications, voltage/frequency (V/f) supply operation and the torque range. The rotor slot shape can be semi-closed, rectangular deep bar, rounded trapezoidal slots with rectangular teeth or completely closed rotor slots. Fig. 2.1 shows typical rotor bar shapes that are used in IM as illustrated in (Boldea & Nasar, 2009). The choice of the shape will therefore depend on the size of the motor and its application. Semiclosed slots can be used for high efficiency induction machines with low power at constant V/f. The round semi-closed slots can be used for variable V/f. As for the rounded trapezoidal slots with rectangular teeth are typically used in small induction machines for medium starting torque. Completely closed rotor slots are used mainly in low power applications for noise reduction and reduction of torque oscillations. For very high starting torque and high rated slip, the rectangular deep bar rotor slots are used (Boldea & Nasar, 2009).. 18.

(37) (a). (b). (c). (d). (e). (f). Figure 2.1:Typical Rotor Bar Types (a) Rectangular, (b) Double cage, (c) Conventional (semi closed), (d) Trapezoidal, (e) Conventional (fully closed) and (f) Round. Fig. 2.1 Rotor Bar Shapes (a) Bar 1, (b) Bar 2, (c) Bar 3, (d) Bar 4, (e) Bar 5 and (f) Bar 6 The rotor bar shape has direct influence on the performance of squirrel cage induction machines. By varying the geometric parameters of the rotor, different torque-speed curves can be achieved, the design of rotor bars particularly have a significant impact on the starting behaviour of an induction machine, for example, choosing a particular rotor bar design can lead to increased starting torque, reduced starting current which will reduce the efficiency as a result of a greater slip (Gyftakis, et al., 2010). A particular rotor bar shape can be selected to suit a given application, for example use of large rotor bars result in reduced rotor resistance which in turn yields reduced starting torque. According to (Gyftakis, et al., 2010), rotor bar variables (rotor bar depth, rotor bar width, rotor bar bottom shape and rotor slot opening width) can be optimized in order to better the performance of SCIMs. These authors applied FEM software to model and analyse the behaviour of this induction machine by optimising the motor’s starting behaviour, output power and efficiency. From the results, it is evident that finding an optimal rotor slot can yield an improved efficiency, starting torque and output mechanical power. A study by (Galindo, et al., 2002) shows how rotor slots can be redesigned in order to improve the performance of squirrel cage induction motors and this can be achieved using computing tools based on numerical analysis. In this study the authors modified the geometrical parameters of the rotor slot until an optimal performance of the motor is achieved. Galindo and his colleagues 19.

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