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RELIABILITY BASED MULTI-OBJECTIVE DESIGN OPTIMIZATION FOR SWITCHED RELUCTANCE MACHINES A Dissertation Presented to The Graduate Faculty of the University of Akron In Partial Fulfillment of the Requirements of the Degree Doctor of Philosophy Lavanya Vadamodala March 2021 RELIABILITY BASED MULTI-OBJECTIVE DESIGN OPTIMIZATION FOR SWITCHED RELUCTANCE MACHINES Lavanya Vadamodala Dissertation Approved: Accepted: _____________________________ _____________________________ Advisor Department Chair Dr. Yilmaz Sozer Dr. Robert Veillette _____________________________ _____________________________ Committee Member Interim Dean of the College Dr. Alexis De Abreu Gracia Dr.

Craig Menzemer _____________________________ _____________________________ Committee Member Dean of the Graduate School Dr. Malik Elbuluk Dr. Marnie Saunders _____________________________ _____________________________ Committee Member Date Dr. Nao Mimoto _____________________________ Committee Member Dr.

Dane Quinn ii ABSTRACT In this thesis, a numerical model is developed for estimating the reliability of a Switched Reluctance Machine (SRM), and is then used in its design optimization. SRM design optimization is performed using the multi-objective surrogate optimization method. The multi-objective surrogate optimization method is chosen because of its ability to find a global solution within a given number of function evaluations. In this study, optimization considers reliability as one of the objectives or constraints to obtain an optimal design with high reliability.

The optimum design should operate for the target lifetime (20000 hours) before maintenance or complete replacement. Since optimization using 2D FEA is slow, a modified analytical model is developed to more quickly obtain a suitable design. This model predicts flux linkage and torque for a given phase current and rotor position with minimum error. Tapering in the stator and rotor poles is introduced in addition to traditional rectangular poles to reduce the error in predicting flux linkage and torque at unaligned and partially aligned positions.

An improved BH curve model with a knee adjustment factor is used to predict the magnetic characteristics of steel used in the machine. Assumptions and detailed derivation of models to estimate flux linkage, co-energy, and torque are included. Reliability is defined as the probability of a component or system operating for a given time. The probability of a component to operate is calculated based on its failure rate.

The failure rate of the machine is obtained as the combination of the machine's base failure rate and the failure rate of the windings, rotor, and shaft. The reliability of the machine is obtained using state transition diagrams associated with the Markov model under normal iii and fault conditions. Along with the machine's reliability, Mean Time to Failure (MTTF) is also predicted for all operating conditions. Using the developed analytical and reliability models for SRM, optimization is performed in two stages.

In first stage, sensitivity analysis is performed using the Taguchi methodology, where the sensitivity of objectives to change in each independent variable is calculated. Based on this, sensitive and non-sensitive variables are identified. In second stage, optimization using the multi-objective surrogate optimization method is carried out. Both single and double-level optimization methods are performed to look at the advantages and disadvantages of the optimization methods and optimum designs obtained based on the number of iterations and design performance.

In this thesis, the reliability models are developed for a 32 kW SRM. This machine's target application is Front End Motor Generator (FEMG) to drive engine accessories in an electric truck. The optimum design obtained for the 32 kW SRM is verified with Finite Element Analysis (FEA), and the prototype is built. The performance of the machine is validated using experimental results from the testing of the prototype.

The failure factor and MTTF are calculated using measurements. It was found that there is good agreement between predictions from simulation and experimental measurements. iv ACKNOWLEDGMENTS I will be forever grateful to the single most influential person in my academic and professional journey, Dr. Yilmaz Sozer, my Professor, Advisor, Supervisor, and Mentor.

This thesis would not have been possible without his continuous teaching, guidance, and mentoring. He is a very patient, passionate, and caring human being who always ensured that I have everything I need to complete my graduate studies. I am grateful to my professors, Dr. Malik Elbuluk, Dr.

Alexis De Abreu Garcia, and Dr. Robert Veillette, for their help and guidance during my studies at the University of Akron. I would also like to thank my committee members for their valuable comments and suggestions to improve the dissertation's quality. I am thankful to Dr.

Nao Mimoto and Dr. Dane Quinn for their valuable inputs, comments, and suggestions that improved my research and my dissertation's quality. I want to thank Bendix Commercial Vehicle Systems for funding this research. I especially thank Fernando Venegas, David Colavincenzo, and Jeffery Geither for their profound insights throughout my research.

I would like to thank my colleagues at the Alternative Energy Laboratory for their support and for creating a healthy and enjoyable learning atmosphere during our work. Finally, I would like to thank my Mom, Dad, and Sister for their unconditional love, support, and encouragement all the time. v TABLE OF CONTENTS Page LIST OF TABLES. xi LIST OF FIGURES.

Research motivation and objectives. Reliability formulation and estimation .Factors effecting the reliability of electric machines .Prediction of reliability of Electric motor. Design of SRM .Modeling of SRM .Optimization of SRM. ANALYTICAL MODELING OF SRM.

Difference between Modified and Arthur Radun’s analytical models .Flux linkage when Rotor/Stator poles overlap.Calculation of Energy and Torque. Reliability for Electric Machines. Failure modes of SRM. Reliability and Mean Time to Failure (MTTF).

Failure rate models .Failure rate model for windings. Current differential multiplying factor. Current density multiplying factor. Altitude multiplying factor .Failure rate model for rotor.

Torque ripple multiplying factor. Net radial force multiplying factor .Reliability prediction for SRM. Fault occurrence only in stator. Fault occurrence only in rotor.

Fault occurrence in both stator and rotor. RELIABILITY BASED MULTI-OBJECTIVE DESIGN OPTIMIZATION. Design parameters and limits. Stator and rotor pole angle selection.

Lamination’s material selection. Winding, Number of turns, and stator pole height. Signal to Noise ratio. Multi-level design optimization.

Key terms in surrogate optimization. Construct surrogate model. Search for minimum. Comparison of optimum designs.

PERFORMANCE AND FAILURE RATE PREDICTION. Verification of Modified Analytical model .Finite Element Analysis (FEA). Performance verification of SRM under Normal and Fault conditions .Performance verification under Normal conditions. Finite Element Analysis (FEA) .Performance verification under Normal and Fault conditions .1 Finite Element Analysis (FEA).

Fault occurrence only in the stator. Fault occurrence only in the rotor. Fault occurrence in both the stator and the rotor .3 Comparison of Failure rate and Mean Time to Failure (MTTF). SUMMARY AND FUTURE WORK .172 x LIST OF TABLES Table Page 4.

Stator failure modes and system status. Winding faults and states. Rotor failure modes and system status. Elements and their values of matrix A for fault in rotor.

Endurance states and corresponding failure modes for fault in stator and rotor. Failed states and corresponding failure modes for fault in stator and rotor. Non-zero elements of state transition intensity matrix A and their values. Estimated Quantities of experiments.

Experimental Performance comparison. Quantities for failure rate estimation at 2000 rpm, 87 Nm under stator faults. Multiplying factors and failure rates at 2000 rpm, 87 Nm under stator faults. Quantities for failure rate estimation at 3500 rpm, 87 Nm under stator faults.

Multiplying factors and failure rates at 3500 rpm, 87 Nm under stator faults. MTTF comparison for fault occurrence in stator. Quantities for failure rate estimation at 2000 rpm, 87 Nm under rotor faults. Multiplying factors and failure rates at 2000 rpm, 87 Nm under rotor faults.

Quantities for failure rate estimation at 3500 rpm, 87 Nm under rotor faults. Multiplying factors and failure rates at 3500 rpm, 87 Nm under rotor faults. MTTF comparison for fault occurrence in rotor. MTTF comparison for fault occurrence in both stator and rotor.

Quantities for failure rate estimation at 500 rpm, 87 Nm. Multiplying factors and failure rates at 500 rpm, 87 Nm. Quantities for failure rate estimation at 1000 rpm, 87 Nm. Multiplying factors and failure rates at 1000 rpm, 87 Nm.

Quantities for failure rate estimation at 1000 rpm, 40 Nm under stator faults. Multiplying factors and failure rates at 1000 rpm, 40 Nm under stator faults. Quantities for failure rate estimation at 2500 rpm, 40 Nm under stator faults. Multiplying factors and failure rates at 2500 rpm, 40 Nm under stator faults.

Quantities for failure rate estimation at 3500 rpm, 40 Nm under stator faults. Multiplying factors and failure rates at 3500 rpm, 40 Nm under stator faults. MTTF comparison for fault occurrence in stator at different operating points .166 xii LIST OF FIGURES Figure Page 1. Types of electric machines.

Failure rate by EPRI. Failure rate by IEEE. Fault detection and diagnosis. Snapshot of motor drive Markov reliability model [27].

Reliability over time [31]. Power converter for SRM [32]. Markov models under dynamic analysis. Reliability curves for four reliability model for DLSR system [36].

System reliability model [37]. System to estimate reliability of electric machines [39]. Structure of the control loop with additional blocks for the reliability-based lifetime prediction and optimization [40]. Pole shapes considered by Modified and Arthur Radun’s analytical models.

BH curves comparison. Error in the prediction of B from Arthur Radun’s and Modified models. SRM with poles overlap and Contours for phase A. Section of SRM with main and fringing flux.

Triangle approximation for stator pole height. Magnified stator pole. Triangle approximation for rotor pole height. Area of pole overlap.

Area of pole with no overlap. Different faults in windings of SRM. Current differential multiplying factor. Current density multiplying factor.

Torque ripple multiplying factor. Net radial force multiplying factor. Reliability block diagram. Reliability block diagram for fault occurrence in stator.

State transition diagram for fault occurrence in stator. Reliability block diagram for fault occurrence in rotor. State transition diagram for fault occurrence in rotor. State transition diagram for fault occurrence in stator and rotor.

A systematic procedure to obtain an optimum design. Torque-Speed-Power curves for the target application. SRM design parameters. Feasible triangle for 18/12 machine with the first condition as βs< βr, second 360 3600 condition as 𝑁 − 𝛽𝑟 > 𝛽𝑠 , and third condition as 𝑚𝑖𝑛(𝛽𝑠 , 𝛽𝑟 ) > 𝑁𝑠.

B-H characteristics of M19 steel. Flowchart for sensitivity analysis. Factor and average effect for electromagnetic torque. Factor and average effect for phase RMS current.

Factor and average effect for current density. Factor and average effect for failure factor. SNR Average for outputs. Surrogate optimization procedure.

Single-level Optimization: Method A- Scatter plots showing Torque and Phase RMS current on x-y axis and objective function, current density, failure factor on color bar. Single-level Optimization: Method B- Scatter plots showing Torque and Phase RMS current on x-y axis and objective function, current density, failure factor on color bar. Double-level Optimization: Level 1- Scatter plots showing Torque and Phase current on x-y axis and objective function, current density on color bar. Double-level Optimization: Level 2- Scatter plots showing Torque and Phase current on x-y axis and objective function, current density, failure factor on color bar.

Comparison of optimization methods based on failure factor, efficiency, and number of iterations. Three phase currents of Single-level optimization: Method A and B, and Double- level optimization designs. Flux linkage comparison at different positions for one phase. Torque comparison at different current levels for one phase.

Flux linkage profiles comparison for Modified, AR, and FEA models. Torque profiles comparison for Modified, AR, and FEA models. Phase current from Modified, AR, and FEA models at 500 rpm .