The student will be able to: • explain the main electromagnetic, magnetic material and electromechanical conversion principles used in electrical machines; • interpret the technological and performance specifications of electrical machines for mechatronic applications; • compare DC, induction and permanent magnet machines with respect to torque density, efficiency, controllability, thermal limits and application suitability; • formulate and use steady-state and dynamic models of electrical machines in electrical drive applications; • derive and use the dq model of permanent magnet machines, including torque production, saliency effects and voltage/current limits; • analyse the interaction between machine, inverter and mechanical load in variable-speed drives; • evaluate torque-speed characteristics, efficiency maps, duty cycles and field-weakening operation for traction and robotic applications; • perform a preliminary sizing and design of a permanent magnet motor starting from application specifications; • use simulation tools to validate machine-drive models and to support design choices; • prepare and present a technical design report with assumptions, calculations, results and critical discussion.

Students are expected to have basic knowledge of electrical engineering, electromagnetic fields, and numerical methods. Familiarity with scientific computing and simulation tools, such as MATLAB or equivalent environments, is also useful. A previous introductory course on electrical machines is helpful but not mandatory, since the required fundamentals are recalled at the beginning of the course.

1. Electromagnetic fields and electromechanical energy conversion fundamentals for electrical machines (6 hours of theory + 3 hours of exercises) Flux density, field strength, flux linkage, electromotive force, Lorentz force and Maxwell stress interpretation. Magnetic materials, B-H characteristics, saturation, hysteresis and eddy-current losses. Electrical losses in windings and basic thermal considerations. Energy and co-energy concepts. Torque production in electrical machines. 2. Reference machines and steady-state characteristics (6 hours of theory + 3 hours of exercises) DC motor as an introductory reference for torque-speed characteristics, voltage control and current control. Three-phase induction motor: rotating field, equivalent circuit, slip, mechanical characteristic and speed regulation by frequency control. Comparison between induction machines and permanent magnet machines for mechatronic applications. 3. Permanent magnet machines: principles and topologies (9 hours of theory + 3 hours of exercises) Permanent magnet excitation and brushless torque production. Surface-mounted PM machines, inset PM machines and interior PM machines. Radial-flux and axial-flux layouts. Concentrated and distributed windings. Sinusoidal and trapezoidal back-EMF. Saliency, reluctance torque and flux barriers. Main advantages and limitations of PM machines in traction and robotic systems. 4. Performance metrics for traction and robotic actuation (6 hours of theory + 3 hours of exercises) Rated, peak and continuous torque. Torque density, power density, specific power, efficiency, overload capability, torque ripple, cogging torque, inertia, acceleration capability, dynamic response, acoustic noise and vibration. Thermal classes, duty cycles, cooling assumptions and short-time operation. Torque-speed and power-speed envelopes for vehicle traction and servo/robotic axes. Vehicle traction load profiles and robotic actuator load profiles. Efficiency-map use and simplified loss models. 5. Reference-frame transformations and dynamic modelling (6 hours of theory + 3 hours of simulations) Three-phase to two-phase transformation (Clarke transformation). Stationary and rotating reference frames (Park transformation). Dynamic equations of AC machines. dq model of permanent magnet machines. Electromagnetic torque equation for SPM and IPM machines. Mechanical equation, load coupling and state-space/block-diagram representation for simulation. 6. Inverter-fed PM motor drives (3 hours of simulations) Voltage source inverter structure. Six-step and PWM operation. Current control principles. Voltage and current limits. Torque control of PM machines. Maximum torque per ampere operation. Field weakening and maximum torque per voltage operation. Effects of inverter non-idealities on machine performance. 7. Design-oriented simulation (6 hours of theory + 3 hours of simulations) Principles of Magnetostatic Finite-Element-Analysis. Introduction to FEMM and SyR-e. Guided FEA simulation of torque and flux map characteristics using the SyR-e platform in Matlab. 8. Preliminary design of permanent magnet machines (6 hours of theory + 3 hours of design laboratory) From specifications to motor requirements: speed, torque, power, voltage, current, duty cycle, cooling and packaging constraints. Selection of topology and pole-slot combination. Preliminary electromagnetic sizing: air-gap diameter and length, current loading, magnetic loading, winding factor, number of turns and base speed. Magnet selection, demagnetization considerations, saliency and mechanical speed limits. Introduction to finite-element verification and design iterations. FEA characterisation of the selected design. 9. Final project workshops (6 hours of project laboratory) Guided project sessions on the preliminary design of a permanent magnet motor from assigned specifications. Definition of assumptions, analytical sizing, operating envelope, simplified thermal check, dynamic model setup, simulation results and preparation of the final technical report. Total: 80 hours.

The course includes lectures, numerical exercises, and application-oriented activities based on simplified models of permanent magnet machines. The course includes lectures, numerical exercises, and application-oriented activities based on simplified models of permanent magnet machines. Simulation activities cover: - circuital models of electrical machines for dynamic simulation - FEA models for performance evaluation and electric motor characterisation Case studies may address, for example, urban electric traction, light electric vehicles, or robotic actuation systems. Each group works on assigned specifications and develops a preliminary machine design consistent with the stated constraints. A significant part of the course assesment is devoted to a group design project carried out by teams of 2–3 students.

Lecture notes available on the “Portale della Didattica”. Datasheet of electric motors. Excerpts of books and additional references will be indicated by the instructors. SyR-e platform for preliminary design and simulation (https://github.com/SyR-e)

Lecture slides; Exercises; Exercise with solutions ; Video lectures (current year); Simulation tools;

You can take this exam before attending the course

Exam: Written test; Compulsory oral exam;

The exam consists of compulsory written and oral tests. The oral test focuses on the presentation of the final project. • Written test: theoretical and numerical questions. 45 minutes. (maximum score 20/30) • Final project: preliminary design of a permanent magnet motor from assigned specifications, including technical report and short presentation, made individually or in teams of 2-3 members. (maximum score 13/20) The written test may include multiple-choice questions, short open questions and numerical exercises. During the written test, the use of books, notes or electronic material is not allowed unless explicitly authorized by the professor. The test includes: - 2 multiple-answer quizzes (2 points each if right, -0.67 points if wrong) - 2 numerical quizzes (4 points each) - 2 open quizzes (4 points) Maximum score is 20. Admission to oral with scores >= 12. The project is evaluated based on correctness of assumptions, consistency of calculations, quality of the motor model, interpretation of results, technical justification of design choices and clarity of the final report. For the project, students may use the course material and simulation tools, but the submitted work must clearly report all assumptions and must be original. For team works, the final score will be individual (may be different for the members of the same team). ------------------------------------------------------------------------------------ Example project breifs: Electric traction motor - Design a permanent magnet motor for a light electric vehicle traction application. Given the DC bus voltage, wheel speed range, gearbox ratio, peak torque requirement, continuous power requirement and cooling assumption, select a suitable PM topology and produce a preliminary electromagnetic design. Estimate the torque-speed envelope, base speed, field-weakening capability and main design trade-offs. Robotic joint actuator - Design a compact permanent magnet motor for a robotic joint. Given peak torque, continuous torque, maximum speed, inertia limit, external diameter limit and duty cycle, select a motor topology and perform a preliminary sizing. Evaluate torque density, current requirement, thermal feasibility and dynamic response. Discuss the trade-off between torque density, inertia, cooling and controllability. Electric compressor or high-speed actuator - Design a high-speed permanent magnet motor for an electric compressor or similar mechatronic load. Given power, maximum speed, supply voltage, cooling condition and packaging constraints, define the preliminary motor dimensions and winding data. Discuss voltage limit, mechanical speed limit, losses, magnet retention and field-weakening requirements.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.