Looking for a quick, guided introduction to electromagnetic coil modeling with the COMSOL Multiphysics® software and the AC/DC Module? We put together a series of video lectures that walk you through the modeling of electromagnetic coils, designed to show the key aspects of building such models. Let’s quickly review what’s in these videos and how to use the series to your best advantage!

### Getting Started with Modeling Electromagnetic Coils

The simplest electromagnetic coil is a single turn of current-carrying wire, as you’ll see in almost any introduction to the topic. It’s often a reasonable engineering simplification to assume that the coil can be treated as a closed loop, meaning that it is axisymmetric, or invariant around the centerline.

*A simple one-turn coil can also be modeled using a 2D axisymmetric assumption.*

It is with this assumption that our coil modeling lecture series begins. The first session contains five videos in which we’ll work in the 2D axisymmetric space.

#### Session 1 Videos

- Part 1: Modeling Electromagnetic Coils
- Modeling a single conductor coil under DC operating conditions
- Truncating the modeling domain
- Refining the mesh

- Part 2: Strategies for Modeling Electromagnetic Coils
- Modeling a single-turn coil at varying excitation frequencies
- Adjusting the mesh to account for the skin depth
- Extracting impedance and losses
- How and why to use impedance boundary conditions when the skin depth is small

- Part 3: Modeling a Coil Connected to an Electric Circuit
- Modeling a single-turn pickup coil that interacts with a transmit coil
- Computing induced currents and voltages under different conditions
- Connecting a coil to an external circuit model

- Part 4: Modeling a Multiturn Coil
- Coils with several turns and different winding patterns
- Modeling coils up to and around the first resonant frequency
- Modeling coils with many turns and flat coils

- Part 5: Using the Magnetic Fields Interface for Coil Modeling
- Reduced or background field formulation
- Boundary conditions for modeling thin-walled structures
- Periodic structures
- Modeling of moving domains

Once completing the videos in this introductory session, you will have seen the foundations for 2D axisymmetric coil modeling techniques.

### Electromagnetic Heating in Coils

One of the common uses of COMSOL Multiphysics with the AC/DC Module and Heat Transfer Module is for modeling inductive heating, the process by which a coil is used to heat up a workpiece over time. In this second lecture session, we address this topic in depth.

*Workpiece being inductively heated over time, with nonlinear material properties.*

#### Session 2 Videos

- Part 1: Modeling Inductive Heating in a Coil
- Setting up an inductive heating problem
- Using the various solver types to model steady-state and transient cases
- Incorporating temperature-dependent material properties

- Part 2: Features for Modeling Inductive Heating in an EM Coil
- Improving modeling accuracy via mesh and tolerance refinement
- Using the
*Events*interface to capture instantaneous changes in loads and operating frequencies - Solving at several different frequencies

- Part 3: Modeling Radiation in an Electromagnetic Coil
- Thermal modeling in more detail
- Modeling radiation and view factors
- Incorporating multiple spectral bands when parts are heating up significantly

- Part 4: Modeling Convection and Thermal Damage in an Electromagnetic Coil
- Multiple approaches for modeling of convection in the surrounding air
- History tracking
- Tracking of damage

- Part 5: Modeling the Heating of Moving Parts in an Electromagnetic Coil
- Several different approaches for modeling parts that are moving relative to the coil

Once completing this lecture session, you should be confident in addressing most coil heating problems.

### Modeling of Forces, Motion, Nonlinearities, and More

The third lecture session addresses another kind of multiphysics: the coupling of electromagnetic forces to the deformation and motion of parts, such as in solenoids.

*Displacement of a solenoid actuator over time.*

#### Session 3 Videos

- Part 1: Computing Electromagnetic Forces on Parts
- Modeling forces between coils
- Issues of geometry, meshing, and accuracy
- Modeling magnets

- Part 2: Modeling Induced Currents from a Magnet Moving Through a Coil
- Considering the small and large motion of a magnet within a coil, and how this time-varying change in the magnetic field induces currents in the coil

- Part 3: Modeling a Solenoid Actuator
- Coupling the computed forces to the small and large deformation of a solenoid plunger via moving domains

- Part 4: Modeling an Inductor with a Nonlinear Core
- Modeling materials that have a nonlinear B-H curve, and how these will introduce higher-order harmonics into a device such as a transformer
- Extracting cycle-averaged data

- Part 5: Optimizing an Electromagnetic Coil to Achieve a Desired B-Field
- Using the Optimization Module for optimizing the fields within a coil
- Adjusting current
- Adjusting coil position via the
*Moving Mesh*functionality

### Modeling of 3D Coils

The last session in the coil modeling lecture series addresses issues related to modeling 3D coils. Although most of the concepts of coil modeling can be learned solely on a 2D axisymmetric model, there are some unique issues that need to be addressed in 3D.

*A 3D coil model showing current magnitude on the coil and the surrounding magnetic field.*

#### Session 4 Videos

- Part 1: Introduction to Modeling Electromagnetic Coils in 3D
- Building a 3D coil model from scratch, using both the
*Magnetic Fields*and*Magnetic and Electric Fields*interfaces

- Building a 3D coil model from scratch, using both the
- Part 2: Exciting 3D Electromagnetic Coil Structures
- Special features for modeling of multiturn coils, thin pancake coils, and tightly-packed coils
- Estimating coil capacitance
- Correct interpretation of boundary conditions as current return paths, electric insulators, or symmetry conditions

- Part 3: Using Infinite Elements to Terminate Domains for 3D Coil Models
- Using
*Infinite Elements*for modeling domain truncation - Built-in coil modeling options
- Using edges to excite coils or compute intercepted flux

- Using
- Part 4: Frequency-Domain Modeling of Electromagnetic Coils in 3D
- Delineating the three modeling regimes, the low-, mid-, and high-frequency regimes, and how to address them via the
*Magnetic Fields*and*Magnetic and Electric Fields*interfaces - Issues of meshing and solver convergence

- Delineating the three modeling regimes, the low-, mid-, and high-frequency regimes, and how to address them via the
- Part 5: Modeling Resonance and Coupling Between Electromagnetic Coils
- Modeling resonant frequency of the coil
- Computing the coupling between coils in 3D
- Summary of the various modeling approaches

Once you’ve gone through this last session of lectures, you’ll have the foundations to solve 3D coil models. We hope that these videos will educate and inspire you to build coil models in COMSOL Multiphysics and the AC/DC Module, and do to so faster and with confidence in your modeling!

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