# Optimal and Cost-Effective Machine Design Using FEM Magnetic Simulation

October 13, 2020

### Key Takeaways

• Finite Element Method ❲FEM❳ magnetic simulation software helps predict the effects of electromagnetic and electrostatic fields in a system.

• FEM magnetic simulation addresses electrostatic, magnetostatic, and electromagnetic problems.

• FEM magnetic simulation includes flux path plotting, flux density mapping, magnetic field mapping, 2D and 3D modeling,  and electromagnetic field motion mapping. Electrical machines are an inevitable part of our daily routines.

Whether it's a mobile charger with inductors, or an electric oven using transformers, we are in touch with various electrical components in our daily life, and Faraday’s laws of electromagnetic induction is the basic working principle governing all of them. The law states the interaction between the magnetic and electric fields, which becomes critical when dealing with electric voltage and currents.

Finite Element Method ❲FEM❳ magnetic simulation software helps predict the effects of electromagnetic and electrostatic fields in a system. It is very advantageous when designing magnetic and electric circuits.  The magnetic properties can be determined from simulation, and designs can be optimized based on the simulation results. FEM Magnetic simulation addresses electrostatic, magnetostatic, and electromagnetic problems.

## FEM Magnetic Simulation and Modeling

FEM magnetic simulation is a finite element analysis tool that can address the magnetic and electric field problems in an engineering system before its hardware development. It addresses linear and non-linear electromagnetic, magnetostatic, and electrostatic problems in a system. It offers a magnetic vector control approach as well as an electric scalar potential approach to simulation models. FEM magnetic simulation is fast, and the results obtained are accurate. The analysis of the simulation results can prevent prototyping defects caused by electromagnetic field interactions.

Large capital investment is involved in electrical machine manufacturing, and it is not easy to let go of the money spent on prototypes or design defects. When you are designing a motor or generator, you can virtually view the interactions of electric and magnetic fields in FEM magnetic simulation. The customer requirements, constraints, and boundary conditions can be incorporated into the simulation model. If there is a requirement for a certain flux density in the motor or generator, the simulation model can be modified until the required value is obtained in the results. By following the same parameters as in simulation for machine prototyping, you can attain the motor as specified in the design.

The magnetic field geometry can be simulated and observed using FEM magnetic simulation. The features such as 2D and 3D modeling aids in getting a 360° view of the magnetic field geometry of the machine. Most FEM magnetic simulations come with features such as magnetic field mapping and electromagnetic field motion mapping. You can study the influence of various grades of ferrite cores on the magnetic properties such as flux and flux density, and the flux path plots and flux density maps give you a better understanding of these quantities. The ability to calculate the torques and forces in a system prevent monetary losses from design issues. The design to cost, design to operational requirements, and improved equipment performance can be achieved through FEM magnetic simulation and modeling.

Assume you are designing a transformer and are deliberating on which type of core and its material to choose. You are deciding whether to go for two E cores or E and I cores. In such instances, FEM magnetic simulation can aid you in your decision by providing numerical values supporting the most suitable cores for the given application. The procedure is to run the simulation with the two models and see which simulation results are closer to your requirement. Fine-tune the model until the values are closer to the expected design.

## Field Problems Addressed by FEM Magnetic Simulations

The following field problems are commonly addressed by FEM magnetic simulation, and can always offer reliable solutions to these issues:

Magnetostatics- In magnetostatic problems, fields are time-invariant and the FEM magnetic simulation solves the problem by taking a magnetic vector control approach. The field solution is obtained by solving equations involving flux density, field intensity, current density, and permeability.

Electrostatics- In electrostatic problems, the fields are time-invariant and an electric scalar potential approach is taken by FEM magnetic simulation.  Gauss law and Ampere’s loop law are the two conditions to be satisfied by the parameters such as electric field intensity, electric flux density, and permittivity in this simulation model.

Low frequency time-harmonic magnetic problems- When the fields oscillate at one fixed frequency, the problems arising are often low-frequency time-harmonic magnetic problems. The magnetic and electric fields are time-varying, and the solution is obtained by solving equations involving current, magnetic flux density, electric voltage, and magnetic permeability.

Electromagnetic boundary problems- The electromagnetic field is mathematically expressed using equations with terms such as electric field intensity, flux density, and current density. Maxwell’s equations are used to represent these problems, and boundary conditions are imposed on the field using Dirichlet, Neuman, or Robin functions.

Current flow problems- The current flow problem is related to quasi-electrostatic fields, which give more weightage to the displacement current terms. The magnetic field terms in Maxwell’s equations are neglected in quasi-electrostatic field problems.

## Eddy current problem in electrical machines.

## Example of FEM Magnetic Scalar Potential Approach

FEM magnetic simulation is found to be very effective at solving the eddy current problems in electrical machines. The method introduces a scalar magnetic potential in a non-conducting region, and deals with the topological configuration of the conducting region.  The eddy current problem is the approximation of Maxwell’s equation with displacement currents neglected. The eddy current problem is an example of low-frequency time-harmonic magnetic problems, can be applied to magnetic levitation, induction heating, and transformer-based problems.

FEM magnetic simulation helps designers visualize the effects of electric and magnetic fields in the design prior to prototyping. The computer-aided FEM magnetic simulation is accurate, adaptable, and absorbs all the boundary conditions and physical limitations into modeling. The optimization of system design through the use of FEM magnetic simulation will result in reduced cost, successful projects, and happy customers.

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