Electromagnetic Plunger with Dynamics k D

Introduction

• Linear plungers/actuators feature in voice coils, electromagnetic relays,

electromagnetic valves etc.

• Main parts are coil, stator core, spring and moving plunger.

• The plunger end is attached to a spring and damper.

• The magnetic core and plunger are modeled with both linear and nonlinear B-H

Curves separately.

• A current pulse is applied to the coil, actuating the plunger.

• The electromagnetic force on the plunger is computed.

• The equations of motion of the plunger are modeled using the Global state variables.

• The model is parameterized to facilitate parametric sweeps.

k D

3D View

Magnetic core

Multi-turn coil

Guider

Plunger/armature

Plunger motion direction

Air region

2D Axi-symmetric View

Modeling Approach

• Geometry dimension: 2D-axisymmetry

• Geometry finalized: using Form Assembly

• Physics used:

1. Magnetic Fields

2. Moving Mesh

3. Global ODEs and DAEs

• Study type: Time Dependent

• Results:

– Electromagnetic force on the plunger vs time

– Dynamic position of the plunger vs time

– Dynamic velocity of the plunger vs time

Model Variables

• A Rectangular waveform is used to model the current in the coil

Magnetic Fields Modeling

• Plunger and Magnetic Core settings when using linear material

• The Magnetic Core and Plunger are modeled using separate ‘Ampere’s Law’ nodes. A linear relationship between B and H is defined using Magnetic Permeability.

• The relative permeability for linear material are: mur_plunger = 4000, and mur_core = 1200.

• Above figures show the setup for plunger and similar settings are applied for the Magnetic Core as well.

Magnetic Fields Modeling

• Plunger and Magnetic Core settings when using nonlinear material

• The non-linearity of Magnetic Core and Plunger is modeled using separate ‘Ampere’s Law’ nodes.

• Above figures show the setup for plunger and similar settings are applied for Magnetic Core as well.

Magnetic Fields Modeling

• Coil settings

• The current in the coil is defined using a rectangular waveform defined in the variables

tab. The number of turns, coil conductivity and coil cross-sections are defined as

shown in the above figure.

• Force Calculation

• Since magnetic materials are used in the

model, the Lorentz method for force

calculation cannot be used as it only

supports the conductive but nonmagnetic

materials.

• Maxwell’s Stress Tensor is used to

compute the forces on the plunger.

• When using Stress Tensor to compute

forces, the mesh around the boundaries

should be very fine to get accurate results.

Magnetic Fields Modeling

Magnetic Fields Modeling

• A continuity boundary condition is added to ensure a continuity between the stationary and moving domains. Weak constraints improves numerical stability.

• The Identity pair is created using ‘Form Assembly’ feature in the Geometry node.

Modeling Plunger Dynamics

• Global ODEs and DAEs interface is used to solve the equation of motion

𝑀𝑑2𝑝

𝑑𝑡2+ 𝐷

𝑑𝑝

𝑑𝑡+ 𝑘𝑝 − 𝐹𝑧 𝑝, 𝑣, 𝑡 = 0

• The above equation can be rewritten into two separate equations as

𝑀𝑑𝑣

𝑑𝑡+ 𝐷𝑣 + 𝑘𝑝 − 𝐹𝑧 𝑝, 𝑣, 𝑡 = 0

𝑑𝑝

𝑑𝑡− 𝑣 = 0

Where, p = z-position v = velocity M = mass D = damping coefficient k = stiffness Fz = electromagnetic force

Moving Mesh Settings

• Since COMSOL 5.3a, the “Moving Mesh” node is to be found under “Definitions”

• Moving Mesh interface is used to model the ‘Translational Motion’ of the plunger.

• The ‘Fixed Boundary’ and ‘Prescribed Mesh Displacements’ are defined as shown in the figure.

• The displacement of Plunger is given by position variable ‘p’ obtained from ‘Global ODEs and DAEs’ interface.

• Same method as in example:

• https://www.comsol.com/model/voltage-induced-in-a-coil-by-a-moving-magnet-14163

Moving Mesh physics is only solved in the moving domains.

Fixed boundary

Fixed boundary

Mesh Settings

• The Destination boundary from the Identity pair should be finer than the Source

boundary to properly map resolve the continuity between moving and

stationary parts.

• Mapped mesh is used in the moving domains (excluding Plunger).

Mesh Settings

• A very fine mesh is generated along the boundaries of the Plunger in order to

accurately measure the forces using Maxwell’s Stress Tensor.

• Boundary layers are defined on Plunger and Magnetic Core to properly resolve the

induced eddy currents.

• For fast and robust computation, use

linear elements by changing the

Discretization to Linear. This is strongly

recommended when having nonlinear

materials (B-H curve). The reason being

that the spatial transition from

magnetically unsaturated to saturated

regions is often not resolved by the

mesh. That is handled better by linear

elements whereas higher order

elements can develop

numerical instabilities.

Changing Discretization

Solver settings

• For physics involving moving mesh, applying some manual solver tuning

is recommended.

• Time-Dependent Solver

– Time stepping and Error estimation

• Fully Coupled

– Nonlinear Solver settings

• Direct Solver

– Pardiso is usually faster than MUMPS

• Exclude algebraic states in the error

estimation. The Lagrange multipliers in

weak constraints are algebraic and

noisy. Other algebraic variables may

arise in circuit couplings.

Time-Dependent Solver

• Frequent Jacobian update is required

due to the motion (couplings change).

• Increase the Maximum number of

iterations and tightening the

Tolerance Factor.

• Try using Anderson acceleration.

Fully Coupled

• PARDISO is usually faster than MUMPS

Direct SOlver

Figure: Magnetic flux density in the plunger at t=0.2011 s.

Results: Magnetic Flux Density

Results: Electromagnetic Force

Figure: The electromagnetic force acting on the plunger depending on the current in the coil for different ‘Damping

Coefficients’.

Results: Plunger Position

Figure: The change in the position of the plunger as the current varies in the coil for different ‘Damping Coefficients’.

Results: Plunger Velocity

Figure: The velocity profile of the plunger w.r.t time as the current varies in the coil for different ‘Damping Coefficients’.

Induced Current

NOTE: You need to click on “Slide Show” mode to visualize the animation.

Plunger Dynamics

NOTE: You need to click on “Slide Show” mode to visualize the animation.