Using FEMM software tool - Università di Padova

Using FEMM software tool 

Electric Drive Laboratory 

May 10, 2006 

Introduction 

Rules for the use of FEMM (Finite Element Method Magnetics) in the analysis of the 

electrical machines. 

The elements of the problem can be divided in: 

Drawing Mark Properties Operations 

points labels materials pre–processing 

segments groups boundary conditions mesh 

arcs circuits solution 

post–processing 

1

Nicola Bianchi Using FEMM 

Part I 

Simple examples 

1 A first example: the electromagnetic actuator 

Let us consider the electromagnetic actuator of Fig. 1. It includes a fixed iron yoke 

around which a coil is wound, and an iron plate. When the coil carries current, the 

iron yoke attracts the iron plate, due to the magnetic pressure on its surface. 

Neglecting the end effects, the simulation is carried out by assuming a planar 

symmetry. This is that all the magnetic fields are repeated equal for each section of 

the electromagnetic actuator. Then an unitary length is assumed, that is, Lstk=1 m. 

1.1 Problem setting 

Figure 1: Sketch of the electromagnetic actuator 

The first step is to define the problem: 

Type: the symmetry is planar, 

Units: the unity is millimeter, 

Frequency: since this is a magneto–static problem, the frequency is set to be zero, 

Depth: a unity length is selected (this corresponds to 1000 mm). 

1.2 Drawing 

At first all the points of the structure are drawn, as shown in Fig. 2. The points can 

be chosen by using the mouse (in this case it is suggested to use the snap to the grid) 

or by using the keyboard (press TAB and insert the point coordinates). 

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Figure 2: Points of the drawing 

After drawing the points, they have to be connected by segments. Select two 

points at a time by the left bottom of the mouse, so that they are connected together. 

Fig. 3 shows the segments that connect the points of Fig. 2. 

Figure 3: Segments of the drawing 

At this point the drawing of the structure is completed. 

1.3 Boundary conditions 

In a field problem, the the magnetic fields are required to satisfy suitable conditions 

on the boundary of the domain. These conditions are called boundary conditions. In 

a two–dimensional problem, they are imposed along the segments of the border. 

There are four main boundary conditions: 

Dirichlet: this condition prescribes a given value of the magnetic vector potential Az 

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along a segment. Thus, the flux lines results tangential to this segment. This 

condition is used to confine the field lines into the domain. 

Neumann: this condition imposed the flux density lines to be normal to the selected 

segment. This condition is a natural condition. This means that it is 

automatically satisfied, if other conditions are not assigned. 

Periodic: this condition is assigned to two segments and imposes that the magnetic 

vector potential behavior is the same along the two segments, i.e. Az,segment1 = 

Az,segment2. 

Anti–periodic: this condition is assigned to two segments and imposes that the 

magnetic vector potential behavior is the one opposite to the other along the 

two segments, i.e. Az,segment1 = −Az,segment2. 

It is worth noticing that the boundary conditions are defined to confine the field 

analysis to a given region, reducing the domain as minimum as possible. 

In this specific problem, it will be assigned that no flux lines can cross this boundary: 

1. A boundary condition Az = 0 is defined in the problem. 

2. The external lines, that is, the segments of the box are selected, using the right 

bottom of the mouse. 

3. The boundary condition is assigned. 

1.4 Materials 

The material of the objects that form the structure have to be defined. They can be 

new materials, suitably defined for this analysis, or they can be selected from a given 

Material Library. This includes the commonly used materials. 

In the example, the materials that are used are Air, Iron and Copper. 

A label is defined for each object. Then, the appropriate material is assigned to 

the object: Iron is assigned to the two magnetic pieces, Copper is assigned to the two 

coil sides, and Air is assigned to the remanent space. 

Fig. 4 shows the label of the electromagnetic actuator. 

1.5 Mesh 

The subdivision of the structure in finite elements is automatic. This process is 

commonly called ”to create the mesh”. Each object will be subdivided in small 

elements (the finite element), which are triangles in FEMM. 

It is possible to force the maximum mesh size in each object. The mesh size 

refers to the area of the triangle used for this subdivision. The choice of the mesh 

size depends on the problem to be analyzed. It is better to refine the parts of the 

problem, in which the higher field gradients are expected. 

Fig. 5 shows the final mesh of the electromagnetic actuator. 

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1.6 Current sources 

Figure 4: Labels of the drawing 

Figure 5: Mesh of the structure 

The current is imposed in the coil sides by defining two current sources, or circuits. 

In our example, we define two circuits: 

CurrentPos: the positive current, for instance equal to 100 A. 

CurrentNeg: the negative current, whose value has to be –100 A. 

After their definition, they are assigned to the two coils of the structure, as shown 

in Fig. 6. 

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1.7 Groups 

Figure 6: External circuits connected to the coil sides 

A group of objects can be defined to belong to the same group, defined by an identification 

number. The group can also contain one object only. 

The group definition is useful when the automatic analysis is adopted, as will be 

shown when the script files are dealt with. 

In this example, we define the upper coil side as group 1001, the lower coil side as 

group 1002 and the moving keeper as group 10. 

1.8 Plot 

Once all the steps above have been completed, the problem is ready to be solved. The 

problem is analyzed. Then the results can be 

At first the flux lines are plotted as shown in Fig. 7. This plot give us a rapid idea 

if the problem has been correctly set. 

A further visual analysis refers to the flux density map, shown in Fig. 8. This 

gives an indication of the range of flux density values reached in the structure. 

2 Use of the LUA script 

The purpose of the LUA file is to automatize a series of computations using the 

FEMM code. 

A series of instructions can be written in a unique file (the LUA file) and they are 

executed consecutively when the file is read within a FEMM editor or viewer. Often 

a FOR loop is implemented, in which one or two parameters are changed. 

This kind of programming is useful when several simulations have to be carried 

out searching the dependence of the machine performance on one parameter, e.g. the 

working frequency, the operating currents, or the geometrical position. 

Some examples are given in the following. Further informations and documen- 

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Figure 7: Flux lines of the solved structure 

Figure 8: Flux density map of the solved structure 

tation can be found in the chapter ”LUA Scripting Documentation” of the ”FEMM 

User’s Manual” (Press key Help topics in the menu Help of the application. 

2.1 Scripts for the Pre–processing 

An example is given to modify the current of the circuits. 

At first we could need to compute the maximum current from the geometrical 

data 

S_coil = 600 -- (mm2) 

k_fill = 0.4 

J_max = 6 -- (A/mm2) 

I_max = S_coil * J_max 

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\begin{verbatim} 

% 

where the text following \verb"--" is a comment. 

Then a series of analysis at various currents can be implemented as 

follows. Ten simulations are considered with linear variation of the 

current: 

\begin{verbatim} 

N_sim = 10 

for n = 1, (N_sim + 1), 1 do 

I_coil = I_max * (n - 1) / N_sim 

Once the value of the current is computed, the correspond circuits have to be 

modified. The instructions that have to be used are 

modifycircprop("CurrentPos", 1, I_coil) 

modifycircprop("CurrentPos", 1, -I_coil) 

It is also convenient to operate as follows: 

1. to open an original FEMM file, 

2. to modify as required, 

3. to save in a temporary FEMM file, which becomes a copy of the original project 

but with the modifications, and 

4. to analyze the temporary FEMM file. 

In this way, the original file is not modified. The LUA code becomes 

openfemmfile("electromagnet.fem") 



savefemmfile("tempfile.fem ") 

analyse() 

A copy of the original project ”electromagnet.fem” to save in the temporary file 

”tempfile.fem”, with the modifications implemented. This allows the original project 

to remain unchanged. 

The command analyse() start the finite element computation. 

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2.2 From Pre– to Post–processing 

Sometimes there is the needs to transfer one or more data from the pre–processing 

to the post–processing. This can be accomplished by write the information in a text 

file that will be read when the post–processing will run. 

An example of writing (e.g. the value of the current of the coil) in the ”temp.txt” 

file is 

handle = openfile("temp.txt", "w"); 

write (handle, I_coil, "\n"); 

closefile(handle); 

Finally, once the problem is analyzed, it is necessary that the solved problem is 

processed. Then the last command within the FOR loop of the pre–processing file 

is the call to the post–process LUA file. This procedure will be described in the 

following subsection. It is called as follows 

runpost("postprocess.lua") 

All the command that have written in the file ”postprocess.lua” will be executed. 

Then the complete ”preprocess.lua” becomes 

S_coil = 600 -- (mm2) 

k_fill = 0.4 

J_max = 6 -- (A/mm2) 

I_max = S_coil * J_max 

N_sim = 10 

for n = 1, (N_sim + 1), 1 do 

I_coil = I_max * (n - 1) / N_sim 

openfemmfile("electromagnet.fem") 



savefemmfile("tempfile.fem ") 

analyse() 

handle = openfile("temp.txt", "w"); 

write (handle, I_coil, "\n"); 


runpost("postprocess.lua") 

end 

2.3 Post–processing 

The post–processing file contains the instructions that have to executed after the field 

problem has been solved. This file can be called separately or can be launched by the 

pre–processing, for instance when it is included within an analysis loop. 

At first, the value of some parameters are assigned, e.g. the z–axis length and the 

number of turns of the coil: 

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-- length (m) 

L_z = 0.100 

-- number of turns 

N_t = 80 

The first operation of the post–process is to read the data written in the temporary 

file during the pre–processing. 

handle = openfile("temp.txt", "r"); 

I_coil = read (handle, "*n"); 


Then, some operations are executed. The same conventions used in the pre– 

processing have to be of course used. Some examples are reported hereafter. 

Each operation is divided in two steps: 

1. at first, an element (line, object, group) or a set of elements is selected, 

2. an operation is executed referring to this element or this set of elements. 

In the following example, the line on the top of the moving keeper is selected by 

means of the two extremes of the line. Then the computation of the force along the 

line is required. Fcx and Fcy are the constant component of the force along the x 

and y directions respectively, while Fpx and Fpy are the pulsating force components 

along the x and y directions respectively. The latter components are equal to zero in 

magneto–static problems. 

seteditmode(contour) 

selectpoint(-60, -10) 

selectpoint( 60, -10) 

F_cx, F_px, F_cy, F_py = lineintegral(3) 

Alternatively, the moving iron keeper could be selected by means of its group 

number 10, and the force components are achieved from the Maxwell stress tensor: 

groupselectblock(10) 

F_cx = blockintegral(18) 

F_cy = blockintegral(19) 

F_px = blockintegral(20) 

F_py = blockintegral(21) 

In the following example, the flux linkage with the coil is computed. The two 

coils can be selected by means their group number (1001 and 1002 for the upper 

and the lower coil side respectively). The coil side surface is firstly computed. Then 

the magnetic potential is integrated over the two surfaces, and the flux linkage is 

computed from their difference. 

10


-- surface 


Sup = blockintegral(5) 

clearblock() 

-- integral of Az 


intg_Are_1, intg_Aim_1 = blockintegral(1) 

clearblock() 


intg_Are_2, intg_Aim_2 = blockintegral(1) 

clearblock() 

-- flux linkage 

flux_re_1 = (intg_Are_1 / Sup) * L_z * N_t 

flux_im_1 = (intg_Aim_1 / Sup) * L_z * N_t 

flux_re_2 = (intg_Are_2 / Sup) * L_z * N_t 

flux_im_2 = (intg_Aim_2 / Sup) * L_z * N_t 

In order to compute the magnetic energy all the elements of the domain are selected. 

No number is specified in the command groupselectblock() so as all blocks 

are selected. Then, magnetic energy density, magnetic coenergy density and the product 

A · J are integrated. 

groupselectblock() 

Energy = blockintegral(2) 

Coenergy = blockintegral(17) 

AJ_intgr = blockintegral(0) 

Once the computation is finished, the results have to be stored into a file. The 

file ”results.txt” is open to append (note the command ”a”) the results of the computation. 

In the example hereafter the values are written on the same row, spaced by 

some blank spaces, followed by a line end command (”\n”). 

handle = openfile("results.txt", "a") 

write(handle, 

I_coil, " ", 

F_cx, " ", 

F_cy, " ", 

flux_re_1, " ", 

flux_im_1, " ", 

flux_re_2, " ", 

flux_im_2, " ", 

Energy, " ", 

Coenergy, " ", 

AJ_intgr, 

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"\n") 

closefile(handle) 

At last, the view editor is closed: 

exitpost() 

3 A second example: a cylindrical actuator 

According to the cylindrical actuator shown in Fig. 3, the pre– and post–processing 

files are reported in the following. 

The pre–processing is 

(a) Pre–processor (b) Post–processor 

Figure 9: Actuator 

PRE_ATT.LUA 

-- Current density is defined 

jm=3 

handle = openfile("result.txt", "a"); 

write(handle, jm, " "); 

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-- Loop of simulations varying the air--gap thickness 

-- dz is the variation with respect to the initial position 

for dz = 0,-0.6,-0.2 do 

-- Its value is stored in the result file 


write(handle, dz, " "); 


-- The actuator structure is loaded 

open_femm_file("actuator.fem") 

-- The current density is assigned to the coil 

modifymaterial("Copper", 4, jm) 

-- Mover (group=1) is selected and moved 

selectgroup(1) 

move_translate(0, dz) 

-- The changed structure is save in a temporary file 

save_femm_file("temp.fem") 

-- Solving the problem 

analyse(1) -- (0) show window 

-- (1) hide window 

-- Post-processing 

runpost("post_att.lua", "-windowhide") 

end 

The post–processing is 

POST_ATT.LUA 

-- selection of the line to integrate the flux density 

seteditmode(contour) 

selectpoint(0,10.5) 

selectpoint(3,10.5) 

Flux, B_avg = lineintegral(1) 

-- unselection 

clearcontour() 

-- Data storage 


write(handle, Flux, " ", 

B_avg, "\n") 


-- post-processing end 

exitpost() 

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4.1 Mathematic functions 

4.2 Vectors 

4 Useful functions 

sin(x) Sine of x 

cos(x) Cosine of x 

tan(x) Tangent of x 

asin(x) Inverse sine of x [−π/2, π/2], x ɛ [−1, 1] 

acos(x) Inverse cosine of x [0, π], x ɛ [−1, 1] 

atan(x) Inverse tangent of x [−π/2, π/2] 

atan2(x, y) Inverse tangent of x/y [−π, π] 

sinh(x) Hyperbolic sine of x 

cosh(x) Hyperbolic cosine of x 

tanh(x) Hyperbolic tangent of x 

esp(x) Exponential e x 

log(x) Natural logarithm of x, with x¿0 

log10(x) Common (base 10) logarithm of x, with x¿0 

pow(x, y) Power x y 

sqrt(x) Square root √ x 

ceil(x) Round towards plus infinity of x 

floor(x) Round towards minus infinity of x 

abs(x) Absolute value of x 

When a vector of numbers has to be defined, we can use the curly brackets. For 

instance, a vector of three number is 

Vector = {number1, number2, number3} 

The values of the vector are gained by using the squared brackets: 

number1 = Vector[1] 



4.3 Indexed variables 

Sometimes it is needed to adopt some variables whose name has a common root 

followed by a varying number. 

For example, CoilSide1 and CoilSide2 that are used in the first example. 

These names can be obtained by link the common root CoilSide2 with an index 

that assumes the numerical value 1 and 2. The link is achieved as 

"CoilSide" .. index 

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Acknowledgment 

This report has been possible thanks to contribution of many students and PhD students 

of the Electric Drive Laboratory of the Department of Electrical Engineering, 

University of Padova, Italy. In particular, the big work of PhD. Eng. Fabio Luise, 

PhD. Eng. Giorgio Grezzani, Eng. Diego Bon and Eng. Michele Dai Prè is acknowledged. 

Contacts 

Prof. Nicola Bianchi, Prof. Silverio Bolognani, Electric Drive Laboratory, Department 

of Electrical Engineering, University of Padova, Via Gradenigo 6 A Padova, 

Italy. Phone: +39 049 827 7500, Fax: +39 049 827 7599, email: [bianchi] [bolognani] 

@die.unipd.it. 

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