# The permeance

## Курсовой проект - Физика

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ABSTRACT

of investigation - direct current electromagnet.of the work - to get skills of electromagnet calculation.of investigation - empirical formulas.calculation of dc-current electromagnet was made.course project consists of four parts. In the first part the so-called direct problem is solved and the magnetic-moving force is found. In the second part the winding is calculated and the pure MMF of the coil is found. The third part includes the so-called inverse problem, the magnetic flux is being determined. And the last, the fourth part includes defining of the actuation time of the electromagnet.ELECTROMAGNET, AIR-GAP, WINDING, ACTUATION TIME, MAGNETIC MOTIVE FORCE, INDUCTION.

INTRODUCTION

course design is intended for getting skills on calculation of electromagnets. In this work next problems are solved:

-direct problem. Condition of the work of electromagnet: the armature is in open stage. Here such parameters are calculated: permeances of the air-gaps, magnetic fluxes, magnetic potential drops in metal and, as a result, magnetic motive force;

-calculation of winding. Here such parameters are calculated: diameter and cross-section of wire, resistance of wire, current, flowing in wire and precise value of magnetic motive force;

inverse problem. Conditions of the work: armature is in closed stage. Here such parameters are calculated: permeances of air-gaps, magnetic flux, inductance of metal and magnetic intensity;

calculation of dynamic characteristics of electromagnet. Here such characteristics are found: moving, pick up, actuation time and electromagnetic force for actuation of calculated electric apparatus.special computer programs are made for computing electromagnets and their characteristics. But the importance of this work is to understand and to learn the stages of finding one or another thing during calculation of contacting electric apparatus.

1. MMF determination

1.1.Initial data

dc electromagnet with next parameters is given on Figure 1.1:

=10 mm; d=25 mm; d2=20 mm; l=250 mm; h=80 mm; dп=10 mm; d2=0.25 mm; dк=0.2 mm; induction at d=dп, B=0.1 T; winding power voltage U=36 V; magnet circuit material is steel of quality 50HXC.1.1. - Calculated electromagnet

-to determine MMF of electromagnet winding;

-to design electromagnet winding;

to define electromagnetic forces;

to find actuation time of the electromagnet.

1.2.Completing of the equivalent circuit

first step is to set up equivalent magnetic circuit without taking into account reluctance of iron subcircuits. The scheme is represented on the Figure 1.2.MMF that is produced by flowing current through the coil is drawing as the source of power. The magnetic resistances of operating and parasitic air gaps are drawn as resistors.is the magnetic resistance of the operating air-gap. Rm2 and Rm3 are the magnetic resistances of the parasitic air-gaps.

1.2. - Equivalent circuit

1.3.The permeance of the air-gaps determination

permeance of the operating air-gap is determined according to the method of probable flux passes. The fluxes in this air-gap are shown on the Figure 1.3.

1.3.1. - Fluxes flowing between core and armature (1) and between yoke and armature (2)

magnetic permeances of the operating air-gap by the method of probable fluxes can be calculated

0 - is magnetic constant, or vacuum permeability, ;

δп - is the value of the operating air-gap, m.

where δп - is the value of the operating air-gap, m.lets find the front magnetic flux permeance of the operating air-gap:

.it is possible to find the full magnetic permeance of the operating air-gap:

,

.

The next step is to find the magnetic permeance of parasitic air-gap δ2. It can be found using specific permeance for coaxial cylinders . The flux through δ2 can be calculated without taking into account fluxes of bulding, because the dimensions of the pole are more than the air-gap in 240 times.

where d2 - is the value of the parasitic air-gap, m.

.lets find the permeance of the parasitic air-gap between the yoke and the armature using Roters method.first, lets find square of a high yoke surface:

;front magnetic flux permeance of the parasitic air-gap is determined:

;

.

For Λδ1z1 the formula of half-ring is used :

,

For Λδ1p1 the formula of half-cylinder is used :

For Λδ1p2 the formula of quarter-cylinder is used :

,

For Λδ1z2 the formula of quarter-ring is used 

,total permeance of the parasitic air-gap is found:

1.4.Determination of magnetic flux

it is necessary to find the flux of the pole:

where Bδ - is magnetic induction, T;δ - is the pole face area, m2;

σвп - is the coefficient of bulging.bulging coefficient is to be found:

,

where Λδ - is the permeance of the operating air-gap, H;

ΛδT - is the front magnetic flux permeance of the operating air-gap, H.

Then the pole face area is calculated

;

;

where Bδ - is magnetic induction, T;

σвп - is the coefficient of bulging;is the diameter of the core, m.

1.5.Determination of the steel magnetic potential drops

lets find the magnetic potential drops of the magnetic circuit by the method of leakage ratio. The division of the electromagnet is shown on the Figure

1.5.1 At first the core is divided by 5 equal parts (x) equaled to

1.5.1. - Dividing of a magnetic circuit on subcircuits

Now the leakage ratios of every subcircuit must be defined:

where xi - is the length from the top of the core to the middle of the investigated subcircuit;

λS - is the specific permeance; in this case this is the specific permeance of coaxial cylinders:

.that, the total permeance ΛδΣ is found:

;

;

,Λδ, Λδ1, Λδ2 - are the permeances of the air-gaps, H., the calculations for the first subcircuit are made. The bulging coefficient σX1 is found

,

where λS - is the specific permeance, ; in this case this is the specific permeance of coaxial cylinders;

ΛδΣ - is the total permeance, H.the magnetic flux through the first subcircuit is made:

;

,Фδ - is the magnetic flux through the circuit, Wb;

σX1 - is the bulging coefficient of the subcircuit.

After it, the induction of the core is found:

,ФX1 - is the magnetic flux through the subcircuit, Wb;- is the diameter of the core, m.induction of the yoke is found:

;

.

From the graph of magnetic curves  the magnetic intensity is taken:

;

.

lets find magnetic potential drop of the first subcircuit:

;

.

for the next subcircuits are done by analogy to the first one.

the magnetic potential drop in the armature can be found. At first, the magnetic flux through the armature is found:

;

it, the induction of the armature is found:

From the graph of magnetic curves  the magnetic intensity is taken:

.

lets find magnetic potential drop:

;

.

Now the magnetic potential drop in the base of the electromagnet can be found. The parasitic air-gap can be neglected and the base can be decided to be entire, because the existence of such a little air-gap almost doesnt influence on the flux. The bulging coefficient σX6 is found:

,

where λS - is the specific permeance, ; in this case this is the specific permeance of coaxial cylinders;

ΛδΣ - is the total permeance, H.

Then the magnetic flux through the base is found:

;

;

After it, the induction of the base is found:

;

,

where Фbase - is the magnetic flux through the base, Wb.the graph of magnetic curves  the magnetic intensity is taken:

Now lets find magnetic potential drop:

;

,Hbase - is the magnetic intensity of the base, .

1.6.Determination of the magnetic motive force of the electromagnet

lets find the MMF

Umi - are magnetic potential drops, A;

Фi - is the magnetic flux, Wb;

Λδi - is the permeance, H.

1.7.Results of the computation of electromagnet subcircuit parameters

1.7.1. - Parameters of the electromagnet subcircuits

σiФi, mWbBi, THi, A/mU

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