Magnetic Measurements

Objective of Magnetic Measurement

The measurement of magnetic field strength.

Determination of B-H curve and hysteresis loop for softferro - magnetic materials.

Testing of permanent magnet.

Determination of eddy current and hysteresis losses forsoft ferro - magnetic materials when they are subjected toA.C. magnetic fields.

Types of Test:

•Ballistic test: These tests involves sudden changes inmagnetization and usually include measurements ofcorresponding changes in magnetizing force H and flux density B.The change in magnetic flux density is measured by a flux meteror a ballistic galvanometer. These tests are generally employed forthe determination of B-H curves and hysteresis loop of ferro-magnetic materials.

•A.C. test: These may be carried out at power audio or radiofrequencies and are usually intended to give information aboutpower loss in the material.

•Steady-state test: These are performed to obtain the steadyvalue of flux density existing in the air gap of the magnetic circuit.

Measurement of flux density:

Φ = Flux linking of the search coil R = Resistance of the Ballistic Galvanometer Circuit N = Number of turns in the search coilt = Time taken to reverse the flux Kq= Galvanometer Constant

Average emf induced in the search coil

tN

dtdNe φφ 2==

Average Current through the Ballistic GalvanometerRt

Ni φ2=

Charge passing through Galvanometer coilR

NitQ φ2==

If θ1 throw of the galvanometer due to flow of charge

Charge indicated by ballistic galvanometer = Kqθ1

12 θφ

qKRN

= Flux Density N

RKq

21θφ =

s

q

s NARK

AB

2AreaFlux 1θφ

===

Observed value of flux =True value of flux in specimen + flux in the air space between specimen and search coil

)(' scoss AAHBAAB −+= µ

True value of flux density

−−= 1'

s

co A

AHBB µ

Measurement of value of magnetizing force (H)

Magnetic potentiometer

A = Area of the strip (m2)n = Number of turns per unit length of the stripH1 = tangential component of the magnetizing force A/mR = resistance of the ballistic galvanometer circuit

Flux linkage of a small infinitesimal part of strip of length dl = Flux × turns

AndlHndlAH oo 11 )( µµ =

Total flux linkage of the strip dlHAnAndlH oo ∫∫ = 11 µµWhen the current in the magnetizing winding is reversed, change in flux linkages

dlHAno ∫= 12µ

MdlH =∫ 1= Magnetic potential difference between A and B

Change in flux linkages AnMoµ2=

ChargeRAnM

tRtAnM

tReitQ oo µµ 22

====

Charge indicated by the deflection of galvanometer1θqKQ =

Magnetic potential difference An

RKM

o

q

µθ

21=

The value of constant of galvanometer can be found with the help of acalibrating circuit.

Determination of B-H curve

i. Method of reversals

ii. Step by step method

Determination of Hysteresis loop of B-H curve

i. Step-by step method

ii. Method of reversal

Permeameter

a. Hopkinson permeameter (Bar and Yoke method)

N = Number of turns on the magnetizing windingI = Current in the magnetizing windingl = Length of the bar specimen between two halves of the yokeAs = Area of cross section of the specimenμs = Permeability of the specimen when the magnetizing current is I.Ry = Reluctance of the yokeRj = Reluctance of the joints between the bar specimen and the yokeΦ= Flux in the magnetic circuit

This device measures themagnetizing force or field intensityinside a specimen of bar shape.

Reluctance of the specimen ss

s AlR

µ=

Flux,

++

==

ssjy A

lRR

NI

µ

φcircuit magnetic of reluctance

mmf

Flux density in the specimen)/( ssjyss AlRRA

NIA

Bµ

φ++

==

Magnetizing force )/( ssjysss AlRRA

NIBHµµµ ++

==

)(/specimen of reluctance

joints)(yoke of reluctancejy

ss

ss

jy RRlA

AlRR

m +=+

=+

=µ

µLet

)1( mlNIH+

=∴ )1( ml

NIH −=

b. Ewing double bar permeameter

n = Number of turns per unit length of magnetizing coil,I1 = Current in the coils when the specimen length is lI2 = Current in the coils when the specimen length is l/2

H1 = Apparent magnetizing force for sample of length lH2 = Apparent magnetizing force for sample of length l/2M = mmf required for yokes and the jointsB = Flux density in specimen

11

1 nIl

nlIH ==

22

2 2/2/ nI

lInlH ==

c. The National Physical laboratory permeameter

A.C. Magnetic testing

A magnetic material is subjected to an a.c. magnetic field, loss in power occurs owing to hysteresis & eddy currents.

This loss is called iron or core loss.

Hysteresis loss may be computed from the hysteresis loop test carried out & D.C. connection.

The eddy current loss can be measured only under a.c. condition.

The iron loss in ferromagnetic material depends on the maximum operating flux density, freq. of a.c. magnetization, geometrical thickness of the material.

A typical iron loss/kg vs. flux density for different thickness

Epstein Square

The ferromagnetic materials are shaped into this rectangular sheet. Four stacks are formed by these thin sheets.

The individual sheets are insulated from each other & are slipped into from magnetizing coils of equal no. of turns.

The ends of the four stacks are interleaved & clamped corners so that a square specimen is formed.

Lloyd-Fisher Square

The ferromagnetic materials are shaped into strips of usually 25cm long & 5-6cm wide.

These strips are built up into 4 stacks.

Each stack is made up of two types of strips –one cut in the direction of rolling & the other cut perpendicular to the direction of rolling.

The strips are stacked together in such a manner that the plane of each strip is perpendicular to the plane of the square. The magnetic circuits completed by bringing the 4 stacks together in the form of a square and joining them at the corners. The corner joints one made by a set of standard right angled corners pieces. The corner pieces one of the same materials as strips. There is an overlapping of corner piece and strips at the corners due to which cross-section of iron is doubled at the corners.

Test setup

Induced secondary voltage

E = 4 kf фm f N2 = 4 Kf Bm As f N2

Kf = Form Factorфm = Maximum Flux linking the secondary coils.As = Effective cross-section of the specimen.N2 = No. of turns of secondary winding

Maximum flux density24 fNAK

EBSf

m =

Actual value of flux density in the specimen

−−= 1'

S

Cmmm A

AHBB µ

Ac = cross-section area of coil.Hm = magnetizing force corresponding to maximum density

Pi = total iron loss occurring in the specimen.P = wattmeter reading.V = voltage applied to wattmeter pressure coil.E = voltmeter reading = Voltage induced in coil S2.rp = resistance of wattmeter pressure coil.rs = resistance of coil S1.Ip = current in the pressure coil circuit

Since, the voltage induced in S1 is equal to the voltage induced in S2 since both of them have equal no. of turn and they link with the same flux.

Voltage induced in S1 coil = E

If the leakage reactance of coil S1 & pressure coils are neglected then E = Ip (rp + rs)

Total iron loss in specimen + total copper loss in the secondary circuit VEP.=

Total copper loss in the secondary circuit SP rr

E+

=2

Total iron loss in the specimen

SPP

S

SPi rr

ErrP

rrE

VEPP

+−

+=

+−=

22

1.

Separation of Iron Losses

Hysteresis loss per unit volume

kfBP mh η= η = Hysteresis co-efficient.K = Steinmets co-efficient (1.6 to 2).

Eddy current loss per unit volume

ρ34 2222 tBfK

P mfe =

Kf = Form factor of a.c. voltaget = Thickness of specimenρ = Resistivity of material

Total iron loss per unit volume

Pi = Ph + Pe

Total iron loss in a specimen

Pi = (AS × I)Ph + Pe

l = Mean length of the magnetic circuit formed by the specimen.As = Cross section of the specimen

( )

+×=

ρη

34 2222

2 tBfKfBIAP mf

mSi22

mfek

mh BKKfBK += η××= IAK Sh

××=

ρ34 2tIAK S

e

Variation of frequency

Variation of Form factor

Kf , Bm constant and f varied

Pi = K1f + K2f2Total Iron Loss

where K1 = KhBmk & K2 = KeKf

2Bm2 are constants

fKKfPi

21 +=

Hysteresis Loss Ph = K1f1 Eddy Current Loss Pe = K2f12

Bm , f constant and Kf varied

Total Iron Loss Pi = K3 + K4Kf2

where K3 = KnfBmk , K4 = Kef2Bm

2 are constants

Hysteresis Loss Ph = K3 & Eddy Current Loss Pe = K4Kf12

Bridge Method

( )224

3 rRRRRS +=

Resistance & Inductance

24

3 LRRLS

=

Effective Resistance ( )2

1

21

IRIPR Wi

S+

=

Total Iron Loss ( )WSi RRIP += 21

( ) 414231 RIIRIRI −==

IRR

RI

+

=43

41

( )WS RRRR

RI −

+

=2

43

42Total Iron Loss

At Balance voltage drop

Iron Loss Measurement using A.C. Potentiometer