iv) magnetic measurements
TRANSCRIPT
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