CHAPTER X 

HYSTERESIS MOTOR 

98. In it revolving magnetic field, a circular iron disk, or 
iron cylinder of uniform magnetic reluctance in the direction of 
the revolving field, is set in rotation, even if subdivided so as to 
preclude the production of eddy currents. Thin rotation is due 
to the effect of hysteresis of the revolving disk or cylinder, and 
such a motor may thus be called a hysteresis motor. 

Let / be the iron disk exposed to a rotating magnetic field 
or resultant m.m.f. The axis of resultant magnetization in the 
disk, /, does not coincide with the axis of the rotating field, but 
lags behind the latter, thus producing a couple. That is, the 
component of magnetism in a direction of the rotating disk, /, 
ahead of the axis of rotating m.m.f., is rising, thus below, and 
in a direction behind the axis of rotating m.m.f. decreasing, that 
is, above proportionality with the m.m.f., in consequence of the 
lag of magnetism in the hysteresis loop, and thus the axis of 
resultant magnetism in the iron disk, /, does not coincide with 
the axis of rotating m.m.f., but is shifted backward by an angle, 
«, which is the angle of hysteretic lead. 

The induced magnetism gives with the resultant m.m.f. a 
mechanical couple: 

D = mS'b sin a, 
whore 

S = resultant m.m.f., 
4> = resultant magnetism, 
« = angle of hysteretic advance of phase, 
m = a constant. 
The apparent or volt-ampere input of the motor is: 

P ■ wiS*. 
Thus the apparent torque efficiency: 


Q = volt-ampere input, 


HYSTERESIS MOTOR 169 

and the power of the motor is: 

P = (1 - s) D = (1 - s) m$$ sin a, 
where 

s = slip as fraction of synchronism. 

The apparent efficiency is: 

p 

n = (1 — *) sin a. 

Since in a magnetic circuit containing an air gap the angle, 
a, is small, a few degrees only, it follows that the apparent 
efficiency of the hysteresis motor is low, the motor consequently 
unsuitable for producing large amounts of mechanical power. 

From the equation of torque it follows, however, that at 
constant impressed e.m.f., or current — that is, constant SF — 
the torque is constant and independent of the speed; and there- 
fore such a motor arrangement is suitable, and occasionally used 
as alternating-current meter. 

For s<0, we have a < 0, 

and the apparatus is an hysteresis generator. 

99. The same result can be reached from a different point 
of view. In such a magnetic system, comprising a movable 
iron disk, 7, of uniform magnetic reluctance in a revolving 
field, the magnetic reluctance — and thus the distribution of 
magnetism — is obviously independent of the speed, and conse- 
quently the current and energy expenditure of the impressed 
m.m.f. independent of the speed also. If, now: 

V = volume of iron of the movable part, 
(B = magnetic density, 
and 

rj = coefficient of hysteresis, 

the energy expended by hysteresis in the movable disk, 7, is 
per cycle: 

Wo = VV®1\ 

hence, if / = frequency, the power supplied by the m.m.f. to 
the rotating iron disk in the hysteretic loop of the m.m.f. is: 

p0 =/Fi?(B,-e. 

At the slip, sfj that is, the speed (1 — s) f, the power expended 
by hysteresis in the rotating disk is, however: 

Pi = s/FtjCB1-6. 


17(1 ELECTRICAL APPARATUS 

Hence, in the transfer from the stationary to the revolving 
member the magnetic power: 


has disappeared, and thus reappears as mechanical work, ami 
the torque is: 


D = 


(1 -«)/ 


. IV 


that is, independent of the speed. 

Since, as seen in " Theory and Calculation of Alternating-cur- 
rent Phenomena," Chapter XII, sin a is the ratio of the energy 
of the hysteretic loop to the total apparent energy of the mag- 
netic cycle, it follows that the apparent efficiency of such a motor 
can never exceed the value (1 — s) sin a, or a fraction of the 
primary hysteretic energy. 

The primary hysteretic energy of an induction motor, as repre- 
sented by its conductance, ij, being a part of the loss in the 
motor, and thus a very small part of its output only, it follows 
that the output of a hysteresis motor is a small fraction only of 
the output which the same magnetic structure could give with 
secondary short-circuited winding, as regular induction motor. 

As secondary effect, however, the rotary effort of the magnet ic 
structure as hysteresis motor appears more or less in all induction 
motors, although usually it. is so small as in be neglected. 

However, with decreasing size of the motor, the torque of the 
hysteresis motor decreases at a lesser rate than that of the in- 
duction motor, so that for extremely small motors, the torque 
as hysteresis motor is comparable with that as induction motor. 

If in the hysteresis motor the rotary iron structure has imi 
uniform reluctance in all directions — but is, for instance, bar- 
shaped or shuttle-shaped — on the hysteresis-motor effect is 
superimposed the effect of varying magnetic reluctance which 
tends to bring the motor to synchronism, and maintain it 
therein, as shall be more fully investigated under "Reaction 
Machine" in Chapter XVI. 

100. In the hysteresis motor, consisting of an iron disk of 
uniform magnetic reluctance, which revolves in a uniformly 
rotating magnetic field, below synchronism, the magnetic mix 
rotates in the armature with the frequency of slip, and the 
resultant line of magnetic induction in the disk thus lags, in 
space, behind the synchronously rotating line of resultant m.m.f 


HYSTERESIS MOTOR 171 

of the exciting coils, by the angle of hysteretic lead, or, which is 
constant, and so gives, at constant magnetic flux, that is, con- 
stant impressed e.m.f., a constant torque and a power propor- 
tional to the speed. 

Above synchronism, the iron disk revolves faster than the 
rotating field, and the line of resulting magnetization in the disk 
being behind the line of m.m.f. with regard to the direction of 
rotation of the magnetism in the disk, therefore is ahead of it in 
space, that is, the torque and therefore the power reverses at 
synchronism, and above synchronism the apparatus is an 
hysteresis generator, that is, changes at synchronism from motor 
to generator. At synchronism such a disk thus can give me- 
chanical power as motor, with the line of induction lagging, or 
give electric power as generator, with the line of induction 
leading the line of rotation m.m.f. 

Electrically, the power transferred between the electric cir- 
cuit and the rotating disk is represented by the hysteresis loop. 
Below synchronism the hysteresis loop of the electric circuit 
has the normal shape, and of its constant power a part, propor- 
tional to the slip, is consumed in the iron, the other part, pro- 
portional to the speed, appears as mechanical power. At syn- 
chronism the hysteresis loop collapses and reverses, and above 
synchronism the electric supply current so traverses the normal 
hysteresis loop in reverse direction, representing generation of 
electric power. The mechanical power consumed by the 
hysteresis generator then is proportional to the speed, and of 
this power a part, proportional to the slip above synchronism, 
is consumed in the iron, the other part is constant and appears 
as electric power generated by the apparatus in the inverted 
hysteresis loop. 

This apparatus is of interest especially as illustrating the 
difference between hysteresis and molecular magnetic friction: 
the hysteresis is the power represented by the loop between 
magnetic induction and m.m.f. or the electric power in the 
circuit, and so may be positive or negative, or change from the 
one to the other, as in the above instance, while molecular mag- 
netic friction is the power consumed in the magnetic circuit by 
the reversals of magnetism. Hysteresis, therefore, is an electrical 
phenomenon, and is a measure of the molecular magnetic fric- 
tion only if there is no other source or consumption of power in 
the magnetic circuit.