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and incoming air is not to exceed 19C., it will be necessary to
provide at least 100 cu. ft. of air per minute for each kilowatt
lost in the machine.

The power required to drive the ventilating fan is not very
easily estimated as it depends upon the velocity of the air
through the passages. The velocity of the air through the ducts
and over the cooling surfaces is usually from 2,000 to 4,000 ft.
per minute and should preferably not exceed 5,000 ft. per minute;
with higher velocities the friction loss might be excessive.

As a very rough guide to the power required to drive the
ventilating fans, the following figures may be useful :

For 50-kw. dynamo, 150 watts.
For 200-kw. dynamo, 500 watts.
For 1,000-kw. dynamo, 2,000 watts.

34. Cooling Surfaces and Temperature Rise of Armature.
Specifications for electrical machinery usually state that the
temperature rise of any accessible part shall not exceed a given
amount after a full-load run of about 6 hr. duration. The
permissible rise of temperature over that of the surrounding air
will depend upon the room temperature. It usually lies between
40 and 50C. The surface temperature is actually of little
importance and is no indication of the efficiency of a machine,
but, by keeping the surface temperature below a specified limit,
the internal temperatures are not likely to be excessive, and
the durability of the insulation upon which the life of the ma-
chine is largely dependent will thereby be ensured. The de-
signer must, however, see that ventilating ducts or surfaces are
provided at sufficiently frequent intervals to allow of the heat

1 MILES WALKER: "Specification and Design of Dynamo-electric Ma-
chinery," LONGMANS, GREEN & Co.



108 PRINCIPLES OF ELECTRICAL DESIGN

being carried away without requiring very great differences of
temperature between the internal portions of the material
where the losses occur and the surfaces in contact with the air.
The thermal conductivity of all materials used in construction,
and of the combinations of these materials, must be known before
accurate calculations can be made on the internal temperatures;
but, as an indication of how the insulation tends to prevent the
passage of the heat to the cooling surfaces, the following figures
are of interest. The figures in the column headed "Thermal
conductivity" express the heat flow in watts per square inch of
cross-section for a difference of 1C. between parallel faces 1
in. apart.

Material Thermal conductivity

Steel punchings, along laminations 1 . 6
Steel punchings, across laminations

(8 per cent, paper insulation) . 038

Pure mica . 0091

Built-up mica 0.0031 to 0.0026

Empire cloth, tightly wrapped (no

air spaces) . 0063

Presspahn 0.0042

The maximum temperatures to which insulating materials
may be subjected should not exceed the following limits:

Asbestos 500C. or more

Mica (pure) 500C. or more

Micanite. 125 to 130C.

Presspahn, leatheroid, empire cloth,
cotton covering, insulating tape, and

similar materials 90 to 95C.

If ventilating ducts are provided at sufficiently frequent
intervals to ensure that the internal temperatures will not be
greatly in excess of the surface temperatures, it is merely nec-
essary to see that the cooling surface is sufficient to dissipate
the watts lost in the iron and copper of the armature.

Temperature Rise of Self-ventilating Machines. In calculating
the losses and the cooling surfaces of the armature, we shall
assume that the current density in the conductors has been
so chosen that the end connections will not be appreciably hotter
than the armature as a whole. If this density does not exceed
the value as calculated by formula (51) of Art. 29, it may be
assumed that the temperature rise of the end connections will



LOSSES IN ARMATURES 109

not exceed 40C., and the watts to be dissipated by the cooling
surfaces of the armature core will consist of:

1. The hysteresis and eddy-current losses in the teeth.

2. The hysteresis and eddy-current losses in the core below
the teeth.

3. The PR losses in the " active" portion of the armature
winding.

All these losses can be calculated in the manner previously
explained. The copper loss to be taken into account is not
the total'/ 2 /? loss in the armature winding, but is this total loss

21
multiplied by the ratio ^ [-y> where l a is the gross length of

Zl a -\- L e

the armature core, and l e is the length of the end connections
of one coil, as calculated by formula (52) of Art. 29.

The various cooling surfaces may be considered separately,
and the watts carried away from each surface computed
independently. The total cooling surface may conveniently
be divided into:

1. The outside cylindrical surface of the (revolving) armature.

2. The inside cylindrical surface over which the air passes
before entering the radial cooling ducts.

3. The entire sur-face of the radial ventilating ducts, and
the two ends of the armature core.

The cooling effect of the external surface at the two ends of
the armature core is generally similar to that of the radial venti-
lating spaces, and it is convenient to think of the two end rings
as being equivalent to an extra duct. Thus, in Fig. 35, the
number of ducts is shown as five, and the cooling surface of each

duct (both sides) is ~ (D 2 - d 2 ). The calculations would be

made on the assumption that there are six ducts. If the number
of radial vent ducts provided is n, the total cooling surface of
the ducts and the two ends of the armature will be

I (> 2 - <* 2 )(n + 1).

The outside cylindrical surface of the armature will be taken
as irDla, where l a is the gross length, no deduction being made
for the space taken up by the vent ducts. The cooling surface
of the end connections beyond the core is not taken into account.

The area of the inside cylindrical surface is irdl a .



110 PRINCIPLES OF ELECTRICAL DESIGN



/1,500+jA
' 1A \ 100,000 / (53)



The watts dissipated by the cylindrical cooling surfaces may
be calculated by the formula

1,500 + v\

100,000
where W = the watts dissipated.

T = the surface temperature rise in degrees Centigrade.
A = the cooling area in square inches.
v = the peripheral velocity in feet per minute.

This formula is generally similar to one proposed some years
ago by DR. GISBERT KAPP.

If w c is a cooling coefficient representing the watts that can
be dissipated per square inch of surface for 1C. difference of
temperature, we have

1,500 + v ,'.



and the temperature rise will be

r- w



w c A

where W stands for the watts that have to be dissipated through
the cooling surface A.

The watts dissipated by the air ducts and end surfaces may
be calculated by the formula

w - TA (55)



where W, T, and A have the same meaning as before, but v d
stands for the average velocity of the air through the ducts in
feet per minute. This velocity is very difficult to estimate in
the case of self-ventilating machines, but the constant in the
formula has been selected to give good average results if v* is
taken as one-tenth of the peripheral velocity of the armature.

If Wd is a cooling coefficient representing the watts that can
be dissipated per square inch of duct surface for each degree
Centigrade rise of temperature, we have

/K\



and the temperature rise of the vent duct surfaces will be



where W stands for the watts that have to be dissipated through
the surface of area A.



LOSSES IN ARMATURES



111



Example. In order to explain the application of the formulas
for armature heating, numerical values will be assumed for the
dimensions in Fig. 35.
Let D = 32 in.,
d = 23 in.,
l a = 15 in.,

n = 5 (the number of air ducts in the armature core),
N = 400 revolutions per minute,
whence



and



v = 400 X -^ = 3,360



12



v d = 336.




FIG. 35. Section through armature core.

Let us further assume that the total armature losses, con-
sisting of hysteresis and eddy-current losses in teeth and core,
together with the PR losses in the portion of the armature wind-
ing that is buried in the slots, amount to 7 kw.

The cooling surfaces to be considered are:

1. The outside cylindrical surface of area A\ = TT X 32 X
15 = 1,510 sq. in.

2. The inside cylindrical surface of area A* = TT X 23 X
15 = 1,085 sq. in.



112 PRINCIPLES OF ELECTRICAL DESIGN

3. The ventilating duct surface, including the two ends of

the armature coil, of area A 3 = ^ (32* - 23 2 ) ( 5+ 1) = 4,680

z

sq. in.

The radiating coefficients to be used are calculated by formulas
(54) and (56); thus, for surface (1),

1,500 + 3,360
Wc= 100,000

and the watts that can be dissipated per degree rise of temperature
are

Wi = w c Ai

= 0.0486 X 1,510 = 73.4
For surface (2),

1,500 + (3,360 X )

- - - 100,000 - ' 0391

and the watts that can be dissipated per degree rise of temperature
are

Wz = w c A 2

= 0.0391 X 1,085 = 42.5
For surface (3),

a 1344



and the watts that can be dissipated per degree rise of temperature
are

Ws = w d A,

= 0.01344 X 4,680 = 63

The total watts that can be dissipated per degree rise of tem-
perature are 73.4 + 42.5 + 63 = 178.9; whence the rise in
temperature to be expected will be

7 ' 000 _ oo oC

17^9 -

Temperature Rise of Machines with Forced Ventilation. When
a machine is designed for forced ventilation, suitable ducts
whether radial or axial must be provided in the armature, and
the frame must be so arranged as to provide proper passages for
the incoming and outgoing air. The fan or blower may be out-
side or inside the enclosing case. It is usual to allow 100 cu. ft.
of air per minute for every Idlowatt lost in heating the arma-



LOSSES IN ARMATURES 113

ture and field coils of the machine. This will result in a dif-
ference of about 20C. between the average temperatures of the
outgoing and incoming air.

In order to ensure that there shall be no unduly high local
temperatures in the machine, the air ducts or passages must be
suitably proportioned, and provided at frequent intervals. When
the paths followed by the air through the machine, and the
cross-section of these air channels, are known, the average velocity
of the air over the heated surfaces can be calculated. Formula
(56) can then be used for determining approximately the dif-
ference in temperature between the cooling surfaces and the
air.

35. Summary, and Syllabus of Following Chapters. All
necessary particulars have been given in this and the fore-
going chapters for determining approximately the dimensions
and windings of an armature suitable for a given output at a
given speed. A suggested method of procedure in deisgn
will be explained later; but, so far as the preliminary design
of the armature is concerned, the dimensions are determined
by using an output formula (Art. 19, Chap. IV) and deciding
upon the diameter D and the length l a of the armature core.
When proportioning the slots to accommodate the winding, the
diameter D should be definitely decided upon, but slight altera-
tions in the length l a can readily be made later if it is found
necessary to modify the amount of the flux per pole (<l>) or the
air-gap density (B g ). Once the calculations for temperature rise
have been made, and the design so modified if necessary
as to keep this within 40 to 45C., the dimensions of the arma-
ture will require no further modification. The question of
commutator heating will be taken up later; but, in designing
the armature for a given temperature rise, the assumption is
made that no appreciable amount of heat will be conducted to
or from the commutator through the copper lugs connecting the
armature winding to the commutator bars.

The flux per pole necessary to generate the required voltage
being known, the remainder of the problem consists in designing
a field system of electromagnets capable of providing the re-
quired flux in the air gap. This problem is similar to that of
designing an electromagnet for any other purpose, and it has
been considered in some detail in Chaps. II and III. It might
appear, therefore, that little more need be said in connection with



114 PRINCIPLES OF ELECTRICAL DESIGN

the design of a continuous-current generator, but it must be
remembered that certain assumptions were made in order that
the broad questions of design might not be obscured by too much
detail, and in order also that the leading dimensions of the
machine might be decided upon.

It was assumed that the flux in the air gap was uniformly dis-
tributed under the pole face; but is it so distributed, and if not,
how does this affect the tooth saturation and the ampere-turns
required to overcome the reluctance of the teeth and gap?
What is the influence of the air-gap flux distribution on arma-
ture reaction and voltage regulation, and how can we calculate
the field excitation required at different loads in order that the
proper terminal voltage may be obtained? These and similar
questions cannot be answered without a more thorough study
of the magnetic field cut by the conductors, at full load as well
as on open circuit.

Again, with a non-uniform field under the poles, the flux
density in the teeth may be much higher than would be indicated
by calculations based on a uniform field, and this might lead to
excessive heating.

Perhaps the most important problem in the design of direct-
current machines is that of commutation which, so far, has barely
been touched upon. It is proposed to devote a whole chapter
to the study of commutation phenomena.

These various matters will be taken up in the following
order: First, a study of the flux distribution over the armature
surface, and what follows therefrom in relation to tooth densities,
regulation, and the excitation required at various loads; next,
commutation and the design of commutating poles; and finally,
some notes on the design of the field system, with a brief
reference to the factors that must be taken into account when
calculating the efficiency of a continuous-current generator.



CHAPTER VII
FLUX DISTRIBUTION OVER ARMATURE SURFACE

An experienced designer may go far and obtain good results
without resorting to the more or less tedious process of plotting
flux-distribution curves; but occasions arise when his experience
and judgment fail him, and when a reasonably accurate method
of predetermining the distribution of flux density over the sur-
face of the armature would give him all necessary information.
A method of designing electric machinery whether continuous-
current dynamos or alternating-current generators which in-
volves the plotting of the flux distribution curves, has much to
recommend it, not only to the student, but also to the professional
designer. The advantage from the student r s point of view is
that a more accurate conception of the operating conditions
can be obtained than by using empirical formulas, or making
the unscientific assumptions which are otherwise necessary.
The designer will be glad to avail himself of a practical method
of plotting flux curves when departures have to be made from
standard models, or when it is desired to investigate thoroughly
the effects of cross-magnetization upon commutation or pressure
regulation.

36. Air-gap Flux Distribution with Toothed Armatures.
The determination of the flux densities in all parts of the tooth
and slot for various values, of the average air-gap flux density
is so difficult and complicated that it is safe to say no correct
mathematical solution may be looked for, although empirical
rules and formulas of great practical value may serve the
purpose of the designer.

The reluctance of the magnetic paths between pole face and
armature core can be calculated with but little error for the two
extreme cases of very low and very high average flux density
over the tooth pitch; but for intermediate values the designer
has still to rely on his judgment, based on familiarity with the
laws of the magnetic circuit.

To calculate the permeance of the air paths over one slot
pitch at the center of the pole face, when the density is low, the
magnetic lines are supposed to follow the paths indicated in

115



116



PRINCIPLES OF ELECTRICAL DESIGN



Fig. 36. The tooth is drawn, for convenience, with parallel
sides, and the magnetic lines entering the sides of the tooth are
supposed to follow a path consisting of a straight portion of
length 5, equal to the actual clearance, and a circular arc of
radius r, all as indicated in the figure. This is obviously an
arbitrary assumption, but it is convenient for calculation and
gives very good results. It agrees very closely with the results
obtained by MESSRS. H. S. HELE-SHAW, ALFRED HAY, and P.
H. POWELL in their classic Institution paper 1 and also with the
i i

W&Z



FIG. 36. Flux lines entering toothed armature. (Low flux density.)

correct mathematical conclusions arrived at by MR. F. W.
CARTER 2 based on certain assumptions, including that of infinite
permeability of the iron in the teeth.

Considering a portion of the air gap 1 cm. long axially (i.e.,
in a direction normal to the plane of the section shown in Fig.
36), the permeance over the slot pitch of width X is seen to be
made up of two parts: (1) the permeance PI between pole face

and top of tooth, of value PI = T, and (2) the permeance 2P 2

where P 2 is the permeance between the pole face and one side
of the tooth. Consider any small section of thickness dr as
indicated in Fig. 36. The permeance of such a path, of depth
1 cm. measured axially, is

dr



dr



2

- X

7T



1 " Hydrodynamical and Electromagnetic Investigations Regarding the
Magnetic-flux Distribution in Toothed-core Armatures," Proc. Inst. E. E.,
vol. 34, p. 21.

2 Electrical World, vol. 38, Nov. 30, 1901, p. 884.



and



FLUX DISTRIBUTION
2 r* dr



117




The average permeance per square centimeter over the slot pitch
at center of pole is, therefore,

Pi + 2P 2



sq. cm.



,



(57)



The reciprocal of this quantity is the reluctance per square
centimeter of cross-section, or the equivalent air-gap length 5 e .
Thus

t + S (58)'



Consider now Fig 37, which illustrates the case of a highly
saturated tooth. The lines of flux are shown parallel over the














1 1 1 j 1 II 1 1 1 1










3




*"-




.




.^ - t *










t

1






















I



FIG. 37. Flux lines entering toothed armature. (High flux denxity.)

whole of the slot pitch, a condition which is approached but
never attained as the density in the tooth is forced up to higher
and higher values. It is obviously only when the permeability

1 If the ventilating ducts are closely spaced, or exceptionally wide, the gap,
5 t , for the equivalent smooth-core armature, as given by formula (58), might
have to be slightly modified; but the calculation of fringing at the sides of
vent ducts is usually an unnecessary refinement.



118 PRINCIPLES OF ELECTRICAL DESIGN

of the iron in the tooth becomes equal to unity that is to say,
equal to the permeability of the air paths that this parallelism
of the flux lines would occur, and the equivalent air gap would
be b e = 5, to which would have to be added another air gap of
length d (Fig. 37) to represent the reluctance of the teeth and
slots. This is an extreme, and indeed an impossible, condition;
but, since the actual distribution of the lines of flux in tooth and
slot cannot be predetermined, the calculations for very high
densities are usually made by assuming the flux lines to be
parallel, as indicated in Fig. 37. It is when this assumption is
made for low values of the density that appreciable errors are
likely to be introduced. The following method of calculating
the joint reluctance of tooth and slot should not be used for tooth
densities below 20,000 gausses.

Considering 1 cm. only of axial net length of armature core
(i.e., I cm. total thickness of iron), the reluctance of the air
gap and tooth, taken over the width of one tooth only, is,

_ d d _ (d + M g)
Kl ~ t + id ~ tf

The reluctance of the slot portion of the total tooth pitch is,



The air gap of the equivalent smooth-core armature being the
reluctance per square centimeter or the reciprocal of the perme-
ance per square centimeter is, therefore,



e=



which can be put in the form,

(*+)(<*+)



(59)



This equivalent air gap includes the reluctance of the tooth itself
when the flux density is high, but does not take account of the
flux in the vent ducts and spaces between stampings. It is
seen to depend upon the permeability of the iron, and, therefore,
upon the actual flux density in the tooth. In order to make use
of formula (59), a value for the flux density in the tooth must be
assumed. A method of working which involves a change in the



FLUX DISTRIBUTION 119

equivalent air gap for various values of the flux density would
be unpractical, and, since no exact method is ever likely to be
developed, some sort of compromise must be made.

Length of Air Gap. The air-gap clearance 5 must, of course,
be decided upon before the calculation of tooth and slot reluctance
can be made. The controlling factor in determining this clear-
ance is the armature strength or the ampere-turns per pole of
the armature. If the m.m.f. due to the armature greatly exceeds
the excitation on the field poles, there will be trouble due to field
distortion under load, which will lead to poor regulation and
commutation difficulties. The field ampere-turns at full load
should be greater than the armature ampere-turns. A safe rule
is to provide an air gap such that the open-circuit ampere-turns
required for the air gap alone assuming a smooth core and no
added reluctance due to slots would be equal to the ampere-
turns on the armature at full load. Thus if (SI) g are the ampere-
turns per field pole required to overcome the reluctance of an
air gap of length 6, we may write (SI} = (SI) a where (*$/)<,
stands for the armature ampere-turns as calculated by formula
(48) page 80. This gives for 6 the value:



or, approximately,



(SI)g X 0.4rr .
2.54J9,



where B g may be taken as the apparent flux density in the
air gap under the pole face on the assumption that there is no
fringing. (For approximate values of B a , refer to the table on
page 75.)

The length of air gap may be somewhat reduced if corn-
mutating interpoles are provided, especially if pole-face windings
(see Art. 50, Chap. VIII) are used.

Another factor which may influence the air-gap clearance is
the possibility of unbalanced magnetic pull due to slight decen-
tralization of the armature. This becomes of importance only
in machines of large diameter with many poles and rarely
necessitates a clearance greater than that obtained by applying
the above rule.

37. Actual Tooth Density in Terms of Air-gap Density.
It is convenient to think of the reluctance of air gap, teeth, and



120 PRINCIPLES OF ELECTRICAL DESIGN

slots as consisting of two reluctances in series, (a) the reluctance
of the equivalent air gap (as calculated by formula (58) for the
center of the pole face), and (6) the reluctance of the tooth.
The calculation of this latter quantity depends upon a knowledge
of the actual flux density in the tooth. For low densities in the
iron up to about 20,000 gausses the actual tooth density will
be approximately equal to the apparent density; that is to say,
practically all the flux entering the armature over one tooth
pitch will pass into the core through the root of the tooth. For
densities exceeding 20,000 gausses, a closer estimate of the correct
value of the tooth density may be made by assuming the con-
dition of Fig. 37.
Let the meaning of the symbols be as follows:

B g = the average air-gap flux density at armature surface;
i.e., the average density over one tooth pitch of width
t -\- s and length l a .

B t = the actual tooth density.

B 8 = the density in the slot and air spaces.

<I>x = the total flux entering armature core in the space
of one slot pitch.

l n = the net length of the armature core (iron only).
The other dimensions as given on the sketch Fig. 37.

If the assumption is made that the lines of flux lie in a plane
exactly perpendicular to the axis of rotation, it might be argued
that the flux in the ventilating ducts and in the insulating spaces
between the iron laminations does not enter the iron of the
armature core; and the reluctance of the paths followed by this
flux would therefore be very high. This argument is not justi-
fied since the flux lines in the ventilating ducts will actually



Online LibraryAlfred StillPrinciples of electrical design; d. c. and a. c. generators → online text (page 10 of 30)