IMPROVEMENTS IN CENTRIFUGAL GOVERNORS FOR REGULATING STEAM ENGINES AND OTHER MOTORS ALSO APPLICABLE FOR THE CONSTRUCTION OF SPEED INDICATORS FOR ROTATING SHAFTS
Year: 1882

page_text: LETTERS PATENT to William Phillips Thompson of the Agency for Foreign
Patent Solicitors 6 Lord Street Liverpool in the county of Lancaster and of
323 High Holborn in the county of Middlesex Civil Engineer for an inven--
tion of "IMPROVEMENTS IN CENTRIFUGAL GOVERNORS FOR REGULATING STEAM
ENGINES AND OTHER MOTORS ALSO APPLICABLE FOR THE CONSTRUCTION OF
SPEED INDICATORS FOR ROTATING SHAFTS Communicated to him from abroad
by Johann Selwig of Brunswick in the Empire of Germany
.
COMPLETE SPECIFICATION filed by the said William Phillips Thompson at
the Office of the Commissioners of Patents on the 7th June 1882.
WILLIAM PHILLIPS THOMPSON of the Agency for Foreign Patent Solicitors
6 Lord Street, Liverpool in the County of Lancaster and of 323 High Holborn in
the County of Middlesex, Civil Engineer "IMPROVEMENTS IN CENTRIFUGAL
GOVERNORS FOR REGULATING STEAM ENGINES AND OTHER MOTORS ALSO APPLI-
CABLE FOR THE CONSTRUCTION OF SPEED INDICATORS FOR ROTATING SHAFTS
"
Communicated to me from abroad by Johann Selwig of Brunswick in the Empire
of Germany
The following is an exact translation of the specification forwarded to me by my
correspondent along with the drawings annexed hereto with orders to file
The construction of this governor designed for regulating steam engines and
other motors also applicable for the construction of a speed indicator for rotating
shafts, consists in the employment of a rotating pendulum oscillating in a circular
path and in which the moment of the centrifugal force is proportional to the sine
of the angle which the pendulum arm (the normal let fall from the centre of
gravity of the pendulum upon its axis) or a line drawn through the point of
suspension of the pendulum in its plano of oscillation and inclined to it at any
angle, makes with a plane parallel to the axis of rotation passing through the axis
of the pendulum.
Now if ym be the angle which the pendulum arm makes with this plane and m

page_text: case, man possible positions of one pendulum (of 10 any
me
constant sin Ym
A pendulum possessing this property may be called a "sine pendulum" or in
contradistinction to the one hereafter mentioned, "a perfect sine pendulum
In the second case, we should have for all positions of the pendulum
m = constant sin (m + n)
A pendulum possessing this property may be called an "imperfect sine pendulum,"
when is greater or less than 90°. In this last, as we have sin (7m + n) = cos
sin sin cosm, me depends as much on sin Ym as cos Ym and not on cos m
alone, since cannot = 90° and consequently cos cannot = 90°
"
The pendulum becomes a "cosine pendulum" when = 90°. because then we
have me constant cos Ym This cosine pendulum may be called a
" cosine
pendulum with inclined axis.'
The characteristic property of each of these sine pendulums and of this new
cosine pendulum with inclined axis consists in their having the axis inclined at an
acute or obtuse angle upon the axis of rotation or upon the plane of rotation
perpendicular to this latter; the other properties which it must also possess will
be examined hereafter
Figs 5, 6 and 7 (sheet 1) represent respectively projections upon the planes xy,
yz, and xz, and Fig 8 a projection upon the plane of oscillation of the pendulum.
In these figures y y is the axis of rotation and AO the axis of the pendulum which
cuts yy at the point O at an acute angle a = 90° - B-The pendulum which
oscillates around AO is only represented in the drawing by two particles (supposed
to be of infinitesimally small size) situated at the points S, and S₂ their weights
being G, and G, and their arms S₁n and S₁n may be designated by r, and r₂.
Let G be the total weight of the pendulum, S its centre of gravity, 7m the
normal Sn upon A O (that is to say its arms) Let 7, 7, and ym be the angles
which r₁r, and Ym make with the plane A Oy. Let &, and d₂ be the angles which
the pendulum arms r₁ and r₂ make with the plane drawn through S or 7m and the
axis of the pendulum AO, angles which are of constant magnitude so that
₁ = m₁ and Y2
7m+
Let b₁, b, and bm be the distances between n₁, n, and n, the centres of rotation
of the pendulum arms, and the point 0 (the point where the axis of the pendulum
cuts the axis of rotation, or the plane yz, if these two axes do not intersect)
Let ₁ = nn₁ Նջ: =nn, et cetera, be the distances of the points S, and S, from the
plane of oscillation of the pendulum arm Sn so that thus b₁ b + b₂ = b + l₂
and so on. Let C, and C₂ be the centrifugal forces generated in S, and S₂,
Mc, and Mc, their moments about the pendulum axis (in the positive direction)
Let D, and D, E, and E, be their components parallel to Ox and Oz, the
moments of which components are respectively Md, and Md., and Me, and Me,
=
Let as above designated, Mc be the total moments of the centrifugal forces
produced in the pendulum; Mg the moment of the weight G of the pendulum, the
axis of rotation being in a vertical position; Mp the moment of a force P parallel
to yy, and acting at a point situated in the plane ASO at a distance rp from AO
Now suppose that the axis A O of the pendulum is rotating around yy, with au
angular velocity of w per second. Then the moment of centrifugal force C₁ of the
particle of the pendulum situated at S, is

page_text: If the pendulum axis does not intersect the axis of rotation but lies towards OZ
at a distance e from y y, or from the plane x y₁ we have
II
Ma
=
w2G
g
1
(r₁b₁ sin cos ẞ siny₁ + er₁ cos ₁ + 7³, cos² ẞ sin ✗₁ cos ₁)
If we substitute for y, in equation II its value 7 +ò̟₁, we get
w2G,
III
M C₁
-
g
IIIa Mc
1
[(sin ß cos Br, b₁ cos d₁-r₁ e sin d₁) sin 7m + (sin ẞ cos Br₁ b₁ sin d₁
+re cos d₁) cos m + cos² B) r², cos² 2, sin² 6) sin Ym cos Ym
+cos, sin ₁ cos d₁ (cos² m sin² 7m)]
or replacing 6, by bm + ↳₁
woºG.
g
-
1
== [(sio ẞ cos ẞr, bm cos d₁ + sinẞ cos Br₁₁ cos à₁-r₁ e sin ₁) sin m
+(sin ẞ cos ẞr, bm sin d, + sin ẞ cos Br₁ 4 sin d₁ + r₁e cos d₁) cos m
+ cos(r², cos³ 2, sin³) sin 7m cos m + cos³ Br², sin d₁ cos &₁
102
-
(cos² Ym sin² 7m)]
-
In this expression 7m is the only variable quantity. But the total moment of the
centrifugal force of the pendulum is Mc Mc₁ + Mc₂ +
= Σ (M c) then
{[sin ẞ cos BΣ (Grb cos d) + e Σ (G r sin 6)] sin m + cos³ B
[Σ (Gr² cos² 8). Σ(Gsin)] sin m cos m + [sin ẞ cos BΣ
(Grb sin ) + e Σ (Gr cos 8)] cos m + cos² BΣ (Gr³ sin & cos 6)
Mc =
[cos² Ym
-
----
sin³]}

page_text: In the first case (a) we must have Lv=Bv=O because sin ẞ cos ẞ is greater orð
less than O
Lv is, amongst others, equal to O in pendulums in which the plane drawn
through the centre of gravity and the axis of the pendulum, or the plane drawn
through the centre of gravity perpendicular to the axis of the pendulum (in Fig 1
the planes ASO or S, N, S₁), is a plane of symmetry, as in the case in the
pendulums employed in the regulator represented in the drawing.
But we must at the same time have e Grm=0, that is to say e=0˚or rm=0.
In this case then the pendulum axis must intersect the axis of rotation, or the
distance rm of the centre of gravity from the pendulum axis must = 0 that is to
say, that the moment of the weight of the pendulum must = 0.
This last case deserves special consideration. Sine pendulums, in which rm=0,
we may regard as sine pendulums in equilibrium and possess this peculiar property,
that BzLz is independent of the distance bm of the pendulum from the point 0:
and consequently constant, and that further Mc is also independent of the distance e
of the pendulum axis from the axis of rotation. In these pendulums then, the
moment of the centrifugal force only depends on the inclination of the pendulum:
axis to the plane of rotation, but not on any other position that it can occupy in
relation to this latter. Amongst others, a sine pendulum in equilibrium may be
obtained by combining with any sine pendulum, a pendulum sinilar to it in such
way that the two pendulum arms make upon their axis between them an angle
of 180°, though they must still be a certain distance apart, upon the amount of
which distance Lz depends
that is to say that if the distance e of the pendulum axis from the axis of rotation
is given, there exists a certain distribution of the masses determined by the
preceding relation, which makes the pendulum a perfect sine pendulum. Inversely,
for every pendulum in which Lv is greater or less than O, there exists a certain
distance e for which the pendulum becomes a perfect sine pendulum.
In the perfect sine pendulum, Mc can always be replaced by the moment of a
single constant force acting parallel to the axis of rotation, such for example as
gravity, the point of application of which is in the plane ASO, drawn through the
centre of gravity of the pendulum and through the pendulum axis. In the imperfect
sine pendulum, the plane drawn through the point of application of this force and
through the pendulum axis makes an angle 7 (see equation IX) with the plane A SO.
In the cosine pendulum this angle is 90°.
102
g
-
In the cosine pendulum with inclined axis, for which we have (see equation X).
Mc
(sin cos Bv + e Grm) cosy, the distribution of the masses must be
such that we have BzLz+bm Grm=O and Bv is greater or less than 0; but e
and rm can have any magnitude and even be equal to O. In order that BzLz+
|bm Grm=0, bm or rm and at the same time L2 must=0 or bm Grm must = − Lz.
A cosine pendulum may be obtained for example in the following manner.
If in the double pendulum G₁ G, represented in Sheet 1 (Fig. 1), one of the
pendulums G, is brought nearer to the axis y y, so as to bring it into the position
shown in dotted lines, in which its centre of gravity is at S₁, this pendulum
becomes first an imperfect sine pendulum, in which then Bv = G₁ (- SS, x
N, O+S S, x N, 0) = — G₁ × SS, xN, N, whilst Bz = G, × SN, (N, O+N, O).
But as soon as the arm of the pendulum S, N, passes above the point O, N, O
becomes negative, whilst then the negative quantity Bv increases with the distance
N, N, Bz becomes continually smaller and O when N, O
-
=
-
N, O
The pendulum is then a perfect cosine pendulum in which in the position
represented Mc= O and in general Mc is negative-So if, whilst the pendulum G,
remains in its position, the pendulum G, is pushed beyond the point O, we get

page_text: equally a perfect cosine pendulum, but one in which Mc is positive. As in these
cosine pendulums Bi has exactly the same magnitude as Bz in the sine pendulum
from which they proceed the maximum moment of the centrifugal force has also
exactly the same magnitude in both.
The cosine pendulum with inclined axis remains, as shown by equation X, a
perfect cosine pendulum when its axis is transported to a distance e from the axis
of rotation Mc then increases only from the quantity Le Grm cos 7m)
102
The cosine pendulum with inclined axis in which rm = O, possesses with the
sine pendulum in equilibrium this common property, that Mc is independent of e
so that its axis can be situated at any distance from the axis of rotation without
Mc varying.
As all the pendulums above described, that is to say the perfect sine pendulum,
the imperfect sine pendulum, and the cosine pendulum with inclined axis, can, as
previously stated, be replaced by the moment of a constant force in a constant
direction, all these pendulums are suitable for obtaining regulators completely
astatic.
The perfect sine pendulum is by itself a completely astatic regulator provided
that rm is not = O and that the axis of rotation is vertical, since the moment of
the weight of the pendulum Mg is constantly proportional to Mc. But, further,
the moment Mp of a force P parallel to the axis of rotation and applied at a
point situated in the plane ASO at a distance rp from the pendulum axis, can still
act upon the pendulum in the same direction as the weight or eventually in a
contrary direction.
The pendulum is in equilibrium when M c + Ma + M = O. or. as Maand M

page_text: 610 B (Lz+bmĠrm)
0
In the cosine pendulum w² = 1, that is to say that the velocity remains
indeterminate. We must then introduce Lv instead of Lz and we then get
XVIIa
شروح
Prp sin 3 cos B
= 9 sin ẞ cos B L v + e Gr m
It is self evident that in all the cases hitherto considered, the force P may act
at a point situated with the point of application of the force G in the same plane
A SO, only the direction in which P acts must then be different to that of G; this
direction must be inclined to the axis of the regulator at an angle ( 3)
=
In many cases, when for example the axis of the regulator oscillates, we cannot
by the aid of gravity obtain the force P constant and acting in a constant direction.
But its moment Mp constant x Prp sin ym can be replaced or produced by the
variable push or pull of a spring (preferably a spiral one) as soon as there is given
to this spring a direction which is not parallel to the axis of rotation, but variable.
The spring must then be arranged in the manner represented in Fig. 9.
Fig. 9 shows a vertical section through the axis of a sine pendulum G the arm
of which makes an angle Y with the plane NN, drawn through its axis parallel
to the axis of rotation. The moment M p must then also = constant x Prpsin ym¨¨
The point T situated at a distance rp from the axis O of the pendulum, is the point
of application of the force P; the pressure Q exerted by a spiral spring F is also
applied at this point and in such a way that this pressure is constantly directed
towards a point W situated in the plane N N₁ and at a distance h from the
point O.
か
It is convenient to arrange this point, as in the case represented, so that the
plane TWO is perpendicular to the pendulum axis. The spiral spring F is placed
between the discs V and W, this latter can turn in lateral axles. A shaft
terminating at the point T traverses the two discs. It results from this arrange-
ment that as soon as y increases, the spring is compressed since it turns in the
same time around W.
If the angle TWO made by the spiral spring with N N₁ be e, we get for the
moment of the pressure exerted by the spring
sin €
TP
But as
sin Y
TW
Мр
===
Qh sin €
rpsin Yea
we get
TW
=l
which gives sin € =
Qhrp sin Y
Mp =
TW
=
or putting TW
Mp = hrpsin ym

page_text: Instead of employing the pressure of the spiral spring one can also use the pull
exerted by it by fixing it to the disc V and fastening to this latter a socket
extending to the disc W and provided at this point with axles, in which socket the
spring is placed. In this case the extremity of the spring acts directly on T, whilst
the distance V W remains constant.
As Mp depends on h, we can by increasing or diminishing h, increase or diminish
at will the moment Mp if the same spring be used. The displacement of the
point W furnishes then, since the angular velocity w depends on Mp an exceedingly
convenient means of adjusting the regulator for different velocities. If the
value hrp must increase in proportion as 7m increases Q must = O when lis
greater than O.
In practice, the regulators cannot in the majority of cases be completely astatic ;
they can only be nearly astatic, that is to say that the velocity of rotation w must
be a little greater in the highest position of the regulator than in the lowest, so
that it must increase a little with the angle Ym
This result is obtained in various ways:
(1) By employing an approximately sine or cosine pendulum in which the value
(Tz-Tv)= [Σ (Gr 2 cos² 8) - Σ (G² sin²)] is not = O but positive or negative.
In the greater number of cases, as for example in the regulators represented in the
accompanying drawings, we are obliged to use this method of making the regulator
non-astatic.
(2) By employing an imperfect sine pendulum in which the value (sin ẞ cos B
Le Grm) is positive.
(3) By causing the force P to act in such a way that the angle Ym of the
pendulum for which (Mg + Mp) is a maximum may be less than the angle for
which me is maximum.
The sine pendulum or the cosine pendulum with inclined axis may be employed
like most other rotating pendulums for the construction of tachometers (measurers
of the velocity of revolving shafts) which we consider well known.
Mc
In this case for a constant velocity of rotation, the relation M9+ MP cannot be
constant, but must increase rapidly when the angle 7m increases. It is no longer
necessary that Mc should be proportional to sin (m +7) For this reason, we can
employ for the construction of tachometers not only sine or cosine pendulums,
but in general, pendulums with inclined axes which do not consequently possess the
distribution of mass required by the relations Vid and VIe
Generally, to produce the moment Mc, a sine or cosine pendulum is used in
which rm= O, and to produce the moment Mp a spring is used. The length of
path of the pendulum or the angle ym which is measured in any manner by
transmission to an indicator, then determines the velocity of rotation of the axis of
the tachometer.
Sheet 1 of the accompanying drawings represent a regulator which is composed
essentially of two approximately perfect sine pendulums, and which may be called
a sine regulator. Fig 1 is a front elevation (in the plane of the two pendulum
axes) Fig. 2, a side elevation. Fig. 3 a part plan looking at the top and part
section on line qq of Fig. 1. Fig 4 a transverse section on line uu of Fig 1,
parallel to the plane of oscillation of the right pendulum.
The two sine pendulums G are entirely alike and they are arranged at the same
height and diametrically opposed to each other. They are represented in their
mean position, in which the pendulum arm SN is horizontal, that is to say
rm = 90°
Each pendulum consists of two spherical balls G, and G, fastened together and
arranged symmetrically with relation to the plane A SO drawn through the centre
of gravity of the pendulum axis and these two pendulums make between them an
angle of 90°. The pendulum axis is formed in some sort by a second sine pendulum,
that is to say by a casting C in the form of a hollow semi-cylinder turning round

page_text: =
determine by their ascending and descending motion the adjustment of the regu-
lating mechanism of the motor. (b) with perfect or imperfect sine pendulums or
with cosine pendulums with inclined axis, which are combined by means of levers
fixed to them, with an ascending and descending loading weight or with stretched
springs, so that the sum of the moment of rotation (Mp) exerted by the weight or
spring upon the pendulum, and of the moment of the weight (M 9), may be pro-
portional to the moment of the centrifugal force (Mc) in all positions of the
pendulum and for a constant velocity of rotation, that is to say that we
Mp + Mg
have
constant, the pendulums determining by their ascending and
descending movement the adjustment of the regulating mechanism of the motor.
Approximately astatic regulators are obtained in the manner described above
by fulfilling only approximately the conditions which make regulators astatic,
and specially by employing pendulums in which the distribution of mass is only
approximately that prescribed by the relations VId and VIe, or by combining the
pendulum with a loading weight or a spring in such a way as that for a constant
velocity of rotation the relation Mp+M is not constant, but increases slightly
when the angle m of oscillation of the pendulum increases.
"
Mc
Mc
2nd The manufacture of "tachometers" by means of "pendulums with inclined
axis in the manner indicated in the immediately preceding paragraphs, exactly
as a very non-astatic (static) regulator
In these instruments, the pendulums are connected to a movable index upon a
fixed scale in such a way that the index shows directly the position of the
pendulum, and thus at the same time the velocity of rotation of the axis of the
tachometer which corresponds to this position.
In witness whereof I the said William Phillips Thompson have hereunto
set my hand and seal this Sixth day of June in the year of our Lord One
Thousand eight hundred and eighty-two.
W. F. THOMPSON
(L.S.)