Improvements in and relating to Ball Bearings.
Year: 1895

page_text: Date of Application, 19th Feb., 1895-Accepted, 13th July, 1895
Improvements in and relating to Ball Bearings.
I, CESARE CASALEGNO, of 25-27 Via Ormea, Turin, in the Kingdom of Italy,
Manufacturer, do hereby declare the nature of this invention and in what manner
the same is to be performed, to-be-particularly described-and-ascertained in and
by the following statement:-
My invention relates to ball bearings.
"
Among the ball bearings heretofore proposed and applied to velocipedes there is
none which presents such a shape that each ball, while serving as a suitably firm
support for the surface of contact of the bearing which it keeps apart by its
interposition, may nevertheless be adapted for the perfect rolling and development
against these surfaces so as to transform the ordinary sliding friction into rolling
friction of the balls in a complete manner such as is rendered possible by the most
delicate mechanical means of construction.
In all the well-known bearings of this kind the ball rolls exteriorly with regard
to the axis of the shaft or axle upon conoidal surfaces, and interiorly upon
spheroidal surfaces, whose action in an axial plane of the shaft or axle presents a
radius of curvature almost equal to that of the balls; consequently these surfaces
or zones for the rolling embrace a very large arc of the circumference of the balls
instead of bearing upon a single point of each of them. There is therefore a
notable difference in the linear velocity between all the points in contact (except
one of them) of the ball and the corresponding points of the zone. Supposing the
zone Z Figure 1 to rotate and admitting that the linear velocity is equal at any
point 1 of the contact of the ball B with Z', the linear velocity at any other
point 2, 3 etc. will evidently be a function of that of the point 1 proportionately to the
relation of the two radii of rotation of 1 and of the fresh point considered, this
being the case upon the ball as well as upon the zone; now these relations one in
respect of the ball and the other in respect of the zone will be different from each
other. For example if the point 1 is the mean point of the arc of contact, and if
the two points 2 and 3 on the ball are at an equal distance, one being on each side
of 1, it is clear that their linear velocity is the same by reason of the equality of
their radii of rotation 2m, 3n, while on the other hand the linear velocity on the
zone at the point 3 will be greater than at the point 2, the radius of rotation 3r
being greater than 2g. Accordingly the rolling of the ball upon the said zone
will be accompanied by much sliding, so that this movement takes place with
considerable friction. Such is also the case when the movable surface should be
on the exterior Z'. This defect is very noticeable in the bearing for the handle-
bar shaft of the velocipede, where the ball must roll on four zones which are
not arranged more suitably than those of the bearings for the pedals or the
wheels.
It is true that some manufacturers have already attempted to modify the
construction of these zones for the rolling with the object of diminishing the
beforementioned defect of too great friction to be tolerated in these types of
vehicles; but no one has heretofore proposed a practical arrangement, that is to
say one based on the rules of kinematics and therefore capable of giving a perfect
rolling movement unaccompanied by sliding.
Now my invention has for its object to obviate the aforesaid inconvenience in an
absolute manner theoretically, and also approaching practically as nearly as
Dossible exactitude by the most careful and most perfected construction.

page_text: constituting the other zone. Either of these two zones may be fixed, while the
other is movable.
The simplest case of this construction is represented in Figure 2, wherein the
two tangents n' N', n² N³, acting as generatrices are perpendicular one to the
other at V, and the two surfaces whose connection constitutes the first zone are
plane (that is to say conical, with the centre or apex at an infinite-distance); B is
the ball having its centre at O and its tangent points at N¹ N. These latter are
obviously the centres of instantaneous and simultaneous rotation of the ball upon
this zone; and therefore the straight line N N which connects these two points is
the axis of instantaneous rotation, and the straight line m² 0 m² diametrical and-
parallel to N N is the axis of rotation of the ball. The second zone, having
always to be at the same distance from the first in relation to the diameter of the
ball, will also be a plane, and its generatrix n n will be a straight line parallel to
the axis of rotation'm² m² and therefore to the straight line of junction of the two
centres N¹ N' of instantaneous rotation, that is to say will be the tangent to the
circumference at the point N situated at the opposite extremity of the diameter ON
perpendicular to N¹ Ñ.
I will now pass to the general case of the conic zones (that is to say having
their centre apex of the cone at a finite distance) represented in Figure 3.
✗' X2 is the common axis of the shaft or axle and bearing; O is the centre of the
ball B having a diameter suitably fixed beforehand in relation to the distance of
the axis X'X' at which its centre is placed; n' N' and n² N2 are the two tangents
and generatrices of the two surfaces constituting the first zone for the rolling.
The tangent points N¹ N³ are here also the centres of instantaneous rotation, and
the straight line N' N2 is the axis of the same; and the point of intersection M
of this axis of instantaneous rotation with the axis X'X' of the general movement
of the machine is the centre of continuous rotation of the whole-system, that is to
say is the apex of the virtual cone upon which the centre of the ball must roll, so
that the straight line MO is the axis of rotation of the ball. Accordingly the
second zone is a couic surface enveloping the ball in its movement; and its
generatrix is the tangent M N exterior to the circumference which is easily traced
according to the well-known simple rules of geometry.
For having this construction well defined and ready to be applied in practice it
will be sufficient to determine beforehand the angle n' V n² and its position with
regard to the axis X' X2 of the general movement; which is obtained by the study
of the forces to which the bearing will be submitted both perpendicularly and
parallel to the axis X1 X2 (which forces it will be easy to calculate for each special
application), and on the principle of reducing to a minimum the normal pressure on
each surface resulting from the decomposition of the said forces. Without giving
here the calculations which any engineer will easily make it may be mentioned that
for bearings of wheels of roadsters, by taking into account the ordinary normal
weight of the machine, the mean additional load which it has to bear, and also the
oscillations and vibrations produced in the riding by the most probable unevenness
of the ground, I may give to the angles n' V n² and X' M N the mean values
respectively of about 112° to 115° and 20° to 25°. Figure 4 represents one-half of
such a bearing for the axle of the front wheel of a bicycle.
For other cases I may vary these values more or less without however departing
too much therefrom, for they are very suitable in most cases and very approximately
give rise to a minimum wear of the several parts of the bearing.
For example Figure 5 represents the arrangement to be used for opposing
longitudinal forces (parallel to the shaft or axle) which are more considerable than
in the previously mentioned instances by reason of a greater inclination X' M N
equal to about 40° and the angle N¹ V N³ equal to about 110° to 112°. On the
other hand Figure 6 shows the arrangement to be used for example for the
bearings of the pedal shaft of all types of velocipedes; where the longitudinal forces
are much less sensible than in the preceding examples relatively to those which are
perpendicular to the shaft; and where consequently there may be a much smaller

page_text: conical surfaces, two of these three surfaces being connected to constitute one of
the zones for the rolling, preferably the interior, and the third surface alone con-
stituting the other zone conjugated with the first, and the arrangement of these
two zones for the rolling of the balls so that the cone of the single zone and that
of the axis of instantaneous rotation of the. ball upon the double zone have a
common apex situated in the axis of the shaft or axle of the machine preferably
at a finite distance, or in certain special cases at an infinite distance, for the
purpose of entirely preventing the sliding of the balls and rendering their rolling
perfect and of obtaining upon the entire periphery of the bearing an absolute
uniformity in the resistance opposed to the movement of the latter, substantially
as hereinbefore set forth with reference to the drawings.
Dated this 19th day of February 1895.
HASELTINE, LAKE & Co.,
45 Southampton Buildings, London, W.C., Agents for the Applicant.