Improvements in the Production of Bevel Gear Wheel Teeth
Year: 1894

page_text: Date of Application, 8th May, 1894
Complete Specification Left. 6th Nov., 1894-Accepted, 8th Dec.. 1894
PROVISIONAL SPECIFICATION.
Improvements in the Production of Bevel Gear Wheel Teeth.
A communication from abroad by GEORGE B. GRANT, of Lexington, in the State
of Massachusetts, one of the United States of America, Manufacturer.
ALFRED GEORGE BROOKES of 55 & 56 Chancery Lane, in the County of
London, Chartered Patent Agent do hereby declare the nature of this invention to
be as follows:-
This invention has for its object the production of a bevel gear having a novel,
theoretically correct tooth.
A bevel gear embodying my invention has teeth the flanks of which are
planes, and faces which are curved surfaces conjugate to the plane flanks of a
mating tooth.
The term "conjugate" as herein used may be defined as follows; viz. :-When
the pitch circles of two mating gears are rolled together without slip, any curve on
one gear is conjugate to a curve or line on the mating gear when it works in
contact with the said curve or line during the rolling of the two pitch circles
together.
This form of a bevel gear tooth, so far as my correspondent is aware, is entirely
new and original with him, and he, therefore, designates it the "planoid" bevel
gear tooth, the name being taken from the peculiar curve of the face which he has
termed a "planoid curve.
To generate the curved tooth face of a planoid tooth embodying this invention,
he employs a cutting tool, preferably a milling tool, having a straight cutting edge
or edges which coincide with an imaginary plane in the position of the flank of a
tooth with which the tooth being generated is to mate.
The gear blank in which the tooth is to be generated or formed, and the cutting
tool are given a relative motion as of the pitch cones of the gear blank and mating
gear (the latter pitch cone carrying the cutting tool) rolling one upon the other,
whereby the cutting edge of said tool in moving in the position of the plane flank
of the mating tooth, is caused to generate or sweep up a curved tooth surface
conjugate to the plane flank of a mating tooth in the plane of which said cutting
edge lies and coincides.
The flanks of the improved tooth may be of any desired practicable planes, they
being preferably, however, planes which are radial with relation to the axis of the
gear; and I have made reference herein in describing my invention to a radial
flanked tooth, but it is to be expressly understood that the invention is not restricted
to the use of radial flanks.
I have described my improved tooth with radial flanks, as not only preferable
because of convenience in manufacture, but also because it is the nearest like
a so-called "radial
flanked epicycloidal tooth," from which it must be
distinguished.
The lines of action (i.e., the curved lines in arcs of which the moving points of
contact between two mating teeth travel) in the case of two mating radial flanked
planoid teeth, said lines of action being non-circular, that is oval in shape,
when the flanks of the teeth are radial, pass through the axis of the respective
gears.

page_text: Where the flanks of the planoid tooth are not radial planes but planes drawn
tangent to a circle or circles about the axis of the gear, tangent to the circles, the
lines of action of the teeth, instead of passing through the axes of the gears will be
tangent to the circles to which the plane flanks of the teeth are tangent.
In order that my invention may be clearly understood it is necessary to
differentiate my improved tooth with the form of tooth which is the nearest
approach to it, viz. :-the "so-called radial flanked epicycloidal tooth," in order
that the difference between the two may be clearly understood.
It will be noticed that I speak of this nearest approach to the improved tooth, as
the so-called " radial flanked epicycloidal tooth.
This is because there can be no theoretically correct epicycloidal tooth having
flanks which are planes, for the face of an epicyeloidal tooth is an epicycloid, and
it is a demonstrable fact that if the face of a tooth is an epicycloid the mating
flank must be a hypo-cycloid and not a plane; therefore a tooth having faces
which are epicyeloids and flanks which are planes is not and cannot possibly
be a theoretically correct tooth and for this reason it cannot have a definite line
of action.
The true epicycloid bevel gear tooth is a theoretically correct tooth but it cannot
have flanks which are planes.
Although the divergence of the flanks from the plane flanks of a planoid tooth is
slight, yet there is a divergence which may be proven by comparing the lines of
action of the two teeth.
If we project on paper the lines of action of two theoretically correct epicycloidal
bevel gear teeth corresponding in size with the planoid teeth, also shewn in said
drawing, it will be noticed that these lines of action are true circles passing through
or intersecting the axes of the respective gears.
While the line of action of a planoid tooth is never a true circle, the line of action
of an epicycloidal bevel gear tooth is always a circle within the line of action of the
radial flanked planoid tooth corresponding to it.
The divergence between the lines of action of the two teeth compared is only
slight, but the two lines of action for bevel gears can never coincide, though the
divergence gradually lessens as the radius of the sphere increases until the radius
of the sphere becomes infinite when the divergence disappears entirely, both forms
of gear then becoming the common epicycloidal spur gear.
While the divergence between the plane flank of the planoid tooth and the curved
flank of the epicycloidal bevel gear tooth is only slight, yet in connection with the
actual formation of the tooth it is a very material divergence, for while the plane
Hank of the planoid tooth may be easily and quickly formed by a simply cutting
tool having a straight cutting edge or edges it has heretofore been found
impracticable to form the slightly curved flank of the true epicycloidal bevel
gear tooth.
The difference between the two teeth then is the difference between a tooth
which has never yet been practically produced and a tooth which can and has been
practically produced.
It is not essential that the flanks of the planoid teeth of both gears of the
mating pair be similar, for while it is preferable on account of simplicity and case
of construction that both should have radial flanks, yet one may have radial flanks,
and the other flanks which are not radial.
Dated the 8th day of May 1894.
WM. BROOKES & SON,
55 & 56, Chancery Lane, London, Agents for the Applicant.

page_text: A communication from abroad by GEORGE B. GRANT, of Lexington, in the State
of Massachusetts, one of the United States of America, Manufacturer.
I ALFRED GEORGE BROOKES of 55 & 56 Chancery Lane, in the County of
London, Chartered Patent Agent 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 :-
This invention has for its object the production of a bevel gear having a novel,
theoretically correct tooth.
A bevel gear embodying my invention has teeth, the flanks of which are planes,
and faces which are curved surfaces conjugate to the plane flanks of a mating
tooth.
-When
The term "conjugate" as herein used may be defined as follows, viz. :-'
the pitch circles of two mating gears are rolled together without slip, any
curve on one gear is conjugate to a curve or line on the mating gear when it
works in contact with the said curve or line during the rolling of the two pitch
circles together.
This form of a bevel gear tooth, so far as my correspondent is aware, is entirely
new and original with him, and he therefore, designates it the "planoid " bevel gear
tooth, the name being taken from the peculiar curve of the face which he has
termed a planoid" curve.
6:
To generate the curved tooth face of a planoid tooth embodying this invention,
he employs a cutting tool, preferably a milling tool, having a straight cutting edge
or edges which coincide with an imaginary plane in the position of the flank of a
tooth with which the tooth being generated is to mate.
The gear blank in which the tooth is to be generated or formned, and the cutting
tool, are given a relative motion as of the pitch cones of the gear blank and mating
gear (the latter pitch cone carrying the cutting tool) rolling one upon the other,
whereby the cutting edge of said tool in moving in the position of the plane flank
of the mating tooth, is caused to generate or sweep up a curved tooth surface
conjugate to the plane flank of a mating tooth in the plane of which said cutting
edge lies and coincides.
One form of apparatus for generating teeth upon a bevel gear embodying this
invention is shewn and described in my application for Patent No. 402 dated
January 8th 1894, to which reference may be had.
The accompanying drawing Fig. 1, represents in end view a bevel gear having
teeth embodying my invention; and Fig. 2 represents upon the surface of a sphere
parts of the outlines of two meshing bevel gears embodying this invention, the lines
of action of the teeth being shewn by dotted lines, said drawing also shewing the
lines of action of the so-called radial flanked epicycloidal tooth, the nearest
approach to my improved tooth and easily mistaken for it, in order that the
invention and the difference between it and this nearest approach to it may be
clearly understood.
Referring to the drawing Fig. 1, B is an end view of a gear embodying my
invention, and in Fig. 2 A and B represent in outline upon the surface of a sphere
the gear shewn in Fig. 1 and another in mesh with it, said bevel gears having
planoid teeth A', B', embodying my invention, the same having, respectively,
flanks a, a, and b, b, which are planes, and faces a', a', and b¹, b', which are
curved surfaces conjugate to the planes constituting the flanks of the mating
tooth.

page_text: I
The flanks of the improved tooth may be of any desired practicable planes,
they being preferably, however, planes which are radial with relation to the axis of
the gear; and I have therefore, herein illustrated my invention in connection with
a radial flanked tooth, it being expressly understood that the invention is not
restricted to the use of radial flanks.
I have shewn my improved tooth with radial flanks as not only preferable
because of convenience in manufacture, but also because it is the nearest like
the so-called “radial flanked epicycloidal tooth" above referred to, from which it
must be distinguished.
Referring to the drawing, the dotted lines a, a, and a, a, composed of short
regular dashes, shew the lines of action (i.e. the curved lines in arcs of which the
moving points of contact between two mating teeth travel) of two mating radial
flanked planoid teeth, said lines of action being non-circular, that is, oval in shape,
said lines of action, when the flanks of the teeth are radial, passing through the axis
of the respective gears.
Where the flanks of the planoid tooth are not radial planes but planes drawn
tangent to a circle or circles about the axis of the gear, as illustrated by the light
linez, tangent to the circles z', 2, the lines of action a³, a', of the teeth, instead of
passing through the axes of the gears will be tangent to the circles to which the
plane flanks of the teeth are tangent.
In order that my invention may be clearly understood, it is necessary to compare
my improved tooth with the form of tooth which is the nearest approach to it, viz. :-
the "so-called radial flanked epicycloidal tooth," in order that the difference
between the two may be clearly understood.
It will be noticed that I speak of this nearest approach to the improved tooth, as
the "so called" radial flanked epicycloidal tooth.
This is because there can be no theoretically correct epicycloidal tooth having
flanks which are planes, for the face of an epicycloidal tooth is an epicycloid, and
it is a demonstrable fact that if the face of a tooth is an epicycloid the mating flank
must be a hypo-cycloid and not a plane; therefore a tooth having faces which
are epicycloids and flanks which are planes is not and cannot possibly be a
theoretically correct tooth and for this reason it cannot have a definite line
of action.
The true epicycloid bevel gear tooth is a theoretically correct tooth, but it cannot
have flanks which are planes.
Although the divergence of the flanks from the plane flanks of a planoid tooth is
slight, yet there is a divergence which may be proven by comparing the lines
of action of the two teeth.
Referring to the drawing, the dotted lines y, y, and y¹, y', consisting of alternate
long and short dashes, shew the lines of action of two theoretically correct
epicycloidal bevel gear teeth corresponding in size with the planoid teeth, also
shewn in said drawing, and it will be noticed that these lines of action are true
circles passing through or intersecting the axes of the respective gears.
While the line of action of a planoid tooth is never a true circle, the line of action
of an epicycloidal bevel gear tooth is always a circle within the line of action of the
radial flanked planoid tooth corresponding to it.
The divergence between the lines of action of the two teeth compared is only
slight, it being shewn in the drawing somewhat exaggerated in order that it may
be clearly understood, but the two lines of action for bevel gears can never
coincide, though the divergence gradually lessens as the radius of the sphere
increases until the radius of the sphere becomes infinite when the divergence
disappears entirely, both forms of gear then becoming the common epicycloidal
spur gear.
While the divergence between the plane flank of the planoid tooth and the curved
flank of the epicycloidal bevel gear tooth is only slight, yet in connection with the
actual formation of the tooth it is a very material divergence, for while the plane
flank of the planoid tooth may be easily and quickly formed by a simply cutting

page_text: tool having a straight cutting edge or edges it has heretofore been found
impracticable to form the slightly curved flank of the true epicycloidal bevel
gear tooth.
The difference between the two teeth then is the difference between a tooth which
has never yet been practically produced and a tooth which can and has been
practically produced.
It is not essential that the flanks of the planoid teeth of both gears of the mating
pair be similar, for while it is preferable on account of simplicity and ease of
construction that both should have radial flanks, yet one may have radial flanks,
and the other flanks which are not radial.
Having now particularly described and ascertained the nature of the said inven-
tion, and in what manner the same is to be performed, I declare that what I
claim is :-
1. The herein described bevel gear having teeth the flanks of which are planes
and the faces of which are curved surfaces conjugate to the plane flanks of the
teeth of a gear with which the said bevel gear is adapted to work, substantially as
described.
2. The herein described bevel gear, the same having teeth the flanks of which
are radial planes and the faces of which are curved surfaces conjugate to the
plane flanks of the teeth of a mating gear, substantially as described.
3. The herein described bevel gear, the same having teeth the flanks of which
are radial planes and the faces of which are curved surfaces conjugate to the radial
plane flanks of the teeth of a mating gear, substantially as described.
Dated the 6th day of November 1894.
WM. BROOKES & SON,
55 & 56, Chancery Lane, London, Agents for the Applicant..