FACE GEARING WITH CONICAL INVOLUTE PINION
BACKGROUND OF THE INVENTION
The present invention relates generally to gearing capable of providing torque
and speed transmission through an angle as required in a helicopter transmission.
In particular, the present invention relates to an angular gear drive employing a
conical involute pinion, whose tooth surfaces are involute helicoids generated from a
base cylinder, in mesh with a mating gear that is theoretically generated by the
conical involute pinion.
A typical helicopter transmission includes a large total gear reduction ratio (in
the magnitude of 70:1), one or two angular turns from the engine output to the main
rotor and, preferably, some power splitting features for increasing the overall
capacity within the specified weight and envelope limitations. These same
requirements are also found in other applications.
In order to maximize performance of a helicopter, the gear sets comprising
the drive train must be carefully selected. The performance of a gear set in
transmitting power is judged in terms of, among others, the contact pattern imprinted
on the teeth of each member as the members go through the mesh, the backlash of
the mating teeth and the transmission errors or conjugacy of the mesh. The relative
importance of these factors depends on the arrangement configuration and
application requirements of the helicopter or other system driven by the gear set.
The present invention is concerned with gearing drives which transmit speed
and torque through an angle. There currently exists a variety of gearing types which
may be considered in attempting to accomplish this task. Configuration and
efficiency considerations will exclude worm gears, spiroid gearing and helicon
gearing from consideration in meeting the high-power intersecting shaft applications
associated with helicopter transmissions. This leaves rather limited choices which
are discussed below.
The spiral bevel gear set is a common gear arrangement employed in
angular gear drives when high speed and high torque applications are desired.
Spiral bevel gears have been found not to be suitable when the there is a large
reduction ratio (>5:1) combined with a large shaft angle resulting in a large pitch
angle (> 90° ) in the gear. These limitations to the use of spiral bevel gearing are
due to generation principles and manufacturing methods and are inherent in all spiral
bevel gear sets. In addition, spiral bevel gearing is sensitive to establishing the
proper contact pattern of the pinion (member with the fewer number of teeth) and the
gear (member with the greater number of teeth). This makes it very difficult to adjust
the backlash of a spiral bevel gear set without affecting the contact pattern. As a
result, creating the proper backlash while retaining the proper contact pattern
becomes a tedious, iterative process.
Another gearing type which may be considered are face gears. While this
gear type was developed decades ago, it has only recently been considered for high-speed, high-power applications. Technology advancements in the areas of
computer modeling and computer numerical control (CNC) machining makes it
possible to understand and solve difficult problems in the design and manufacture of
face gears such as complex 3D gear geometry, tooth contact analysis, avoidance of
undercutting, face gear grinding and coordinate measurement of the tooth profile.
Face gears offer designers an alternative to spiral bevel gears in large shaft-
angle, large reduction ratio angular power transmission environments. However, the
backlash of conventional face gears can not be adjusted without adversely affecting
the contact pattern or the conjugate action between the pinion and the gear. In the
real world where manufacturing errors and loaded defections are inevitable, it is
extremely difficult, if not impossible, to achieve both the desired contact pattern and
the desired backlash during assembly. Maintaining proper tooth contact pattern is
vital because the load capacity of a single mesh depends heavily on the proper
location and orientation of the contact pattern. Likewise, the proper amount of
backlash at each mesh is critical for torque-splitting because, as a closed-loop
system, the timing among different power paths has significant impact on the
percentage of power share through each power path.
Typical of the systems employing face gears in a helicopter transmission is
that shown in U.S. Patent No. 5,178,028 issued to Bossier, Jr. This patent teaches
the use of two concentric, counter-rotating face gears, one being an idler gear and
the other an output gear. The gears are in meshing engagement with a driving
pinion connected to an engine output shaft. This system clearly does not
contemplate the use of a conical involute gear as the pinion in mesh with a mating
gear theoretically generated by the conical involute pinion.
In reviewing various types of gearing which could possibly meet the requirement of transmitting power through an angle, one might consider the so-
called conical involute gears. Other names for this type of gearing include tapered
involute gears and beveloids. An advantage of this gearing is its insensitivity to
positioning of both the pinion and gear members and its adjustable backlash without
violating conjuate action. However, in order to achieve this advantage, conventional
conical involute gearing include certain, inherent, drawbacks which make such
gearing unsuitable for high power applications. In particular, the cone or taper angle
must be relatively small (< 10°) or the face width of the gear will be severely limited
by pointing at the large end and undercutting at the small end. In addition, the two
mating conical gears are always in convex-convex point contact which is a
significant limitation on load carrying capacity. During operation of such a gear set,
the high relative curvature at the point of contact causes high contact stresses and
breaks down desirable lubrication conditions. This problem becomes significantly
more serious when the shaft angle is in the range of 70° to 110°, which range
constitutes a common shaft angle arrangement in helicopter transmissions.
There is a clear and present need for a type of gearing suitable for
applications demanding large reduction ratio and large shaft-angle arrangements,
while providing appropriate capacity to transmit an appreciable mount of power.
Such a gear set should also have the capability of adjusting backlash without
affecting the tooth contact pattern and true conjugate action. As will become
evident, the present invention provides a unique type of gearing that fulfills all of
these needs.
SUMMARY OF THE INVENTION
The present invention is directed to a unique gear set including a
conical involute pinion and a mating face gear. The mating gear axis location and
orientation is usually configured, according to typical helicopter transmission
requirements, as intersecting with or slightly offset from the pinion axis with a shaft
angle ranging from 70° to 110°. The pinion tooth surface is formed as an involute
helicoid generated from a base cylinder. The mating gear tooth is defined as the
conjugate surface to the pinion tooth, with the surface generated by the pinion tooth
following the same relative motion as the two gears mesh to transmit power. In
other words, the shape of the flank surfaces of the face gear are directly determined
by the shape of the conical involute pinion teeth as they exist when the two gear
members are relatively positioned so as to perform synchronous rotations about their
respective axes of rotation. This assures that the flank surfaces of the gear teeth
contact the corresponding flank surfaces of the mating pinion teeth along an
instantaneous theoretical line of contact at every instant of the meshing cycle and
thus follow true conjugate action during the entire meshing cycle.
Gearing constructed in accordance with the present invention provides
numerous, distinct advantages as compared with known gear sets.
Because the pinion is a conical involute gear with tapered tooth thickness, its
positioning provides a means of adjusting the backlash of the gear set. The involute helicoid is generated from a base cylinder and, as a result, the axial movement of
the pinion for purposes of adjusting backlash will not affect the contact pattern or
conjugate action of the gear set. This feature of the present invention is not
available with either spiral bevel gears or conventional face gears.
The gear sets of the present invention are especially suitable for large
reduction ratios of approximately 4:1-10:1 and for large shaft angles of
approximately 70° to 110°. Such arrangements result in a relatively small pinion
pitch angle and a relatively large gear pitch angle. A small pinion pitch angle allows
the design of the taper angle to be relatively small. This, in turn, relieves the
limitations on the conical involute pinion in regard to pointing and undercutting The
mating gear will, because of he nature of the generation process, have some
limitation in face width of the gear teeth. However, because the surface of the
mating gear is generated by the pinion rather than as another conical involute gear,
the mating gear does not suffer as severe a limitation on face width of the gear teeth
as the limitations affecting conventional pairs of conical involute gears. This provides
an obvious power advantage as compared to beveloid gearing in which both gear
members are formed as conical involute gears. In addition, this assembly
overcomes the inability of spiral bevel gears to provide large reduction ratios and
large shaft angles.
A further distinct advantage of the present invention is the line contact
conditon between the pinion and gear members provides enhanced load capacity
compared to the point contact created by beveloid gearing. In practice, optimal
contact conditions tend to be obtained by slightly modifying (crowning) the pinion
and/or mating gear tooth to absorb manufacturing errors and deflections arising
under load conditions. When properly crowned, the gear set of the present invention
can be expected to create a localized pattern under light load and, under full load,
create a pattern that will develop i.e., spread out, to cover the tooth flank, thereby
reducing contact stresses and increasing load capacity of the gear set.
The pinion of the present invention includes a conical involute gear generated
with a tapered root and a tapered outer face which helps to reduce sliding at the
corner point; which point is furthermost from the kinematic pitch line, thereby
reducing the scoring probability at the point of contact. This structure provides an
improvement over conventional face gears that employ straight involute pinions
where the kinematic pitch cone runs along the diagonal of the gear tooth.
A further advantage of the present invention is the ease of assembly as
compared to conventional face gears with straight cylindrical pinions. This is due to
the tapered tooth thickness and cone shaped outer face of the pinion which makes
axial assembly of the pinion easier, especially when there is small backlash. It is
expected that repeated disassembly and re-assembly of the pinion during
development of a gear box may occur without movement of the mating face gears.
Conventional spiral bevel gears wherein both gear members are of complex
tooth surfaces are very expensive to manufacture because of the special
requirements for machines and cutting tools. In comparison, the present invention is
much simpler to manufacture because at least the pinion can be made with existing
tooling on spur/helical gear, hobbing or grinding machines that need only be slightly
modified.
BRIEF DESCRIPTION OF THE ATTACHED DRAWINGS
The foregoing and other objects, aspects and advantages will be better
understood from the following detailed description of a preferred embodiment of the
present invention with reference to the drawings, in which:
FIG. 1a is cross sectional view of a conventional, prior art, spur-pinion face
gear;
FIG. 1 b is cross sectional view of a tapered pinion-face gear assembly
formed in accordance with the present invention;
FIG. 2a is a perspective view of a conical involute gear formed in accordance
with the present invention;
FIG. 2b is a perspective view of an involute helicoid tooth in accordance with
the present invention;
FIG. 2C is a perspective view of pinion tooth showing contact lines as created
when in mesh with the mating gear in accordance with the present invention;
FIG. 3 is a perspective view of a conical involute pinion being generated in
accordance with the present invention;
FIG. 4a is and end view of a machining configuration employed in fabrication
of the mating face gear conjugate to the conical involute pinion shown in FIG. 2b:
FIG. 4b is a side view of the machining configuration of FIG. 4a;
FIG. 4c is a perspective view of the face gear tooth showing contact lines;
FIG. 4d is a perspective view of a cutting tool and face gear in normal contact
as would occur during fabrication of the face gear;
FIG. 4e is a perspective view of the face gear formed in accordance with the
present invention; and
FIGS. 5a and 5b show top and sectional views, respectively, of a gear train
including pinions and mating face gears formed in accordance with the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
While the present invention is described herein with reference to illustrative
embodiments for particular applications, it should be understood that the present
invention is not limited thereto. Those having ordinary skill in the art and access to
the teachings provided herein will recognize additional modifications, applications,
and embodiments within the scope thereof and additional fields in which the
invention would be of significant utility.
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Turning now to the drawings and to FIG. 1a, a conventional face gear set 10a
is shown in FIG. 1a and comprises a pinion gear 14a and a mating gear 12a. It is
noted that tooth 16a of gear 12a and meshing tooth 18a of pinion 14a each extends
parallel to a pinion axis PA as well as extending parallel to one another.
In comparison, a unique face gear set 10 formed in accordance with the
present invention is shown in FIG. 1b. Gear set 10 includes a pinion gear 14 and a
mating gear 12. The tooth 16 formed on mating gear 12 forms a gear taper angle 0
to a gear axis GA. Likewise, the tooth 18 of pinion 14 forms a taper angle β with
pinion axis PA. In comparison, the pinion 14a partially shown in FIG. 1a is generally referred to as a straight pinion while the pinion 14 in FIG. 1b is referred to as a
conical or tapered pinion.
A pinion gear 14 formed in accordance with the present invention is shown in
FIG. 2a. Pinion 14 includes a pinion tooth surface 18 which defines an involute
helicoid as shown in FIG. 2b. Pinion tooth 18 includes a large end 26 and an
oppositely disposed small end 28. Tooth 18 has a tapered outer cone 30 and a
tapered root 32. Joining outer cone 30 to root 32 is an involute helicoid shaped
surface 34. Finally, the small end 28 includes a dished or flat front surface 36.
The pinion 14 is a conical involute shaped gear with a tapered tooth
thickness. This configuration provides a means of adjusting the backlash of gear set
12
10 without affecting the contact pattern or conjugate action of the gear set. The
conical involute pinion 14 is especially suitable for large reduction ratios (4:1-10:1) in
which cases the taper angle β can be kept small. While the taper angle 0 on the
mating gear 12 is relatively large, the fact that mating gear 12 is generated by the
pinion 14, rather than as being another conical involute gear, greatly reduces the
limitations to face width as would otherwise occur if mating gear 12 were a conical
involute gear similar to pinion 14. This provides a significant advantage over
conventional beveloid gearing wherein both the pinion and mating gear are typically
generated as conical involute gears.
For purposes of explanation, assume a conical face gear set in which the
number of teeth on the pinion is Np , the number of teeth on the gear is Ng, ωp is the
angular velocity of the pinion and ωg is the angular velocity of the gear, thereby giving
a reduction ratio of:
i^ω^Nfl ωg Np
The pinion can be produced by hobbing or generating grinding processes
utilizing a threaded cutting/grinding tool in synchronous rotation with a pinion blank
on which the teeth are to be generated. The process can be implemented on a
conventional spur/helical involute gear hobbing machine or on a thread wheel
grinding machine having an additional feature of feeding the tool across the face
13
width of the pinion gear teeth along the direction that makes an angle β with the axis
of the pinion as shown in FIG. 3. This angle β is a design parameter of the gear set
10. Hobbing and threaded-wheel grinding methods share the same principle of gear
generation but usually produce gears of differing quality due to the differences in the
methods of material removal. For aerospace applications such as use in a
helicopter drive train, the preferred process is one wherein the pinion blank is first
rough cut by hobbing to form the teeth. After this, the grinding process is employed
to finish the teeth to a high degree of accuracy. The common machining practice is
for the cutting tool 38 to start at the small end 28 of the conical involute pinion gear
14 as shown in FIG. 3 and perform the feed motion along the angle β with respect to
the gear axis A-A until finally reaching the large end 26 of the pinion gear. This
completes the tooth generation process for pinion 14. During the formation process,
the cutting tool 38 and the pinion blank 14 perform synchronous rotations with the
constant ratio determined by:
iprωj N, ω, Np
where N, is the number of threads on the cutting tool 38, i.e., either a hob or a
threaded grinding wheel and ωt is the angular velocity of cutting tool 38.
FIGS. 4a and 4b illustrate the preferred method of fabricating mating gear 12
to be conjugate to the conical involute pinion 14 formed in accordance with the
present invention. The cutting tool 39, either a peripheral milling cutter or a grinding
14
disk, has its axial profile formed to match the tooth profile of the conical pinion at its
small end 28. The axial profile of the cutting tool 39 can be formed either to be one side 41a of the tooth profile of the pinion 14, as it is shown in FIG. 4g, or the axial
profile can be of both sides 41b of a pinion tooth as shown in FIG. 4f. Whichever of
these two cutting tool designs 43a or 41 b is used depends on the specifics of the
machine on which the cutting method of the present invention is implemented. For
example, if the cutting machine is of a type where the cutting tool 39 is intended to
be turned over, that the profile 41 a may be employed. However, if the tool 39 cannot
be turned over, than the profile 41b assures that both flanks of the gear tooth may be
formed. The particular type of cutting tool profile is not essential to the explanation of
the formation of the face gear, because either tool finishes the face gear tooth one flank at a time. The diameter of the cutting tool 39 is designed to be reasonable
from a practical standpoint and in itself makes up no part of the present invention.
As shown in FIG. 4a, face gear 12 is mounted on a rotary table 37. Rotary
table 37 performs continuous, controlled rotary movement to provide required
tangency conditions between the gear 12 and the cutting tool 39 as cutting tool 39 is
traveling and cutting each tooth space across the face width of mating gear 12. After
one tooth space is finished, rotary table 37 indexes gear 12 to the next tooth space
and the cutting operation of tool 39 is repeated.
As cutting tool 39 moves across each tooth 16 formed on mating gear 12, the
position and orientation of both cutting tool 39 and gear 12 are controlled so that the
normal contact alignment between cutting tool 39 and the theoretical tooth surface
15
16 of gear 12 is maintained as shown in FIG. 4d. This normal contact position is
derived from the conjugate action and the meshing condition between pinion 14 and
mating gear 12. Application of the well known theory of gearing to the meshing
process results in creation of a contact line (a 3D curve) between the pinion tooth 18
and the mating gear tooth 16 for every instant of the meshing cycle. Such contact
lines 40 are shown in FIGS. 2c and 4c. This means that the whole active flank of
both the pinion tooth 18 and the mating face gear tooth 16 is covered by an
imaginary pattern of contact lines 40, each corresponding to a different instant, or
different angle of rotation, of the meshing cycle between gear 12 and pinion 14. As
a result, for a certain preset angle of rotation of mating gear 12 to be machined,
there is a given contact line on the gear tooth and corresponding pinion tooth. In
the course of the cutting tool 39 traveling across the mating gear tooth space at the
predetermined angle of rotation of mating gear 12, the position and orientation of
cutting tool 39 is controlled in such a manner as to satisfy the following operating
conditions: (1) the cutting tool 39 is in instantaneous point contact with the mating
gear 12 at a point on the specific contact line. This condition assumes both position
and surface normal coincidence of the gear 12 and cutting tool 39 at their point of
contact; (2) at each instant, the contact point on the cutting tool 39 is spaced a radial
distance from the outer diameter of the cutting tool 39 equal to the distance of the
corresponding theoretical point of contact on the mating pinion 14 to the outer
diameter of pinion 14; and (3) as the cutting tool 39 moves along the face width of the mating gear 12, the point of contact between the gear and the cutting tool 39
moves along the contact line of the face gear 12 corresponding to the current
16
angular position of face gear 12.
Reference is made to figure FIG. 4d which shows a typical position of a
cutting tool 39 engaging gear 12 while satisfying the above conditions (1)-(3) existing
during the process of machining gear 12. In particular, when generating a gear 12 in
accordance with the present invention, the tangency conditions apply continuously to
each theoretical contact line 40 on the gear tooth 16, preferably, starting from the
contact line 40a near the top land of gear tooth 16 and finishing with the contact line
40b close to the root of tooth 16 as shown in FIGS. 4c and 4d. The number of
theoretical contact lines 40 crossing the flank of gear tooth 16 during the machining
process depends on accuracy requirements. For most applications, It is considered
appropriate to have between 20-40 such theoretical contact lines 40 each extending
across the flank of tooth 16.- In forming a gear 12 according to the present invention,
the method of fabrication finishes one flank of one gear tooth 16 at a time. The
same flank of all gear teeth 16 are subsequently fabricated by rotating table 37 until
each gear tooth 16 of gear 12 is subsequently aligned with the cutting tool 39 and
the cutting process is repeated. It should be noted that both the rotary table 37 and
cutting 39 may jointly move as cutting tool 39 crosses gear 12. The process controls
the relative movement to assure that tool 39 follows each theoretical contact line 40.
After the systematic cutting process for the same flank of each tooth 16 is finished, a
similar cutting operation is then applied to the opposite flank of each tooth 16, one
tooth at a time, until all the teeth 16 of gear 12 are formed.
In order to achieve the method of cutting gear 12 discussed hereabove, a
multi-axis (5 or 6 axes) CNC machine providing a continuously controllable motion
for cutting tool 39 and gear 12 may be employed. Several known machines are
available in the gear manufacturing industry and the details of such machines
themselves make up no part of the present invention. Typical of known CNC
machines is the device described in U. S. Patent No. 5,116,173 issued May 26,
1992 to Robert N Goldrich which disclosure is incorporated into the present
application by express reference thereto. It should be emphasized that FIGS. 4a
and 4b of the present application are only intended to show the relative configuration between the cutting tool 39 and the gear 12. The actual mounting configuration of a
gear 12 and cutting tool 39 may vary depending on the design of the particular CNC
machine employed.
The present invention can be utilized for high-speed, high torque gear drive
applications having large reduction ratio and large shaft angle. Of particular benefit
is the ability to adjust the backlash when employed in torque splitting designs in
which it is critical that the proper amount of backlash at every mesh in different
power flow branches be maintained. FIGS. 5a and 5b show a gear arrangement 50
in which the power from two input shafts is transmitted through an angle to one
output shaft of the gear arrangement, with reduced speed and increased torque.
Such an arrangement is provided as an example and is not intended to limit the
present invention to any way. In a similar manner, the reduction gear ratio and
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angular relationships of the various shafts is provided solely for explanation and is
not intended to limit the scope of the present invention.
Gear arrangement 50includes a total of four pinions 52, 54, 56 and 58 and
two face gears 60 and 62, including lower face gear 60 and upper face gear 62
forming eight separate meshes. At each mesh the reduction ratio may be designed
to be approximately 8:1. The shaft angle may be selected to be 78 ° with the upper
gear 62 and 102 ° with the lower gear 60.
Power input is taken from the two input pinions 52 and 54, which splits the
power to the upper, output gear 62 and to the lower, idler gear 60 which is in
concentric relationship with upper gear 62. The power taken by the lower gear 60 is
transferred through the two idler pinions 56 and 58 to the upper output gear 62,
which combines power from all four pinions 52, 54, 56 and 58 and delivers the
power to an output shaft 64. With this gear arrangement 50, each gear mesh ideally
sees only half of the load from one of two input shafts 66 and 68, or % of the total
output.
This arrangement allows the capacity of the transmission to be substantially
increased for a given volume and defined envelope limitations. Such a torque-split
combination gear arrangement essentially works as a closed-loop gear train, wherein the percentage of power shared in each load path depends on the angular
timing of the gear members in each path, and the relative angular timing of the
power paths is affected by the backlash at all meshes of each path combined. Even
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power-split among all meshes can not be achieved unless two conditions are
present: (1) the two input pinions are mounted in floating shafts such that under
actual load conditions they can find a balanced position at which equal torque is
transferred to the upper and the lower mesh; and (2) the backlash at each mesh is
properly set.
The effects of backlash are two-fold and include: (i) the relative backlash
between the input pinion and the idler pinion determining how much the input pinion
has to float or reposition itself to reach a balanced position under load condition
when the load is split; and (ii) the relative backlash between the two idler pinions
determining the percentage of the load transferred through each idler pinion and
delivered to upper gear 62 and output shaft 64. If backlash amounts are not
correctly determined and proper adjustment made, the input pinion may, in seeking
a balanced position, run into the jamming condition by taking up all the backlash in
one mesh, thereby preventing it from delivering equal amounts of torque to the
upper and lower meshes. It is desirable that the backlash of each of the four pinions
52. 54. 56 and 58, either input or idler be individually adjustable to accommodate
manufacturing errors and loaded deflections in order for the gear train 50 to properly
function.
The present invention provides a unique gear set wherein the tooth surface
16 of mating gear 12 is conjugate to the involute helicoid tooth surface 18 of pinion
14. The gear tooth 16 is theoretically generated by pinion 14 following true
conjugate action. When mating gear 12 is in mesh with pinion 14, line contact is
created that will obey conjugate motion of transmission. The present invention
includes the unique capability of providing an adjustable backlash through axial
positioning of pinion 14 without affecting gear set contact characteristics or violating conjugate action. Such adjustment will not change the contact pattern, line contact
condition or the true conjugate action of the gear mesh.
Although preferred embodiments of the present invention have been
described in detail hereinabove, it should be clearly understood that many variations
and/or modifications of the basic inventive concepts herein taught, which may
appear to those skilled in the art, will still fall within the spirit and scope of the present
invention as defined in the appended claims and their equivalents.