U.S. patent number RE28,740 [Application Number 05/517,603] was granted by the patent office on 1976-03-23 for rack and pinion variable ratio steering gear.
Invention is credited to Arthur E. Bishop.
United States Patent |
RE28,740 |
Bishop |
March 23, 1976 |
Rack and pinion variable ratio steering gear
Abstract
A variable ratio steering mechanism for a vehicle having an
axially movable rack meshing with a helical pinion the axis thereof
making an angle with the axis of the said rack, the rack having a
group of teeth at its center of varying form and varying
inclinations with respect to the axis of the rack, the inclination
of the teeth of said group becoming less closely aligned with the
pinion axis as the teeth are more remote from the center of said
rack, said teeth thereby meshing with the teeth of the pinion at
varying effective pitch radii in a predetermined manner.
Inventors: |
Bishop; Arthur E. (Mosman, New
South Wales, AU) |
Family
ID: |
27422919 |
Appl.
No.: |
05/517,603 |
Filed: |
October 24, 1974 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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Reissue of: |
171842 |
Aug 16, 1971 |
3753378 |
Aug 21, 1973 |
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Foreign Application Priority Data
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Aug 17, 1970 [AU] |
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2222/70 |
Apr 5, 1971 [AU] |
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3086/71 |
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Current U.S.
Class: |
74/422;
74/498 |
Current CPC
Class: |
B62D
3/12 (20130101); F16H 19/04 (20130101); F16H
55/0853 (20130101); F16H 55/26 (20130101); Y10T
74/1967 (20150115) |
Current International
Class: |
B62D
3/00 (20060101); B62D 3/12 (20060101); F16H
55/08 (20060101); F16H 19/00 (20060101); F16H
55/02 (20060101); F16H 55/26 (20060101); F16H
001/04 () |
Field of
Search: |
;74/422,498,507,508,462 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Scott; Samuel
Assistant Examiner: McKenzie, Jr.; Frank H.
Attorney, Agent or Firm: Hill, Gross, Simpson, Van Santen,
Steadman, Chiara & Simpson
Claims
I claim as my invention:
1. A variable ratio rack and pinion steering mechanism having an
axially movable rack meshing with a helical pinion the axis of
which makes an angle with the axis of the rack, the rack being
characterized by having a group of teeth at its center said teeth
being of varying forms and varying inclinations with respect to the
axis of the rack, the inclination of the teeth of said group
nearest the center being the most closely aligned with the axis of
the pinion, the inclination of teeth of said group becoming less
closely aligned with the pinion axis and more closely perpendicular
to the axis of the rack as they move away from the center of the
rack, the inclinations and forms of said group of teeth being
associated with engagement of the said teeth with the pinion at
varying effective pitch radii, the effective pitch radius being
least at the center of the rack and increasing on either side
thereof.
2. A variable ratio rack and pinion steering mechanism as claimed
in claim 1, wherein the remainder of the teeth of the rack engage
the pinion at an effective pitch radius substantially equal to the
effective pitch radius at which the pinion is engaged by the
outermost portions of the outer teeth of said group of teeth, said
remainder of the teeth extending substantially at right angles to
the axis of the rack.
3. A variable ratio rack and pinion steering mechanism as claimed
in claim 2, wherein the sides of the remainder of the teeth of the
rack are arcs of circles.
4. A variable ratio rack and pinion steering mechanism as claimed
in claim 3, wherein the form of the teeth of the pinion is
substantially involute.
5. A variable ratio rack and pinion steering mechanism as claimed
in claim 2, wherein the form of the teeth of the pinion is
substantially involute.
6. A variable ratio rack and pinion steering mechanism as claimed
in claim 3, wherein the effective pitch radius increases
symmetrically on either side of the center of the rack.
7. A variable ratio rack and pinion steering mechanism as claimed
in claim 2, wherein the effective pitch radius increases
symmetrically on either side of the center of the rack.
8. A variable ratio rack and pinion steering mechanism as claimed
in claim 1, wherein the said group of teeth comprise a minority of
the teeth of the rack, the majority of teeth being straight sided
and of constant section across the width of the rack whereby they
are adapted to manufacture by broaching.
9. A variable ratio rack and pinion steering mechanism as claimed
in claim 8, wherein the form of the teeth of the pinion is
substantially involute.
10. A variable ratio rack and pinion steering mechanism as claimed
in claim 8, wherein the effective pitch radius increases
symmetrically on either side of the center of the rack.
11. A variable ratio rack and pinion steering mechanism as claimed
in claim 1, wherein the form of the teeth of the pinion is
substantially involute.
12. A variable ratio rack and pinion steering mechanism as claimed
in claim 1, wherein the effective pitch radius increases
symmetrically on either side of the center of the rack.
13. A variable ratio rack and pinion steering mechanism having an
axially movable rack meshing with a helical pinion the axis of
which makes an angle to the axis of the rack, the rack being
characterized by having a group of teeth at its center whose form
is different at every section across the width of the rack, and
having other teeth each side of said group having a constant form
at every section across the width of the rack, said group of teeth
providing a varying effective pitch radius, and said other teeth
providing a substantially constant effective pitch radius, said
constant pitch radius being always greater than the varying
effective pitch radius.
14. In a variable ratio rack and pinion steering mechanism as
claimed in claim 1, a pinion having a form determined by a
generating rack having a tooth space, measured at the mid height of
the tooth, more than twice the tooth thickness. .Iadd. 15. A
variable ratio rack and pinion steering mechanism having an axially
movable rack meshing with a helical pinion the axis of the which
makes an angle with the axis of the rack, the rack being
characterized by having groups of at least one tooth and of varying
forms and varying inclinations with respect to the axis of the
rack, the inclination of the teeth of at least one group being more
closely aligned with the axis of the pinion, the inclination of
teeth of said one group becoming less closely aligned with the
pinion axis as they move away from the one group, the inclinations
and forms of said group of teeth being associated with engagement
of the said teeth with the pinion at varying effective pitch radii,
the effective pitch radius being least at the position on the rack
where the inclination is most closely aligned with the axis of the
pinion and increasing to provide decreasing steering ratio with
movement away from said one group..Iaddend..Iadd. 16. The structure
of claim 15 wherein said one group is adjacent the center of the
rack and the inclination of teeth of said one group becomes less
closely aligned with the axis of the pinion with movement in either
direction away from the center of the rack..Iaddend..Iadd. 17. The
structure of claim 15 wherein said at least one group comprises two
groups of teeth on opposite ends of the rack and the inclination of
the teeth of both thereof becomes more closely aligned with the
axis of the pinion as they approach each of the said one groups
from the direction of the center portion of the rack providing
increasing steering ratio with movement away from the center
towards the ends of the rack.
Description
BACKGROUND OF THE INVENTION
The present invention relates to a variable ratio steering
mechanism of the rack and pinion type. The characteristics and
advantages of rack and pinion steering are well known, as are the
advantages of providing a variable steering ratio and it is
therefore unnecessary to explain these in the present
specification.
Considerable problems have however arisen in devision a practical
construction which incorporates variable ratio steering in a
mechanism of the rack and pinion type. One approach to a solution
to the problem is disclosed in the specification of U.S. Pat. No.
2,865,339, in which a non-round, straight cut pinion engages a
"wavy" rack, producing a varying ratio of engagement which recurs
at each revolution of the pinion and hence also of the steering
wheel. This necessarily requires that the wheels of the vehicle to
be steered must be moved throughout their entire range of movement
from lock to lock by not more than two turns of the steering wheel,
and a very low average ratio results. As a high (numerical) ratio
is needed near center to avoid excess sensitivity at speed, the
change in ratio with this system is generally in excess of 2:1.
This shortcoming can be overcome by the introduction of an
intermediate gear between the steering wheel and the pinion to
allow more turns of the steering wheel or by modifying the rack as
described in U.S. Pat. No. 2,973,658. Such constructions however
introduce complexities into the system which add undesirable
expense.
In addition to directness of the sterring action, it was found very
difficult to achieve a smooth action in a steering mechanism of
this kind in view of the sudden transitions in tooth action
necessitated by the non-round form of the pinion and high pressure
angles. A helical form of the device, which might well have cured
this roughness, was obviously impractical.
A somewhat different approach to the solution of the general
problem of providing a variable ratio steering mechanism of the
rack and pinion type is described in U.S. Pat. No. 3,267,763 and
the corresponding British Pat. No. 977,434. In that construction a
concentrically mounted driving pinion of circular form is meshed
with a rack having teeth of various forms. Teeth of minimum pitch
and pressure angle providing a maximum ratio are provided at the
center of the rack and teeth of maximum pitch and maximum pressure
angle providing a minimum ratio are provided at the ends of the
rack, the intervening teeth on each side of the center having a
progressive variation of pitch and form. Note that the variation of
pitch radius of the pinion in any case is a result solely of the
forms of the rack teeth.
A detailed consideration of that form of mechanism has shown that,
although it is not limited in the number of steering wheel turns,
practical considerations so limit the amount of ratio variation and
pattern thereof that little benefit has resulted from its use. In a
typical passenger car steering gear employing power assist, optimum
steering performance requires a variation of steering ratio of just
less than 2:1, a rapid drop of ratio from the center, a "flare" out
to a more constant ratio with about 21/2 turns stop to stop. If
such characteristics are sought to be obtained by employing the
subject mechanism, the following difficulties are posed:
1. A very low pressure angle must be used for the form of the
central, most frequently used, teeth to such a degree that
considerable weakness in the strength of these teeth results.
2. A very high pressure angle must be used for the teeth at the
ends of the rack in order to obtain the desired low ratio in this
region, as a result there is a large variation of efficiency,
successively, during the engagment of each tooth (as much as 30
percent). The requirement that the driver be able to steer the car
in these low ratio regions when the power assist has failed governs
how low the ratio may be in this region. Intermittently occurring
regions of poor efficiency, such as would occur with this system,
obviously impose a limitation in selecting the low ratio.
3. A rapid ratio drop, or change of pressure angle, particularly
occurring in the high ratio, low pressure angle region, produces
"holes" or cusps in the rack tooth flanks at certain points, and
the intensity of surface loading at these points becomes
unacceptable. Even if this is avoided by reducing the rate of ratio
change to less than that desired, areas of very small radius occur
on the rack tooth profiles, which will be points of high wear
rate.
The first of the difficulties mentioned above is appreciated in the
prior specifications referred to in that it is proposed that in
order to increase the strength of the teeth, an intermediate
reduction pinion be provided between the steering mechanism and the
pinion meshed with the rack. However, as has been pointed out
above, this is an expensive solution.
The object of the present invention is to provide a variable ratio
steering mechanism of the rack and pinion type, the design of which
overcomes these listed difficulties.
SUMMARY OF THE INVENTION
Whereas in the prior proposals the pinions used are of the straight
cut variety, it is proposed in the present invention to use a
substantially concentrically mounted helical pinion the teeth of
which are substantially identical in shape meshing with a rack
having teeth some at least of which are such as to provide a
variable steering ratio, it being preferred that the majority of
the teeth of the rack provide a low steering ratio and be of
constant section across their width, a small group only of teeth at
the center of the rack being of warped configuration to provide, in
cooperation with the helical pinion, a change of steering ratio
from a high ratio to the low ratio.
The use of a helical pinion permits the variation of the steering
ratio by as much as two to one and whereas a non-helical pinion
under these circumstances would give discontinuous tooth action in
the low ratio region at either end of the rack and would result in
poor strength of the teeth in the high ratio region, by the use of
a helical pinion it is possible to design the teeth at the center
of the rack so as to have adequate strength. Although this results
in the use of a pressure angle in the teeth towards the ends of the
rack of about 60.degree., an angle which would be entirely
unacceptable for a straight cut pinion, this is acceptable here,
due to the fact that the resulting discontinuous tooth action can
be accommodated by a helical pinion, since tooth engagement is
staggered across the width of the rack.
If the helical pinion fails to span the coarse low ratio teeth of
the rack for some parts of its rotation this will occur only in one
part of the width of the rack and full engagement will occur across
the remainder of the width. Furthermore, tooth engagement being
staggered across the width of the rack compensates for the
variations of efficiency in rack tooth action.
While the use of a helical pinion has the advantages referred to
above, its use does present some problems in manufacture of the
rack.
An examination of the problems has, however, shown that teeth of
suitable form can be generated, for example, by the use of a cutter
which is an identical facsimile of the pinion, a technique well
known in the manufacture of geared pairs. The difficulties and
expense of the method can be considerably reduced by designing the
rack so that the majority of its teeth can be formed by a
straightforward broaching process, only a small number of teeth
near the middle of the rack having to be generated. The design may
be such that it is possible to broach teeth of the form used at the
ends of the rack over the whole length of the rack and thereafter
modify the teeth at the center of the rack to the required form,
broaching of the central teeth would, of course, be to only a
relatively shallow depth. This reduces the use of the more
elaborate generating technique required for these teeth to a
minimum.
In order that the invention may be better understood and put into
practice a preferred form thereof is hereinafter described, by way
of example, with reference to the accompanaying drawings in
which:
DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagrammatic view of a rack and pinion steering
mechanism;
FIG. 2A is a scrap view in plan of a helical pinion engaging teeth
in a low ratio region of a rack;
FIG. 2B is a sectional view on the line IIb--IIb;
FIG. 3A is a view similar to FIG. 2A showing the pinion engaging
teeth in a high ratio region of a rack, here in a non-varying ratio
form;
FIG. 3B is a section on line IIIb--IIIb of FIG. 3A;
FIG. 4A is a plan view of one half of a rack having low ratio teeth
over the majority of its length and a small group of variable ratio
teeth at the center,
FIG. 4B is a section on IVb--IVb of FIG. 4A;
FIG. 5A illustrates diagrammatically the general case of a helical
pinion arranged in engagement with a rack to illustrate pinion and
mounting dimensions without reference to ratio variation;
FIG. 5B is a sectional view on line Vb--Vb of a part of FIG.
5A;
FIG. 5C is a section on Vc--Vc of FIG. 5A;
FIG. 6 is an enlarged view of the section shown in FIG. 5C;
FIG. 7A is a diagram similar to FIG. 5A, but illustrating the
effect of ratio variation as distinct from the constant ratio of
FIG. 5;
FIG. 7B is a diagrammatic view on the VIIb--VIIb of FIG. 7A;
FIG. 8 is a sectional view to a very much enlarged scale of the
rack and pinion of FIG. 5a showing the particular features of
contact between the rack and the pinion being a section through the
centerline of the rack;
FIG. 9 is a plan view in diagrammatic form of the pinion and the
rack showing the position of various section lines referred to in
the description;
FIG. 10 is a diagram indicating the contact conditions in the true
normal plane of the pinion of FIG. 8;
FIG. 11 is a diagram showing a comparison between ratio curves
provided by a known form of rack and pinion steering and a rack and
pinion steering mechanism according to the present invention,
and
FIGS. 12 and 13 are diagrams illustrating considerations involved
in the use of a pinion having non-involute teeth.
DETAILED DESCRIPTION
Before describing a particular form of the invention a number of
factors connected with the design of rack and pinion steering
mechanisms will be discussed to assit in an understanding of the
invention.
A number of variables are available to the designer of rack and
pinion steering, but in practice, considerations of economy,
strength, and performance narrow the choice.
The space available for the steering gear being limited, it
generally happens that the steering shaft 10 (FIG. 1) and hence the
steering pinion 11, must be angled in the plan view outward from
the car centerline at from 20.degree. to 30.degree.. The stroke of
the rack 12 is also limited by suspension geometry and, as the
minimum number of wheel turns is set by considerations of
sensitivity at high speeds, steering pinions are generally just as
small in diameter as safety allows.
It should be made clear at this juncture that, although in FIG. 1
no indication is given of the use of power assistance, the present
invention is equally applicable to either power assisted or manual
steering mechanisms.
The angular arrangement of the pinion in the plan view may be
exploited to increase the pinion in size as indicated in FIG. 2A,
which is a scrap view in plan of the pinion and rack of a
right-hand drive vehicle, with the steering gear located behind the
wheels (as illustrated in FIG. 1). Here the teeth are arranged
transversely across the rack, and a left-hand spiral pinion is used
of a helix angle just matching the installed angle of the pinion
(.alpha.). Because motion of the pinion teeth lie along the line a
whereas the rack tooth surfaces lie square to the rack axis,
"slippage" occurs, so that one tooth of the pinion of pitch p in
the normal plane drives the rack only the lesser distance p cos
.alpha., and hence a somewhat larger pinion may be used than if a
non-helical non-inclined pinion were used. If on the other hand the
pinion spiral angle were reduced so that the rack teeth lay more
nearly along the installed angle axis of the pinion .alpha., the
"slippage" effect would be lost and the pinion diameter would have
to be reduced in order to keep the same desired pitch diameter.
Now consider the implications of introducing a variable ratio into
the helical rack and pinion steering gear. FIGS. 2A and 2B
illustrate a low ratio region where the pitch radius of the pinion
lies almost at the tips of the teeth. Now in a variable ratio gear
the ratio in this area may, in fact, be quite low so that the pitch
diameter is relatively large. However, because this pitch diameter
is almost equal to the outside diameter of the pinion an
undesirably small pinion will still result unless every advantage
is taken of the preferred arrangement of the helix as mentioned in
the previous paragraph. Note that the teeth here are spaced
relatively far apart as at Pa. If the same pinion is now meshed
with another rack or another section of the same rack at a very
small pitch diameter on the pinion, as illustrated in FIGS. 3A and
3B, the teeth will now be spaced close together as at Pb and it
will be seen that the teeth of the rack are now slanted to more
nearly match the axis of the pinion. This follows as a corollary of
the statement at the end of the last paragraph and because of this,
some of the ratio change that would have resulted from the reduced
pitch has now been lost.
The above description illustrates a feature of steering racks made
according to this invention, namely that the teeth of the rack
typically in one area are arranged at one angle to the rack
centerline and have one pressure angle, and at another point are
angled at another angle to the rack centerline and have another
pressure angle. Such an arrangement is believed to be novel both in
the art of steering racks and, indeed in gearing of any sort.
Whereas the rack thus is highly unusual, the pinion appears
superficially somewhat conventional. However, the optimum
proportions in any given design of steering mechanism require that
the pinion be highly modified from conventional steering mechanism
practice. This is because of the great range of pressure angles
over which the pinion is required to mesh if a desirably large
change of ratio is used. Much more of the involute curve is used
than conventionally, to achieve which the gap at the root of the
pinion teeth is made narrow, and at the tips the teeth are brought
virtually to a sharp point. Thus in the case of the figures given
as an example, relating to a pinion of six teeth, the angle
subtended at the center by any involute flank is 221/2.degree.,
while a conventional seven tooth pinion of a constant ratio version
of the same steering gear would use only 10.degree.. Note that the
proportions of this seven tooth pinion are already highly modified
as compared to conventional gearing, but in a manner well known in
the art of steering mechanisms.
Such unconventional pinion teeth, if used in a constant ratio,
steering mechanism would result in impractical rack tooth forms as
illustrated by line 55 of FIG. 8 (as discussed below). However, the
proper strength balance between rack and pinion teeth in a variable
ratio gear of the type desired is achievable only by using such
pinions.
The unconventional form of the pinion teeth is most readily defined
by considering the proportions of the generating radii of a
conventional pressure angle (say 20.degree.) rack with which it
would mesh. FIG. 8 which relates to the matter of strength, will
serve to show, at line 55, the proportions of such a hypothetical
constant ratio rack. Now conventional racks are proportional with
respect to a plane of symmetry 55b, generally the mid height of the
teeth, in which plane the gap between adjacent rack teeth
conventionally equal the tooth thickness. For the figures given by
way of example of the prevent invention, the pinion is defined by a
20.degree. pressure angle generating rack having a tooth gap more
than double the tooth thickness.
FIGS. 4A and 4B show how a rack according to the invention might
appear, with the rack pitch plane 13, for most of its length near
the root of the course teeth 14 and hence near the tips of the
pinion teeth (not shown) but humping up through center to provide a
reduced pitch radius of the pinion in this region. Note that the
rack pitch plane is a warped surface in that its hump occurs
further to the left in FIG. 4a towards the top of the figure than
it does lower in the same view. This humping must follow the pinion
inclination angle (.alpha.) as the pinion must mesh at the same
pitch radius all along its length at any instant.
It will be seen from FIGS. 4A and 4B that the rack has at its
center a group of inclined teeth 15 of which the center tooth is at
the greatest inclination, the inclination of subsequent teeth being
successively less, terminating in the coarse, low ratio teeth 14
square to the axis, which continue thus to the end of the rack. The
rack is of course symmetrical about its centerline in that right
hand end (not shown) is identical with the left hand end shown, but
rotated 100.degree. about `O`. This arrangement of teeth gives a
variation in steering ratio which is illustrated at H in FIG. 11
and is discussed fully in connection with that figure. It should be
noted that for rack and pinion steering the steering ratio is
defined as the effective radius of the pinion divided by the
average effective length of the steering arm L (see FIG. 1). The
effective radius of the pinion will vary according to variations of
the rack pitch plane 13 (FIG. 4B) and the effective length L
according to the geometry of the steering mechanism of the
particular vehicle to which the invention is applied.
The design details of one particular rack and pinion mechanism
according to the invention are given below and these should be read
in conjunction with FIGS. 5A to 7B, in which the various reference
numerals and letters appear.
______________________________________ PINION AND MOUNTING DETAILS
______________________________________ No. of Teeth: 6 Form
Involute Helix: Left Hand Lead length (16) 6.84029" Base Circ.
Diameter (17) 0.531859 Root Diameter (18) 0.510" Overall Diameter
(21) 0.875" ______________________________________
Installed Angle (.alpha.) 22.degree.
Angle, center of tooth gap to start of involute (B) 6.degree.
Assumed effective length of steering arms 4.92 inches
RATIO CURVE DETAILS
Form of curve (pinion normal plane) -- Sinusoidal
Rack travel -- centerline to constant -- Low ratio value.
(Pinion Normal Plane) (22) 0.800 inch
Rack Axis Plane) (23) 0.86280 inch
Rotation of Pinion, centerline to constant
Low Ratio (D.degree.) 147.7.degree.
Total travel of rack, each side of centerline (24) 3.06 inches
Rotation of Pinion, centerline to end of travel (E) 1.267 turns
Ratio of center 18:1 Ratio-Low Ratio 12.07:1
Rotation of pinion, centerline to end of travel, if ratio constant
at 18:1 1.782 turns
______________________________________ RACK DETAILS
______________________________________ Low Ratio On Center Region
Variable Ratio Section ______________________________________
PINION NORMAL PLANE (Pressure Angle) 52.degree. 48'2" 18.degree.
(Pinion Pitch Rad.) (25) 0.43985" 0.279615 (Circular Pitch) (26)
0.46061 RACK AXIS PLANE (Pressure Angle (G) 50.degree.41'
17.degree.36'51" (Pinion Pitch * Rad. (27)) 0.407822 0.273222
(Circular Pitch* (28)) 0.427068 (*Effective in this Plane) Pitch
Helix Angle (C-A) 22.degree. 13.degree. 4' 43" Rack Skew Angle (C)
0.degree. 8.degree.55' 16"
______________________________________
A clearer understanding of the invention may be gained from a
consideration of FIGS. 8, 9 and 10 of which FIGS. 8 and 10 are
enlarged scale drawings showing particular features of the contact
between the variable ratio rack and six toothed helical pinion
particulars of which are given above. FIG. 8 is a section through
the centerline of the rack showing the pinion at an angle and hence
appearing elliptical. The exact position of the parts as
illustrated in FIG. 9 shows that the section is primarily that
indicated as B--B and for the sake of clarity, in order to show the
condition of engagement at the farthest side of the rack from the
driver, the pinion has been imagined to but cut along line A--A of
FIG. 9. The position shown in FIG. 9 is that in which the pinion is
in the straight-ahead position otherwise known as "on-center"; the
center of the pinion in the centerline section of the rack of FIG.
8 will be point 33 and the center of the pinion in the plane in
which the pinion has been cut will be the point 34 in that same
figure. The pitch line indicated at 32 in FIG. 8 will reach its
maximum value in height corresponding to a minimum steering ratio
at the "on center" position 33, in the centerline section of the
rack at point 35. Now considering the section on plane A--A, the
pitch line 32a will again be at its maximum value here and the
intersection of the crest of the pitch line curve 32a and the
centerline of the pinion will take place at point 36. The
corresponding contact points in planes B and A respectively will be
at points 37 and 38. Note that the lines joining 36 to 38 and 35 to
37 lie at the same angle to the vertical, which angle 39,39 is the
pressure angle corresponding to the pitch radii (also identical) of
the pinion in the two planes at that instant. These pitch radii are
indicated by the length of the line 34-36 and also by the length of
the line 33-35. This pressure angle 39 is of the order of
18.degree. for the on-center position shown in that particular
instant for the particular example chosen and increases from there
to a value of about 52.degree. in the low ratio region. Now whereas
this view shows in general terms the contact conditions, it will be
noted that the curves in this view are those on the slanted plane
as far as the pinion is concerned and hence are not true involutes.
In accordance with the normal technique of laying out gearing
therefore, it is necessary to consider the contact conditions in
the true normal plane of the pinion, which is done in FIG. 10. To
do this a point is taken slightly displaced to the left on the
centerline 40. In order to consider the different meshing
conditions along the pinion axis, four sections are taken as at DD,
EE, FF and GG of FIG. 9.
For the sake of clarity these are all superimposed on a common
center indicated as point 40 in FIG. 10. Note that in this view the
flanks of the pinion are true involute curves and hence several
properties of the involute relating to the contact points may be
illustrated in this section; thus if one sets out in this view,
about center 40, the base circle 41 of the involute and then draws
a line 42 tangent to this base circle through 43, being the pitch
point of engagement between the pinion and rack at that instant,
this line continued will pass through the contact point 44 between
the rack and the pinion. As this construction is valid for each of
the four sections noted, it will be seen that points 44,45,46 and
47 are in a straight line as the pitch radius is the same for each
of these conditions of meshing; it follows that the pressure angle
indicated as 48 will be the same in each case. Now in order to
study the condition of contact at this instant it is the practice
to take a small displacement of the pinion for example to 49,
rolling either backwards or forwards along the plane. Note that in
the case chosen, in plane D the pinion has been rolled along the
line or in the direction of H (FIG. 9) in this plane and in so
doing of course, the point 43 on the pitch line has been departed
from a new intersection of the pinion centerline and the pitch line
occurs at 50; as line 40-50 is shorter than line 40-43 the pressure
angle has changed and the new value 51 is smaller than that
indicated at 48. For this reason it follows that the line tangent
to the base circle 52 passing through point 50 converges towards
the former line tangent to the earlier base circle and meets it at
a point such as at 53, however, it will follow that the
instantaneous curvature or the average curvature occurring over the
interval of movement 40-49 on each of the flanks is approximated by
a circle having its center at 53 and it is obvious then that the
radius of contact for each of the planes D, E, F and G will be
indicated by the lengths 53-47, 53-46, 53-45, and 53-44. Also
apparent is the fact that the radius at 47 is very small for the
case sketched and would be quite unsuited to carry the loads
imposed on a steering mechanism were it not for the fact that this
occurs only this one of the four planes indicated and is backed up
by much more advantageous conditions of contact in other sections.
There are many factors which determine the magnitude of this radius
such as the slope of the pitch line and the oreintation of the
teeth with respect to the pitch line at any instant but it is
important to note that in general in rack and pinion variable ratio
steering it is impossible to construct a satisfactory pitch line in
a practical arrangement that does not involve such very small radii
at at least one section across the width of the teeth.
This is one of the great advantages of the helical rack and pinion
in that conditions as in plane D could not be tolerated if they
occurred across the whole width of the teeth as would be the case
with a non-helical pinion.
Referring again to FIG. 8, the angular disposition of the rack
teeth in the plan view associated with the small pitch radius is
evident by the displacement of the section of the rack teeth in the
centerline plane B--B as compared with the plane A--A. This
displacement indicated as 55a in the on-center condition has
reduced to the value shown as 56a at the first tooth and would
reduce very rapidly to virtually zero at the third tooth. In the
example chosen the low ratio teeth lie transversely across the
rack, and there is of course no displacement of the teeth in
section across the plane of the rack in FIG. 8. This is indicated
by the single dotted line 31 and it will note noted that this
single tooth profile is in fact tangent to the pinion both on the
centerline plane A--A and in the remote plate, B--B.
As has been mentioned elsewhere that are distinct functional
advantages in having the ratio drop rapidly as is made possible by
the use of helical teeth. A second advantage is well illustrated in
FIG. 8, this relates to the question of the strength of the teeth.
If the ratio were substantially constant near the on-center
condition where the pressure angle is relatively small (say
20.degree. in this figure) the teeth would have relatively straight
flanks as indicated at line 55. It will be noted that the strength
of these teeth is considerably less than that given by the variable
ratio form as indicated at 56 where the flaring out of the base of
the tooth is attributable to the rapidly reducing ratio. This is
even more apparent in the second tooth where if the ratio increased
slowly as proposed by some other workers the second tooth would
have the same narrow form indicated by line 55. In contrast to this
the second tooth shows that the rack is very substantial indeed and
contact occurring for example at 37 at the on-center position is
backed by a tooth of equivalent strength to that of the pinion. In
contrast to this a tooth of the general shape indicated by line 55
for this second tooth would have a strength only a fraction of that
of the pinion and be quite incapable of carrying the load required
in this on-center meshing condition. It will be realized that it is
this condition where most loads are carried in the steering gear
and hence it is very important that buttress type teeth shall be
provided in this position.
The practical value of a rack and pinion steering mechanism of the
construction described above is illustrated in FIG. 11 in which
steering ratio as defined above is plotted against angle of turn of
the front wheels of the vehicle taken as an average of right and
left turns. In this the upper horizontal line may be taken as
representing a standard type of steering having a constant steering
ratio of 18:1. The line M illustrates the effect achieved with a
variable ratio rack and pinion steering of the kind described in
the United States and British patent specifications mentioned
above. Taking a typical intersection turn angle as being
20.degree., the area between the upper line and curve M (shaded
solid) represents to some scale the saving in terms of turns of the
steering wheel as between a standard steering system and that
described in those specifications and this amounts to about 5
percent.
The lower curve H represents the results achieved by a rack and
pinion steering employing a helical pinion and constructed
according to the present invention which gives under similar
conditions a saving (represented by the hatched area) of about 25
percent, for the same angle of turn and, as has been shown above,
this is achieved without suffering the disadvantages referred to at
the beginning of the specification.
In the embodiment of the invention described above, the involute
curve has been used, as it results in the simplest possible
generation of the pinion and the least complex form for the broach
teeth in the low constant ratio region of the rack. The many
advantages of the involute, well known in the art of gearing, are
not fully utilized however in this case; for example the
insensitivity to change of center distances and the simplicity with
which a family of gears may be made from the one cutter. The design
parameters in rack and pinion steering are, however, so demanding
that curves other than the involute may be used to advantage, even
though at the penalty of some complexity in making the broach for
the rack and in the generation of the pinion.
It will be found, for example, by departing from the use of a
straight sided rack flank in the low ratio region, (particularly
when pressure angles in excess of 50.degree. are used) and
substituting for example a concave tooth profile some considerable
advantages result. The reason for this is that the limiting value
for pressure angles is determined by the contact at the tips of the
rack teeth, where the combination of high sliding velocity and
steep pressure angle result in near-binding conditions. At the root
of the rack teeth, however, sliding velocity reduces to almost zero
and the pressure angle may be substantially higher, while still
avoiding binding, than is possible at the tip of the teeth.
These advantages may be studied by considering FIGS. 12 and 13 in
which two pinion rack combinations are compared meshed in the low
ratio region having the same pitch 62, tooth height 63 and pitch
radius 64 of the pinion. In FIG. 13 a straight flank is used for
the rack as described previously, whereas in FIG. 12 the root and
tip points have been maintained, but an arc centered at point 65
has been used to join these extremes. Note that, while accurate
broach teeth will be somewhat more difficult to make to the
required order of accuracy than straight-sided teeth, they would be
greatly preferable to higher order or arbitrary curves. Typically,
radius 65 might be five times the length of the rack flank. Note
that certain complications have also been introduced in the system
in the manufacture of the pinion.
Thus in FIG. 13 if a hob were used of the same form as the teeth,
generation would cease at point 69. For this reason the hob must be
used of the least pressure angle with which the pinion is required
to mesh, in this case about 18.degree. as shown by line 71. Because
the pinion flank is an involute, however, line 71 is a straight
line and thus the hob is of the simplest possible form. In the case
of FIG. 12, it is again not possible to use a hob for the pinion of
the same profile as the rack as the form on the pinion between 67
and 68 would not be determined. A suitable hob profile, such as
shown by line 72, may be determined of generally less slope than
that of the rack flank, but this will not be a radius nor indeed
any simple shape.
In the case of the pinion required to mesh with the arcuate form
rack, however, a lower pressure angle hob must be employed whose
teeth will be of some arbitrary form.
Therefore, the following steps must be observed in completing the
design of a hollow rack form variable ratio pinion as illustrated
in FIG. 12. Step 1. Determine the optimum form of the rack tooth
flank, to meet the performance parameters of the steering gear,
preferably a simple radius or combination of radius and straight
line, for the purpose of simplicity in making the broach. Step 2.
Determine the conjugate form of the pinion flank 66 up to a point
67, rolling the pinion at a constant pitch radius. Step 3. The
pitch flank in an arbitrary manner between points 67 and 68 having
regard to the required ratio in the low ratio region and the form
of ratio variation. Taking the pinion flank so derived, roll this
at a predetermined generating pitch radius and so determine the
counterpart form of the generating hob which must be used to
manufacture the pinion, making due allowance for the effects of the
helical form of the pinion.
Naturally, the generating pitch radius will be of the order of the
smallest pitch radius which the pinion is subsequently required to
roll with the actual rack. This procedure for determining the form
of hobs to manufacture arbitrary geared shapes is well known in the
art of gearing and presents no undue problems to those skilled in
the art.
While the embodiment of the invention described above relates to a
variable ratio steering mechanism in which the steering ratio
varies from a high ratio at the center to a constant ratio
extending over the major part of the rack, other configurations may
be adopted, for example, the effective pitch radius (that is to say
the radius which accounts for the lateral movement of the rack for
a given angle of pinion rotation) of engagement with the pinion and
thus the steering ratio may be caused to increase at the extreme
ends of the rack by shaping the teeth of the rack in an appropriate
manner. Such a configuration should be of value in some types of
manually operated steering mechanism to assist in turning the
wheels at extreme positions of lock.
* * * * *