Dual tooth contact type W-N gear

W-N gears of novel basic rack tooth profile designed to have at all times two points of meshing contact located in the same reference plane, one on an addendum arc of first tooth and the other on the dedendum arc of a second tooth neighboring the first tooth on its side opposite to the addendum arc, so that at the respective points of contacts the addendum and dedendum arcs have lines of radius aligned with each other. Such dual tooth contact enables much smoother and quieter gear operation, the points of contact proceeding in the direction of tooth trace.

BACKGROUND OF THE INVENTION 
This invention relates to improvements in W-N gears or gears of the kind 
whose basic rack tooth profile on normal or transverse reference plane or 
the tooth surface is composed of addendum-defining convex circular arcs 
and dedendum-defining concave circular arcs and is intended to provide 
novel double tooth contact or double mesh type gears of the kind described 
which are highly advantageous from the viewpoints of manufacture and 
performance. 
As is well known in the art, a pair of mating W-N gears of the kind 
described operate with their circular arc tooth surfaces successively 
making meshing contact and, having a transverse contact ratio of zero or 
approximately zero, rely for transmission of rotation exclusively upon the 
tooth trace. In this sense, W-N gears in essence can be considered helical 
gears. 
With conventional forms of W-N gear, meshing contact of the addendum and 
that of the dedendum take place at the same time and separately in 
different reference planes, their location shifting progressively in the 
direction of tooth trace with rotation of the mating gears. Accordingly, 
with W-N gears, transmission of rotation can be effected smoothly so long 
as a requisite value of axial overlap contact ratio is obtained. 
Generally, with involute spur gears, it is well known that, as the 
transverse contact ratio is raised to exceed 2, not only torque variations 
but also vibration and noise in operation are substantially reduced owing 
to the fact that they have at all times two teeth held in meshing contact 
and hence their teeth are subjected only to bending load of limited 
fluctuation. 
With conventional W-N gears, however, it is not at all times advisable to 
raise the number of the contact tooth to 2 or above with a view to 
obtaining similar operational effects as it makes it necessary to 
accordingly increase the axial overlap contact ratio and this in turn 
necessitates a greater length of tooth trace as long as the helix angle is 
held within certain limits to maintain the tooth surface strength at a 
level desired, involving some problems to be considered in regard to 
machining and assembling accuracies, tooth deflection, etc.. 
One relatively recent prior art patent upon W-N gears is U.S. Pat. No. 
3,855,874, issued Dec. 24, 1974. Such patent particularly relates to these 
W-N gears that include gear teeth having profiles each including circular 
addendum and dedendum arcs connected by a straight line segment at the 
pitch line area. 
SUMMARY OF THE INVENTION 
Under these circumstances, the present invention has for its object the 
provision of a pair of dual tooth contact and double mesh type W-N gears 
having a basic rack tooth profils designed to give tooth contact at all 
times at two locations in one and the same transverse or normal reference 
plane, one on the addendum, convex circular arc on one side of a tooth 
profile and the other on the dedendum, concave circular are on the same 
side of a neighboring tooth lying on the side opposite to the former 
profile, the addendum and dedendum arcs having at the respective points of 
meshing contact radius lines aligned or lying on a common straight line. 
With W-N gears having such basic rack tooth profile, since the lines 
normal to the surfaces of two neighboring teeth and extending through the 
respective points of meshing contact thereon extend at the same time 
through the pitch point of the meshing gears, the two teeth make meshing 
contact at the same time in the same reference plane. This not only 
reduces variations in stiffness of teeth under bending load but also 
effectively prevents any improper tooth bearing as resulting from 
machining and assembling errors or deflection of teeth when loaded, and 
reduces vibration and noise in operation. The basic rack tooth profile of 
W-N gears of the present invention has an additional advantage that it 
facilitates determination of accuracy of teeth formed and thus helps 
improve the machining accuracy. 
The above and other objects, features and advantages of the present 
invention will become apparent from the following description when taken 
in conjunction with the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Reference is made first to FIG. 1, which illustrates the basic rack tooth 
profile, taken in a transverse or normal reference plane, of one 
embodiment of the present invention. 
In FIG. 1, reference numeral 1 indicates a convex circular arc forming an 
adendum of a rack tooth X on one side thereof, reference character A.sub.1 
indicating a point of meshing contact set on the addendum arc 1. Reference 
numeral 2 indicates a concave circular arc forming a dendum of another 
tooth Y which neighbors the tooth X on its side opposite to the addendum 
arc 1, A.sub.2 indicating a point of meshing contact set on the dedendum 
arc 2. The center C.sub.1 of convex circular arc 1 lies at the point of 
intersection of the straight line A.sub.1 -A.sub.2 and the pitch line l 
of the basic rack and the radius A.sub.1 C.sub.1 of convex circular arc 1 
is equal in length to the segment A.sub.2 C.sub.1 of the straight line 
A.sub.1 -A.sub.2 . As observed, the center C.sub.2 of concave circular arc 
2 lies on the straight line A.sub.1 -A.sub.2 , as with the case of center 
C.sub.1 of convex arc 1, and the length of radius A.sub.2 C.sub.2 of the 
concave arc 2 is a little greater than that A.sub.1 C.sub.1 of convex arc 
1. It is to be noted that such basic rack formation gives a dual tooth 
contact type W-N gear which makes point contact on two neighboring teeth 
simultaneously at respective points A.sub.1 and A.sub.2 when point C.sub.1 
coincides with the pitch point in the same reference plane. 
FIG. 2 illustrates the basic rack tooth profile of another embodiment of 
the present invention, taken in a transverse or normal reference plane. 
As illustrated, the addendum, convex circular arc 3 of the tooth profile 
has a radius equal in length to that of dedendum, concave circular arc 4 
thereof, the centers of the two arcs coinciding with each other at a point 
C.sub.3 on the pitch line l. With this basic rack tooth profile, a line of 
radius A.sub.3 -C.sub.3 of convex circular arc 3 and that A.sub.4 
-C.sub.3 of concave circular arc 4 are aligned with each other to define 
a straight line passing the point C.sub.3 and the points A.sub.3 and 
A.sub.4, respectively, lying on the convex and concave circular arcs 3 and 
4 represent respective points of meshing contact. 
In this manner, such basic rack tooth profile forms a dual tooth contact 
type W-N gear of which two neighboring teeth make line contact with the 
mating gear simultaneously along the convex and concave circular arcs 3 
and 4, respectively, including points A.sub.3 and A.sub.4, when the point 
C.sub.3 coincides with the pitch point in the same reference plane. 
FIG. 3 illustrates the basic rack tooth profile of a further embodiment of 
the present invention, taken in a transverse or normal reference plane. In 
this figure, point A.sub.5 represents a point of tooth contact set on the 
addendum, convex circular arc 5 and point A.sub.6 another point of tooth 
contact set on the dedendum, concave circular arc 6. The centers of convex 
and concave circular arcs 5 and 6 coincide with each other at the 
intersection C.sub.4 of the straight line A.sub.5 -A.sub.6 and the pitch 
line l. As observed, the length of radius A.sub.6 C.sub.4 of the concave 
arc 6 is somewhat grater than that of radius A.sub.5 C.sub.4 of convex arc 
5. 
Such form of basic rack tooth profile gives a dual tooth contact type W-N 
gear of which two neighboring teeth make point contact with a mating gear 
at two points A.sub.5 and A.sub.6 in the same reference plane, as will be 
described in further detail with reference to FIG. 4, which illustrates 
how a pair of such W-N gears are actually placed in meshing engagement 
with each other. 
In FIG. 4, reference characters O.sub.1 and O.sub.2 designate the centers 
of the individual gears D and E formed of the basic rack tooth profile of 
FIG. 3; C.sub.4, the common center of the convex and concave circular arcs 
of gear D including respective points of tooth contact, A and A'; and 
C.sub.4 ', the common center of the convex and concave circular arcs of 
gear E including respective points of tooth contact, A and A'. In actual 
use, however, the pair of gears D and E must be arranged with the center 
distance slightly reduced from O.sub.1 O.sub.2 ' to O.sub.1 O.sub.2 and 
the intermeshing pitch circles are circles centered at O.sub.1 and 
O.sub.2, respectively, and extending through the intermeshing pitch point, 
P, though not shown in FIG. 4. Incidentally, the dotted line E' indicates 
gear E imaginarily positioned retative to gear D as for tooth generation. 
Previously known is the technique of forming on a pair of W-N gears 
accurate convex and concave circular arcs differing in radius from each 
other to obtain correct point contact between such circular arcs of the 
mating gears, as illustrated in the embodiment of FIG. 3. It is to be 
understood, however, that the instant embodiment represents an important 
advancement over the technique which enables dual tooth contact between a 
pair of such line contact W-N gears. 
It will be readily appreciated from the foregoing description that, 
according to the present invention, there are two neighboring teeth 
simultaneously coming into meshing contact in any reference plane for 
tooth profile whenever contact takes place in the reference plane and the 
two points of contact proceed in the direction of tooth trace. It follows, 
therefore, that there are at all times two teeth participating in meshing 
contact within the same reference plane irrespective of the angular 
position of the gear in operation, as illustrated in FIG. 5a, as long as 
an overlap contact ratio is selected which slightly exceeds 1, and hence 
variations in rigidity or stiffness of teeth under bending stress can be 
reduced to a minimum by appropriately relieving the face end to alleviate 
the load fluctuation occurring with load delivery at the face end. It will 
be apparent that in this manner substantial reduction in torque variation 
and hence in vibration and noise can be readily effected and this makes 
application of W-N gears to various fields of high-speed operation much 
easier. 
Further, according to the present invention, even if some tooth deflection 
occurs owing to machining and assembling errors and load applied, its 
influence upon the tooth bearing is small compared with that in the case 
of conventional forms of W-N gear because of the dual tooth contact 
effected in the same reference plane and this forms another characteristic 
feature of W-N gears of the present invention. 
Further, use of the tooth profile of the present invention is desirable 
from the practical viewpoint of quality control of gear teeth in 
production as it makes it possible to determine a sort of normal pitch by 
measuring the distance between the addendum arc of a tooth and the 
dedencum arc of the next following tooth, taking the addendum arc as the 
reference of measurement, as illustrated in FIG. 6. With the system of 
FIG. 1, the vicinity of the contact points is to be taken into account. 
Though a few embodiments of the present invention and more particularly a 
few typical forms of basic rack tooth profiles usable for dual tooth 
contact type W-N gears of the invention have been shown and described, it 
will be apparent to those skilled in the art that many changes and 
modifications may be made therein without departing from the spirit of the 
invention or the scope of the appended claims and any forms of W-N gear 
are within the contemplation of the present invention which are 
approximately the same in tooth profile, meshing mode and effects deriving 
therefrom as the dual tooth contact type W-N gears illustrated herein, in 
comparison with conventional forms of W-N gear.