JPH0694101A - Conical involute gear - Google Patents

Abstract

PURPOSE:To provide a conical involute gear which is meshed in a wide range with a tooth surface so that a high torque can be transmitted. CONSTITUTION:This gear is formed by giving a transposition coefficient x for nearly matching a meshing center distance with a center distance between axes in a tooth orthogonal direction on the arbitary tooth orthogonal surface of an entire tooth width bn1 in relation to a pinion 7 and can be processed by moving the reference pitch line of such tool as a hob and the like along the locus of a pitch circle in a tooth width direction obtained by adding the radius of the reference pitch circle to a product computed by multiplying the transposition coefficient x by a module m and brought in contact with the pinion 7 on a tooth surface whose meshing center distance is nearly equal to the center distance between axes across the nearly entire tooth width bn1. Therefore, touch of a tooth during meshing is not necessarily limited to a part of the tooth width bn1, but applicable to a wide range on the tooth surface so that a high torque can be transmitted. This gear can be formed by a general process.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a conical involute gear used in a power transmission mechanism.

[0002]

2. Description of the Related Art As is known in the prior art, a power transmission mechanism using gears has an arrangement in which gears of various shapes are provided such that a drive gear shaft and a driven gear shaft are provided in parallel or so as to intersect with each other. It is composed of The power transmission mechanism is required to be compact and capable of transmitting high torque, and further, it is desired to have a rotation transmission characteristic with a small backlash and a low noise characteristic with a quiet meshing noise.

Under such circumstances, the conical involute gear (hereinafter, referred to as a conical gear) can be used for both the parallel shaft and the cross shaft, and the backlash can be adjusted small by adjusting the movement in the axial direction. Further, since the meshing is close to that of a helical gear, the meshing sound is quiet.

However, in the meshing of general conical gears obtained by processing with a conventional hobbing machine or tooth surface grinding machine, the tooth contact is limited to a part of the tooth width and it is impossible to make contact with the entire tooth width. It was In particular, it is known that when the inclination of the conical angle of the gear increases, the width of the contact narrows and the points concentrate on one point. Therefore, it is difficult to transmit high torque and it is difficult to put it to practical use. Furthermore, in the case of crossed shafts, the design value of the conical angle of the gear does not match the shaft angle when actually engaged, and one end in the axial direction causes uneven tooth contact, so similarly transmit high torque. Was difficult to put into practical use.

Further, as a contact which can obtain contact at all tooth widths, it is known that a pinion cutter has the same number of teeth as the mating pinion to be meshed in a special case, but it is compatible with a machining tool. It was not general, and it was not a general one obtained by processing hobbing machines.

Under these circumstances, the present inventor has clarified the cause of the tooth contact of a conical gear, which is designed by the conventional design method and which is tooth-cut, is limited to a part due to actual meshing. That is, in the sectional view shown in FIG. 7, the conical gear 1
The reference plane S-S is a plane perpendicular to the axis with zero displacement, and the pitch line 3 of the rack 2 is geared so as to form an angle δ with the conical gear shaft 4. P ₀ is the reference pitch point, d _b is the diameter of the reference pitch circle, m is the gear module,
If z is the number of teeth, it is defined as d _b = m · z (1).

Further, as shown in a schematic sectional view in FIG.
Hobbing of the O ₂
This is done by moving the hob 5 in the direction of arrow A so that the reference pitch circle 6 centered at is in contact with the pitch line 3 inclined at the angle δ. The dislocation coefficient x ₂ of the point P on the pitch line 3 which is separated from the reference pitch point P ₀ by the length b is x ₂ = (b · sin δ) / m (2), and the dislocation occurs in the direction orthogonal to the axis. It indicates that

Next, in the conical gear 1 designed and processed as described above, a cylindrical pinion 7, a conical gear shaft 4 and a pinion shaft 8 form an angle δ _s as shown in the schematic sectional view of FIG.
Consider the case where the meshing state is such that (= δ). Here, the reference pitch point P ₀ of the conical gear 1
Let V ₀ and U ₀ be the points of intersection of the tooth-perpendicular surface of the pinion 7 and the conical gear shaft 4 and the pinion shaft 8, respectively, and let U be the point separated from the point U ₀ on the pinion shaft 8 by the length b. Further, the point of intersection of the pinion 7 including the point U with the conical gear shaft 4 on the plane perpendicular to the teeth is V.

Then, the meshing center distance a between the conical gear 1 and the pinion 7 on the plane perpendicular to the teeth of the pinion 7 is determined. The meshing center distance a is obtained as described below, like the meshing of the cylindrical dislocation involute spur gears.

Inv α _b = 2 [(x ₁ + x ₂ ) / (z ₁ + z ₂ )] tan α ₀ + inv α ₀ (3) y = (z ₁ + z ₂ ) [(cos α ₀ / cos α _b ). −1] / 2 (4) a = [(z ₁ + z ₂ ) / 2 + y] · m (5) where α ₀ : tool pressure angle, α _b : meshing pressure angle, x ₁ , x ₂ : pinion 7 and the dislocation coefficient of the conical gear 1, z ₁ , z ₂ : the number of teeth of the pinion 7 and the conical gear 1, y: the center distance increase coefficient.

On the other hand, since the distance a _s between the rotating shafts of the conical gear 1 and the pinion 7 corresponds to the length of the straight line UV, it can be obtained by the following equation.

A _s = a _s0 + b · tan δ _s (6) where a _s0 is the axial distance in the plane perpendicular to the reference tooth and is the length of the straight line U ₀ −V ₀ , which is obtained from equation (5). It is made to match the meshing center distance a.

Then, the meshing center distance a obtained from the equation (5) and the interaxial distance a _s obtained from the equation (6) are respectively applied from the small diameter end to the large diameter end of the conical gear 1 in detail. Calculated by giving the original. For example, as gear specifications, the tool pressure angle α ₀ = 20 °, the module m = 1.5, the parallel teeth, the pinion 7 has the number of teeth z ₁ = 17, the dislocation coefficient x ₁ = 0.
3 and the conical gear 4 has a tooth number z ₂ = 39 and a tooth width b _n =
13 mm, addendum modification coefficient x ₂ dislocation of a smaller diameter end, as shown in FIG. 10 (referred to as reference pitch point P ₀₎ coefficient x ₂ =
0, and the straight line indicated by the solid line 9 at which the dislocation coefficient x ₂ = 1.4036 at the large diameter end and the angle δ _s = δ = 9 ° between the conical gear shaft 4 and the pinion shaft 8 Is
The meshing center distance a and the interaxial distance a _{s with} respect to the tooth width b _n are as shown by the solid lines 10 and 11 in FIG. In the case of 42 teeth, the values are shown in parentheses in FIG.

That is, the curve 10 of the meshing center distance a
And the solid line 11 of the inter-axis distance a _s do not change in the same manner, and a = a _s at the small diameter end, but a <a _s at other portions up to the large diameter end. This is because the tooth surface of the conical gear 1 and the pinion 7 are in contact with each other at the small diameter end where the meshing center distance a and the axial distance a _s are equal, but the tooth surfaces do not contact at the other parts, and are offset at the small diameter end. It shows that the teeth are in contact with each other.

Further, the solid line 10 of the center distance a meshing match contrast to the straight line shown by the dotted line 12, has a gentle curve convex upward, the center distance a meshing the axial distance a _s So that the conical gear shaft 4 and the pinion shaft 8
Even if the angle δ with respect to δ _{s is} shifted from δ _s = 9 °, only the part of the tooth surface where the conical gear 1 and the pinion 7 contact is changed, and the state of local partial contact does not change.

[0016]

As described above, the conical gear designed by the conventional design method and obtained by general processing using a hobbing machine or the like has a tooth contact at the time of meshing limited to a part of the tooth width. It was difficult to make contact with a wide tooth surface, and it was difficult to transmit high torque, which was difficult to put into practical use. The present invention has been made in view of such a situation,
The object is to provide a conical involute gear that can be processed by general-purpose processing, can be brought into contact with a wide range of tooth surfaces during meshing, and can transmit high torque. .

[0017]

A conical involute gear according to the present invention is a conical involute gear in which a dislocation coefficient is changed in the gear axis direction to form a conical outer shape. It is characterized in that it is formed by giving a dislocation coefficient in the direction perpendicular to the teeth so that the center distance between the shafts meshes with the center distance between the shafts and the center distance between the shafts.

[0018]

The conical involute gear configured as described above has a dislocation coefficient in the direction perpendicular to the teeth on the surface perpendicular to the tooth of any tooth width of the mating gear, which makes the center distance between the shafts substantially coincide with the center distance. It is formed by giving the reference pitch line of the tool such as the hob along the locus of the pitch circle in the tooth width direction obtained by adding the radius of the reference pitch circle to the product of the dislocation coefficient and the module. And the mating gear comes into contact with the mating gear at the tooth surface where the center distance between the shafts and the meshing center distance over substantially the entire tooth width are substantially the same. Therefore, the tooth contact at the time of meshing is not limited to a part of the tooth width, but the tooth contact can be made in a wide range of the tooth surface, and high torque can be transmitted. In addition, this can be formed by general processing.

[0019]

Embodiments of the present invention will be described below with reference to the drawings. Each embodiment was designed based on the result of the above-mentioned inventor designed by the conventional design method, and the tooth contact in the meshing of the toothed conical gear is limited to a part, and the cause of the one-side contact is clarified. Now, embodiments of the present invention will be described below with reference to the drawings.

First, a first embodiment will be described with reference to FIGS. 1 is a sectional view of a conical gear, FIG. 2 is a diagram showing a relationship between a meshing center distance and an axial distance with respect to a tooth width, and FIG. 3 is a diagram showing a relationship of a dislocation coefficient with respect to a tooth width. FIG. 6 is a cross-sectional view showing a state of tooth contact.

First, the basis for processing the conical gear 21 shown in FIG. 1 will be described. That is, in order to bring the conical gear into contact with the mating gear, for example, the tooth surface of the pinion with the total tooth width Bsec δ _s , the meshing center distance a
And the inter-axle distance a _s are required to be equal on any plane perpendicular to the tooth, which is expressed by the following equation.

A = a ₀ + b · tan δ _s (7) Here, a ₀ is the meshing center distance in the plane perpendicular to the reference tooth.

Then, when the meshing center distance a on an arbitrary tooth right-angled surface is determined by the equation (7), the meshing pressure angle α _b becomes the following equation from the equations (4) and (5).

Α _b = cos ⁻¹ [(z ₁ + z ₂ ) m · cos α ₀ ] / (2 · a) (8) Furthermore, substituting equation (8) into equation (3), the dislocation coefficient of the conical gear x is calculated as Expression (9). x = [(z ₁ + z ₂ ) (inv α _b −inv α ₀ ) / (2 tan α ₀ )] − x ₁ (9) The dislocation coefficient x shown in this formula (9) is the tooth right-angled surface of the conical gear. However, the dislocation direction is perpendicular to the teeth.

Here, concrete gear specifications are given and calculated as follows, and the conical gear 21 of FIG. 1 is formed. In FIG. 1, 21 is a conical gear, 22 is a tooth, and 2 is a tooth.
The point P ₁ at the small diameter end of 2 is the reference pitch point P ₀ .
23 is a locus of the pitch circle in the tooth width direction that passes through the point P ₁ , intersects with the tooth right-angled surface at the large diameter end at the point P ₂ , and the point P ₃ on the locus 23 of the pitch circle is the point P ₁ (= P ₀ ). Is an intermediate point between the point P ₂ and the point P ₂ .

As the gear specifications, the tool pressure angle α ₀ = 2
0 °, module m = 1.5, parallel teeth, pinion 7 has tooth number z ₁ = 17, dislocation coefficient x ₁ = 0.3, and conical gear 21 has tooth number z ₂₁ = 39, tooth width b _n1 = 13 mm, the angle δ _s between the conical gear shaft 4 and the pinion shaft 8 = 9 °, and the meshing center distance a and the inter-axis distance a _s for the total tooth width b _n1 are shown in FIG.
When the values are matched as shown by the solid line 24 in FIG. 3, the dislocation coefficient x obtained by the equation (9) is as shown by the solid line 25 in FIG. 3, the dislocation coefficient x = 0 at the small diameter end and the dislocation coefficient x = at the large diameter end. 1.69
84, which changes so as to draw a concave gentle curve on the upper side. Further, when the number of teeth is 42, the value is shown in parentheses in FIG. The dotted line 2 shown in FIG.
6 is a straight line described for comparison.

In the conical gear 21, the dislocation coefficient x obtained by the equation (9) for matching the meshing center distance a with the interaxial distance a _s on an arbitrary right-angled surface over the entire tooth width b _n1 The process is performed by giving the dislocation coefficient x obtained by the equation (9) on an arbitrary right-angled plane in which the locus 23 of the pitch circle passing through the point P ₁ extends over the entire tooth width b _n1. Since it is obtained by adding the reference pitch circle radius (radius at the small diameter end) to the product of the modules m, the reference pitch line of the tool is set at the point P ₁ along the trajectory 23 of the pitch circle.
From an NC hobbing machine of a processing machine that can be numerically controlled to move from a point P ₃ to a point P ₂ .

The conical gear 21 thus formed was meshed with the pinion 7 as shown in FIG. 4, and the tooth contact was confirmed. In the state of uniform contact.
For comparison, the state of tooth contact of the conical gear 1 machined by the conventional design method shown in the figure is a contact state of one side as shown by the shaded portion 13.

Therefore, according to the conical gear 21 of the present embodiment constructed as described above, the backlash can be adjusted, and the meshing noise is not impaired. It is possible to realize high torque transmission by contacting with each other, and high torque transmission can be achieved even when the conical angle of the gear is large. Further, in the case of further processing, a unique tool is not required, and it can be processed by a general method using a hobbing machine or the like.

Next, a second embodiment of the present invention will be described with reference to FIG. FIG. 5 is a sectional view, in which 31 is a conical gear, 32 is a tooth, and 33 is a point P at the small diameter end of the tooth 32.
₁ and the intermediate point P ₃ and the large-diameter end point P ₂ pass through the same three points as in the first embodiment, and the locus of the pitch circle in the tooth width direction is different from the first embodiment. For this reason, an arc passing through the point P ₁ , the intermediate point P ₃ and the point P ₂ is used.
The gear specifications are formed in the same manner as in the first embodiment.

The locus 33 of the pitch circle is the reference pitch point P.
_In a Cartesian coordinate system with ₀ (= P ₁ ) as the origin, centering on the point O ₃ , X = 53.311 mm, Y = 310.264 mm,
R = 314.811 mm, which is an approximation of the pitch circle locus 23 of the first embodiment by an arc. The process is a reference pitch line of the tool to be moved from point P ₁ along the path 33 of the pitch circle to the via to point P ₂ to the point P ₃ performed by the NC hobbing machine and the like.

The conical gear 31 formed in this way
When the tooth contact was confirmed by meshing with the pinion 7 in the same manner as the conical gear 21 of the first embodiment, the tooth contact condition is substantially the same as that of the conical gear 21 of the first embodiment. All tooth surfaces were in uniform contact.

Therefore, also in this embodiment, the same operation and effect as in the first embodiment can be obtained.

Further, a third embodiment of the present invention will be described with reference to FIG. Figure 6 is a sectional view, 41 is a conical gear in FIG, 42 is a tooth, 43 pitch circle of the tooth width direction through the the point P ₄ of the small diameter end and the point P ₅ of the large diameter end of the tooth 42 Unlike the second embodiment, the locus is a straight line for simplifying the gear cutting process, and this straight line defines the meshing center distance a in an arbitrary right-angled surface over the entire tooth width b _n3. Dislocation coefficient x obtained by equation (9) that matches the axial distance a _s
Is a straight line approximation of the locus of the pitch circle when given in the direction perpendicular to the teeth. .

The gear specifications are the pressure angle α _{0 of the} tool.
= 20 °, module m = 1.5, double teeth, pinion 7
Is the number of teeth z ₁ = 17, the dislocation coefficient x ₁ = 0.3, the conical gear 41 has the number of teeth z ₂₃ = 45, the tooth width b _n3 = 13 mm, and the angle δ _s between the conical gear shaft 44 and the pinion shaft 8. = 9 °, the dislocation coefficient x at the small-diameter end point P ₄ is x = 0, and the dislocation coefficient at the large-diameter end point P ₅ is x = 1.6730.

Further, the locus 43 of the pitch circle is different from that of the second embodiment in order to make the gear cutting process simpler.
It becomes a straight line passing through the point P ₄ of the small diameter end and the point P ₅ of the large-diameter end, the straight line equation to match the center distance a mesh of any tooth plane perpendicular to the axis-to-axis distance a _s (9) The locus of the pitch circle when the dislocation coefficient x obtained in (3) is given in the direction perpendicular to the teeth is linearly approximated. The machining is performed by a hobbing machine or the like so that the reference pitch line of the tool is moved from the point P ₄ to the point P ₅ along the locus 43 of the pitch circle.

The conical gear 41 formed in this way
When the tooth contact was confirmed by meshing with the pinion 7 in the same manner as the conical gear 21 of the first embodiment, the tooth contact state is uniformly contacted on all tooth surfaces as indicated by the shaded portion 45. Although it did not reach the state, the conventional conical gear 1
The contact area was larger than that of No. 1 and the contact state of the tooth surface was obtained in a range where there was no contact in the peripheral portion of the tooth surface, which was not a problem in practical use.

Therefore, also in this embodiment, substantially the same operation and effect as in the first embodiment can be obtained.

The present invention is not limited to those described in each of the above-mentioned embodiments. For example, the mating gear may be a conical gear instead of a pinion, and for different gear specifications and different axial angles. Is also applicable. Further, the locus of the pitch circle may be approximated by a plurality of arcs, other curved lines, or straight lines, and the like, which can be appropriately changed and implemented within a range not departing from the gist.

[0040]

As is apparent from the above description, according to the present invention, the dislocation coefficient for making the meshing center distance substantially coincide with the inter-axis center distance on the tooth right angle surface of the entire tooth width of the mating gear is set. Since it is formed by giving it in the direction, it can be formed by general processing, and the tooth contact at the time of meshing is not limited to a part of the tooth width, but contacts in a wide range of the tooth surface. It is possible to obtain the effect that high torque can be transmitted.

[Brief description of drawings]

FIG. 1 is a sectional view showing a conical involute gear according to a first embodiment of the present invention.

FIG. 2 is a diagram showing a relationship between a tooth center width and a meshing center distance and an axial distance in the same as above.

FIG. 3 is a diagram showing a relationship between a dislocation coefficient and a tooth width in the same as above.

FIG. 4 is a cross-sectional view showing a state of tooth contact in the above.

FIG. 5 is a sectional view showing a conical involute gear according to a second embodiment of the present invention.

FIG. 6 is a sectional view showing a conical involute gear according to a third embodiment of the present invention.

FIG. 7 is a sectional view for explaining a conical involute gear.

FIG. 8 is a sectional view for explaining gear cutting of a conventional conical involute gear.

FIG. 9 is a cross-sectional view shown for analyzing a meshing state of a conventional conical involute gear with a pinion.

FIG. 10 is a diagram showing a relationship between a dislocation coefficient and a tooth width in a conventional example.

FIG. 11 is a view showing the relationship between the meshing center distance and the axial distance with respect to the tooth width in the above.

[Explanation of symbols]

7 ... pinion 21 ... trajectory P ₀ ... reference pitch point of conical gears 22 ... teeth 23 ... pitch circle b _n1 ... tooth width m ... module x ... shift coefficient

Claims (1)

[Claims] 1. A conical involute gear in which a dislocation coefficient is changed in the gear axis direction to form a conical outer shape, in which a center-to-axis center distance is set on a surface orthogonal to an arbitrary tooth having a full tooth width with a mating gear. A conical involute gear, which is formed by applying the dislocation coefficient that makes the meshing center distances substantially equal to each other in the direction perpendicular to the teeth.