JPH06304812A - Hourglass shape worm gear generating method - Google Patents

Abstract

PURPOSE:To reduce a grinding margin, and shorten time necessary for generation by generating a worm wheel by a wheel generating tool to which the same shape with a hand drum shape worm or the part is adopted. CONSTITUTION:The whole or a part of an inverted conical surface where a half apex angle (gamma) is set in 90 deg.<gamma<180 deg., is adopted to an hourglass shape worm generating tool as a tooth surface of an intermediate gear, and relational motion similar to an hourglass shape worm wheel is given to this tool, and an hourglass shape worm is generated. Next, a worm wheel is generated by a wheel generating tool to which the same shape with this hourglass shape worm or the part is adopted. Or the whole or a part of two inverted conical surfaces where a half apex angle (gamma) is in 90 deg.<gamma<180 deg., is adopted to the hourglass shape worm generating tool as the tooth surface of the intermediate gear, and the conical principal axis of the two inverted conical surfaces are made to coincide with each other, and the bottom surfaces are made to coincide with each other, and both tooth surfaces of a worm gear are generated simultaneously.

Description

Detailed Description of the Invention

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of grinding an hourglass-shaped worm gear with an inverted conical surface tool.

[0002]

2. Description of the Related Art Conventionally, as a method for creating a drum-shaped worm gear, grinding is performed using a flat tool (developing tooth surface drum-shaped worm gear), grinding is created using a conical tool, etc. Is publicly known (see Japanese Patent Publication No. 62-19970). Comparing the grinding created using a flat tool with the grinding created using a conical surface tool, the grinding created using a flat tool has less design freedom and the teeth of the worm gear. Since it is inconvenient that both sides of the surface cannot be ground at the same time, the method of grinding by using a conical tool is being used more and more.

[0003] Explaining the generating method of grinding by using this known conical surface tool, the tool 2 rotated by the motor 1 is a conical surface as shown in FIG. It creates a drum-shaped worm gear 3 on both sides at the same time. However, the worm using the known conical surface tool 2 has not been satisfactory in terms of cost. The reason is that both the milling time and the grinding time are long.

On the other hand, it has also been proposed to cut an hourglass-shaped worm gear using an inverted conical milling cutter. (See Japanese Patent Publication No. 2-232119)
2, the rotation of the motor 11 is transmitted to the holder 14 by the pulley 12 and the belt 13. Holder 14
The cutting tool 15 for milling is attached to the tool. By turning the holder 14, the cutting tool 15
It is designed to cut the hourglass-shaped worm gear 16.

[0005]

However, in the case where the hourglass-shaped worm gear 16 is cut by the above-mentioned inverted conical cutting tool 15, there is an advantage that the time required for cutting is shortened, while the cutting by the cutting tool 15 is performed. Because of this, the tooth surface is rough and must be ground and finished with a grindstone. Usually, in this finishing grinding, there is a large error between the conical grinding wheel gear that uses a grinding wheel with a conical surface and the thread cutting gear with an inverted conical tool, so the grinding allowance increases, and eventually the grinding time for surface finishing becomes long. The drawback is that it will be lost. Therefore, an object of the present invention is to provide a novel creation method capable of creating a drum-shaped worm gear with a tool in a short time.

[0006]

The features of the present invention are as follows. First, the first feature of the present invention is that, in a drum-shaped worm creation tool as a tooth flank of an intermediate gear, all or one of the inverted conical surfaces having a half apex angle γ of 90 ° <γ <180 °. Part, and gives the tool a movement similar to a drum-shaped worm wheel to create a drum-shaped worm,
And, a method for creating a drum-shaped worm gear by means of a medium gear theory, characterized in that a worm wheel is created by a tool for creating a wheel having the same shape as or a part of this drum-shaped worm. It is in.

A second characteristic of the present invention is that the tool for creating a drum-shaped worm as a tooth flank of an intermediate gear has all two inverted conical surfaces with a half-vertical angle γ of 90 ° <γ <180 °. Or, a part of them is adopted, and the conical main axes of two inverted conical surfaces are made to coincide with each other and their bottom surfaces are made to coincide with each other so that both tooth surfaces of a worm gear can be simultaneously created. It is in the method of creating a drum-shaped worm gear.

[0008]

An embodiment of the present invention will be described below with reference to the drawings. Prior to the description of the embodiments of the present invention, the purpose of the present invention will be described.The present invention focuses on the fact that the cutting time is shortened when the inverted conical milling tool is used, The creation is done using an inverted conical tool. In the following description, in order to facilitate understanding of the present invention, the present invention will be described while adding a description of the case where a conventionally known flat tool, a conical surface tool, and a cutting tool for inverted conical milling are respectively used. .

First, the case of creation using a flat tool will be described. Intermediary Gear Theory (Sakai-Mechanical Society Papers, 1955, Volume 21, No. 102, 164 pages) and Double Contact Theory (Sakai-Maki Mechanical Society Papers, 1972, Volume 38, No. 311, 1895) The developable tooth flank worm gear based on (Page) has already proved its high performance. However, the conventional developable tooth-shaped drum-shaped worm gear (Sakai-Maki-Mechanical Society lecture paper, 740-15)
Was a case where a plane was taken as the tooth flank of the intermediate gear and the plane was parallel to the axis of the intermediate gear. Due to these two conditions, the degree of freedom in design is restricted, and the inconvenience is particularly significant when designing a worm gear with a reduced speed ratio.

Further, when a tool that expresses a flat surface (a flat surface tool) is used in terms of processing, it is inconvenient that both tooth flanks of the worm screw cannot be created at the same time.

The case where the above-mentioned intermediate gear theory and the two-degree contact theory are applied to a drum-shaped worm gear will be described below. In FIG. 1, I ₁ is a worm shaft, I ₂ is a wheel shaft, and I ₃ is an intermediate gear shaft. Also, the absolute coordinate fixed in space is O-xyz in the right-handed rectangular coordinate system, the x-axis is the I ₁ -axis direction,
The z-axis is oriented in the I ₂ -axis direction, and the common perpendicular line O ₂ O ₁ of the I ₁ and I ₂ axes is oriented in the y-axis direction. The I ₃ axis intersects with O ₂ O ₁ at a right angle at an O ₃ point and is inclined with respect to the I ₂ axis by an angle α as shown in the drawing (where O ₁ and O ₂ are the I ₁ and I ₂ axes, respectively). It is the intersection of the common perpendicular line O ₂ O ₁ and the worm axis I ₁ and the wheel axis I ₂ .

Now, the rotational speeds of the worm shaft I ₁ , the wheel shaft I _2, and the intermediate gear shaft I ₃ are ω ₁ , ω ₂ , ω ₃ , and the translational speed of the intermediate gear I _{3 in} the axial direction is ω. ₃ , the rotation ratio is i = ω ₁ /
If ω ₂ , j = ω ₁ / ω ₃ , h = ω ₃ / ω ₃ (converted pitch of screw motion of intermediary gear), O ₂ O ₁ = e, O ₃ O ₁ = e ₁ , According to the gear theory, the following conditions are satisfied.

E ₁ = ecos ² α (1) j = icos α-sin α (2) h = ω ₃ / ω ₃ = esin α · cos α (3)

Conversely, a tool tooth surface of arbitrary shape is attached to the I ₃ axis satisfying the expressions (1) to (3), and a worm blank attached to the I ₁ axis and a worm wheel attached to the I ₂ axis. -If you process the le blank first, a pair of water-
The worm and the wheel are in contact with each other with the same contact line as the contact line between the intermediate gear and the worm (this is called the "first contact line"). This creation method is called an indirect creation method.

Especially when α = 0, the intermediate gear shaft I ₃ coincides with the wheel shaft I _2, and when α = 90 °, the intermediate gear shaft I ₃ coincides with the worm shaft I ₁ . Therefore, it is not necessary to consider the intermediate gear in any case. Therefore, in this case, it is called the direct creation method.

Further, according to the "double contact theory",
When a worm wheel is directly created by a tool having the same shape as or a part of the worm created by the intermediate gears satisfying the conditions of formulas (1), (2) and (3), In addition to the above-mentioned first contact line, the pair of worm and worm wheel has a second contact line (this is referred to as "second contact line").
But they come into contact at the same time. Moreover, at a point where the contact occurs only once (referred to as “limit normal point”), the relative radius of curvature becomes infinite (∞). In practice, it is desirable to bring a line (referred to as "critical normal point curve") in which this relative radius of curvature (∞) can be expected into the range where the worm and the worm wheel mesh. Therefore, for this purpose, there arises a problem of how to determine the tooth profile of the intermediate gear.

In the developable tooth surface drum-shaped worm gear, a plane A (planar tool) parallel to the intermediate gear axis I ₃ is adopted as the intermediate gear tooth surface at a distance a from the intermediate gear axis. Therefore, the fact that the translational motion of the intermediate gear shaft I ₃ can be omitted is an advantage in processing. Also, in terms of performance, the limit normal curve can be brought into the meshing range, and a high-performance worm gear was realized.

Next, a method of creating a drum-shaped worm gear with a conical tool will be described. Hourglass worm with conical tool
The creation of the gear is also based on the above-mentioned intermediate gear theory and the double contact theory. Therefore, the relationship between the axial positions is the same as the positional relationship shown in FIG. And the above formula (1),
Of course, (2) and (3) must also hold. Then, based on these conditions, there is a feature that a conical surface (conical surface tool) is adopted as the tooth surface of the intermediate gear.

FIG. 2 is a diagram when a conical surface B is adopted as the tooth surface of the intermediate gear. Further, FIG. 3 more specifically shows the positional relationship between the intermediate gear shaft and the intermediate gear tooth surface.
Now, let us say that the half-vertical angle of the conical surface B that is the tooth surface of the intermediate gear is γ, and the main axis of the cone is O ₁ O ₅ (O ₁ is the apex of the cone). Also, I ₃ axis is z
₃ as an axis, right rectangular coordinate system fixed O ₃ points to mediate gear shaft having an origin O ₃ take -x ₃ y ₃ z _3. Then the conical main axis O ₄ O ₅
In the plane of y = b so that it has an inclination δ with respect to the x ₃ y ₃ plane. Then, the point O ₅ becomes the intersection of the y ₃ z ₃ plane and O ₄ O ₅ . The point O ₅ is given by (O, b, -c), and O ₄
Let O ₅ = a.

The above-described creation method shown in FIG. 1 can be said to be a creation method using a flat tool.
The creation method described can be referred to as a creation method using a conical surface tool. The creation method of the present invention uses an inverted conical surface instead of the conical surface in FIG.

This will be described with reference to FIG. 4. FIG. 4A shows a conical surface tool. In the conical surface tool, the half apex angle of the conical surface is 0 <γ <90 °. In addition, FIG. 4B shows a flat tool, and the half apex angle of the flat tool is γ =
It is 90 °. On the other hand, FIG. 4C shows an inverted conical surface tool, and in the inverted conical surface tool, the half apex angle of the conical surface (reverse conical surface) is 90 ° <γ <180 °. That is, in the present invention, the half apex angle is 90 ° <γ <180 °
Is one of the features.

Next, a method of creating an hourglass-shaped worm gear using the inverted conical surface tool according to the present invention will be described. First of all, the creation of the hourglass-shaped worm gear with the inverted conical surface tool is also based on the above-mentioned intermediate gear theory and the double contact theory. Therefore, the relationship between the axial positions is the same as the positional relationship shown in FIG. And, the above equations (1), (2), and (3) must be naturally satisfied. Then, based on these conditions, there is a feature in that an inverted conical surface (inverse conical surface tool) is adopted as the tooth surface of the intermediate gear.

The relationship between the axial position of the drum-shaped worm gear according to the present invention, the intermediate gear tooth surface, and the intermediate gear shaft will be described with reference to FIGS. 5 and 6. That is, as in the case of the conical surface tool shown in FIGS. 2 and 3, the half apex angle of the reverse conical surface C, which is the tooth surface of the intermediate gear, is γ, and the conical main axis is O.
₁ O ₅ (O ₁ is the apex of the cone). Further, the I ₃ axis is the z ₃ axis, and a right-handed rectangular coordinate system O ₃ −x ₃ y ₃ z ₃ fixed to the intermediate gear axis with the O ₃ point as the origin is taken. Therefore, the conical main axis O ₄ O ₅ is y
In the plane of = b, the inclination is δ with respect to the x ₃ y ₃ plane. Then, the point O ₅ becomes the intersection of the y ₃ z ₃ plane and O ₄ O ₅ . Point O ₅ is given by (O, b, -c), and O ₄ O ₅ =
a.

FIGS. 7A and 7B are views showing the relative positional relationship between the inverted conical surface tool of the present invention and the worm gear. Here, the case where c = 0 and α = 0 is shown. That is, when c = 0, the opposite conical principal axes of the two conical surfaces forming the left and right tooth surfaces of the hourglass-shaped worm coincide, and the left and right teeth of the worm can be created simultaneously. At the same time, α =
0 is the case of the direct generation method in which the intermediate gear axis and the wheel axis coincide with each other.

Next, in FIG. 8 (A) and FIG. 8 (B), c =
The arrangement positions of the conical surface tool and the inverted conical surface tool when 0 and α = 0 are shown. The conical surface tool shown in this arrangement position is created by K in FIG. 8 (A), and the inverted conical surface tool is created by K in FIG. 8 (B), and the difference in use is clear.

Next, looking at the error of the tooth profile between the conical surface tool and the inverted conical surface tool with reference to FIG. 9, the tooth profile of the conical surface tool shown in FIG. 9 (A) and the inverted conical surface tool shown in FIG. 9 (B). 9C shows the tooth profile error, and it can be seen that there is a large difference in pressure angle as seen in FIG. 9C. This indicates that the finishing allowance (grinding allowance) is large when the screw tooth profile formed by the inverted conical surface tool is finished by the conical tool (grinding stone). Therefore, if the inverted conical tool is used as it is as a finishing tool (grinding stone), the grinding allowance is small and the thread cutting time
It is possible to obtain a drum-shaped worm with less grinding time.

Further, assuming that the inverted conical surface tool is inferior in performance as compared with the conventionally known conical surface tool, this is not preferable, but FIG. ) Shows the contact line by the conical surface tool, and FIG. 10B shows the contact line by the reverse conical surface tool, the contact line both by the conical surface tool and the reverse conical surface tool. Is almost the same, and as shown in Table 1, there is almost no difference in terms of the angle formed by the contact line and the sliding direction, the relative curvature radius, and the length of the simultaneous contact line. Therefore, the inverted conical surface tool of the present invention is conventionally known. It is comparable in performance to the conical tool.

[0028]

[Table 1]

[0029]

According to the present invention described above, the following effects can be obtained. According to the present invention, since the grinding allowance is reduced, the time required for creation is shortened correspondingly, which is a very effective method for creating a drum-shaped worm gear. In that case, in terms of other performance, it is not inferior to the conventionally known creation method using a conical surface tool.

[Brief description of drawings]

FIG. 1 is a diagram showing an axial positional relationship of a worm gear in the case of a flat tool.

FIG. 2 is a diagram showing an axial positional relationship of a drum-shaped worm gear in the case of a conical tool.

FIG. 3 is an enlarged view showing the relationship between the intermediate gear tooth surface of FIG. 2 and the intermediate gear shaft.

FIG. 4 is a view showing a difference in half-vertical angle depending on tools, (A) shows a conical surface tool, (B) shows a plane tool, and (C) shows an inverted conical surface tool. It is a thing.

FIG. 5 is a drum-shaped worm for an inverted conical surface tool.
It is a figure which shows the axial positional relationship of a gear.

6 is a diagram showing a relationship between the intermediate gear tooth surface of FIG. 5 and an intermediate gear shaft.

FIG. 7 is a diagram of a special case where α = 0 and c = 0, (A) is a front view, and (B) is a side view.

FIG. 8 is a diagram showing an arrangement position when c = 0 and α = 0, (A) is a case of a conical surface tool, and (B) is a diagram.
Is the case of an inverted conical surface tool.

9A and 9B show tooth profiles of a conical surface tool and an inverted conical surface tool and their errors, FIG. 9A shows a tooth profile of a conical surface tool, and FIG. 9B shows a tooth profile of an inverted conical surface tool. It is a figure which shows the error of each tooth profile.

FIG. 10 is a diagram showing how the contact line appears,
(A) is a figure in the case of a conical surface tool, (B) is a figure in the case of an inverted conical surface tool.

FIG. 11 is a schematic diagram illustrating a method of creating a drum-shaped worm gear using a conventionally known conical surface tool.

FIG. 12 is a schematic view showing a cutting process of a drum-shaped worm gear by a conventionally known milling machine.

[Explanation of symbols]

I ₁ worm shaft I ₂ wheel shaft I ₃ intermediate gear shaft A A plane parallel to intermediate gear shaft I ₃ ω ₁ rotation speed of worm shaft ω ₂ rotation speed of wheel shaft ω ₃ intermediate gear shaft Axial translation speed ω ₃ Rotational speed of the intermediate gear shaft h Converted pitch of screw motion of intermediate gear = ω ₃ / ω ₃ α Inclined angle of intermediate gear shaft I ₃ B Conical surface Rc Radius δ Conical surface In the plane parallel to the x ₃ y ₃ plane of the main axis O ₄ O ₅ , x
₃ y ₃ (a conical surface) inclination angle γ relative to the plane distance between the apex O ₄ and the bottom surface center O ₅ half apex angle a conical surface (O ₄ O ₅₎ and b conical bottom center O ₅ and x ₃ z ₃ planes Distance c The distance between the center O _{5 of the} conical bottom surface and the y ₃ axis C The reverse conical surface

[Procedure amendment]

[Submission date] July 8, 1994

[Procedure Amendment 1]

[Document name to be amended] Statement

[Correction target item name] 0004

[Correction method] Change

[Correction content]

On the other hand, it has also been proposed to cut an hourglass-shaped worm gear using an inverted conical milling cutter. (See Japanese Patent Laid-open flat 2-232119) which Figure 1
2, the rotation of the motor 11 is transmitted to the holder 14 by the pulley 12 and the belt 13. Holder 14
The cutting tool 15 for milling is attached to the tool. By turning the holder 14, the cutting tool 15
It is designed to cut the hourglass-shaped worm gear 16.

[Procedure Amendment 2]

[Document name to be amended] Statement

[Correction target item name] 0019

[Correction method] Change

[Correction content]

FIG. 2 is a diagram when a conical surface B is adopted as the tooth surface of the intermediate gear. Further, FIG. 3 more specifically shows the positional relationship between the intermediate gear shaft and the intermediate gear tooth surface.
Now, let us say that the half-vertical angle of the conical surface B that is the tooth surface of the intermediate gear is γ, and the main axis of the cone is O ₁ O ₅ (O ₁ is the apex of the cone). In addition, a right-handed rectangular coordinate system O ₃ -x ₃ y ₃ z ₃ fixed to the intermediate gear axis having the I ₃ axis as the z ₃ axis and the O ₃ point as the origin is taken. Therefore, the conical main axis O ₄ O ₅ is set to have an inclination δ with respect to the x ₃ y ₃ plane in the plane where y ₃ = b. Then, the point O ₅ is x ₃ y
_It is an intersection of O ₄ O ₅ and a plane parallel to the ₃ planes and having z ₃ = −c . Point O ₅ is given by ( 0 , b, -c), and O ₄ O
Let ₅ = a.

[Procedure 3]

[Document name to be amended] Statement

[Name of item to be corrected] 0023

[Correction method] Change

[Correction content]

The relationship between the axial position of the drum-shaped worm gear according to the present invention, the intermediate gear tooth surface, and the intermediate gear shaft will be described with reference to FIGS. 5 and 6. That is, as in the case of the conical surface tool shown in FIGS. 2 and 3, the half apex angle of the reverse conical surface C, which is the tooth surface of the intermediate gear, is γ, and the conical main axis is O.
₄ O ₅ (O ₄ is the apex of the inverted cone). I ₃ axis is z ₃
An axis, right rectangular coordinate system fixed _{O 3} points to mediate gear shaft having an origin _O 3 take _{-x 3 y} 3 _z 3. So the conical main axis O
₄ O ₅ is set so as to have an inclination δ with respect to the x ₃ y ₃ plane in the plane of y ₃ = b. Then, the point O ₅ becomes the x ₃ y ₃ plane.
Is an intersection point of a plane parallel to z and a surface of z ₃ = −c and O ₄ O ₅ . Point O ₅ is given by ( 0 , b, −c), and O ₄ O ₅ = a
And

[Procedure amendment 4]

[Document name to be corrected] Drawing

[Name of item to be corrected] Figure 6

[Correction method] Change

[Correction content]

[Figure 6]

Claims (2)

[Claims] 1. A drum-shaped worm generating tool as a tooth flank of an intermediate gear, wherein all or a part of an inverted conical surface having a half-vertical angle γ of 90 ° <γ <180 ° is adopted and the tool is a drum. Shaped worm wheel
To create a drum-shaped worm by giving a relational movement similar to that of the drum-shaped worm, and to create a worm wheel with a wheel-forming tool having the same shape as or a part of the drum-shaped worm. A method of creating a drum-shaped worm gear based on the theory of a medium gear. 2. A drum-shaped worm creating tool as a tooth flank of a transmission gear employs all or part of two inverted conical surfaces having a half-vertical angle γ of 90 ° <γ <180 °, and 2 A method for creating a drum-shaped worm gear based on the theory of intermediate gears, characterized in that the conical principal axes of two inverted conical surfaces are made coincident with each other and the bottom surfaces thereof are made coincident so that both tooth surfaces of the worm gear can be simultaneously generated. . [0001]