JPH0712203A - Tooth profile determining method of cylindrical worm gear, tooth profile obtained therefrom, and device therefor - Google Patents

Abstract

PURPOSE:To obtain an optimum tooth profile of cylindrical worm gear by supposing at first an ideal line of contact, inputting it as a supposed line of contact from an initial value input format, and determining the tooth profile of the worm gear by numerical calculation. CONSTITUTION:One of lines of contact projected on a plane perpendicular to a worm axis is supposed, one point on the tooth profile of a worm to be desired is supposed on the center plane of the worm containing the worm axis, inclination of the tangent of a tooth profile on this point is supposed, and the worm tooth profile and the wheel tooth profile are obtained in order from these suppositions. When one of lines of contact projected on a plane perpendicular to the worm axis is supposed to be a straight line, the rotation angle phi0 of the straight line from the reference axis is adopted in the range of 20 deg.<=¦phi0¦<=45 deg., and inclination (dxsi/dxsi)0 of the tangent of the tooth profile on the supposed point on the worm tooth profile is adopted in the range of 0<=¦tan<-1>(dxsi/dxsi)0¦<=35 deg.. Hereby, the tooth profile of the optimum cylindrical worm gear can be obtained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for determining the tooth profile of a cylindrical worm gear, a cylindrical worm gear tooth profile obtained by the method and an apparatus for determining the tooth profile of a cylindrical worm gear.

[0002]

2. Description of the Related Art Cylindrical worm gears can be improved in performance such as load capacity, efficiency, and service life by using a worm as an involute tooth profile and using a dislocation gear, or a worm with a concave arc tooth profile. Methods for doing so have been proposed. In particular, the concave arc tooth profile is called a Nimann tooth profile or a Cabex tooth profile. Not only does the tooth profile of the worm have a concave surface, but various improvements have been made to this with the concave arc tooth profile as the basic model. .

[0003]

However, even if the tooth profile of the cylindrical worm gear is improved by the above-mentioned conventional method, the contact around the root of the worm wheel (= the contact at the worm outlet side) It cannot be improved up to the tendency that the contact line of) becomes parallel to the relative sliding direction.

Here, the contact line is a contact line between a worm wheel and a worm, and is obtained as follows. The pitch line W _{1 of the} rack is a straight line passing through the pitch point CA as shown in FIG. 6 (b). A line passing through CA and perpendicular to it passes through the axis of the wheel. Cross section A is a surface including pitch points. Each cross section from CA (X from I
The contact line is the curve that hangs the foot of the perpendicular line drawn to the tooth profile curve in I). Here, a vertical line drawn from the point CA to the tooth profile of the section VIII is shown. The contact line m projected on the cross section perpendicular to the axis is obtained by advancing this method also in other cross sections (FIGS. 6A and 7A).

The relative sliding direction is a vector direction in which the difference between the worm speed and the wheel speed at the contact point is vector-synthesized.

As described above, if the contact line is parallel to the relative sliding direction, it hinders the efficiency improvement. On the contrary, if the contact line is almost perpendicular to the relative sliding direction,
The lubricating oil film is most easily formed. That is,
The ratio of power transmission by the oil film of fluid lubrication is relatively large,
Since the oil film is hard to break, the friction coefficient is small.

In the conventional tooth profile, since the contact line is almost parallel to the relative sliding direction, it is difficult to form a lubricating oil film, and the oil film is cut off, so that a large amount of friction work occurs and seizure easily occurs. It also led to a reduction in the life of the worm.

On the other hand, in the conventional concave arc improved tooth profile, while the number of simultaneous meshing teeth is small, there is an improvement in increasing the relative radius of curvature, but the load capacity does not increase so much as a whole. It has the drawback.

This is because the conventional improvement measures could not achieve the design item of increasing the angle formed by the contact line and the relative sliding direction due to restrictions in design and production technology. It is a thing.

In view of the problems of the above conventional improvement measures, the present invention is a method for determining the tooth profile of a cylindrical worm gear that makes the angle formed by the contact line between the worm wheel and the worm larger. And further improve the performance of the cylindrical worm gear in a well-balanced manner.

[0011]

SUMMARY OF THE INVENTION In a cylindrical worm gear, one of the contact lines projected on a plane perpendicular to the worm axis.
Assuming a book, and also in the worm center plane including the worm axis, suppose a point on the worm tooth profile to be obtained, and the tangent slope of the tooth profile at this point. From these assumptions, the worm tooth profile and the wheel tooth profile are sequentially obtained.
When one of the contact lines projected on the plane perpendicular to the worm axis is a straight line, the rotation angle φ ₀ of the straight line from the reference axis is in the range of 20 ° ≦ | φ ₀ | ≦ 45 ° The tangent slope of the tooth profile at one point on the assumed worm tooth profile adopted from
(dζ / dξ) ₀ is 0 ≦ | tan − ¹ (dζ / dξ) ₀ | ≦ 35
The optimum cylindrical worm gear tooth profile is obtained from the above tooth profile determination method by adopting from the range of °. Further, as a means for realizing the above method, a device for determining a tooth profile is constituted by a display unit, an input unit, a memory unit, an output unit and a processing unit.

The display unit has at least items relating to the coordinates of a point on the tooth profile to be obtained in the center plane of the worm including the worm axis and the hypothetical inclination of the tangent line of the tooth profile at this coordinate point, and perpendicular to the worm axis. An initial value input format for sequentially inputting items related to the assumed contact line projected on another plane is displayed.

The memory section stores an initial value file for storing data input using the above initial value input format, and a numerical calculation for a single or a plurality of numerical solution methods in solving a differential equation by numerical calculation. It includes a numerical solution constant file that stores data such as necessary step widths corresponding to each numerical solution, and a design item file that stores at least data regarding load capacity and efficiency of the cylindrical worm gear.

The processing section displays the initial value input format on the display section, and stores the data input from the input section in the initial value file according to the displayed initial value input format. A first processing means for storing,
The data input using the initial value input format stored in the initial value file and the data required for the numerical calculation stored in the numerical solution constant file are used to write the data. Second processing means for sequentially calculating the coordinate values of the tooth profile and the wheel tooth profile for each step size, and the wore from the group of coordinate values of the worm tooth profile and the wheel tooth profile calculated by the second processing means The third processing means for calculating the contact line and the relative radius of curvature between the frame and the wheel, and the contact line and the relative radius of curvature calculated by the third processing means are stored in the design matter file. At least
As a result of the comparison by the fourth processing means for comparing the load capacity and the efficiency with the data, the fourth processing means returns to the first processing means when the desired design items are not satisfied, and the comparison is made. As a result, a fifth processing means for outputting the coordinate value group of the worm tooth profile and the wheel tooth profile calculated by the second processing means when the desired design items are satisfied is output from the output section. There is.

[0015]

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below. FIG. 1 shows an outline of the hard configuration of the tooth profile determining apparatus. The tooth profile determination device has a central processing unit (CPU) 1 as its central device. As the CPU 1, it is preferable to use a so-called personal computer, but an optimum one is selected according to the step size of the numerical solution or numerical calculation.

A keyboard 3, input data, for inputting various data and inputting an output command of the coordinate value group of the determined worm tooth profile and wheel tooth profile, A display, preferably a CRT, for displaying output data, etc.
4, and a printer 5 for outputting the coordinate value group of the determined tooth profile is connected to the CPU 1 as its input / output device.

The CPU 1 is also connected to a hard disk 2 for storing a tooth profile determination program and data necessary for tooth profile determination.

FIG. 2 shows a processing procedure for determining the tooth profile of the cylindrical worm gear. First, according to the initial value input format displayed on the screen of the display 4, the tooth profile designer determines the coordinates (ξ ₀ , ζ ₀ ) of the tip of the tooth profile and the inclination (dζ / dξ) of the tooth profile tangent line. Assume ₀ (FIG. 3) and input it from the keyboard 3 (step 11).

Here, as also shown in the upper right of FIG. 4, the coordinates of the point on the worm tooth profile on the worm center plane (ξ-ζ plane) are (ξ, ζ), and A plane parallel to the central plane and separated from the central plane by Z is hereinafter referred to as an M plane.

Subsequently, in the initial value input format displayed on the screen of the display 4, the value of φ when the simultaneous contact line becomes a straight line is sought, and therefore the designer inputs the value φ ₀ . -Input from board 3 (step 1
2).

Here, φ when the simultaneous contact line is a straight line
The value φ = φ ₀ of is as follows. That is,
First, as shown in FIG.
Set one simultaneous contact line projection line for both teeth.
This is called Mline. In the example of FIG. 5, since a straight line passing through the worm axis O is assumed, Mline is φ = φ ₀ = const
Can be expressed as (where φ is the coordinate O-
The rotation angle from the ξ axis to the Mline in the ξZ coordinate is shown).

Based on the above three assumptions, the following procedure
Find the tooth profile and wheel profile. That is, the conditional expression for the contact between the worm and the wheel is shown in (1).

[0023]

[Equation 1]

Where ψ is the rolling angle of the wheel Rw is the radius of the worm wheel pitch circle Rh is the radius of the worm pitch circle γh is the lead angle on the worm pitch cylinder m is the axis module χ is the axis coefficient (ξ, ζ): Coordinates of the worm tooth profile φ: Coordinates of the cross section orthogonal to the worm axis O-ξ Z in the Z coordinate
The rotation angle from the axis to Mline is. In this _equation , ξ = ξ ₀ , ζ = ζ ₀ , dζ / dξ = (dζ
By substituting / dξ) ₀ , φ = φ ₀ , (ξ ₀ , ζ ₀ )
Parameter ψ for finding the point on the tooth flank that contacts the point
= Φ ₀ = φ (ξ ₀ , ζ ₀ , (dζ / dξ) ₀ , φ ₀ ) can be obtained (step 13).

The equation for obtaining the wheel tooth profile from the worm tooth profile is shown in equation (2).

[0026]

[Equation 2]

However, φ = sin ^-1 (Z / ξ) (X, Y): coordinates of wheel tooth profile

In this expression, ξ = ξ ₀ , ζ = ζ ₀ , φ = φ ₀ , ψ =
Obtaining the point (X ₀ , Y ₀ ) on the wheel tooth profile on the XY reference plane (Z = 0) corresponding to the worm tooth profile (ξ ₀ , ζ ₀ ) by substituting ψ ₀ (Step 14).

In the O-ξζ plane, the tooth profile at a point moved by a minute distance h in the ξ-axis direction is obtained from (ξ ₀ , ζ ₀ ). ξ ₁ = ξ ₀ −h ζ ₁ = ζ ₀ −h · (dζ / dξ) ₀ Substituting ψ = φ ₀ , ξ = ξ ₁ , ζ = ζ ₁ , φ = φ ₀ into the equation (1), dζ / dξ) ₁ = f (ξ ₁ , ζ ₁ ) is calculated. By substituting ξ = ξ ₁ , ζ = ζ ₁ , and ψ = ψ ₀ into equation (2), the point (X ₁ , Y ₁ on the wheel tooth profile corresponding to the worm tooth profile (ξ ₁ , ζ ₁ ) ) Can be asked.

Hereinafter, until the contour of the worm tooth profile is obtained
(1) the base - vinegar _{ξi + 1 = ξi-h,} ζi + 1 = ζi-h · f (ξi, ζi),: is (h increments width, i = 0,1,2,3 ···) holds (step 15), (1) by substituting them into formula _{(dζ / dξ) i + 1} = f (ξi + 1, ζi + 1) is Motomari (step 16), (2) to xi] = .xi.i + _1, ζ =
ζi + _1, Wo by substituting ψ = ψ ₀ - arm teeth (xi]
The points (Xi + ₁ , Yi + ₁ ) on the wheel tooth profile on the plane parallel to the worm axis corresponding to (i + ₁ , ζi + ₁ ) can be obtained by successive calculation (step 17).

In the present embodiment, M = line is set to φ = φ ₀ = const for simplicity in FIG. 5, but it is generally sufficient to give φ = φ (ξ). Further, in FIG. 3, the initial value (ξ ₀ ,
The position that gives ζ ₀ , (dζ / dξ) ₀ ) is the tip of the worm tooth profile, but in general, it may be any position on the worm tooth profile to be obtained.

Next, following this process in reverse, φ and Z are obtained by using equation (1) with ψ = φ (ξ, ζ, dξ / dζ, φ) as parameters, and the contact line in the O-ξZ plane is obtained. Recalculate (step 19). Naturally, one of these is Mline itself. Further, the relative radius of curvature ρ is also obtained (step 20). The appearance of the contact line, the relative curvature radius, the number of simultaneous meshing teeth, etc. are checked as a whole, and if it is confirmed that the performance is improved as expected, the worm screw tooth profile is determined (step 21). . If the degree of improvement is insufficient, M line is further changed to M ₂ line and M ₃ line, and the ideal worm screw tooth profile is determined again through the same process (step 22). ).

Finally, a worm thread cutting (grinding) tool tooth profile is obtained from the worm screw tooth profile. Simply use a general-purpose bite with a tooth profile on the worm shaft to cut the desired wore.
A screw thread tooth profile is obtained.

[0034]

According to the present invention, the ideal contact line is first assumed, and the worm gear tooth profile can be determined by numerical calculation by inputting it as a hypothetical contact line from the initial value input format, so that the conventional concave shape is used. It is possible to set with a considerable degree of freedom the degree of contact wire that has not been improved with the arcuate tooth profile, etc., so that the efficiency and load capacity can be improved.

In this tooth profile determination method, since the parameters φ ₀ and (dζ / dξ) ₀ , which are the parameters that most significantly affect the tooth profile, are narrowed down, the optimum tooth profile can be efficiently determined according to the specifications.

[Brief description of drawings]

FIG. 1 is a block diagram showing an outline of a hard configuration of a tooth profile determination apparatus.

FIG. 2 is a flow chart showing an example of processing for determining the tooth profile of a cylindrical worm gear.

FIG. 3 is a diagram for explaining initial values of worm tooth profile calculation.

FIG. 4 is a diagram for explaining a coordinate system of a worm and a wheel.

FIG. 5 is a view for explaining a simultaneous contact line which is a straight line toward the center of the worm axis.

FIG. 6 is a view for explaining the contact line of the worm gear, (a) shows the position of the contact line on the tooth flank of the worm projected on the cross section perpendicular to the axis of the worm, from I XI indicates the position of the section to be dealt with here. B ₁ to B ₇ are points on the contact line necessary for calculation. These points are the central points of each of the two contact lines. (b) is X from section I
Sectional view of the tooth flank of the worm at I.

FIG. 7 is a view for explaining the contact line of the worm gear, similar to FIG. 6, in which (a) shows the position of the contact line on the tooth surface of the worm wheel in a cross section perpendicular to the axis of the worm. Projected on.
(b) shows the engagement between the worm and the worm wheel, the left is a cross section perpendicular to the axis of the worm, and the right is the cross section of the worm.

[Explanation of symbols]

 1 CPU 2 hard disk 3 key board 4 display 5 printer

Claims (3)

[Claims] 1. In a cylindrical worm gear, assuming one of the contact lines projected on a plane perpendicular to the worm axis, and also in the worm center plane including the worm axis. , One point on the worm tooth profile to be obtained and the inclination of the tangent line of the tooth profile at this point are assumed, and the worm tooth profile and the wheel tooth profile are successively obtained from these assumptions. A method for determining the tooth profile of a cylindrical worm gear. 2. The rotation angle φ ₀ of the straight line from the reference axis when one of the contact lines projected on the plane perpendicular to the worm axis is a straight line, 20 ° ≦ | φ ₀ | ≦ 45 The inclination (dζ / dξ) ₀ of the tooth profile at one point on the assumed worm tooth profile is 0 ≦ | tan − ¹ (dζ / dξ) ₀ |
A cylindrical worm gear tooth profile obtained by the tooth profile determination method according to claim 1, selected from the range of ≤35 °. 3. A display unit, an input unit, a memory unit, an output unit, and a processing unit, wherein the display unit has at least a point on the tooth profile to be obtained in a worm center plane including the worm axis. The initial value input format for inputting the coordinate and the item regarding the assumed inclination of the tooth profile tangent line at this coordinate point and the item regarding the assumed contact line projected on the plane perpendicular to the worm axis is displayed. , The memory unit stores an initial value file that stores data input using the above initial value input format, and a numerical calculation method for solving a differential equation by numerical calculation, which is necessary for numerical calculation. A numerical solution constant file that stores data such as the step size corresponding to each numerical solution, and data related to at least the load capacity and efficiency of the cylindrical worm gear are stored. The processing section displays the initial value input format on the display section, and the data input from the input section according to the displayed initial value input format. To the initial value file, data input using the initial value input format stored in the initial value file, and stored in the numerical solution constant file. Second processing means for sequentially calculating the coordinate values of the worm tooth profile and the wheel tooth profile for each step width by using the data necessary for the numerical calculation which is performed, and the wobble calculated by the second processing means. -Third processing means for calculating the contact line between the worm and the wheel and the relative radius of curvature from the coordinate value group of the tooth profile and the wheel profile, and the contact line calculated by the third processing means And the relative radius of curvature In the case where the desired design items are not satisfied as a result of the comparison by the fourth processing means for comparing with at least the data regarding the load capacity and the efficiency stored in the design item file. To the first processing means, and as a result of comparison, when the desired design items are satisfied, the coordinate value groups of the worm tooth profile and the wheel tooth profile calculated by the second processing means are output to the output section. An apparatus for determining the tooth profile of a cylindrical worm gear, comprising: