JPH0673772B2 - How to cut a worm wheel - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a method for cutting a worm wheel meshing with a cylindrical inworm worm.

(Prior Art) This type worm gear set is generally configured as the Figure 3, the specifications of the worm 1 and worm wheel 2, the lead angle of the gamma ₀ as FIG. 4 for the worm _1, a lead L , The standard pitch circle diameter is d ₀₁ , the standard pitch circle diameter of the worm wheel 2 is d ₀₂ , the tooth right angle module is mn, the number of teeth is z ₂ , the pressure angle is αn, and the axes of the worm 1 and the worm wheel 2 are When the inter-distance is a, it is determined that the following four expressions are established.

When the worm wheel 2 is gear-cut, it has been customary to perform hobbing with a hob having the same shape as the worm 1 that satisfies the above relationship.

(Problems to be solved by the invention) However, in such a worm wheel gear cutting method, when it is desired to increase the gear ratio without changing the shaft distance a, d ₀₂ is increased by increasing z ₂ from the formula (4). As a result, we have no choice but to make d ₀₁ smaller than in equation (1), and it is impossible to make a hob of the same size as this, or even if it can be made, the productivity of the worm wheel is poor, and the strength of the hob is strong. Due to the shortage, there were problems such as not being able to withstand the cutting load.

On the other hand, the meshing efficiency of the worm gear set is such that the friction coefficient is μ when driving from the worm 1 side. When driven from the worm wheel 2 side It is known that each changes as shown in FIG. Here, in order to increase the advance angle γ ₀ in order to improve the bad meshing efficiency, which is a drawback of the worm gear set, it is necessary to reduce d ₀₁ from the above equation (2), and in this case as well, the conventional worm wheel teeth are required. The cutting method causes the same problem as described above.

(Means for Solving the Problems) In view of this situation, the present invention is to use the tool such as a hob having the same specifications as the worm, and instead of using a tool having the specifications of the worm, generate the above problem. There is a hob or a dance tool for cutting the worm wheel with no hob or dance tool, and the hob or dance tool is located farther from the worm wheel than the worm, and the radius of the hob or dance tool is increased by the distance. The hob or mai tool is installed at a predetermined angle further than the intersection angle of the worm and the worm wheel, the rotation ratio of the worm and the worm wheel is i, the rotation ratio of the worm and the hob or mai tool is j, and the worm is The basic cylinder radius is r ₁ , the lead angle on the basic cylinder is γ ₁ , the pitch circle radius of the worm is e ₁ , the basic cylinder radius of the hob or dance tool is
rg, the lead angle on the basic cylinder is γg, the pitch circle radius of the hob or dance tool is eg, and the angle formed by the worm axis and the rotation center line of the hob or dance tool is α, the hob or dance tool is The method is characterized in that a hob or a dance tool that satisfies the following three expressions is established, and the hob or dance tool is rotated to perform gear cutting of the worm wheel.

(Operation) The above cutting blade can cut a worm wheel into a tooth profile that is almost normal. And, in order to make the cutting edge larger than the worm, in order to increase the gear ratio without changing the axial distance between the worm and the worm wheel, and in order to improve the meshing efficiency, it is necessary to increase the lead angle. Even if the worm has to be reduced in diameter, it will be so small that the cutting edge cannot be manufactured, the diameter will be so small that the productivity of the worm wheel will be severely deteriorated, or it will be too small to withstand the cutting load. There is no longer a feeling of fatigue.

(Example) Hereinafter, the Example of this invention is described in detail based on drawing.

FIG. 1 shows an embodiment of the present invention, in which 1 is a worm, 2
Is a worm wheel, 3 is a worm wheel shaft, 4 is a worm shaft, and the worm wheel shaft 3 is inclined at an angle β with respect to a line 5 perpendicular to the worm shaft 4. Also, P is a worm 1 and a worm wheel 2.
, E is the distance between the axes of the worm 1 and the worm wheel 2, e ₁ is the radius of the pitch circle of the worm 1, N is the pitch point P, and the lead angle γ with respect to the worm foundation cylinder 6 of radius r _{1. A} line of action that touches with ₁ is shown.

Reference numeral 7 denotes a hob (cutting blade) used for carrying out the method of the present invention. The shaft 8 is separated from the pitch point P by eg (however, eg> e ₁ ),
Worm wheel center O _H and is inclined by α around the intersection Og of the line 9 and the hob axis 8 passing through the pitch point P, and basic cylindrical hob 7 10 respectively show the radius rg, the lead angle in .GAMMA.g.
In addition, a basic vector in the worm axis (4) direction at the pitch point P is shown by a basic vector in a direction orthogonal to the worm wheel axis 3 and the worm axis 4 in common.

Here, when the rotation of the worm shaft 4 is ω ₁ , the rotation of the hob shaft 8 is ωg, and the rotation of the worm wheel shaft 3 is ω ₂ , the reduction ratio i between the worm 1 and the worm wheel 2 is And the reduction ratio j between the worm wheel 2 and the hob 7
Is It is represented by.

In FIG. 1, in order to determine the condition of the hob 7 for cutting the worm wheel 2 that meshes with the worm 1, in order to satisfy this condition, the hob 7 needs to mesh with the worm wheel 2 like the worm 1. From the line of action N
The movement speeds of worm 1 and hob 7 above should be equal, and Is a necessary condition.

On the other hand, the vector in the direction of action line N is , And the vector in the direction of the hob axis 8 is expressed as ＝ −sin α ・ + cos α ・ ＋ ε ・ eg ・ (−sin α ・ + cos α ・ ... (9), where ε is the imaginary number of vector calculation. , The worm shaft 4 and the hob shaft 8 are α
When the equations (8) and (9) are vector-calculated from the relationship inclining only Is required.

Here, the ratio ω of the hob rotation ωg to the worm rotation ω ₁
If g / ω ₁ and the position eg of the hob axis 8 are arbitrarily given, γ ₁ , r ₁ and e ₁ are determined from the design specifications of the worm 1, so the only unknowns are rg, γg and α. (7), (10), (1
These unknowns can be obtained by solving the simultaneous equations of 1). Based on rg and γg obtained in this way,
The axially converted pitch hg, the axial module mag, and the tooth right angle pressure angle αng, which are respectively expressed by the following equations of the hob 7, can be calculated.

hg ＝ rg ・ tanγg mag ＝ 2hg / zw (where zw is the number of worm threads) (However, γ ₀ g = tan ^-1 (hg / eg) The hob 7 is made by the above calculation parameters, and this hob is used as eg-e ₁ rather than the axial distance e between the worm 1 and the worm wheel 2.
And position it apart, and hob 7
By increasing the radius of the worm wheel and further inclining the hob 7 by α with respect to the worm 1, the worm wheel 2 can be tooth-cut to have a tooth profile that can mesh with the worm 1. . Moreover, since the hob 7 can be made larger than the worm 1 by eg−e ₁ , even if the worm 1 has a small diameter, the hob 7 becomes so small that it cannot be manufactured. The diameter of the wheel 2 will not be so small that productivity will be severely deteriorated, and the diameter of the wheel 2 will not be so small as to withstand the cutting load.

Although the cutting edge is shown as the hob 7 in the above example, it is needless to say that the above idea of the present invention can be similarly applied to the case where the cutting edge is a lathe machining tool.

By the way, the worm specifications are module ma = 2.52, pressure angle αn = 20 °, number of threads 1, pitch circle radius 12.5 mm, axial distance 40
mm, the worm wheel 2 with a gear ratio i = 20,
Hob specifications are mozile ma = 2.51, pressure angle αn = 20 °, distance 50 mm between hob shaft 8 and worm wheel shaft 3 (hob diameter
(20mm increase), when the gear is cut by the hob 7 with the hob inclination angle α = -2.56 °, the tooth profile of the central cross section becomes as shown by the solid line 11 in Fig. 2, and when the conventional method is used. It was confirmed that the tooth tip and the tooth bottom had a slightly different shape compared to the tooth profile indicated by the score 12, but this was not a problem for practical use.

(Effects of the Invention) As described above, according to the gear cutting method of the present invention, the hob or dance tool 7 is positioned further away from the axial distance between the worm 1 and the worm wheel 2, and the hob or dance tool is separated by the distance. The radius of the hob or dance tool is increased, and the hob or dance tool is further inclined by a predetermined angle from the intersection angle between the worm 1 and the worm wheel 2 to make the hob or dance tool a unique item that satisfies the above equation. Or Mai tool,
Since the worm wheel is turned by rotating this, the hob or mai tool can have a larger diameter than the worm even though the worm wheel can be cut into a tooth profile almost as usual. Even if the worm is forced to have a small diameter, it is necessary to increase the lead angle for the purpose of increasing the gear ratio without changing the axial distance between the worm wheel and the worm wheel, and for increasing the meshing efficiency. There is no problem that the tool becomes so small that it cannot be manufactured, that the productivity of the worm wheel is so bad that it becomes too small, or that the tool cannot withstand the cutting load.

[Brief description of drawings]

FIG. 1 is an explanatory view of specifications of a hob used for carrying out the method of the present invention, and FIG. 2 is an explanatory view of tooth profile of a worm wheel tooth-cut by the method of the present invention in comparison with a tooth profile tooth-cut by a conventional method. 3 is a sectional view of the worm gear set, FIG. 4 is a partially cutaway side view of the worm gear set, and FIG. 5 is a change characteristic diagram of meshing efficiency with respect to the lead angle of the worm gear set. 1 ... Worm, 2 ... Worm wheel 3 ... Worm wheel shaft 4 ... Worm shaft, 6 ... Worm basic cylinder 7 ... Hob, 8 ... Hob shaft 10 ... Hob basic cylinder

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Masafumi Nakayama 2 Takara-cho, Kanagawa-ku, Yokohama, Kanagawa Nissan Motor Co., Ltd. (72) Inventor Mitsuru Maki 2-1-7-, Namiki, Kanazawa-ku, Yokohama-shi, Kanagawa 504

Claims (1)

[Claims] 1. When cutting a worm wheel that meshes with a cylindrical involute worm, the hob or dance tool is positioned further away from the worm wheel than the worm, and the radius of the hob or dance tool is increased by this distance. The hob or mai tool is installed at a predetermined angle further than the intersection angle of the worm and the worm wheel, the rotation ratio of the worm and the worm wheel is i, the rotation ratio of the worm and the hob or mai tool is j, and the worm is Of the basic cylinder radius of r ₁ , the advancing angle on the basic cylinder γ ₁ , the radius of the worm pitch circle e ₁ , and the basic cylinder radius of the hob or dance tool.
rg, the lead angle on the basic cylinder is γg, the pitch circle radius of the hob or dance tool is eg, and the angle formed by the worm axis and the rotation center line of the hob or dance tool is α, the hob or dance tool is A hob or a dance tool that satisfies the following three expressions, and the hob or dance tool is rotated to perform the gear cutting of the worm wheel.