JPS60155054A - Gear having circular addendum and root - Google Patents

Abstract

PURPOSE:To provide a conical gear which can attain good engagement by forming circular addendum and root by the rotary cutting motion of a hob having a rotary shaft at a designated position. CONSTITUTION:A hob shaft 2a of a hobbing machine, a gear cutting machine special for a cylindrical gear is brought close to a conical gear material 6 up to a regulated position indicated by H and V. After that, with the shaft retained at the regulated position, gear cutting is completed, and a hob 2 is kept from moving along the conical surface of the gear material 6. The root line 8a of a conical gear 8 is circular, and the gear can accomplish engagement mechanically completely on the inner and outer end sides of a face width. Thus, a conical gear attaining good engagement can be produced by a hobbing machine to improve machining efficiency in a large scale.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for manufacturing a gear, including a gear cutting method and a gear shape compatible with the gear cutting method.

Since the ideal rotation of a gear involves practical rolling motion of each pitch plane on the driving side and the driven side, the tooth profile and the tooth profile are arranged in a C along the pitch plane. The shape of the pitch surface changes depending on the relative position of the drive shaft and driven shaft.
If the two wheels are parallel, it will be cylindrical, and if the two axes intersect, it will be circular. Therefore, for the former, the tooth traces are placed along the cylindrical surface, and for the latter, the teeth are placed along the conical surface.

In the former, the tooth profile, pitch, etc. are the same throughout the cross section perpendicular to the axis, but in the latter, the tooth profile, pitch, etc. are different for each...1ifiil-. Therefore, it is impossible to use the same gear cutting machine to manufacture C for both departments, and separate dedicated gear cutting machines with completely different gear cutting mechanisms are used. However, while gear cutting machines with circular (1-shaped gears) are popular and have a large capacity, gear cutting machines with conical gears are few in number and are much smaller in size. Machining efficiency is also low, which is a major obstacle in manufacturing this type of gear.

The present invention eliminates this difficulty in manufacturing dowel-shaped gears, and makes it possible to cut even round-shaped gears using a highly popular conventional machine dedicated to cylindrical gears, that is, a hobbing machine. The gear cutting method and tooth width shape will be described below.

3. Detailed description of the invention 1. Principle and method of gear cutting FIG. 1 shows a gear cutting mechanism of a typical dedicated IN (bob machine) for cutting gears of cylindrical gears. The horizontal distance between the axis of the cylindrical gear material 1 and the axis of the threaded cutter (11\-f>2) is set to the pitch radius of the gear material and the cylindrical radius of the hob.
- While maintaining this distance, the hob shaft rotates with the number of teeth equal to 7 for one revolution of the gear material. 1.11 Replace gear 3 and force drive it, and set the tooth profile. The pitch is automatically and continuously cut out.

Same +1. 'l', the feed screw 5 is rotated through the tooth width 4, the hob being rotated and cut is lowered in the axial direction of the gear material, and the healed tooth sushi is shaved off in a circular manner. Therefore, in this case, the rotational motion of B and the 11 linear movement i+1 of C in FIG. 2 are the basic movement iFb of the hobbing machine.

According to the present invention, a rigid gear is manufactured without making any changes to the hobbing machine having the above configuration, and this is carried out by the method shown in FIG. 3. In other words, in this gear cutting method, △ in the same figure,
(The rotation ratio of 3 is exactly the same as in the case of Fig. 2, but the luck of C 11 is the same as in the former case, all <'I1. 1-1. Simply move the hob shaft close to the position specified by V.
Afterwards, the knife is finished cutting while maintaining that position, and the knife does not move along the sushi. Therefore, as shown in Fig. 4, the tooth root line is different from the tooth root line of the conventional cupped gear shown by the dotted line, and it has a circular arc shape that is tangent to this.This is the feature C of this gear cutting method. - Since the threads of silk are cut and interlocked using this method, the tips of the teeth also have an arc-shaped shape, which is unique to this method.

However, it can be proven that a complete mechanistic movement can be performed.

In addition, the value of l-1, V, which determines the position of the rotation axis of the hob, is
It can be calculated from the specifications of the gear material and the radius of the hob, and since the bob machine has a configuration that allows its position to be freely determined, it can accommodate a free chair setting 81 with a four-sided pitch circle. Therefore, even if you do not use the gear cutting machine for the circular color painting mentioned above, there is an alternative gear of the same type (21) that can be manufactured by a dedicated machine for cylindrical gears. Therefore, by applying this gear cutting method, the following effects are produced.

(a) By changing the tooth bottom line to an arc shape, the tooth width can be used for the same purpose as conventional conical gears, and the tooth width can be made into a circle with a large degree of expansion.

(l) It is also possible to manufacture a trapezoidal tooth width that exceeds the limit W of the conventional circular J-shaped tooth width.

(C) The machining rap rate is comparable to the machining efficiency of cylindrical gears, and the machining efficiency of conical gears is significantly improved.

The above can be summarized as follows.

Using a specialized machine for cylindrical gears, which is the most widely used machine for producing tooth widths, ie, a hobbing machine, and without making any changes to the conventional cutter, ie, bob, used for it,
This has made it possible to cut gears other than conical shapes, which previously required a completely separate dedicated machine.In addition, this new gear has arc-shaped tooth tips and tooth bottoms to accommodate this gear cutting method. This is the first step in developing the shape.

The present invention will be explained in more detail.

1. #R word The bevel tooth width gear cutter is the original bevel gear tooth l.
, it is legitimate to use the 7J board. If this could be cut with a regular hobbing machine, it would be extremely convenient.

Therefore, it seems that some attempts have been made in the past, but they were done by attaching a special device to the hobbing machine to move the bob along the pitch cone generatrix (or the 5- or bottom cone line 11). sending. the result,
I can make something fit, but teeth? There is an extremely large bulge on the first tooth, and the contact in the tooth width direction is extremely narrow. The purpose of this research is to suppress this excessive bulge as much as possible, and to cut the bevel gear using E without adding any type of processing device to the hobbing machine.

2. Gear cutting using a simple rack (Fig. 5) costs just $1! /7 This is a basic diagram of cutting a bevel gear with a rack-shaped knife, and this corresponds to the case where the hob is fed in the pitch direction. As can be seen from the same figure (a), the point on the pitch cone where the moving speed of the rack matches the circumferential speed of the gear material is defined as P fish, and this point is located at the center of the tooth width. (a
) In the figure, for an equivalent spur gear on plane B at a position separated by B in the tooth width direction (the top being positive), the pitch circle is 3.
1 - What is the cutting state of the negative shift in relation to the angle δ? (
When B is negative, it is a positive dislocation). amount of dislocation) (@=-Btal'l
The tooth profile created by δ, that is, plane B, rolls against the rack on the circumference of radius re as shown in the same figure (C), and the pressure angle of the rack is α. moves to the gear material on this circle.

The resulting tooth profile has a condition that it meshes with the mating tooth profile that is generated by cutting the same rack. At this time, the half-tooth thickness sb at radius rb on the pitch cone is calculated as follows.

S11 = [(Km /4 +X, tan (1',
) /ro+inv α, -1nv CXh lrb
7: (9 number nl: module α11 = CO3 ((
+', (,O8α-/rb) )ro = mZ/2
・Substituting CO3δ, rb=ro Btanδ, C8b=(yrcos δ/27-2 sin δ・
I-an Q'c/ l1lZteninv rx, -1n
v ab) (r, -Btan δ)...(1) Now, with respect to the gear in Table 1, calculate the escape amount cb from the correct position using sb of B=O as a reference. This results in Table 2.

(When the sheep assembles these gears, there will be a gap of K h = Cb, 10 Cb, at position B.

Figure 6 summarizes this, and the gap between the gear and pinion curves and the BSM is the amount of clearance, +3
The curve tangent to the line indicates the value of Kb.

It can be seen that even though they are in contact at the center, there is a large gap at the inner and outer ends. The diagram on the left compares the thickness of the tip of the tooth, calculated in the same way, with that of the center, and shows the difference in half-tooth thickness. It can be seen that the thickness of the tooth tip becomes extremely thin at the outer end.

3. Gear cutting when no feed is applied to the hob a) Aim of this gear cutting method Figure 7 shows a case in which the rack is replaced with a bob. Similarly, it is assumed that the two velocities match at one point in the center of the tooth width. The hob shaft is tilted by an advance angle γ of C and A in a plane parallel to the pitch plane of the rack in FIG. This relational position can be achieved using the method described below. Bore 1 only cuts J to this state, and does not feed in the tooth 1 direction. Therefore, the rack working at each position of B (, 1, gradually moves away from the inner and outer ends of the tooth rlJ, which naturally means that the tooth η
This results in an increase of 110 in the tooth 11 direction, and a decrease in the distance between -1 and Q in the tooth 11 direction.

This is the effect we are aiming for. In this case, both bottoms are arc-shaped, so the tips of the teeth of the C white must also be arc-shaped, taking into account the size of the opponent. Therefore, the tooth height gradually decreases toward the inner and outer ends, but this is unavoidable.

+1') Rack acting on the B plane Figure 8 (a) shows the Q-X-Y-Z- system shown in Figure 7,
X'Y''' is drawn horizontally, and in the case of a right-handed hob, the hob axis is inclined by δ in the vertical plane in the direction of the diagram. be. What acts as the cutting edge of the rack in this case is the line of intersection between the spiral of the cutting blade with the axis ``■'' and this plane. That is, the same figure (b
), the cutting edge is located at P, P, P, and the line tracing the erosion falls at point r% t3e P4 in the same figure (C), and this is the cutting edge working on the plane of B=O. be. Let B be the point of ten pitch cylinders, and F? ,P.

is determined from the module and axis plane pressure angle as shown in the figure. Now, when 1) is at the distance of the kidney, a spiral line passing through β can be calculated using equation (2) using the angle θ around the y-axis. However, this applies to right-handed hobs.

Ro: Hob pitch cylindrical radius, - lead/3600 as 10 - Therefore, 2 - = 0 and (3) equation J, subtracting θ, then X
The coordinate values of point p on the ``Y'' plane are rounded.

RC-sin θcos 7--(y, -k O) s
in 7 = 0...(3) Treat B and I in the same way and obtain Re in (C) of the same figure.
Determine p. These three points are taken as representative points indicating the shape and position of the cut %1.

By the way, these three points are not necessarily d on the i8i line -1-, and their inclination angles are not equal to αc (=20°). Then Haru, [? . Place the line connecting (′,
Let the pressure angle be J, and look at the angle △ε from which the heat deviates in the Y'-axis direction at 81. This value indicates the straightness of the cutting edge.

α=jan (YreY76) / (Xte
,-)Δε=Y,,--Y,e--<XzM
-X, stone) 劃an a...(4) When considering this on the B plane, [Well, Z"=B and 1'-
io- and formula (5) is used.

Rcsinθcos 7- (ve-toθ) sin
7-8・(5) Figure 8 (C) shows this general case. When B≠0, the 11 points on the 8 plane are X' wheel axis even if yξ- It's not like it's going to go up. Also, the way the cutting edge curves as the hob rotates is not parallel to the Y' axis, so it is difficult to imagine a rack that is driven by a B spur gear.

Therefore, P6 when 4-<, Ve=O is shown in the same figure (C).
A line passing through the point, that is, point 8D and parallel to the Y' axis is the pitch line of the rack in this case, and the position of the cutting edge for each of y2 (defined on this line).

That is, U = Y*e=-+ (X+t-Xza-
) tan (X...(6) Comparing this cutting edge with the cutting edge of the single rack shown in Fig. 5(b), when this cutting edge comes to the position of l/e -cosγ, it is correct. Since the rack can be seen, the deviation from this position is defined as Δ[, and this is the cutting edge position error.

Δt=F-yt・COSγ...(7) Now, m==3.
75, pitch cylinder radius Rc = 35.

25. The above α, Δε, and Δt are shown on each plane of B −5, O, and −5 mm for the right cutting edge of a right-handed hob with αG −20° and helix angle γ−3.05°. This is shown in Figure 9.

The horizontal axis indicates the position in the Y direction in FIG. When B = 0, α-20° is maintained in a possible range j to the left of the center point, and △ε, △t is a small value at the 11th point in JL, but B =
5. In a plane with R=-5, the center point is also 1 and the interior angle is 20°
That's Tatsumi, and what's more, 11^ changes when you turn 11 to the right.

The degree of change in Δε and Δ[ is also large. In particular, if 3 is positive, the change will be large if 3 is negative.

The behavior of the cutting edge of this J: sea urchin and B top ten is the most complex in the world as a rack, so the tooth profile and tooth trace that are created are as follows:
You cannot calculate h1 in between. Therefore, this will be handled as follows.

C) Tooth profile, 1fiI line i1 First, focus on △ε. This is because if this is too large, a large error will occur in the dislocation 11 tightening as an involute tooth profile. However, this value (,1,B-±5m111 is as shown in the figure, and B=10111111.E-
Even in the range of 20, it is about 10 to 16/1 m, so the cutting edge is assumed to be a straight line and formula (1) is used.

Next is the pressure angle. This makes the average value of the inclination angle of the cutting edge during the generating mesh period to be 0.

FIG. 10 is a view of the outer end, and the meshing start point is set to [1,
Let the ending point be [,. For example, to calculate the coordinate values [η and pressure angle α] of 12 points, use equation (4) and (
8) Combine the equations to create Snake 2. The solution IJ is sufficient for α, and α at this time is adopted as a false value. Point E1 can also be determined in the same way using Sh.

When the above-mentioned hob is used to cut the gears shown in Table 1, the values of E and -E2 are as shown in FIG. 11 for the value of B.

13- Therefore, on each of the 13 planes, F3. [Calculate the pressure angles α, , αs at Y, and calculate the average value α of A (1
) is applied to the equation. .

Next, the processing of the cutting edge position error Δ1 is 5. In the ideal state of Δ1-0, the circumferential speed of the corresponding spur gear at ``1'' and ``6'' matches the moving speed of the cutting blade. It should be 1J.

However, between 1, E, and -IE U where the generation gear cutting occurs,
Rack cutting edge 1. iΔ11−Δ1. The position of DAIJ is shifted. This is i! with the cutting edge at a circumference of r°1Δr. Linen can be used to match and cover things. If Δr is increased by the radius increase, then 2π
(r, 1△r)−2πr”−2πryu(Δ[1−Δt1
) / (ELl-Ei) ,', △r-ro(Δ1pi △t, ) / (F,, -
F,,) - (9) When the above 3111 is incorporated into equation (1), the following becomes t) 1・r: -= r, +Δr, r II =ra Bta
n δXs-=-B tan δ+Rc (1-cos
(5in-'B/Rc)1-△r αb = =CO3'(r,--CO3αn/D,
-Btan δ)) 14- Jb = ((yrm /4+Xs-tanam)
y'ra-+inv α+n-1nv ah-)
r b = (7rCO9δ/ 27-2 sin δ-t
an am 7m z+inv am-inv ah
-) r b ・(10) Incisor 4 (t
@Error is related to increase/decrease in tooth thickness. Lever [to l・17
Using the average position error Δtm between 5h−Jb+Δt m −r 11 , /r,−,′,
Sb −(yr cos δ/27+inv am −1n
v rx−+−(X ” 1all α m −1−△
tm/r, -) r b - (11) Using 4.1 above, calculate the gears in Table 1, and close the gap between the two sides in the same way as Moe, as shown in Figure 12 ()i- tooth surface), 13th
Figure (right south view). Compared to Fig. 6, the allowable gap on the south face has decreased, but on the left flank, there is a slight effect that can be seen numerically. Fig. 14 shows β-±2.
This gap was calculated within the range of 5111111.

In addition, Figure 15 shows the measurement results using a single-sided meshing accuracy tester.
When compared with the runout of the mountain, it can be seen that the mesh is reasonably good.

4. Selection of toothed circle 1 The above example is a case where the tooth height is given along a pitch cone based on a conventional rolling cone. However, in the case of this gear cutting method, C' is the only generating motion of the rack where the circumferential speeds match only at the center P point of south rlJ, and b P on the bit generatrix.
The circumferential speeds do not match except for Ir'a. At points other than the center point, equivalent spur gears with shifted gears mesh with each other 1°, and the amount of shift is shown in Fig. 16 as shown in Fig. 4. At gear It is treated as the distance from the busbar, and has nothing to do with the conventional pitch busbar. In other words, there is no need to stick to the conventional pitch cone for the cone used for tooth alignment. If it is dark blue, there is no need for the vertices of the cone to match.

Based on this free thinking, it is possible to create a design with fewer gaps.

Therefore, if we leave the number of teeth, modulus L-ru, and pressure angle the same as in the previous example, and freely consider the conical angle that provides the tooth swivel, it is possible to create a design with fewer gaps.

Therefore, the number of teeth, 7 joules, and pressure angle remain the same as in the previous example.
Freely set the design cone angle that gives the tooth swivel 1, (the installation cone angle of the binion is its complementary angle)B±1. +21m
FIG. 17 shows the calculation of the gap in . According to this, it is determined that if the cone angle is set to around 52° for gears (around 38° for binions), the combination will have the smallest gap on both the left and right south faces. Therefore, this corner was selected and the aforementioned gap was closed, as shown in Fig. 18 (left tooth surface) and Fig. 19 (right south surface). Although the reduction in the gap is not significant, there is a significant difference in the thickness reduction at the tip of the tooth.

Figure 20.21 shows this combination. Note that the dotted line in FIG. 20 is the reduction value in the case of gear cutting using a rack. The effect in the central part of the mountains can be seen.

5. Gear cutting reset ^ Regarding the method of tilting the hob shaft in the direction shown in Fig. 7 as described in 11 (3di). To achieve 17-, keep the relative position as shown in the same figure <a) and rotate the 7th axis J: ψ [-] so that the overlap plane including the hob axis is in the same direction as the hob axis of the bobbing machine. 3. The rotation angle ψ and the inclination angle γ- of the hob shaft in the vertical plane are as follows.

Using QS in the figure, ψ−jan−′(Q S sin 7 sin δ/QS
cos 7) = tan-'(tax negative 1'-s'+nδ
) r --sin-'(QSsin7-cosδ/Iru5in-'(Sin7'-CO3δ)
Reference position J: Move the rework axis closer to the hob axis by ΔG, and correct the height of the hob axis by Δh.

18-6. An example of load and meshing accuracy. Figure 23 shows an example of load and meshing accuracy.
J) This is an example of a single tooth surface meshing accuracy test at 0 load of a S45C bevel gear with an angle of 20° and a number of teeth of 38 x 38. The value of the load is the tangential force of the pitch circle. When the load is very small, there is an error in the engagement of each tooth, but compared to the runout when a thin piece of steel of 0°06ml 1l is sandwiched, this error is 4i if it is very large. This error almost disappears when the load is 102Kof and 4i, resulting in extremely good meshing.

[Brief explanation of drawings]

Fig. 1 is a drive system diagram showing the gear cutting mechanism that cuts the cylindrical gear and the tooth number ratio of each gear, Fig. 2 is a perspective view showing the movement of the hob and gear material, and Fig. 3 is the invention of the present invention. FIG. 4 is a cross-sectional view of the gear of the present invention, and FIG. 5(a) is an explanatory view. (11) is a perspective view, (C) is an explanatory view, Fig. 6 is a graph,
FIG. 7 is a perspective view, and FIG. 8(a) is a perspective view. <1N) and (C) are explanatory diagrams, Figure 9 is a graph, and Figure 10 is
The figure is an explanatory diagram. Go to Figure 11. Figure 15 is a graph. Figure 16 is a partial side view of the gear. Figures 17 to 21 are graphs. Figure 22 (a) is an oblique tta view. (h) is an explanatory diagram, No. 23
There are graphs. Gear material 1, hob 2, index change gear, 3, feed change gear 4, feed screw 5゜Patent Applicant Restoration Jiko fee Buried Patent attorney On 1) Hirosen table 1 (> 3- SID rb, /r-However, Sha is B=
Sb at O Table 2 21-325 Fig. 5 (C) Fig. 8 Re Hob pitch cylinder radius, = Leet'/860
"6 mm) Δε (mm) 6) Figure 11 Figure 28
11 (1Japanese b 94T05 23
/3 table small+++isum') 9(1'1!1llTl@lεflO
r) B ri 112532 Name of the invention Yamanaka 3 with arc-shaped tooth tip and tooth bottom, supplementary 11- to 1 no.
1 Shikiyama Newcomer] 2] - No. 19 L46” Mr. Niji Name
(General 11 Kuwa Jiko 4, Agent (1 location)
1. ．． <0582> 田) 1810 (Representative) 6, Amendment against poverty drawing J, Contents of amendment Purification of the drawing (no change in content) I] - Bu de Ding Fu my tE group 1ift April 1, 2016 ! It 11 Mr. Manabu Shiga, Commissioner of the Patent Office 2, Name of the invention: Tooth width with arc-shaped tooth tip and tooth bottom 3, Person responsible for amendment I? Relationship with 1: Special J1 applicant name: Osamu Fukuto V (Name) 4. Agent address: 2 Hatazume-cho, Gikushi City, 500 January - <0582> 65-1810 (Representative) 6. Details of the amendment The text and all directions are as per the attached sheet. Specification 10 Name of the invention Conical gear 2, Claim 1 Formed by the rotary cutting movement of a hob holding a rotating shaft in a predetermined position A conical gear characterized by having a tooth tip and a tooth bottom formed in an arc shape. 2. The predetermined position is perpendicular to the rotation axis of the conical gear within a plane substantially parallel to a plane in contact with a pitch conical surface of the conical gear. Claim 1, which forms a predetermined angle with the plane
Conical gears as described in section. 3. The conical gear according to claim 2, wherein the predetermined angle is an advance angle of the hob. 3. Detailed Description of the Invention Object of the Invention (Industrial Application Field) The present invention relates to a conical gear formed by cutting with a hobbing machine for manufacturing a cylindrical gear. (Prior Art) Since the ideal rotation of a gear is to realize rolling motion of each pitch plane of the drive 1111+gear and driven gear, the tooth profiles and tooth traces are arranged along this pitch plane. The shape of the pitch surface changes depending on the relative position of the rotation axis of the drive side gear and the rotation axis of the driven gear. If both rotation axes are parallel, it will be cylindrical, and if both rotation axes intersect, it will be conical. . Therefore, AiJ's cylindrical gear has a tooth heave along the cylindrical surface, and the latter's conical float has a tooth heave 4=J along the conical surface. The tooth profile, pitch, etc. are the same everywhere in the cross section perpendicular to the axis of rotation in the former, but they are different in the latter. Therefore, it has conventionally been impossible to manufacture both gears using the same gear cutting machine, and separate dedicated gear cutting machines with completely different gear cutting mechanisms are used. However, while gear cutting machines for cylindrical gears are popular and have a large capacity, gear cutting machines for conical gears are fewer in number, have a much smaller capacity, and add more. - "Efficiency is also low, which is a major obstacle in the production of conical gears. In order to solve these problems, several attempts have been made to produce conical gears using a hobbing machine. However, , a special device is attached to the hobbing machine to send the hob along the pinch cone generatrix (or tooth bottom cone generatrix), and as a result, although some meshing is possible, there is an extremely large bulge in the tooth trace. , and the contact in the width direction is extremely narrow. (Problems to be Solved by the Invention) The present invention attempts to solve the above-mentioned difficulties in manufacturing conical gears. For cutting conical gears, which conventionally required a dedicated machine completely separate from the hobbing machine, the most widely used hobbing machine for manufacturing cylindrical gears was used, and the conventional cutter used for it, i.e. It is an object of the present invention to provide a conical gear that enables gear cutting of a conical gear without making any changes to the hob, and also provides a conical gear with good meshing in which the tooth tips and tooth bottoms are arcuate. (Means for Solving the Problems) For this purpose, in the present invention, the tips and bottoms of the teeth are cut in an arc shape formed by the rotary cutting to 1 movement of the hob holding the rotating shaft at a predetermined position to form a conical gear. (Function) The present invention manufactures conical gears by the method shown in FIG. 3 without making any changes using a dedicated gear cutting machine for cylindrical gears shown in FIG. 1, that is, a hobbing machine. When cutting and forming a cylindrical gear using a hobbing machine (not shown in FIG. It is set to the sum of the pitch circle radius of material 1 and the pitch cylinder radius of hob 2, and the rotation speed of hob 2 is set to be equal to the number of teeth set for one rotation of gear material 1 while maintaining this distance. The index change gear mechanism 3 is set.Then, the single rotation driving force is transmitted to the gear material 1 and the hob 2 via the same gear mechanism 3, so that the gear material 2
A predetermined tooth profile and pitch are automatically and continuously cut out. At the same time, the feed screw 5 is rotated via the feed transfer gear mechanism 4, and the hob 2, which is being rotated and cut, is lowered in the direction of the axis 1a of the gear material 1, thereby cutting the tooth trace along the cylindrical surface of the gear material 1. Served. In other words, A and H in Figure 2
The rotational motion shown in and the vertical descending motion shown in C are the basic movements of a hobbing machine that cuts and forms cylindrical gears. On the other hand, in the present invention, the rotation ratios of the rotational movements shown by A and B in FIG. 2 are the same as those described above, but the movement shown by C is completely different from the above and is essentially not performed. However, although the hob shaft 2a is brought closer to the conical gear material 6 up to the specified positions indicated by H and V in FIG. No movement of the hob 2 along the 60-conical surface is performed. Therefore, as shown in FIG. 4, the tooth bottom line 8a of the conical gear 8 of the present invention is different from the tooth bottom line of the conventional conical gear shown by the chain line in the same figure, and has an arcuate shape tangent to this tooth bottom line. This is a feature of the gear cutting method of the present invention, and since two sets of gears are cut and meshed by the gear cutting method of the present invention, the tooth tip line 8b naturally also has an arc shape, and the gear of the present invention has a unique shape. Become. In addition, in the present invention, the hob shaft 2a is located within a plane parallel to the plane in contact with the pinch conical surface S shown in FIG. Since gear cutting is performed while being inclined at a predetermined angle, it can be proven that the gears perform mechanically perfect meshing motion on the inner and outer sides of the face width. In addition, the values of H and V that determine the position of the rotating shaft 2a of the hob 2 can be calculated from the specifications of the gear material 6 and the radius of the hob 2, and the hobbing machine has a configuration in which the position defined by H and V can be freely determined. , the pinch cone angle can be freely designed. Therefore, the conical gear of the present invention can be manufactured using a machine exclusively designed for cylindrical gears without using the gear cutting machine exclusively for conical gears described above. As a result of the above, the present invention produces the following effects. First, by changing the tooth bottom line to an arc shape, a conical gear that can be used for the same purpose as a conventional conical gear can be manufactured using a machine dedicated to cylindrical gears, which is highly popular. Second, it is possible to manufacture large gears that exceed the size limits of conventional conical gears. Thirdly, the machining efficiency is comparable to that of cylindrical gears, making it possible to significantly improve the machining efficiency of conical gears. (Example) Hereinafter, the present invention will be explained in more detail based on FIGS. 5 to 23. First, as a comparative example with the present invention, the basic operation when gear-cutting a conical gear with a medium-line rank-shaped cutter 7 will be explained based on FIG. This gear cutting corresponds to the case where the hob 2 is fed in the generatrix direction of the pitch conical surface S of the conical gear material 6. Figure 5 (
As shown in a) and (b), the point on the pinch cone surface 310 where the moving speed of rank 7 matches the circumferential speed of gear material 6 is defined as P, and the same point P is defined as the center of the face width. No.! l! As shown in 1(a), for an equivalent spur gear on a plane (hereinafter referred to as one plane B) at a position B apart in the face width direction (the upper side is positive in the figure), the relationship with the pitch cone angle δ is This results in a negative gear cutting state. When B is negative, a positive dislocation occurs. The amount of dislocation is as follows (see FIG. 5(d)). XB=-Btanδ In other words, in one plane B, the tooth profile created is the 5th [ffl
As shown in (C), rolling with the rack 7 is performed on the circumference of the radius ro, and the pressure angle αC of the rack 7 is transferred to the gear material 6 on this generating rolling circle. The tooth profile formed is the same rack 7
It has a condition that it meshes with the mating tooth profile that is created by cutting the tooth. At this time, the half tooth thickness sb at the radius rb on the pitch cone
is as follows, where m is a module. Sb = ((yrm/4 +
It is. By substituting the following two relational expressions % expression % where Z is the number of teeth into the sb expression, the following expression (1) is obtained. 5b=(yrcos δ/2Z −2sin δ ・t a n αc /mZ teninv
αc-1nvαb) . The calculation results in Table 2. However, Sb. is the value of sb at B=0. The following margin is 1, and the left hand is 10. Therefore, when the gears in Table 1 are assembled, there will be a gap at position B as shown by Kb = Cbl + Cb2. Figure 6 summarizes this and shows the curve C of gear 8.
The distance between I and the opposing pinion 90 curve 11C2 and the BS line is the clearance amount, respectively, and the curve tangent to the BK line is the K
Indicates the value of b. According to this curve Kh, it can be seen that even if the center part of the face width makes contact, there is a large gap between the inner and outer ends. The curves C3 and C4 on the left side compare the thickness of the tooth tip of the gear 8 and pinion 9, which were similarly closed, with the center part, and show the difference in half tooth thickness. According to both curves C3 and C4, it can be seen that the thickness of the tooth tip becomes extremely thin. Now, let's move on to embodiments of the invention. In FIG. 7, the rack 7 is replaced with a bob 2, and it is assumed that the speeds of the bob 2 and the conical gear material 6 match at point P in the center of the tooth width. ; h axis 2 a 4j pitch plane sl of rack 7 in FIG. (Q-Y'Z' plane 1 in FIG. 7) is set aside by its advance angle γ. This positional relationship can be set by a method described later. bob 2
The cut is only made to the state shown in Fig. 7, and feed in the face width direction is not applied. Therefore, the cutting edge of the hob 2 working at each position B, that is, the cutting edge of the rack 7, gradually moves away toward the inner and outer ends of the tooth width, which naturally causes an increase in the tooth thickness, and the tooth width increases. This will reduce the gap between the inner and outer ends. In this case, as explained in FIG. 4, the tooth bottom 8a has an arc shape, so the tooth tip 8b must also have an arc shape in consideration of mutual meshing with the other gear. As a result, the tooth height gradually decreases toward the inner and outer ends. Figure 8(a) is drawn with the Q-X'Y'Y' plane of the Q-X'Y'Z'" coordinate system shown in Figure 7 horizontally, and in the case of a cloth-wound hob, the hob axis 2a is Q-x'y
It is tilted by an angle γ within the perpendicular plane Q-Y'Z'' to the plane as shown in the figure. In this case, the Q-X'Y' plane represents the plane of B=0. This B=O plane In the above, the part 2 that acts as the cutting edge of the rack is the hob axis 2a, that is, the intersection line of the helical plane of the cutting edge of the hob 2 with the coordinate axis y shown in Fig. 7.8 as the axis and the plane B=0. In other words, Pl, P3.P shown in FIG. 8(b)
When there is a cutting edge surface at 5, the line tracing this is shown in Figure 8 (C
) appears at the Pie, P3e, and P5e points, which is 13
= Plane of O -] It becomes a cutting edge that works at 2. If P3 is a point on the pitch cylinder of hob 2, PI and P5 are the points on the pitch cylinder of hob 2.
8 (
It is determined as b). As shown in FIG. 8(b), when P3 is at a distance of ye, Rc is the pitch cylinder radius of the hob 2, k = lead/360
In the case of a cloth-wound hob, the helical wire passing through P3 is expressed as the following equation (2) using the angle θ around the y-axis. X'=Rc 3cosθ Y'=(θ to ye-) cozy +Rc-sinθ・s+nr Z'=Rc −5inθ・C09r −(θ to ye-)sinγ... (2) 3 The following formula with Zo-0 (3) 0=Rc-sinθ'CO37-(ye-toθ)siny... (3) If θ is subtracted from this, the coordinate value of the P2O point on the Q-X'Y' plane is calculated. Pl and P5 are treated in the same way to determine Pie and P5O in Figure 8(c), and these three points Pi
Let e, P3O, and P5O be representative points indicating the shape of the cutting edge and its position. By the way, the above three points are not on the same straight line, and their inclination angle is also not equal to the pressure angle αC. Therefore, the line connecting Ple and P5O is defined as the pressure angle α at this position, and the amount Δ that the PUe point deviates from that line in the Y'-axis direction is
Calculate ε. Pressure angles α and Δε are expressed as in the following equation (4). tx= tan ((Y'5e-Y'le)
/(X'1e-X'5e) ) Δa=Y'3e-Yle (X'1e-X'3e) t a na...
(4) 4 When considering this on the B plane, the following equation (5) is used with Z' = 13. B=Rc - sin θ - CO9r - (ye- to θ) siny... (5) Figure 8(c) shows this general case, and B
When ≠0, even if ye=0, P] point L on the B plane;
l: Not on the X' axis. Also, since the appearance of the cutting edge as the hob 2 rotates is not parallel to the Y" axis, it is difficult to imagine a rack that moves in the B plane - L. Therefore, as shown in No. 8 ffl (c), ye = The pinch line of the rack in this case is the 23 points when o, that is, the line passing through the Pa o point and parallel to the Y' axis, and the position of the cutting edge for each point of ye is defined on this line. In other words, if the distance of point Pae in the Y'-axis direction is E, then E=Y'le+ (X'1e-X'3e) tanα...
- (6) Comparing the cutting edge expressed by this equation (6) with the cutting edge of an m-pure rack (not shown in Fig. 5(b) 5), the above cutting edge is 31'e-Co! When it comes to position 17 (Y' coordinate value of point ye), it can be considered as the correct rank, so the difference between this position and -E in the equation is set as Δt as shown in the following equation (7), and this is the cutting edge position. It is treated as an error. Δt=E-ye-cosγ... (7) Figure 9 (
In a), (b), and (c), module m = 3.75, pitch cylinder radius Rc = 35.25, pressure angle αc = 20 degrees,
For the right cutting edge of a cloth hob with an advance angle of γ-3.05 degrees, B =
5.0. The above α, Δε, Δt on each plane of −5 mm
It is shown. The abscissa axis indicates the position in the Y' force direction shown in FIGS. 8(a) and (C). In the case of 13 = 0, which is not shown in Fig. 9(b), α = 20 degrees is maintained to a considerable extent to the left and right from the center point, and both Δε and Δt are extremely small values, but as shown in Fig. 9(a). B shown in = 5 m
On the plane B=-5mrn shown in FIG. especially,
When B is positive, the degree of change is larger than when B is negative. As described above, the behavior of the cutting edge of the hob 2 acting as a rack on the B-plane is complicated, and the moon shape and tooth line that are created cannot be calculated using the simple equation 11. Therefore, we will handle it as follows. First, let's focus on Δε. If this Δε is too large, a large error will occur in the dislocation calculation as an involute tooth profile, but this value is
The condition is as shown in (c), and B=] Omm,
Even in the range of E=20 mm, it is about 10 to 16 μm, so the cutting edge is assumed to be a straight line and the above formula (4) is used. Next, for the pressure angle α, the average value of the inclination angle of the cutting edge during the generating engagement period is taken. That is, as shown in Fig. 10, the meshing start point of the gears is set to E.
If l, the end point is set to E2, and c and sh are taken as shown, the following equation (8) holds true. r'a -(-E2y-tanα+ro)2+E"2y
ra=ro-Btanδ+C C= m - (RC+ m) 7 x (1-cos (sin (B/ <Rc+m>)
))・・・・(8) Y coordinate value E2y of point R2 and pressure angle α at the same point E2
2, it is sufficient to solve the equation (4) and the equation (8) simultaneously for E2Y and α, and use α at this time as the value of α2. The pressure angle α1 at point R1 can be determined similarly using sh. When calculating the case where the gears shown in Table 1 are cut using the hob 2 described above, E1 to E2 are as shown in FIG. 11 for the value of B. Therefore, on each plane B, the pressure angle α1 at El and R2. α2 is calculated and its average value αm is applied to the above equation (1). Next, regarding the cutting edge position error Δt, in the ideal state of Δt=Q, the circumferential speed at the radius ro of the equivalent spur gear should match the moving speed of the cutting blade. However, between E1 and E2 where generating gear cutting is performed, the position of the rank cutting edge is shifted by Δ[1-Δt2. This can be considered to mean that the speed with the cutting edge matches at the circumference of ro+Δ8r, where Δr is the amount of radius increase. Zunawaji, the following formula holds true. 2π(ro+Δr) 12πr o し'lπro(Δt1−Δt2)/(
El y - E2y) Therefore, Δ"2ro(Δt1-Δt2) / (Ely-E2y) ... (9) And if r'o-ro+Δr, then the amount of dislocation X'B, the angle α"b, the half tooth The thickness S"b is expressed as the following equation (10). -C08ot/(ro-Bt
anδ)) S'b - ((yrm/4+X'B tanαm)/r
'o+invcrm-1nvα'arb 9-(πcos-d/2Z-2sin δ×tanαI
ll /mZ +jnvcrm-invα'b) rb・・・
(10) Furthermore, the incisor position error during the generation period is related to the increase or decrease in tooth thickness. Therefore, if the average position error Δto+ between E1 and E2 is used, 5b=s'b +Δatta-rb/r'. Therefore, 5b=(πcosδ/ 2 Z + i n'v α閑−1nvα”b + (X'B tanα1+Δtrn
) /r' o) rb... (11) Calculate for the gears in Table 1 in the same way as in the case of Fig. 6,
Figures 12 and 13 show curves DI, D2. D3. D4 and D'l, D'2, D'3.
This is a graph indicated by D'4, and Fig. 12 shows the left tooth surface and the 13th
The figure shows the right tooth flank. Compared to the case shown in FIG. 6, a slight effect can be seen in the numerical values on the right tooth flank, but the gap on the left tooth flank has been significantly reduced. In Figure 14, B=±2
．． The figure shows the calculated gap within a range of 5 mm. In addition, Figure 15 shows the measurement results using a single tooth surface meshing accuracy tester, and when compared with the run-out of the peak due to the film with a thickness of 0°14 mm sandwiched in between, it seems that the meshing is good. I know that there is. The embodiment described above is a case in which tooth shear is applied along a pinch cone based on a conventional rolling cone. However, in the present invention, in the generating motion with the rack, the peripheral speeds match only at the center point P of the tooth width, and even on the pinch generatrix, the peripheral speeds do not match at points other than point P. In other words, at points other than the center point of the face width, the gears mesh with each other as equivalent spur gears with shifted teeth. As shown in FIG. 16, in the gear 8, this amount of dislocation is treated as the distance from the cylindrical generatrix of radius r in the radius R1 binion 9, and has nothing to do with the conventional pitch generatrix. In other words, there is no need to stick to the conventional pitch cone 1 as the cone to which the tooth trace is attached. As shown in FIG. 16, when the gear 8 and pinion 9 are assembled, the apex 01 of both,
There is no need for 02 to match. Based on this free thinking, a design with even fewer gaps becomes possible. Therefore, in the next example, the number of teeth, module, and pressure angle are the same as in the previous example, and the design cone angle δ that gives the tooth trace of the gear 8 is freely set, and the design cone angle of the pinion 9 is the complement angle of the design cone angle δ. If the gap at 13-11.12 mm is calculated, it will be as shown in FIGS. 17(a) and (b). FIG. 17(a) shows the case of the left tooth flank, and FIG. 17(b) shows the case of the right tooth flank. According to the same figure, the cone angle of gear 8 is 52
It is estimated that setting the angle to 38 degrees (therefore, 38 degrees for the pinion 9) results in a combination with the smallest gap on both the left and right tooth surfaces. Therefore, the cone angle δ of gear 8 is 52
By selecting the degree and setting the gap Kb between the left and right flanks as in the case of Fig. 12.13, the curve FLF2 shown in Fig. 18.19
．． F3. F4 and F'1゜r'''2, F'3.F'4
become that way. Figure 18 shows the two left tooth flanks, and Figure 19 shows the right south flank. Although the decrease in the gap Kb is not significant compared to the previous example, there is, however, a significant difference in the degree of decrease in the thickness of the tooth tips. Figure 20 shows B-±2.5m as in the case of Figure 14 above.
This is a calculation of the fine gap Kb within the range of m,
FIG. 21 shows the measurement results using a single tooth surface meshing accuracy tester, as in the case of FIG. 15. The curve shown by the broken line in FIG. 20 represents the calculated value in the case of gear cutting with a simple rack, that is, the curve in FIG. 6, and in this example, the effect at the center of the face width is clearly shown. FIG. 23 shows the results of a single-sided meshing accuracy test under load for a bevel gear with a module of 3.75, a pressure angle of 20 degrees, a number of teeth of 38×3B, and 345C+4 according to the present invention. The load value is expressed as the tangential force of the pinch circle. When the load is extremely small, for example 14 kgf, there is a meshing error for each tooth, but it is not as large as the runout when a 0.06 mm thin steel piece is sandwiched. This error 3 difference almost disappears when the load reaches 102 kgf, resulting in extremely good meshing. Finally, a means for tilting the hob shaft 2a in the direction shown in FIG. 7 will be explained. FIG. 22(a) shows a state in which the hob shaft 2a is tilted in a desired direction. To achieve this on a hobbing machine, see Figure 22(a).
It is sufficient to turn the hob by an angle ψ around the Z axis while maintaining the relative position shown in , so that the vertical plane including the hob axis 2a is in the same direction as the hob axis of the hobbing machine. The turning angle ψ and the inclination angle T' in the vertical plane H of the hob shaft 2a are calculated using the following equation (
12). ψ−tan−′(QS′5inr・sinδ/QS′c
osT) = tan (tanr φs inδ) r'=s+n
(QS'5inT9cosδ/S') = s+n (stnr-cosδ) (12) Note that since the Q point moves to the position shown in Figure 22 (b), the calculation in Figure 22 (a) is The work shaft is brought closer to the hob shaft by ΔC shown by the following equation (13) from the reference position, and the height of the hob shaft is also corrected by Δh shown by the following equation. ΔC= (Zm/2+Rc −cosδ)X(1c
osψ) Δh= (Zm/2+Rc −cosδ)xsinψ'
tanr' ... (13) Effects of the invention As detailed above, in the present invention, a conical gear with good meshing can be obtained by using a hobbing machine exclusively for cylindrical gears, and the machining efficiency can be greatly increased by using a hobbing machine. It has the excellent effect of improving the 4. Brief description of the drawings Figure 1 is a schematic perspective view showing the mechanism of a conventional hobbing machine, Figure 2 is a perspective view showing the basic movement of a hobbing machine, and Figure 3 is a diagram showing the gear manufacturing method of the present invention. 4 is a sectional view of the gear of the present invention, FIGS. 5(a), (b), (c), and (d) are all explanatory views, and FIG. 6 is a gear manufactured by simple rank 5. Figure 7 is a perspective view showing the state where the hob is tilted, Figure 8 (a) is also a perspective view, and Figures 8 (b) and (C) are explanatory views. , Figures 9(a), (b), and (C) are all graphs, Figure 10 is an explanatory diagram, Figure 11 is a graph, 12.13.1
Figure 4 is a graph showing the gap state on the south face of the gear of the first example, Figure 15 is a graph showing the meshing test results of the first example, Figure 16 is an explanatory diagram of the second example, and Figure 17 is a graph showing the meshing test results of the first example.
Figures (a) and (b) are graphs for setting the cone angle, Figures 18, 19, and 20 are graphs showing the gap state on the tooth surface of the gear of the second embodiment, and Figure 21 is the graph of the second embodiment. 22(a) is a perspective view for explaining the method of tilting the hob, FIG. 22(b) is an explanatory diagram, and FIG. 23 is a graph showing the load test results. . Hob 2, conical gear 8゜ Patent Applicant 1 & Yasushi Fuji Representative Patent Attorney On 1) Hironobu 6 341- ■ Hase Uta > − Ku Aji

Claims (1)

[Claims] 1. The tip and bottom of the tooth width are made into an arc shape that matches the shape formed by the rotary cutting movement of the cutting edge, and the south face of the double-cut T shell body is machined while remaining in the fixed position. gear.