CONICAL INVOLUTE GEAR AND GEAR PAIR

Abstract

A gear pair includes a small-diameter conical involute gear having a conical angle, and a large-diameter conical involute gear having a conical angle. The small-diameter conical involute gear and the large-diameter conical involute gear are constituted by an aggregate of imaginary cylindrical gears.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(A) is an explanatory view showing a concept of the present invention;

FIG. 1(B) is an explanatory view showing a concept of a conventional structure;

FIG. 2 is a perspective view partially showing a conical involute gear in accordance with the present embodiment;

FIG. 3 is an explanatory view showing an addendum modification state and a spiral angle of a tooth;

FIG. 4(A) is a diagrammatic front elevational view showing an engagement state of the teeth;

FIG. 4(B) is a diagrammatic front elevational view showing the engagement state of the teeth;

FIG. 5 is a perspective view partially showing a contact locus of the teeth;

FIG. 6 is an explanatory view showing an engagement state of a conical involute gear;

FIG. 7 is an explanatory view showing dimensions and angles of various portions of the conical involute gear;

FIG. 8 is an explanatory view showing a gear generating process by a gear hobbing machine;

FIG. 9 is an explanatory view showing another gear generating process by the gear hobbing machine;

FIG. 10(A) is an explanatory view showing an engagement state of a conventional bevel gear;

FIG. 10(B) is an explanatory view showing machining by a milling cutter;

FIG. 10(C) is an explanatory enlarged view showing a tooth of a bevel gear; and

FIG. 11 is an explanatory view showing a gear pair having a conventional structure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A description will be given of one embodiment of the present invention with reference to FIG. 1(A) and FIGS. 2 to 9.

As shown in FIGS. 2, 3 and 6, a gear pair 31 is constituted by a small-diameter conical involute gear (hereinafter, referred to as a small-diameter conical gear) 32, and a large-diameter conical involute gear (hereinafter, referred to as a large-diameter conical gear) 33. The gears 32 and 33 are engaged with each other, and have predetermined conical angles δ1 and δ2, respectively. The conical gear 32 has a set of teeth 34, of the number of teeth z₁, and the conical gear 33 has a set of teeth 35, of the number of teeth z₂. The teeth 34 and 35 have an involute tooth profile and are constituted by helical teeth having a spiral angle β.

An addendum modification coefficient of each of the teeth 34 and 35 is non-linearly changed in each of a face width direction. In other words, as shown in FIGS. 3, 6 and 7, the addendum modification coefficient (an addendum modification amount) of each of the teeth 34 and 35 is zero in an arbitrary intermediate portion in the face width direction thereof, is negative in a small-diameter side from the center portion, and is positive in a large-diameter side from the center portion. In this embodiment, a position at which the addendum modification coefficient is zero is defined as a reference pitch point P. FIG. 3 shows a tooth 34A existing at the position at which the addendum modification coefficient is zero, a tooth 34B profile shifted to the negative side, and a tooth 34C profile shifted to the positive side, respectively.

In this case, values of the conical angles δ1 and δ2 can be optionally set in correspondence to a specification of each of the gears 32 and 33. In this embodiment, these values are set in such a manner as to satisfy a relationship of numerical expression 1 in the present embodiment. In the expression 1, δ1 denotes the conical angle of the small-diameter conical gear 32, δ2 denotes the conical angle of the large-diameter conical gear 33, z₁ denotes the number of teeth of the small-diameter conical gear 32, and z₂ denotes the number of teeth of the large-diameter conical gear 33.

$\begin{array}{cc}\sum ={\delta }_1+{\delta }_2\tan {\delta }_1=\frac{\sin \sum }{\frac{z_2}{z_1}+\cos \sum }\tan {\delta }_2=\frac{\sin \sum }{\frac{z_2}{z_1}+\cos \sum }& \mathrm{Numerical}\mathrm{Expression}1\end{array}$

In this embodiment, the small-diameter conical gear 32 and the large-diameter conical gear 33 constructing the gear pair 31 are defined as an aggregation of infinitude of imaginary cylindrical gears 321 and 331 in which a face width is zero, as shown in FIG. 1A and FIGS. 6 and 7. These imaginary cylindrical gears 321 and 331 respectively have a center axis u-u and a center axis v-v which are in parallel to a line g-g (hereinafter, the line g-g is referred to as a conical line) extending along a conical surface passing through the reference pitch point P of the gears 32 and 33. Accordingly, in the same manner as the imaginary cylindrical gears 321 and 331, there exist infinitude of center axes u-u and center axes v-v. Further, on one line w-w orthogonal to the conical line g-g at the reference pitch point P, the imaginary cylindrical gears 321 and 331 are defined as a helical spur gear (hereinafter, the helical spur gear in which the addendum modification amount is zero is set to standard imaginary cylindrical gears 321A and 331A) in which the addendum modification amount is zero. The positions of the standard imaginary cylindrical gears 321A and 331A are optionally set. As shown in FIG. 3, the imaginary cylindrical gears 321 and 331 in a smaller diameter side than the standard imaginary cylindrical gears 321A and 331A are profile shifted to the negative side, and the imaginary cylindrical gears 321 and 331 in a larger diameter side than the standard imaginary cylindrical gears 321A and 331A are profile shifted to the positive side.

Parameters of the imaginary cylindrical gears 321 and 331 are set in accordance with a numerical expression 2. Reference symbol m_v, in the expression denotes a module of the imaginary cylindrical gears 321 and 331, reference symbol β denotes a spiral angle of the teeth of the imaginary cylindrical gears 321 and 331, that is, the conical gears 32 and 33, reference symbol m_n, denotes a module of the imaginary cylindrical gears 321 and 331 in a vertical cross section of a tooth which is set such that a cross sectional involute tooth profile can be obtained or which is perpendicular to the spiral angle β in the imaginary cylindrical gears 321 and 331, reference symbol α_v, denotes a pressure angle of the imaginary cylindrical gears 321 and 331, reference symbol α_n denotes a pressure angle of the imaginary cylindrical gears 321 and 331 in the vertical cross section of the tooth, reference symbol z denotes the number of teeth of the conical gears 32 and 33, reference symbol z_v denotes the number of teeth of the imaginary cylindrical gears 321 and 331, and reference symbol δ denotes a conical angle of the conical gears 32 and 33, respectively.

Numerical Expression 2

Module m_v=m_n/cos β

Pressure angle α_v=tan⁻¹(tan α_n/cos α)

Number of teeth Z_v=Z/cos δ

Accordingly, in the case where the spiral angle β does not exist in the conical gears 32 and 33, in the numerical expression 2, that is, in the case where the spiral angle β is 0, the module m_v and the pressure angle α_v of the imaginary cylindrical gears 321 and 331 are equal to the module m_v, and the pressure angle α_v of the conical gears 32 and 33 having no spiral. In the case where the spiral exists in the conical gears 32 and 33, the module m_v and the pressure angle α_v of the imaginary cylindrical gears 321 and 331 are equal to values corresponding to the spiral angle β. As mentioned above, the module m_v and the pressure angle α_v are set in correspondence with the value of the spiral angle β of the tooth with respect to the infinitude of imaginary cylindrical gears 321 and 331, in accordance with the numerical expression 2. Further, the number of teeth z_v of the imaginary cylindrical gears 321 and 331 is determined in correspondence with the conical angles δ1 and δ2 of the conical gears 32 and 33. Accordingly, the present embodiment is different from the structure disclosed in Japanese Laid-Open Patent Publication No. 6-94101, in which the number of teeth z of the conical gears 32 and 33 is used as it is.

If the imaginary cylindrical gears 321 and 331 set as mentioned above are engaged with each other without being in biased contact or being in point contact with each other, as shown in FIG. 5, it is possible to obtain a continuous engagement over a whole region in an axial direction (in the face width direction) of the gear pair 31. Respective data of the conical gears 32 and 33 in this case can be set in accordance with the following expressions. FIG. 5 expresses an engagement locus 35a of the teeth. Accordingly, if all the teeth of the gear pair 31 shows a linear engagement locus shown in FIG. 5, it is possible to bring the teeth 34 and 35 of the gears 32 and 33 into surface contact with each other in a wide range.

In FIG. 7, a center distance a between the imaginary cylindrical gears 321 and 331 engaging with each other is expressed by numerical expression 3. Reference symbol r₁′ in the expression denotes a diameter of a pitch circle of the imaginary cylindrical gear 321, reference symbol r₂′ denotes a diameter of a pitch circle of the imaginary cylindrical gear 331, reference symbol R denotes a con-distance of the conical gears 32 and 33, and reference symbol y denotes a distance from a large-diameter end of the gears 321 and 331 on the conical line g-g to the imaginary cylindrical gears 321 and 331, respectively.

Numerical Expression 3

a=r ₁ ′+r ₂′=(R−y)(tan δ₁/cos δ₂)

r ₁′=(R×y)tan δ₁r₂′=(R−y)tan δ₂

A center distance a₀ of the standard imaginary cylindrical gears 321A and 331A is shown in numerical expression 4. Reference symbol y₀ in the expression denotes a distance from the large diameter end of the gears 321 and 331 to the standard imaginary cylindrical gears 321A and 331A, reference symbol z_v1 denotes the number of teeth of the small-diameter standard imaginary cylindrical gear 321A, and reference symbol z_v2 denotes the number of teeth of the large-diameter standard imaginary cylindrical gear 331A, respectively.

$\begin{array}{cc}{a}_0=r_1+r_2=\left(R-y_0\right)\left(\tan {\delta }_1+\tan {\delta }_2\right)\begin{array}{c}{r}_1=\left(R-y_0\right)\tan {\delta }_1=\frac{m_vz_{v1}}{2}\\ r_2=\left(R-y_0\right)\tan {\delta }_2=\frac{m_vz_{v2}}{2}\end{array}\begin{array}{c}{y}_0=\frac{R\tan {\delta }_1-m_vz_{v1}/2}{\tan {\delta }_1}\\ y_0=\frac{R\tan {\delta }_2-m_vz_{v2}/2}{\tan {\delta }_2}\end{array}& \mathrm{Numerical}\mathrm{Expression}4\end{array}$

Next, an engagement pressure angle α_v′ in the right-angled surface of the conical line of the imaginary cylindrical gears 321 and 331 is shown in numerical expression 5. The right-angled surface of the conical line corresponds to the surface perpendicular to the width direction of the conical involute gear. Reference symbol α_v in the expression denotes a pressure angle of the standard imaginary cylindrical gears 321A and 331A, reference symbol x₁ denotes an addendum modification coefficient of the small-diameter imaginary cylindrical gear 321, reference symbol x₂ denotes an addendum modification coefficient of the large-diameter imaginary cylindrical gear 331, respectively. Accordingly, if the imaginary cylindrical gears 321 and 331 satisfy the expression (1) in the numerical expression 5, all the imaginary cylindrical gears 321 and 331 can achieve a normal engagement with no gap, as shown in FIGS. 4(A) and 4(B). As a result, it is possible to obtain a continuous engagement in all the regions in a tooth trace direction of the gear pair 31.

$\begin{array}{cc}\mathrm{Numerical}\mathrm{Expression}5& \\ \cos {\alpha }_v^{\prime }=\frac{a_0}{a}\cos {\alpha }_v\mathrm{inv}{\alpha }_v^{\prime }=\frac{2\left(x_1+x_2\right)}{z_{v1}+z_{v2}}\tan {\alpha }_v+\mathrm{inv}{\alpha }_v& \left(1\right)\end{array}$

in which

invα=tan α−α

The radii of the imaginary cylindrical gears 321 and 331 are expressed as numerical expression 6.

$\begin{array}{cc}{r}_1^{\prime }=r_1\frac{\cos {\alpha }_v}{\cos {\alpha }_v^{\prime }}r_2^{\prime }=r2\frac{\cos {\alpha }_v}{\cos {\alpha }_v^{\prime }}& \mathrm{Numerical}\mathrm{Expression}6\end{array}$

The relationship between the addendum modification coefficients x₁ and x₂ of the imaginary cylindrical gears 321 and 331 is shown in numerical expression 7.

$\begin{array}{cc}{x}_1+x_2=\frac{\left(z_{v1}+z_{v2}\right)\left(\mathrm{inv}{\alpha }_v^{\prime }-\mathrm{inv}{\alpha }_v\right)}{2\tan {\alpha }_v}& \mathrm{Numerical}\mathrm{Expression}7\end{array}$

In order to suitably engage the imaginary cylindrical gears 321 and 331 with each other, it is necessary to bring the thickness of the tooth into line with the width of the tooth space on the pitch circle in which the imaginary cylindrical gears 321 and 331 are engaged with each other, as shown in FIGS. 4(A) and 4(B). In other words, if the thickness of the tooth and the width of the tooth space are equal on the pitch circle in which the imaginary cylindrical gears 321 and 331 are engaged, it is possible to suitably engage the gears with each other. In this case, a relationship of numerical expression 8 is satisfied. Reference symbol p′ in the expression denotes a tooth pitch on the engagement pitch circle after being profile shifted, and reference symbols p₁′ and p₂′ denote tooth pitches of the imaginary cylindrical gears 321 and 331 on the engagement pitch circle after being profile shifted, respectively. Reference symbols s₁′ and s₂′ denote tooth thicknesses of the imaginary cylindrical gears 321 and 331 on the engagement pitch circle after being profile shifted, respectively. Reference symbols e₁′ and e₂′ denote widths of the tooth spaces of the imaginary cylindrical gears 321 and 331 on the engagement pitch circle after being profile shifted, respectively. Reference symbol s denotes a tooth thickness on the engagement pitch circle of the standard imaginary cylindrical gears 321A and 331A, and reference symbol x denotes an addendum modification coefficient of the standard imaginary cylindrical gears 321A and 331A, respectively.

$\begin{array}{cc}{p}^{\prime }=p_1^{\prime }=\frac{2\pi r_1^{\prime }}{z_{v1}}=p_2^{\prime }=\frac{2\pi r_2^{\prime }}{z_{v2}}p^{\prime }=s_1^{\prime }+e_1^{\prime }=s_2^{\prime }+e_2^{\prime }s_1^{\prime }=e_1^{\prime }=s_1^{\prime }=e_2^{\prime }s^{\prime }=s\frac{r^{\prime }}{r}+2r^{\prime }\left(\mathrm{inv}{\alpha }_v-\mathrm{inv}{\alpha }_v^{\prime }\right)s=m_v\left(\frac{\pi }{2}+2\times \tan {\alpha }_v\right)& \mathrm{Numerical}\mathrm{Expression}8\end{array}$

The addendum modification coefficients x₁ and x₂ of the imaginary cylindrical gears 321 and 331 are determined on the basis of numerical expression 9.

$\begin{array}{cc}{x}_1=\frac{z_{v1}\left(\mathrm{inv}{\alpha }_v^{\prime }-\mathrm{inv}{\alpha }_v\right)}{2\tan {\alpha }_v}=z_{v1}f\left(\mathrm{inv}{\alpha }_v^{\prime }\right)x_2=\frac{z_{v2}\left(\mathrm{inv}{\alpha }_v^{\prime }-\mathrm{inv}{\alpha }_v\right)}{2\tan {\alpha }_v}=z_{v2}f\left(\mathrm{inv}{\alpha }_v^{\prime }\right)& \mathrm{Numerical}\mathrm{Expression}9\end{array}$

The addendum modification coefficients x₁ and x₂ are functions of the pressure angles α_v and α_v′, which are variables. Accordingly, the addendum modification coefficients x₁ and x₂ are non-linear functions. An allocation of the addendum modification coefficients x₁ and x₂ is not only related to the conical angles δ1 and δ2 of the imaginary cylindrical gears 321 and 331, but also related to the number of teeth of the imaginary cylindrical gears 321 and 331, as shown in numerical expression 10. Accordingly, the conical involute gears 32 and 33 can obtain a non-linear addendum modification coefficient, and can accordingly obtain an engagement of being in line contact with each other.

$\begin{array}{cc}\frac{x_1}{x_2}=\frac{z_{v1}}{z_{v2}}=\frac{z_1\cos {\delta }_2}{z_2\cos {\delta }_1}& \mathrm{Numerical}\mathrm{Expression}10\end{array}$

As mentioned above, in accordance with this embodiment, a concept of the imaginary cylindrical gears 321 and 331 is introduced, and the conical gears 32 and 33 are respectively defined as the aggregate of the imaginary cylindrical gears 321 and 331. Further, the structure is made such as to precisely engage the imaginary cylindrical gears 321 and 331 with each other by changing the addendum modification coefficient by using the number of teeth taking the conical angles of the conical gears 32 and 33 into consideration in the respective imaginary cylindrical gears 321 and 331 (refer to the numerical expression 10). Accordingly, it is possible to achieve a smooth engagement between the conical gears 32 and 33, under a condition having the same module, pressure angle and number of teeth, and being different only in the addendum modification coefficient.

Further, in each of the cross sections perpendicular to the face width, the pressure angle and the engagement angle come into line in the case where the profile shift does not exist. However, the pressure angle and the engagement angle are different in the case where the profile shift exists. Accordingly, in each of the surfaces perpendicular to the face width, it is necessary that a total of the addendum modification coefficients of the gear pair satisfy a predetermined relationship as shown in the numerical expression 7 and the numerical expression 9, and the pitches of the gears on the engagement pitch circle come into line as shown in the numerical expression 8. In other words, if these relationships are satisfied in each plane perpendicular to the face width, it is possible to obtain an engagement position at one point as shown in FIGS. 4(A) and 4(B). Accordingly, it is possible to obtain the conical involute gear which is simultaneously engaged in all the regions of the face width and comes into surface contact. Further, even if the spiral angle β exists in the conical gears 32 and 33, the module and the pressure angle are set in correspondence with the spiral angle β as is apparent from the numerical expression 2. Accordingly, it is possible to bring the conical gears 32 and 33 into contact with each other in a wide area, and it is possible to further smoothly engage with each other.

Each of the conical gears 32 and 33 can be formed by gear cutting by using a gear hobbing machine shown in FIGS. 8 and 9. As shown in FIG. 8, a position of a hob spindle Ha is fixed in a state in which an axis C of each of the conical gears 32 and 33 (the workpieces) is inclined. Further, the gear cutting work of each of the conical gears 32 and 33 is executed such that the addendum modification coefficient is changed to be non-linear by moving the work in a direction of arrow Q shown in FIG. 8 while rotating the workpiece axis C as well as moving the hob H along the tooth trace at a time of executing the gear cutting.

Further, as shown in FIG. 9, the workpiece axis C may be operated as follows without inclining the workpiece axis C. In other words, the workpiece axis C may be moved in a direction of arrow Q shown in FIG. 9 in such a manner that the gear corresponding to the conical angles δ1 and δ2 of the conical gears 32 and 33 can be generated in correspondence to the movement in the gear trace direction of the hob H. In this case, the other movement than the movement mentioned above in the direction of arrow Q is executed to the work axis C, in such a manner that a change amount of the addendum modification coefficient is generated in addition to the generation of the tooth.

Further, in place of moving the workpiece axis C in the direction of arrow Q, a hob axis Ha may be moved in the direction of arrow Q. As mentioned above, it is possible to easily execute the gear generating tooth cutting with respect to each of the conical gears 32 and 33, only by controlling the movement of the workpiece axis C or the hob axis Ha in the direction of arrow Q, while using the gear hobbing machine in the same manner as the generation of the normal involute gear. Further, since the modules, the numbers of teeth, and the pressure angles of the respective conical gears 32 and 33 are equal, it is possible to execute the gear generating process using the same cutter.

The embodiment mentioned above has the following advantages.

(1) The conical gears 32 and 33 respectively correspond to the aggregates of the imaginary cylindrical gears 321 and 331. Accordingly, it is possible to change the addendum modification coefficient of each of the imaginary cylindrical gears 321 and 331 by using the number of teeth of each of the imaginary cylindrical gears 321 and 331. Accordingly, it is possible to bring the conical gears 32 and 33 into surface contact with each other, and it is possible to achieve a suitable engagement between the conical gears 32 and 33.

(2) Since the spiral angle β of the conical gears 32 and 33 is reflected on the change of the addendum modification coefficient, it is possible to obtain a precise engagement in a wide area on the basis of the involute tooth profile, regardless whether the conical gears 32 and 33 are constituted by straight teeth or helical teeth.

(3) Since it is possible to properly allocate the addendum modification coefficient to each of the conical gears 32 and 33, it is possible to engage the conical gears 32 and 33 with no gap in all the regions in the tooth trace direction of the conical gears 32 and 33.

(4) Each of the conical gears 32 and 33 can be easily generated and machined by using the gear hobbing machine. Further, since the modules, the numbers of teeth, and the pressure angles are equal in the conical gears 32 and 33 constructing the gear pair 31, it is possible to generate and machine teeth by the same cutter. Accordingly, it is possible to simplify an initial setup at a time of machining, and it is possible to further easily manufacture each of the conical gears 32 and 33.

(5) It is possible to set the standard imaginary cylindrical gears 321A and 331A in which the addendum modification amount is zero, in an arbitrary intermediate portion in the face width direction, and it is possible to respectively set the imaginary cylindrical gears 321 and 331 that are profile shifted to a positive side, and the imaginary cylindrical gears 321 and 331 that are profile shifted to a negative side, on both sides of the imaginary cylindrical gears 321A, 331A having no addendum modification. Accordingly, it is possible to form the conical gears 32 and 33 having a large conical angle.

The present embodiment may be modified as follows.

The teeth of the conical gears 32 and 33 may be changed to straight teeth.

One of the two gears 32 and 33 constructing the gear pair 31 may be a cylindrical gear.

The present invention may be applied to a structure in which a plurality of gears are engaged with one gear, or a structure in which a plurality of gears are continuously engaged so as to form gear train. In this case, the gear pair is constructed by a pair of gears engaging with each other.

The diameters of the conical gears 32 and 33 may be equalized.

Claims

1. A conical involute gear having an involute tooth profile, wherein the conical involute gear includes an aggregate of a plurality of imaginary cylindrical gears, and wherein each of the imaginary cylindrical gears has an axis which is in parallel to a conical surface of the conical involute gear passing through a reference pitch point.

2. The conical involute gear according to claim 1, wherein each of the imaginary cylindrical gears has the same module.

3. The conical involute gear according to claim 2, wherein an addendum modification coefficient of each of the imaginary cylindrical gears changes non-linearly in a face width direction of the conical involute gear.

4. The conical involute gear according to claim 1, wherein the imaginary cylindrical gear in which the addendum modification amount is zero is a standard imaginary cylindrical gear, the standard imaginary cylindrical gear is arranged between a large-diameter end and a small-diameter end of the conical involute gear, the imaginary cylindrical gears between the smaller diameter end and the standard imaginary cylindrical gear are negatively profile shifted, and the imaginary cylindrical gears between the larger diameter end and the standard imaginary cylindrical gear are positively profile shifted.

5. The conical involute gear according to claim 1, wherein, in the case of setting the number of teeth of the conical involute gear to z, setting a conical angle of the conical involute gear to δ, and setting the number of teeth of the imaginary cylindrical gear to zv, a relational expression zv=z/cos δ is satisfied.

6. The conical involute gear according to claim 1, wherein each imaginary cylindrical gear has helical teeth.

7. A gear pair in which at least one of two involute gears engaging with each other is a conical involute gear, wherein the conical involute gear is the conical involute gear according to claim 1.

8. The gear pair according to claim 7, wherein, in the case of setting a pressure angle of the imaginary cylindrical gears to αv, setting a pressure angle of the imaginary cylindrical gear in a vertical cross section of a tooth to αn, setting a module of the imaginary cylindrical gear to mv, setting a spiral angle of a tooth to β, and setting a module of the imaginary cylindrical gear in a vertical cross section of a tooth to mn, relational expressions mv=mn/cos β, and αv=tan−1(tan αn/cos β) are satisfied.

9. The gear pair according to claim 7, wherein in the case of setting the imaginary cylindrical gear in which the addendum modification amount is zero to a standard imaginary cylindrical gear, setting a pressure angle of the standard imaginary cylindrical gear to αv, setting an engagement pressure angle in a surface perpendicular to a conical line of the imaginary cylindrical gear to αv′, setting an addendum modification coefficient of a small-diameter imaginary cylindrical gear to x1, setting an addendum modification coefficient of a large-diameter imaginary cylindrical gear to x2, the number of teeth of the small-diameter imaginary cylindrical gear to zv1, and setting the number of teeth of the large-diameter imaginary cylindrical gear to zv2, a relational expression invαv′=[2(x1+x2)/zv1+zv2] tan αv+invαv, in which invα=tan α−α, is satisfied.

10. The gear pair according to claim 7, wherein, in the case of setting an addendum modification coefficient of a small-diameter imaginary cylindrical gear to x1, setting an addendum modification coefficient of a large-diameter imaginary cylindrical gear to x2, the number of teeth of the small-diameter imaginary cylindrical gear to zv1, setting the number of teeth of the large-diameter imaginary cylindrical gear to zv2, setting the number of teeth of a small-diameter conical involute gear to z1, setting the number of teeth of a large-diameter conical involute gear to z2, a conical angle of a small-diameter conical gear to δ1, and setting a conical angle of a large-diameter conical gear to δ2, a relational expression (x1/x2)=zv1/zv2=z1cos δ2/z2cos δ1 is satisfied.