JPH0225732B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention relates to a generating gear cutting method for a gear for an increasing/decelerating drive machine using a wave gear device.

[Prior Art] The so-called harmonic
A drive (wave gear device) is a drive device that utilizes the deflection of a flexible material, and its constituent elements, circular splines (rigid gears) and flex splines (wave gears), have linear or involute tooth profiles. has been used.

However, the tooth profile is not determined based on a strict gear mesh theory, but is based on an approximate analysis result when the reduction ratio is large. One of the reasons for the low efficiency of current harmonic drives is the forced meshing caused by improper tooth profiles. Tooth profile becomes a particular problem when the reduction ratio becomes smaller.

In this way, including harmonic drive,
Regarding gears that move in a wave motion, there is still less research compared to general gears, and in order to obtain smoother meshing, sufficient analysis of the geometric motion of gears that move in a wave motion and the meshing of teeth is required. It is necessary to determine the tooth profile accordingly.

[Problems to be Solved by the Invention] The purpose of the present invention is to create a method for processing the gears of a wave gear device used in an acceleration/deceleration drive machine so that the gears have an appropriate tooth profile determined based on sufficient analysis. The objective is to provide a tooth cutting method.

[Means for Solving the Problems] In order to achieve the above object, the generating gear cutting method of the present invention uses a rigid gear (referred to as a "rigid gear" in this specification) that does not deform on one side, and , the other is a gear that moves in a wave-like manner (referred to as a "wave gear" in this specification), and a mechanism that generates wave motion in the wave gear (referred to as a "wave generator" in this specification). By this, the rigid gear and the wave gear are meshed with their plurality of wavy convex portions,
At this time, by creating a difference in the number of teeth between the rigid gear and the wave gear between adjacent convex parts, relative movement between the rigid gear and the wave gear is made possible as well as movement of the meshing part. During generation gear cutting of a gear in a strain wave gear device, a virtual motion plate (referred to as a "rolling motion plate" in this specification) performs the same relative movement as each of a pair of teeth of a rigid gear and a wave gear that mesh with each other. Let the shape be a trajectory drawn by the instantaneous center of the relative movement of the teeth on a plane fixed to each tooth, and the condition that the common normal of both tooth profiles at the meshing point of the teeth passes through the contact point of the rolling plate. In addition, the tooth profiles of the rigid gear and wave gear are determined, and when cutting the rigid gear or wave gear, the cutting edge of the cutter that commonly contacts both gears at the meshing point of both gears and the rolling motion of both gears are determined. The third rolling motion plate that makes contact with the plate at the same contact point is defined as the rolling contact between the rolling motion plate of the rigid gear or wave gear and the third rolling motion plate, assuming that the plate and the third rolling motion plate make relatively the same motion. Generative gear cutting is performed by applying relative motion to the cutting blade.

[Example] Hereinafter, the generative tooth cutting method of the present invention will be explained in more detail along the analysis process.

The wave gear device shown in Fig. 1a includes an internal gear and an external gear with slightly different numbers of teeth (number of internal teeth > number of external teeth), and does not deform one of the internal gears. Assuming that a rigid gear 1 is now fixed, the other external gear is a thin-walled hollow cylindrical strain wave gear 2 that can be flexibly deformed in the radial direction, and the strain wave gear 2 is rotatably disposed inside it. The rollers 4, 4 of the wave generator 3, which function as cams, flex and deform in the radial direction to mesh with the rigid gear 1 at a plurality of convex portions, and the meshing portions are rotated by the rotation of the wave generator 3. By moving the wave gear, the wave gear can be rotated in a direction opposite to the rotation of the wave generator.

Fig. 1b shows a different example of a strain wave gear device, in which the external gear is replaced by a rigid gear 11, contrary to that shown in Fig. 1a.
and the internal gear is wave gear 12 (number of internal teeth >
number of external teeth), a roller 14 on the outside of the wave gear 12,
A wave generator 13 equipped with a wave generator 14 is rotatably provided. If the rigid gear is fixed, the wave gear rotates in the same direction as the wave generator.

Basic conditions In the wave gear device described above, if we consider the case where the wave gear is made of a thin flexible material, the plate thickness at the bottom of the tooth is extremely thin compared to the tooth area, so deformation occurs only when the teeth are bent. It is thought that this occurs at the bottom. That is, although different teeth move relative to each other, each tooth can be considered to be a rigid body. To explain this more clearly, the motion of a strain wave gear is exactly the same as that of a chain, with the teeth serving as links and the tooth bottoms serving as hinges. Also, when a thin plate is elastically deformed, there is a neutral line that maintains the same length as before deformation, and this can be thought of as the same line that smoothly connects the centers of the hinges of a chain.

Therefore, as shown in Figure 2, in a coordinate system fixed to each tooth of the strain wave gear, a point on the neutral line is
A rectangular coordinate system (M _{i −u i ,} v _{i : i} is the tooth number )think of. At this time, we make the following assumptions.

``When a wave gear moves, the tooth profile does not change when the tooth is observed from the coordinates (M-u, v) fixed to the tooth. Further, on the neutral line, the pitches M _i and M⌒ _i+1 of each tooth are constant. ” This assumption is considered valid if the amount of deformation of the strain wave gear is small.

If we consider each tooth as a rigid body, we can determine the tooth profile by examining the motion of the tooth using the general tooth profile solving method. That is, as shown in Figure 3,
If the tooth profile C ₁ and the rolling motion plate P ₁ are integrated, and the tooth profile C ₂ and the rolling motion plate P ₂ are integrated, the common normal T of the tooth profiles at the meshing point C of the teeth will perform the same relative motion. Rolling contact point (instantaneous center) P of rolling motion plates P ₁ and P ₂
The tooth profile can be determined by giving the mechanistic requirement that the tooth pass through.

Movement of wave gears Devices using wave gears can be thought of as those that perform linear motion in the form of planar motion or those that perform rotary motion. Here we will examine rotational motion, which makes linear motion easier to understand.

Now, it is assumed that the rigid gear and the wave gear can each rotate around the same fixed center.
The wave gear performs a wave motion due to the rotation of the wave generator at the same time as the rotational motion, and n
Assume that the gear has several convex parts and is meshed with a rigid gear near the apex of each convex part. Here, the rigid gear is a cylindrical gear with a reference pitch circle diameter d ₀ and the number of teeth Z _R , and the strain wave gear is a cylindrical gear whose neutral line has a diameter d _n and the number of teeth Z _W before deformation.
Further, it is assumed that the neutral line does not change its length due to deformation, becomes a reference pitch curve, and meshes at the same pitch as the pitch on the reference pitch circle of the rigid gear. Normally, number of teeth Z _W and number of teeth
Z _R are not equal, and FIG. 1a is the case when Z _W <Z _R , and FIG. 1 b is the case when Z _W >Z _R.

In addition, here, the wave generator is considered to be a non-circular cam with n convex parts, and its neutral line is fitted inside the thin wave gear without expanding or contracting.
Consider the case shown in FIG. 1a in which a wave motion is generated in a wave gear by the rotation of a cam. Also, it is assumed that there is no frictional force between the cam and the wave gear.

Now, at a certain point in time, as shown in Figure 4, consider orthogonal coordinates (O-x, y) fixed to a rigid gear whose origin is the rotation center O of the shaft, and the y-axis is the neutral line of the wave gear. Assume that it passes through the convex vertex M ₀ . Counting from this state, the number of teeth of the rigid gear Z
Assuming that the non-circular cam (wave generator) is rotated so that the apex of the convex portion moves by the same amount, and that the apex M ₀ moves to point M, this trajectory is examined.

Assuming that the peak of the convex portion of the neutral line of the strain wave gear moves to point Q as the cam rotates, at the beginning (O-
The coordinates (O-X, Y) fixed on the cam, which corresponded to x, y), rotate as shown in Figure 4,
The rotation angle φ of the cam with respect to the rigid gear is equal to the angle M ₀ OQ, and φ=2π/Z _R ×Z (1).

Next, finding the arc length S of the neutral line MQ⌒, we get
The number of teeth of the wave gear between point M and point Q is also Z, and the pitch is πd _n /Z _W on the neutral line l, so S = πd _n /Z _W ×Z … (2) ( From equations 1) and (2), S=Z _R /Z _W ×d _n /2×φ (3).

Here, the shape of the neutral line l after deformation has the rotation center O of the shaft as its origin, θ as the angle from the axis connecting the convex apex Q and point O (hereinafter referred to as the long axis), and the distance from the origin O as the origin. Let r be expressed in the following polar coordinates.

r=f(θ) ...(4) Now, the non-circular cam has n convex parts, and f
Assuming that (θ) is a function with a period of 2π/n, this can be generally expressed as a Fourier series as follows.

f(θ)=a ₀ /2+ _∞ 〓 ^k=1 {a _k cos(knθ)+b _k sin(knθ)} …(5) Here, If the length of the arc from the vertex of the convex part of this curve to the angle θ is S, then S=∫〓 ₀ √{()} ² + {()} ² dθ...(7).

After all, if we consider equations (3) and (7) to be equal and express them including the sign, we get S=Z _R /Z _W ×d _n /2×|φ| =∫|〓| ₀ √{()} ² + {′()} ² dθ…(8
) becomes.

However, from now on, the angle is positive clockwise, and φ is the angle formed by the long axis with the y-axis as the reference.
θ is the angle formed by the radius vector MO with the long axis as the reference.

From equation (8), the relationship between angle θ and angle φ cannot be expressed by a simple elementary function, but it can definitely be determined by numerical integration.

Now, if the (x, y) coordinates of point M on the neutral line l are (x _M , y _M ), then x _M = rsin (φ+θ) y _M = rcos (φ + θ) (9).

Next, in FIG. 4, the coordinates fixed to the tooth, that is, the orthogonal coordinates (M-u,v) with the tangent u at point M on the neutral line l as the abscissa and the normal v as the ordinate,
Examine the relative movement with the coordinates (O-x, y) fixed to the rigid gear.

Letting ψ be the angle between the v-axis and the y-axis with the y-axis as a reference, ψ=φ+θ+μ...(10).

However, if μ is the angle formed by the v-axis with reference to the radius vector MO, then μ can be found from -tanμ=1/r dr/dθ (11).

In the end, the (M-u,v) coordinates are (O-x,y)
Translate by (x _M , y _M ) and rotate by ψ with respect to the coordinates.

The coordinate conversion formula is: u=(x- _xM )cos(-ψ)+(y- _yM )sin(-ψ)v=(y- _yM )cos(-ψ)-(x- _xM ) sin(−ψ) …(12).

Tooth profile solution In Figure 5, assume that rigid gear C _R and wave gear C _W mesh at point C. Now, when we move the cam slightly, we assume that both gears move relative to each other with point P as the center (instantaneous center), and this point P is based on _{the coordinates} (O-x,
y) or from the coordinates (M-u,v) fixed to the wave gear C _W , it should appear to be stationary.

Expressing this in a formula, the (x, y) coordinate values (x _P , y _P ) and (u, v) coordinate values (u _P , v _P ) of point P
is a fixed point and differentiating equation (12) with respect to φ, du _P / dφ = −dx _M / dφcos (−ψ) + (x _P −x
_M ) dψ／dφsin(−ψ) −dy _M ／dφsin(−ψ)−(y _P −y _M )dψ/
dφcos(−ψ)=0 dv _P ／dφ=−dy _M ／dφcos(−ψ)＋(y _P −y
_M ) dψ/dφsin (−ψ) +dx _M /dφsin (−ψ) + (x _P −x _M ) dψ/
dφcos(−ψ)=0…(13) From equation (13), becomes. Substituting this into x and y in equation (12), we get
(u _P , v _P ) can also be found.

Now, if we rotate the wave generator (cam) and find the trajectory drawn by this point P at the coordinates fixed to each tooth, this will be the trajectory of the rolling motion plates P _R and P _W that make the same relative movement as each tooth. It becomes the shape.

In the end, the solution for the tooth profile is that when we give the tooth profile fixed to one of the rolling motion plates we just found,
This comes down to the problem of finding the tooth profile of the conjugate partner. The mechanical requirement then is that the common normal T at the engagement point C of the teeth passes through the contact point P of the rolling plate.

Here, the explanation regarding the above-mentioned rolling movement plate will be supplemented.

Now, if we consider the meshing state of ordinary internal gears and external gears, there are pitch circles in these gears that roll into contact with each other. The rolling contact plate described above corresponds to this pitch circle. In the case of a wave gear device, the teeth of a rigid gear are arranged at equal intervals on a cylinder, and the teeth of a wave gear are arranged at equal intervals on a convex, non-circular neutral line (soft standard pitch curve), but a pair of meshing teeth The relative motion of cannot be expressed by the rolling motion between the cylinder and the soft pitch curve. That is, in order to replace the relative motion of a pair of teeth with rolling contact motion, it is necessary to consider another curve (rolling motion plate) that causes rolling contact.

When a certain relative motion is given between meshing gears, the motion of those gears can be replaced by the rolling motion of a curved plate that performs the same motion as each gear. The curved plate is a rolling plate, and its shape is expressed as a locus drawn by the instantaneous center (pitch point) of the relative motion of the two gears in the coordinate system of each gear.

For simplicity, rigid gears are used in Fig. 5.
If C _R and rolling plate P _R are assumed to be stationary, wave gear C _W and rolling plate P _W try to rotate around point P.
At this time, the minute line segment near point C of the wave gear C _W attempts to move in a direction perpendicular to the straight line.

Here, if the minute line segment of rigid gear C _R and the minute line segment of wave gear C _W that are in contact at point C,
If it is not perpendicular to the straight line, when C _W moves a little, the C _R line segment and the C _W line segment will move away from each other. That is, at point C, the two teeth separate from each other or bite into the substantial part of the other, and the process of meshing the gears does not hold.

After all, at the meshing point C, the rigid gear C _R and the wave gear C _W must be at right angles to the straight line. Also, it can be seen that at this time, at the meshing point C, the rigid gear C _R and the strain wave gear C _W are sliding in a direction perpendicular to the straight line.

This provides the important mechanical requirements for gear meshing as explained above.

Specific calculation example - 1 Shape of rolling plate As a result of the analysis so far, equation (4) or (5)
When the shape of the neutral line l after deformation of the strain wave gear is given by equation (6), the relationship between the relative rotation angles of the rigid gear and the wave gear can be found from equation (8), and equation (14),
It was found that the shape of the rolling plate can be found from equation (12).

Therefore, we will perform a specific calculation using the shape of the cam currently used in harmonic drives as an example.

The shape of a non-circular cam with two convex parts resembles an ellipse, and assuming that no gap is created between the wave gear (flexspline) and the cam due to load, the neutral position of the wave gear The shape of the line is expressed in polar coordinates as shown below.

r=d/2+δ/2cos2θ...(15) This is an even function that is symmetrical about the long axis and has a period of π, and is the simplest form of equation (5).

Diameter of the neutral line before the wave gear is deformed d _n
When you ask for becomes.

Next, the pitch on the reference pitch circle of the rigid gear (circular spline), t ₀ = πd ₀ /Z _R , and the pitch on the neutral line of the wave gear, t _n = πd _n /Z _W , are equal, so d ₀ = Z _R /Z _W ×d _n …(17) There is a relationship.

Here, the maximum diameter of the neutral line of the strain wave gear d+δ
and the reference pitch circle diameter d ₀ of the rigid gear are connected by a coefficient λ as follows.

d+δ=λd ₀ …(18) When λ=1.0, that is, the state where the reference pitch circle of the rigid gear touches the neutral line at its maximum diameter point, it just corresponds to the standard gear of the involute gear, and , λ≠1 corresponds to meshing of shifted gears.

From equations (17) and (18), δ/d=λZ _R /Z _W ×d _n /d−1 (19), and an equation giving the amount of deformation δ can be found.

Equation (14) is in the form differentiated with respect to φ, but this is the same even if differentiated with respect to θ, so in the end, Then, the shape of the rolling plate can be found.

Figure 6 a, b, and c show rolling motion plates of rigid gears and strain wave gears for λ=1.0, λ<1.0, and λ>1.0, respectively, taking the tooth ratio Z _R /Z _W = 1.1 as an example.
This shows P _R and P _W , and shows the state in which the convex non-circular cam has been rotated by φ (=20 ⁰ ) relative to the rigid gear from the time when the tooth of the wave gear was located at the apex of the convex part. . This rolling motion board is (20)
As can be seen from equation (21), dψ/dθ→0
It has a shape that approaches a certain asymptote at . Then, these perform a rolling contact movement without slipping, and the contact point is at point P in FIGS. 6a, b, and c. Also, before the strain wave gear is deformed, that is, when the neutral line is circular, let the coordinate position of the rotation center O of the gear in the coordinates (Mu, v) fixed to the teeth be O', and M and
The trajectories L _M and L ₀ ′ for the rigid gear of O′ are shown. At this time, since point M and point O' perform the same relative movement as P _W , the normal to the locus L _M or L ₀ ' set at point M or O', respectively, passes through point P.

-2 Tooth profile of wave gear when rigid gear has involute tooth profile There are countless tooth profiles for gears, but here we will give the involute curve, which is currently the most widely used in practice, as the tooth profile for rigid gears.
An example in which the mating tooth profile conjugate with this is the tooth profile of a strain wave gear will be described.

In FIG. 7, the tooth profile C _R is the tooth profile of a rigid gear, and is an involute curve with a base circle radius r _gR . The tooth profile of the wave gear that meshes with it is defined as the tooth profile C _W , and now the tooth profile
Assuming that C _R and tooth profile C _W are in mesh at point C, the common normal T of the tooth profile set at point C is the rolling contact of a rolling plate that performs the same relative movement as tooth profile C _R and tooth profile C _W. At the same time as it passes through point P, it touches the base circle of the involute gear at point E.

Now, let us assume that the coordinates fixed to the teeth of the rigid gear with the axis passing through the center of the teeth as the y-axis are (O-x, y), and the coordinate values of point C at those coordinates (x _c ,
Find _yc ).

The angle γ _R with the y axis is γ _R = tan ^-1 (x _P /y _P )...(22) If the angle POE is τ _R , τ _R = cos ^-1 (r _gR /√ _P ² + _P ² ) …(23) becomes. However, x _P , y _P are (x, y) of point P
The coordinate value is given by equation (20).

Also, if the half angle of the tooth groove width on the base circle is σ _R , then σ _R = π/2Z _R + invα ₀ + 2tanα ₀ /Z _R x _R …(24) However, α ₀ is the standard pressure angle of the involute tooth profile, x _R is the dislocation coefficient.

From the properties of involutes, =BE⌒=r _gR (±γ _R +τ _R +σ _R ) …(25) Also, =r _gR tan (±γ _R +τ _R 〓ν _R ) …(26) Therefore, ν _R = γ _R ±{τ _R −tan ^-1 (±γ _R +τ _R +σ _R )} …(27) After all, x _C = sinν _R = r _gR √1+ (± _R + _R + _R ) ² sinν _R y _C = cosν _R = r _gR √1 + (± _R + _R + _R ) ² cosν _R …(28).

For double numbers, the upper number corresponds to the left tooth flank, and the lower number corresponds to the right tooth flank.

When these coordinates x _C and y _C are observed from the coordinates (M-u, v) fixed to the wave gear, the tooth profile of the wave gear can be determined. That is, when the coordinate values x _C and y _C are substituted for x and y in equation (12), u and v become the tooth profile to be found.

Figure 8 shows a rigid gear with a standard involute tooth profile C _R with the number of teeth Z _R = 22 and a pressure angle of 20°.
The tooth profile C _W of a strain wave gear with the number of meshing teeth Z _W =20 in the state of no backlash and λ=1 is shown based on a calculation example.

In addition, in the same figure, the number of teeth meshing with the rigid gear is 20,
Pressure angle 20° Standard involute gear tooth profile C _S
is shown by a dotted line. From now on, the tooth profile of the wave gear
It can be seen that the tooth thickness of C _W is reduced at the tooth tip and root compared to the standard involute tooth profile C _S.

FIG. 9 shows the state in which the strain wave gear is in motion with respect to the tooth profile shown in FIG. 8. In FIG. 9, the dotted line indicates the trajectory of the motion of the point that meshes with the rigid gear on the base circle. When actually manufacturing gears, it is necessary to design them appropriately so that the teeth do not interfere.

Generating gear cutting method for wave gear devices - 1 Overview of gear cutting method As a result of the results so far, the shapes of the rolling motion plates P _R and P _W can be found from the motion of the rigid gear and the wave gear, and the shapes of the rolling motion plates P _R ，
We were able to find the tooth profiles C _R and C _W that have the same relative motion as P _W.

Now, in Fig. 10, consider a third rolling plate P _K that makes rolling contact with both rolling plates P _R , P _W , and these rolling plates P _R , P _W , P _K are at the same point P. It is assumed that there is rolling contact. In this case, there is no need to consider which side is the real one. Also, rolling exercise board
Assuming that C _K is a tooth profile that makes the same relative movement as P _K , and that these tooth profiles C _R , C _W , and C _K are in sliding contact at the same point C, tooth profiles C _R , C _W , and C _K mesh with each other. become.

Here, when the tooth profile C _K is the cutting edge of the gear cutter and the rolling motion plates P _R and P _K are rolling between the cutter and the workpiece,
Alternatively, if the rolling plates P _W and P _K are given the same relative motion as when rolling, the tooth profiles C _R and C _W of a rigid gear or wave gear are created by the cutting blades.

There are countless shapes of cutter blades,
For example, it is possible to use the tooth profile of the mating gear to form the cutting edge shape, but for practical purposes, a cutter with a straight tooth profile is often used.
Next, we will discuss the generation tooth cutting method using a cutter with a straight tooth profile.

-2 Generating tooth cutting method using a linear tooth profile cutter First, find the shape of the rolling plate of the linear tooth profile cutter.

In Figure 11, considering the relative motion between the rigid gear and the cutter, the coordinates fixed to the rigid gear are (O
-x, y), and the coordinates fixed to the cutter are (K
−ξ, η). Both rolling motion plates P _R and
It is assumed that P _K is in rolling contact at point P, and tooth profile C _R and cutter cutting edge C _K are in contact at point C.

Now, when the wave generator is minutely rotated by an angle dφ with respect to the rigid gear, the rolling contact point P moves by a minute amount dS on both rolling curves, and the rolling contact point P moves by a minute amount dS on both rolling curves.
Assume that it comes to P ₁ and point P ₂ . The shape of the rolling motion plate of a rigid gear is given by x=x _P (φ), y=y _P (φ) ...(29) with the rotation angle φ of the wave generator with respect to the rigid gear as a parameter. Then, the minute movement dS
The relationship between and the angle dφ is given by the following equation.

Next, the angle between the common normal of both rolling plates at point P and the η axis is Ω〓, and the radius of curvature of the cutter's rolling plate at point P is ρ _K
Then, dΩ〓/dS=1/ρ _K (31). Also, since there is the relationship dξ／dS＝cosΩ〓, dη／dS＝sinΩ〓 …(32), in the end, the point P (ξ,
η) If the coordinate values are (ξ _P , η _P ), then or, Therefore, if the radius of curvature ρ _K is found, the shape of the rolling plate of the cutter can also be found.

Here, the radius of curvature at point P of the rolling plate of the rigid gear is ρ _R , and the radius of curvature of the tooth profile C _R and cutting edge C _K at point C are R _R and R _K
Then, according to the Euler-Savary formula, the following relationship holds true.

1/ρ _R −1/ρ _K = (1/R _K −r−1/R _R −r) sin
β...(34) where r is the length of PC, β is the angle between PC and the common tangent of the rolling plate at point P, and ρ _R is given by the following equation.

In addition, in the case of a cutter with a straight tooth profile, the radius R _K
=∞, and since the radius R _R , length r, and angle β are given as a function of the angle φ once the tooth profile of the rigid gear is determined, the radius of curvature ρ _K is given as a function of the angle φ.

Next, as in the example described in Section 1, we will specifically calculate the case where the rigid gear has an involute tooth profile.

In Fig. 11, the (x, y) coordinate values of point P and point C (x _P , y _P ) and (x _C , y _C )
is known from equations (20) and (28), so r=√( _P − _C ) ² + ( _P − _C ) ² …(36) R _R is the same as CE in equation (25), and R _R =CE=r _gr (±γ _R +τ _R +σ _R ) …(37) Also, the angle between the common normal of both rolling motion plates at point P and the y-axis is Ω.
If _y , Ω _y = π/2−tan ^-1 (−dx _P /dφ/dy _P /dφ)…(38), so β=γ _R +τ _R −Ω _v …(39), and (34) From the equation, 1/ρ _K = 1/ρ _R + sinβ/R _R −r …(40), and by substituting equations (40) and (30) into equation (33)′, we can calculate the rolling motion of the linear tooth-shaped cutter. board
Find the shape of P _K.

In addition, the integral of (33)' converts the (ξ, η) coordinate values of point P when φ=0 to (ξ _P0 , η _P0 ), and
It is sufficient to integrate from 0 to φ by setting Ω〓 at that time to _Ω〓0 . If the same relative motion as that between the rolling motion plate of the cutter with the linear tooth profile obtained in this way and the rolling motion plate of the rigid gear or wave gear is applied to the cutter and the workpiece gear, the rigid gear or wave gear A tooth profile can be created. Based on the calculations, the rolling motion plate of the cutter with a linear tooth profile is shown in FIG. The figure also shows the situation when the cutter is fixed and the rigid gear is moved. When the rolling plate P _R of the rigid gear rolls without slipping against the rolling plate P _K of the cutter, the tooth profile C _R of the rigid gear is in sliding contact with the cutter C _K , which has a linear tooth profile.

[Brief explanation of drawings]

Figures 1a and b are cross-sectional views showing parts of different wave gear devices, Figure 2 is an explanatory diagram of the coordinates of the wave gear, Figure 3 is an explanatory diagram showing the relationship between the tooth profile and the rolling motion plate, Figure 4 is an explanatory diagram showing the movement of one tooth of the wave gear, Figure 5 is an explanatory diagram showing the meshing of the rigid gear and the wave gear, and Figures 6 a to c are the rolling movement plates of the rigid gear and the wave gear. An explanatory diagram showing a different example; Fig. 7 is an explanatory diagram showing the meshing of a rigid gear with an involute tooth profile and a wave gear; Fig. 8
The figure is an explanatory diagram showing the tooth profile of a wave gear that meshes with a rigid gear having an involute tooth profile. Figure 9 is an explanatory diagram showing the motion of the wave gear that meshes with the rigid gear.
The figure is an explanatory diagram showing the relationship between the tooth profile of the rigid gear, the wave gear, and the cutter, and the rolling motion plate. Figure 11 is an explanatory diagram showing the positional relationship between the rigid gear and the cutter. Figure 12 is an explanatory diagram showing the relationship between the tooth profile of the rigid gear and the cutter. Figure 12 is an explanatory diagram showing the relationship between the tooth profile of the rigid gear and the cutter. FIG. 2 is an explanatory diagram showing the motion of a rigid gear. 1,11...rigid gear, 2,12...wave gear, 3,
13...Wave generator.

Claims (1)

[Claims] 1 One side is a rigid gear made of a rigid body that does not deform, and the other side is a wave gear that moves in a wave-like manner,
A wave generator that generates a wave motion in the wave gear meshes the rigid gear and the wave gear with their plurality of wavy convex portions, and at this time, the rigid gear and the wave gear between the adjacent convex portions are engaged with each other. By setting a difference in the number of teeth, a rigid gear and a wave gear can be meshed with each other during generation gear cutting in a wave gear device that allows relative movement between the rigid gear and wave gear as well as the movement of the meshing part. The shape of a rolling plate that makes the same relative movement as each of a pair of teeth is a locus drawn on a plane where the instantaneous center of the relative movement of the teeth is fixed to each tooth, and the common method of both tooth profiles at the meshing point of the teeth is calculated. Under the condition that the line passes through the contact point of the rolling plate, determine the tooth profile of the rigid gear and wave gear, and when cutting the rigid gear or wave gear, the line passes through the contact point of the rolling plate, and when cutting the rigid gear or wave gear, the line passes through the contact point of the rolling plate. The cutting edge of the cutter is in common contact with the
A third rolling motion plate that contacts the rolling motion plates of both gears at the same contact point is defined as a rolling motion plate of a rigid gear or a strain wave gear and the third rolling motion plate mentioned above, assuming that the rolling motion plates of the rigid gear or wave gear and the third rolling motion plate of the gears move in the same manner relative to each other. A generating gear cutting method for a gear for an acceleration/deceleration drive machine, characterized in that generating gear cutting is performed by applying relative motion to the cutting blade when rolling contact occurs.