JPS6314216B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Field of Application] The present invention relates to 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] An object of the present invention is to provide a gear of a wave gear device used in an acceleration/deceleration drive machine, which has an appropriate tooth profile determined based on sufficient analysis. be.

[Means for Solving the Problems] In order to achieve the above object, the gear of the present invention has one of the gears as a rigid gear that does not deform (referred to as a "rigid gear" in this specification), and the other as a rigid gear that does not deform. A gear that moves in a wave pattern (referred to as a "wave gear" in this specification) is used, and a mechanism that generates wave motion in the wave gear (referred to as a "wave generator" in this specification) is used to achieve the above. By meshing a rigid gear and a wave gear with their plurality of wavy convex portions, and creating a difference in the number of teeth of the rigid gear and wave gear between adjacent convex portions, movement of the meshing portion is achieved. In a wave gear device that enables relative movement between a rigid gear and a wave gear, a virtual motion plate (this specification) that 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 (In books, it is called a "rolling motion plate." is constructed by forming the tooth profiles of the rigid gear and the wave gear under the condition that the rolling motion plate passes through the contact point of the rolling plate.

[Function] The tooth profiles of the rigid gear and strain wave gear that mesh with each other have been given an appropriate shape through thorough analysis, so the meshing of these gears is extremely smooth, and the operation as an increase/decrease drive is stable. It will be held on.

[Effects of the Invention] Since the wave gear device meshes smoothly, it is possible to obtain an acceleration/deceleration drive machine with excellent operating performance, load capacity, and service life.

[Example] Hereinafter, an example of the present invention will be described 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.
The internal gear is a wave gear 12, and the wave gear 12 is a wave gear 12.
Wave generator 1 equipped with rollers 14, 14 on the outside of
3 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 the coordinate system fixed to each tooth of the wave gear, the point M _i on the neutral line
A rectangular coordinate system (M _i − u _i , _{v i} where i is the number of the tooth) has the tangent _u i at the abscissa and the normal V _i (which passes through the center of the tooth) as the ordinate. think. At this time, we make the following assumptions.

When the 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 Fig. 3, the tooth profile
If 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 profile at the meshing point C of the teeth
are rolling motion plates P ₁ , P ₂ that perform the same relative motion
The tooth profile can be determined by giving the mechanistic requirement that the tooth pass through the rolling contact point (instantaneous center) P.

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.
Linear motion can thereby be easily understood.

Now, it is assumed that the rigid gear and the wave gear can each rotate around the same fixed center. It is assumed that the wave gear performs wave motion due to the rotation of the wave generator at the same time as the rotational motion, has n convex portions, and meshes with the rigid gear near the apex of each convex portion. . 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 wave gear has a neutral line with a diameter d _n before deformation.
Gear Z _w is a cylindrical gear, and the neutral line does not change its length due to deformation and becomes a reference pitch curve, meshing at the same pitch as the pitch on the reference pitch circle of the rigid gear. shall be taken as a thing. Normally, the number of teeth Z _w and the number of teeth Z _R are not equal, and Figure 1 a is
This is the case where Z _w <Z _R , and b in the same figure is the case where Z _w > Z _R.

In this case, the wave generator is considered to be a non-circular cam with n convex parts, and its neutral line is fitted inside a thin wave gear without expanding or contracting, and the rotation of the cam generates a wave in the wave gear. Consider the case of FIG. 1a in which motion is generated, and consider 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, rotate the non-circular cam (wave generator) so that the apex of the convex part moves by the number of teeth Z of the rigid gear, and then suppose that the apex M ₀ moves to point M, and examine this trajectory. .

Assuming that the peak of the convex part of the neutral line of the strain wave gear moves to point Q as the cam rotates, at the beginning (O-x,
The coordinates (O-
X, Y) rotate as shown in FIG. 4, and 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, the number of teeth of the wave gear between points M and Q is also Z, and the pitch is πd _n /Z _w at the neutral line l. , 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(θ)
Assuming that is a function with a period of 2π/n, if this is generally expressed as a Fourier series, it becomes as follows.

here, If the length of the arc from the apex of the convex part of this curve to the angle θ is S, then S=∫〓 ₀ √{()} ² +{′()} ² dθ……(7
) becomes.

In the end, 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
+ {f′(θ)} ² dθ……(8).

However, from now on, the positive angle is clockwise, φ is the angle formed by the long axis with the y-axis as the reference, and 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 = r sin (φ + θ) ... (9) y _M = r cos (φ + θ)} becomes.

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 motion 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 respect to the radius vector MO, then μ can be obtained from −tan μ=1/r dr/dθ (11).

As a result, the (M-u, v) coordinate is translated by (x _M , y _M ) and rotated by ψ with respect to the (O-x, y) coordinate.

The coordinate conversion formula is {u=(x−x _M )cos(−ψ) +(y−y _M )sin(−ψ) ……(12) u=(y−y _M )cos(−ψ) − (x−y _M ) sin (−ψ)}.

Tooth profile solution In Figure 5, the rigid gear C _R and wave gear C _W are C
Suppose that the points are engaged. Now, when the cam is moved slightly, both gears are centered at point P (momentary center)
If it moves relative to
Even when observed from the coordinates (O-x, y) fixed to the rigid gear C _R , the coordinates (M-u, y) fixed to the wave gear C _W are
Even when observed from point v), it should appear to be stationary.

Expressing this in a formula, consider the (x, y) coordinate values (x _p , y _p ) and (u, v) coordinate values (u _p , v _p ) of point P as fixed points, and use formula (12) as φ When differentiated by, 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. By substituting this into x and y in equation (12), we get (u _P ,
v _P ) can also be found.

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

In the end, solving the tooth profile comes down to the problem of finding the other tooth profile that is conjugate to the tooth profile that is fixed on one of the rolling plates just found.
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.

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

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 follows.

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).

Determining the diameter d _n of the neutral line before the wave gear is deformed, we get: 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, it is assumed that the maximum diameter d+δ of the neutral line of the wave gear 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 is as follows:
It just corresponds to the standard gear of the involute gear, and the state of λ≠1 corresponds to the meshing of the shifted gear.

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

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

Figure 6 a, b, and c take the tooth ratio Z _R /Z _W = 1.1 as an example,
The rolling motion plates P _R and P _W of the rigid gear and wave gear are shown for λ = 1.0, λ < 1.0, and λ > 1.0, respectively. From the time when the tooth of the wave gear is located at the apex of the convex portion, Convex non-circular cam to rigid gear φ
It shows the state rotated by (=20 ⁰ ). As can be seen from equations (20) and (21), this rolling motion plate is
It has a shape that approaches a certain asymptote at dψ/dθ→0. Then, these perform a rolling contact movement without slipping, and the contact point is at point P in FIGS. 6a, b, and c. In addition, before the wave gear is deformed, that is, when the neutral line is circular, the coordinate position of the rotation center O of the gear in the coordinates (Mu, v) fixed to the teeth is O', and the rigidity of M and O' is The loci L _M and L _O ′ for the gear are shown. At this time, point M and point O′ are
Since it performs the same relative motion as P _W , the normal to the locus L _M or L _O ' set at point M or O', respectively, passes through point P.

-2 Tooth profile of a strain wave gear when the rigid gear has an 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 of a rigid gear, and find its conjugate counterpart. An example in which the tooth profile is that 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 . Then, the tooth profile of the wave gear that meshes with it is tooth profile C _W , and now tooth profile C _R and tooth profile C _W are at point C.
Assuming that the teeth are in mesh at point C, the common normal T of the tooth profile set at point C passes through the rolling contact point P of the rolling plate that makes the same relative movement as the tooth profile C _R and the tooth profile C _W , and at the same time, the involute gear It touches the base circle of at point E.

Now, let the coordinates fixed to the teeth of the rigid gear whose y-axis is the axis passing through the center of the teeth be (O-x, y), and find the coordinate values (x _c , y _c ) of point C at those coordinates.

The angle γ _R that OP makes 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 /√ _P2 + _P2 ) ...(23) becomes. However, x _P and y _P are the (x, y) coordinate values of point P, which are given by equation (20).

Also, if the half angle of tooth groove width on the base circle is σ _R , 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) In the end, becomes.

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

The _coordinates ( _M
- u, y), the tooth profile of the strain wave gear can be determined. That is, when the x and y coordinate values x _c and y _c of equation (12) are substituted, u and v become the tooth profile to be found.

Fig. 8 shows the number of teeth Z _W = 22, pressure angle 20°, standard involute tooth profile C _R for a rigid gear with no backlash and λ = 1 _.
The tooth profile _CW of 20 strain wave gears is shown based on a calculation example.

In addition, in the same figure, the tooth profile _Cs of a standard involute gear with a number of teeth of 20 and a pressure angle of 20° that meshes with a rigid gear is shown by a dotted line. From this, it can be seen that the tooth profile _CW of the wave gear has a reduced tooth thickness at the tooth tip and tooth 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.

[Brief explanation of the drawing]

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 meshing with a rigid gear having an involute tooth profile, and FIG. 9 is an explanatory diagram showing the motion of the wave gear meshing with the 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. In a wave gear device that allows relative movement between a rigid gear and a wave gear by providing a difference in the number of teeth as well as movement of the meshing part, each of a pair of teeth of the rigid gear and wave gear that mesh with each other. The shape of a rolling motion plate that performs the same relative motion as , is set as a locus drawn by the instantaneous center of the relative motion of the teeth on a plane fixed to each tooth, and the common normal of both tooth profiles at the meshing point of the teeth is the same as the above rolling motion. A gear for an increasing/decelerating drive machine, characterized in that the tooth profile of the rigid gear and wave gear is formed under the condition that the gear passes through a contact point of a moving plate.