JP2719780B2 - Gears for acceleration / deceleration drive - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to a gear for an acceleration / deceleration drive,
More specifically, the gears are provided with internal and external gears meshing with each other, one of which is a rigid gear made of a rigid body that is not deformed, and the other is a soft gear that performs wavy motion. In addition, the number of teeth of the hard gear and the soft gear between the adjacent meshing portions is different, and the wave generator generates a wave motion on the soft gear and moves the meshing position of the hard gear and the soft gear, The present invention relates to a gear for an accelerating / decelerating drive device (hereinafter, this accelerating / decelerating drive device is referred to as a “wave gear device”) in which a hard gear and a soft gear are relatively rotated with the movement. [Prior Art] A linear tooth profile or an involute tooth profile has been used as a tooth profile of a hard gear and a soft gear in a conventional wave gear device. However, the tooth profile conforms to the conventional common sense of the same module and the same reference pressure angle obtained based on the approximate analysis result when the reduction ratio is large. In a hard gear and a soft gear in a wave gear device, since correct meshing is not performed with such a conventional tooth profile, one of the present inventors determined a tooth profile based on a strict gear meshing theory, And Japanese Patent Application Laid-Open No. 61-228142. The above proposal describes a method of analyzing the motion of the wave gear device and the meshing of the teeth to obtain the tooth profile of the hard gear and the soft gear, and gives the most widely used involute tooth profile as the tooth profile of the hard gear. And a method of finding the tooth profile of the soft gear that meshes with it. That is, the above-described method of finding a tooth profile that performs theoretically correct meshing involves, in the above-described wave gear device, the shape of a rolling motion plate that performs the same relative motion as each of a pair of teeth of a hard gear and a soft gear that mesh with each other. , The instantaneous center of the relative movement of the teeth is set as a trajectory drawn on a plane fixed to each tooth, under 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 motion plate In addition, the tooth forms of the above-mentioned hard gear and soft gear are formed. However, generating the tooth profile of the theoretically required soft gear has some problems in that a complicated mechanism is required for the generating device. [Problems to be Solved by the Invention] The present inventor has conducted a rigorous analysis in consideration of approximating the tooth profile of a soft gear that meshes with a hard gear having an involute tooth profile with an involute tooth profile that is currently most frequently used. As a result, they found that it was effective to engage involute gears with different tooth sizes (modules) and reference pressure angles, which were not common sense in the past. Based on such knowledge, the present invention attempts to approximate the tooth profile of a gear for a wave gear device with an involute tooth profile closest to a tooth profile based on a strict gear meshing theory, thereby simplifying and facilitating creation of the tooth profile. Things. [Means for Solving the Problems] The acceleration / deceleration drive gear of the present invention for achieving the above object is the wave gear device described above, wherein the rigid gear and the soft gear meshing with each other have an involute tooth profile, and the rigid gear and the soft gear Since the common normal of the tooth profile at the gear meshing point touches the base circle of the soft gear, the size of the base circle of the soft gear is determined, and the half thickness of the tooth thickness on the base circle of the soft gear is determined. , The reference pressure angle, and the dislocation coefficient, one of the three design parameters is given to determine the remaining two, so that the tooth profile of the soft gear can be changed from the involute tooth profile of the hard gear to an involute having a different module and pressure angle. It is characterized by approximating a tooth profile that theoretically engages correctly. [Operation] Since the gears in the wave gear device having the above-described configuration are theoretically close to correct tooth shapes, the gears are smoothly engaged with each other, and the tooth shapes are easily and easily formed with a normal involute gear cutting machine. It becomes possible. Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. The wave gear device shown in FIG. 2 (a) includes an internal gear and an external gear having slightly different numbers of teeth (the number of internal teeth> the number of external teeth). A rigid gear 1 made of a rigid body that does not deform, and the other external gear is a thin hollow cylindrical soft gear 2 that can bend and deform in the radial direction.
Is deformed in the radial direction by the rollers 4, 4 of the wave generator 3 functioning as a cam rotatably disposed therein, so that the hard gear 1 and the soft gear 2 are formed at a plurality of convex portions of the soft gear. At the same time, the number of teeth of the hard gear and that of the soft gear between the adjacent meshing parts are set to be different, and the meshing parts are moved by the rotation of the wave generator 3 so that the rotation of the wave generator 3 And rotate in the opposite direction. That is, for example, when the wave generator 3 is rotated with the rigid gear 1 fixed, a deceleration output can be obtained from the soft gear 2. FIG. 2 (b) shows a different example of the wave gear device. Contrary to FIG. 2 (a), the outer gear is a hard gear 11, the inner gear is a soft gear 12, and the soft gear 12 is Roller 1 outside
A wave generator 13 provided with 4, 14 is rotatably provided. When the hard gear is fixed, the soft gear rotates in the same direction as the wave generator. In the above-described wave gear device, considering that the soft gear is made of a thin flexible material, the thickness of the bottom portion is extremely thin compared to the tooth portion, so that the deformation occurs exclusively at the bottom portion. it is conceivable that. That is, each tooth moves relatively, but each tooth can be considered a rigid body. Prior to the description of the embodiment, the above-described method of finding a tooth profile that performs theoretically correct engagement will be described in detail along with the analysis process. I. Basic conditions now, as shown in Figure 6, a coordinate system fixed to one tooth one tooth of soft gear abscissa tangent u _i at the point M ₁ of the neutral line, and the ordinate the normal v _i (M ₁ −u _i , v _i : i is the tooth number). If each tooth is considered to be a rigid body, it is possible to determine the tooth profile by examining the movement of the teeth according to a general tooth profile solution.
That is, as shown in FIG. 7, the tooth profile C ₁ and the rolling motion plate
If P ₁ is integrated and the tooth profile C ₂ and the rolling motion plate P ₂ are integrated, the common normal line T of the tooth profile at the tooth meshing point C will be the rolling motion plates P ₁ , P performing the same relative motion. _Two
The tooth profile can be determined given the mechanistic requirement of passing through the rolling contact point (instantaneous center) P. II. Motion of the soft gear The soft gear performs a wave motion due to the rotation of the wave generator simultaneously with the rotational motion, and has n convex portions, and meshes with the hard gear near the apex of each convex portion. Suppose you have Here, rigid gear, the reference pitch diameter d _o, a cylindrical gear tooth number Z _R, flexible gear, the neutral line diameter before deformation d _m,
A cylindrical gear tooth number Z _W, and, the neutral line is without changing its length by deformation, become the reference pitch curve, and which are engaged at the same pitch as the pitch of the reference pitch circle of the rigid gear I do. It is assumed that the wave generator is a non-circular cam having n convex portions, and the case of FIG. 2 (a) in which a wave motion is generated in the soft gear by rotation of the cam will be considered. At some point, the rectangular coordinates (O
-X, consider y), y-axis is assumed to pass through the protrusion apex M _o of the neutral line of the flexible gear. Counting from this state, the number of teeth of the hard gear Z
The non-circular cam (wave generator) is rotated so that the peak of the convex portion moves by the distance, and the trajectory is examined assuming that the vertex _Mo has moved to the point M at that time. With the rotation of the cam, the convex vertex of the neutral line of the soft gear
, The coordinates (O-X, Y) fixed to the cam that coincided with the beginning (O-x, y) are rotated as shown in FIG. φ is equal to the angle M _o OQ, Becomes the neutral line The arc length S of Becomes Here, the shape of the neutral line l after the deformation is such that the origin is the rotation center O of the shaft, the angle from the axis (hereinafter referred to as the long axis) connecting the convex vertex Q and the point O is θ, and the distance from the origin 0. Is r,
It is assumed to be represented by the following polar coordinates. r = f (θ)... Now, the non-circular cam has n convex portions, and f (θ) is 2
Assuming that the function has a period of π / n, this can be generally expressed by a Fourier series as follows. here, (K = 1, 2,...). Assuming that the length of the arc from the apex of the curve to the angle θ is S, Becomes In the end, if we put the equation and the equation as equal and include the sign, Becomes Hereinafter, the angle is positive in the clockwise direction, φ is the angle formed by the long axis with respect to the y-axis, and θ is the angle formed by the moving radius MO with respect to the long axis. Now, let the (x, y) coordinates of the point M on the neutral line 1 be (x _M , y _M )
Then Becomes Next, in FIG. 8, the coordinates fixed to the teeth, that is, the orthogonal coordinates (M-u, v) with the tangent u at the point M on the neutral line l as the abscissa and the normal v as the ordinate, and the rigid gear Investigate the relative motion with the fixed coordinates ((O−x, y). Assuming that the angle between the v axis and the y axis is ψ with respect to the y axis, ψ = φ + θ + μ... And the angle μ formed by the v axis is Can be obtained by After all, the (M−u, v) coordinate is translated by (x _M , y _M ) with respect to the (O−x, y) coordinate and rotated by ψ. Becomes III. Solution of Tooth Profile In FIG. 9, it is assumed that the hard gear C _R and the soft gear C _W mesh at point C. Now, when slightly moved cams, if the gears are intended to movement about (instant center) point P, the point P, the coordinates fixed rigidly gear C _R (O-x,
be observed from y), the coordinates fixed to the flexible gear C _W (M-u,
If you observe from v), you should see it stopped. When this is represented by an equation, the (x, y) coordinate value (x _P ,
y _P) and (u, v) coordinates (U _P, considered fixed point V _P), Differentiating equation with phi, From the formula, Becomes This expression for x, by substituting the _{y, (U P, V P} ) is also determined. Now, if the wave generator (cam) is rotated and the locus of the point P is obtained, the locus becomes the shape of the rolling motion plates P _R and P _W which perform the same relative motion as each tooth. In the end, the solution of the tooth profile is reduced to a problem that, when a fixed tooth profile is given to one of the rolling motion plates just obtained, a tooth profile conjugate with the given tooth profile is obtained. The mechanistic requirement at that time is that the common normal T at the tooth meshing point C is
Passing through the contact point P of the rolling motion plate. IV. Specific Calculation Examples IV-1. Shape of Rolling Motion Plate As a result of the above analysis, if the shape of neutral line l after deformation of the soft gear is given by the formula The relationship between the relative rotation angles was found, and it was found that the shape of the rolling motion plate could be obtained from the formula and the formula. Therefore, a specific calculation will be performed by taking the shape of the cam currently used in the wave gear device as an example. The shape of the non-circular cam having two convex portions resembles an ellipse, and assuming that there is no gap between the soft gear (flex spline) and the cam due to the load, the neutral line of the soft gear The shape is represented by the following polar coordinates. This is an even function that is symmetric about the long axis and has a period of π, and is the simplest form of the equation. When the diameter d _m of the neutral line before the soft gear is deformed, Becomes Next, the pitch t _o = πd _o / Z _R on the reference pitch circle of the hard gear (circular spline) and the pitch on the neutral line of the soft gear
Since t _m = πd _m / Z _m is equal, There is a relationship. Here, the maximum diameter d + [delta] and rigid gear reference pitch diameter d _o of the neutral line of the flexible gear, and those connected with the coefficient as follows: lambda. d + δ = λd _o ... λ = 1.0, that is, the state where the reference pitch circle of the hard gear is in contact with the neutral line at the point of its maximum diameter corresponds to the standard gear of the involute gear. From the formula, And the equation giving the deformation amount δ is obtained. The equation is differentiated by φ, but this is the same even when differentiated by θ. And the shape of the rolling motion plate is determined. IV-2. Tooth profile of wave gear when rigid gear has involute tooth profile Next, an example in which an involute curve is given as a tooth profile of a hard gear and a mating tooth profile conjugate to the tooth profile of a soft gear will be described. In Figure 10, tooth profile C _R is a tooth of the rigid gear, the base circle radius is involute curve and r _gR. And the tooth profile of the soft gear that meshes with it is the tooth profile _CW .
Assuming that the tooth profile C _R and the tooth profile C _W are engaged at the point C, the common normal T of the tooth profile at the point C is the rolling contact of the rolling motion plate which performs the same relative movement as the tooth profile C _R and the tooth profile C _W. At the same time as passing through the point P, it contacts the base circle of the involute gear at the point E. Now, let (Ox, y) be the coordinate fixed to the tooth of the hard gear whose axis is the y-axis passing through the center of the tooth, and C
Find the coordinate values (x _c , y _c ) of the point. Angle gamma _R which OP makes with the y axis, when the ^{_{γ R = tan -1 (x P}} / y P) a ... angle POE tau _R, Becomes Where x _P and y _P are the (x, y) coordinate values of point P,
Given by the formula. When the half width of the tooth groove width on the base circle is σ _R , However, alpha _O is the reference pressure angle x _R of the involute tooth is shift coefficient. From the nature of involute, Therefore, ν _R = γ _R ± ｛τ _R −tan ⁻¹ (± γ _R + τ _R + σ _R ) Becomes The coordinates x _c, coordinates with a fixed y _c a flexible gear (M-u, v)
Observing from, the tooth profile of the soft gear is determined. That is, u, v when the coordinate values x _c , y _c are substituted for x, y in the expression are the tooth profile to be obtained. Next, a description will be given of an embodiment of the present invention in which an involute tooth profile closest to the above-described theoretically correct tooth profile is approximated. Now, when the soft gear is in a circular state without deformation,
It is assumed that the theoretical tooth profile of the soft gear substantially coincides with and overlaps the involute tooth profile having the same number of teeth. The gear for the wave gear device of the present invention, as described above,
The involute tooth profile most similar to the tooth profile based on the strict gear meshing theory is used. Therefore, the shape of the gear with the most approximate involute tooth profile (hereinafter referred to as a soft involute gear) will be described below. . Referring to FIG. 3, coordinates (Ox, y) are coordinates fixed to the involute toothed gear 1 and the center O of the gear.
, And the y-axis passes through the center of the tooth groove of the hard gear. The coordinates (OX, Y) are coordinates fixed to the wave generator 3, and the Y axis passes through the vertex of the meshing convex portion. Now, with the Y-axis rotated by φ with respect to the y-axis, the teeth of the hard gear with the y-axis at the center of the tooth groove are assumed to mesh around the center of the teeth of a certain soft gear. . The coordinates (M−u, v) are coordinates fixed to the teeth of the soft gear 2, the origin is a point M on a soft reference pitch curve (neutral line of the soft gear deformed into a convex non-circle), and the u axis is The tangent to the soft reference pitch curve and the v-axis pass through the center of the teeth of the fixed soft gear. Assuming that the teeth of this soft gear have an involute tooth profile, the center O 'of the involute gear is on the extension of the v axis, and the length of M0' is 1 / the diameter d _OF when the soft reference pitch curve is circular. Equal to 2. From this, the (x, y) coordinate value (x ₀ ′,
y ₀ ′) is Becomes Where (x _M , y _M ) is the (x, y) coordinate value of point M,
ψ is the angle between the y-axis and the v-axis, and represents the shape of the soft reference pitch curve 極 in polar coordinates where r is the radial radius and θ is the argument, and μ
Is the angle between the v axis and the radial radius OM, (x _M , y _M ) and ψ are given by the following equations. ψ = θ−φ + μ (3) Now, assuming that the common normal line T of the tooth profile established at the meshing point C between the hard gear and the soft gear is in contact with the base circle of the hard gear at the point E, Since the base circle of the soft involute gear is in contact with the base circle at point E ', the size of the base circle of the soft involute gear is determined. That is, the base circle radius ▲
If ▼ is r _gF , r _gF = ▲ ▼ _{cosα bF} (4) Here, α _bF is an angle between O′C and O′E ′ and is given by the following equation. α _bF = ± ξ ± γ _R + α _b (5) Further, _assuming that the half angle of the tooth thickness on the base circle of the soft involute gear is σ _F , σ _F = _{tanα bF} − (± ψ ± γ _R + α _b ) (6) Here, the coordinates (x _c , y _c ) of the meshing point C are (Ν _R is the angle between OC and the y-axis), so that O′C and ξ are also obtained. The gamma _R, alpha _{b ^{are, γ R = tan -1 (x}} P / y P) ··· (8) From. Here, x _P and y _P are (x, y) coordinate values of the pitch point P, and r _gF is a base circle radius of a hard gear that is an involute gear. Thus, the base circle radius r _gF of the soft involute gear and the half thickness σ _F of the tooth thickness on the base circle are obtained, and the module m _F ,
Reference pressure angle alpha _OF, among the three parameters of addendum modification coefficient x _F, any one remaining two Given is determined. Next, a practical method of approximating the theoretical tooth profile of the soft gear meshing with the rigid gear with the involute tooth profile with the involute tooth profile will be specifically described. FIG. 1 shows a state where the y-axis and the v-axis at the coordinates (0-x, y) and (Mu, v) described above overlap. As mentioned earlier, a soft reference pitch curve is determined as a neutral line of the flexible gear, d _oF and root circle diameter d _fF of flexible gear is determined. Further, the number of teeth Z _R of the rigid gear, given a number of teeth Z _F of the flexible gear, the relative reference pitch circle diameter d _oR Tsuyoshi gear is determined. Now, the shape of the soft reference pitch curve is such that r is radial, θ is declination,
_Assuming that d and δ are constants and expressed in a shape similar to an ellipse as shown below, a deviation coefficient λ = (d + δ) / d _oR which is a ratio between the maximum diameter d + δ and _doR is given. d and δ are determined. Then, Tsuyoshi the gear gives the top drama c _R of, determines the tip diameter d _aR rigid gear. _Further , if any two of the tooth groove / tooth thickness ratio e _{R on} the _{addendum circle of the hard} gear and the dislocation coefficient X _R , the reference pressure angle α _oR , and the module m _R are given, the remaining one is determined. . Then, Tsuyoshi given a tooth depth h _R of the gear, the root circle diameter d _fR rigid gear, also given a top drama c _F of flexible gear, the addendum circle diameter d _aF of flexible gear is determined. Finally, if any one of m _F , α _oF and X _F of the soft gear is given, the remaining two are determined. FIG. 4 illustrates the relationship between the above-mentioned design parameters and the parameters obtained sequentially by giving the design parameters. Table 1 shows the results calculated for the specific examples according to the above procedure. The dislocation coefficient was set to zero for both the hard gear and the soft gear. Also, the reference pressure angle of the hard gear can be given appropriately, but depending on how the value is selected, the contact ratio between the hard gear and the soft gear changes as shown in FIG. Therefore, a reference pressure angle of 28.5 degrees was selected to maximize the contact ratio. In this case, the geometric contact ratio is 1.0
However, the actual contact ratio when a load is applied is 1.0 or more because the soft gear is slightly bent. Table 2 shows the difference between the radial position of the soft gear in the above design example and the theoretical tooth profile at that position. In the above wave gear device, the soft gear may have an involute tooth profile, and the theoretical tooth profile of the rigid gear meshing with the soft gear may be approximated by an involute tooth profile. Normally, a pair of involute gears meshing with each other
Created with tools of the same module and the same reference pressure angle.
However, according to the above-described method, when the hard gear and the soft gear are involute gears, they are created by using different modules and tools having different reference pressure angles.
Although such a method cannot be considered with common sense, it is possible to obtain a gear that meshes smoothly. [Effects of the Invention] As described above in detail, according to the wave gear device of the present invention, since the gear is theoretically close to the correct tooth profile, the gear meshes smoothly, and the driving performance, load capacity, A wave gear device excellent in life and the like can be obtained, and products can be provided simply and inexpensively by making each gear in the gear device an involute tooth profile that is easy to manufacture.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is an explanatory view of design parameters in gears of a wave gear device according to the present invention, and FIGS. 2 (a) and (b) are cross-sectional views each showing a part of a different wave gear device. Figure, third
The figure is an explanatory diagram of the coordinates and symbols of the hard gear and the soft gear,
FIG. 4 is an explanatory diagram showing the relationship between the design parameters of the soft gear and the parameters sequentially obtained by giving the design parameters. FIG. 5 is a graph relating to the meshing ratio of the hard gear and the soft gear, and FIG. , FIG. 7 is an explanatory view showing the relationship between the tooth-shaped biasing motion plates, FIG. 8 is an explanatory view showing the movement of one tooth of the soft gear, and FIG. 9 is an explanatory view showing the engagement between the hard gear and the soft gear. FIG. 10 is an explanatory view showing the engagement between a hard gear having an involute tooth profile and a soft gear. 1,11… Hard gear, 2,12… Soft gear, 3,13… Wave generator.

   ────────────────────────────────────────────────── ─── Continuation of front page    (72) Inventor Junji Nakatani               1-49-10 Oi, Shinagawa-ku, Tokyo Hitachi               Taisei Building Harmonic Dora Co., Ltd.               In Eve Systems                    Panel     Referee Isamu Hama     Judge Yasuhiko Suzuki     Referee Masatoshi Koike                (56) References JP-A-61-228142 (JP, A)                 Tokiko 45-41171 (JP, B1)                 USSR Patent 750182 (SU, A)

Claims (1)

(57) [Claims] Equipped with internal and external gears that mesh with each other, one of which is a rigid gear made of a rigid body that does not deform, and the other is a soft gear that performs wavy movement, and both gears mesh at multiple places by deformation of the soft gear, and are adjacent The difference in the number of teeth between the hard gear and the soft gear between the meshing parts is provided, the wave generator generates a wave motion in the soft gear, and the meshing position between the hard gear and the soft gear is moved. In a speed increasing / decelerating drive in which the gear and the soft gear rotate relatively, the gear and the soft gear meshing with each other have an involute tooth profile, and the gear tooth has a common normal line at the meshing point between the gear and the soft gear. The size of the base circle of the soft gear is determined from the contact with the base circle of the gear, the half thickness of the tooth thickness on the base circle of the soft gear is determined, and the other design of the module, the reference pressure angle, and the dislocation coefficient By giving one of the parameters and determining the remaining two, the tooth profile of the soft gear is an involute tooth profile having a module and a pressure angle different from that of the involute tooth profile of the hard gear, and a tooth profile that theoretically engages correctly. A gear for an accelerating / decelerating drive, characterized by approximating