TW201350711A - Rigid annular gear and flexible planetary gear of harmonic speed reducer and manufacturing method thereof - Google Patents

Abstract

This invention relates to a rigid annular gear and a flexible planetary gear of a harmonic speed reducer and a manufacturing method thereof. The manufacturing method of the rigid annular gear comprises a preparation step and a rigid annular gear fabrication step. After that, a flexible planetary gear fabrication step is performed so as to produce a flexible planetary gear. In the preparation step, a hobbing cutter is prepared, with the longitudinal cross-section of the gear cutter surface being formed as the curved line of a generating hobbing cutter, wherein the curved line equation of the generating hobbing cutter is defined by any of the following mathematical formulae (1) to (5). Using the aforementioned method, a rigid annular gear and a flexible planetary gear of a harmonic speed reducer can be made. Thus, this invention achieves the advantages and efficacies of low relative slip ratio, low abrasion, low temperature rise, low contact stress, high speed reduction ratio, high efficiency and low energy consumption.

Description

Rigid ring gear and flexible planetary gear of harmonic reducer and preparation method thereof

The invention relates to a rigid ring gear and a flexible planetary wheel of a harmonic reducer and a method for manufacturing the same, in particular to a rigid ring gear and a flexible planetary wheel with a toothed continuous harmonic curve reducer and a method for manufacturing the same, It has the advantages and functions of low relative sliding ratio, low wear, low temperature rise, low contact stress, high reduction ratio, high efficiency and low energy consumption.

The technology of the traditional harmonic gear (or harmonic reducer, English harmonic drive) has long been known. The main mechanism has harmonic generators, flexible planetary gears and rigid ring gears from the inside to the outside. Its harmonic generator is like the sun gear of a planetary gear train. The center of rotation is fixed, with a non-circular pitch curve and pushing the flexible planet wheel to deform.

In the conventional harmonic reducer, the tooth shape of the flexible planetary gear and the rigid ring gear is mostly a conventional involute tooth type, as shown in the first figure is an internal mesh involute tooth profile, which includes a rigid ring gear tooth profile. Line 91 and flexible planet gear line 92.

Next, as shown in the second figure, another conventional harmonic reducer of the U.S. Patent No. 4,974,470 has an S-shaped tooth profile, and the tooth profile is formed by joining three segments of curves a, b, and c.

In addition, as shown in the third figure, it is a conventional conventional harmonic reducer, that is, US Pat. No. 7,694,607 B2, which proposes a circular arc line a1, a straight line a2, a circular arc line a3, and a circular arc line b1. The straight line b2 and the circular arc line b3 are joined to each other.

However, the tooth shapes of the above two cases are all multi-segment joints, and the theory of inductive meshing is time-consuming and labor-intensive, and the mathematically non-differentiable points (ie, singular points) are easily generated due to the continuous segments.

The key technology of the harmonic gear lies in the design of the tooth profile. The tooth profile is constructed on the circular curve 93 (refer to the first figure) by the envelope equation. The involute tooth profile and the crown circle 94 and the root are constructed. Circle 95 is used for line segment bonding. However, from involute teeth The mathematical model of shape generation can be found:

(1) It is impossible to construct the entire gear tooth shape through an equation, which is a discontinuous continuous tooth shape. The discontinuous continuous tooth shape is easy to generate a discontinuity point (cusp) at the joint, and it is difficult to design the tooth shape meshing overcut. The discontinuity point is also mathematically indivisible, and it is easy to cause jumping during operation.

(2) Due to the discontinuous convex to convex meshing tooth shape, with a large relative sliding ratio, no smooth curvature radius change and a large relative curvature radius, the contact stress of the tooth surface is large, high wear and high temperature rise.

Therefore, it is necessary to develop new technologies to solve the above shortcomings.

The object of the present invention is to provide a rigid ring gear and a flexible planetary gear of a harmonic reducer and a method for manufacturing the same, which have a low relative sliding ratio, low wear, low temperature rise, low contact stress, high reduction ratio, high efficiency, Low energy consumption and other advantages. In particular, the problems to be solved by the present invention include that the conventional device cannot construct the entire gear tooth shape via an equation, the bounce is likely to occur during operation, the contact stress of the tooth surface is large, and the high wear and high temperature rise are caused.

The technical means to solve the above problems are: A method for manufacturing a rigid ring gear of a harmonic reducer, comprising: [a] a preparation step; and [b] a rigid ring gear manufacturing step.

A method for manufacturing a flexible planetary gear of a harmonic reducer, comprising: [a] preparation step; [b] rigid ring gear manufacturing step; [c] flexible planetary wheel manufacturing step.

A rigid ring gear and a flexible planetary gear of a harmonic reducer include a rigid ring gear and a flexible planetary gear, wherein the rigid ring gear and the tooth profile of one of the flexible planetary wheels are : L ₁ =[ x 1 y 1 0] ^T

The other equation of the tooth profile is: L ₂ =[ x 2 y 2 0] ^T

among them:

Where: h is the tooth height coefficient, the minimum value of the range of values is 0, and the maximum value is defined by the following equation:

The tooth height coefficient is between 0 and the maximum value of the above formula; Φ is an input parameter; i is an arbitrary number; m is a modulus; z1, z2 are one of the rigid ring gear and the flexible planetary gear The other number of teeth.

The invention relates to a rigid ring gear and a flexible planetary wheel of a harmonic reducer and a manufacturing method thereof, which comprise two parts of a manufacturing method and a finished product.

Please refer to the fifth to eighth figures. In terms of the manufacturing method, the general method is as follows: a hobbing cutter (a conventional structure, not shown) is first prepared, whereby the hobbing cutter produces a rigid ring gear 21 according to a conventional creation method. The flexible planet gear 22 is then fabricated from the rigid ring gear 21 in accordance with a conventional meshing equation. Of course, the order of the latter two can also be reversed, and the hobbing cutter is first produced, whereby the hobbing cutter produces the flexible planetary gear 22 according to the conventional creation method, and then the flexible planetary gear 22 is in accordance with the conventional meshing equation. A rigid ring gear 21 is produced. Thereafter, in combination with a harmonic generator 23, it becomes a harmonic reducer 20.

Referring to FIG. 4A, a method for manufacturing a rigid ring gear of a harmonic reducer according to the present invention includes: [a] preparation step 11: preparing a hobbing cutter and a rigid annular processing component, the hobbing cutter system Forming a graph of a toothed knives (as shown in the ninth figure), the curve equation of the hobbing cutter is defined by one of the following mathematical formulas (C1) to (C5): f(Φ)= h . g(i.Φ).........(C1)

f(Φ)= h . g(g(i.Φ))............(C2)

f(Φ)= h . g(g(g(i.Φ)))............(C3)

f(Φ)= h . g(g(g(g(i.Φ)))))......(C4)

f(Φ)= h . g(g(g(g(i.Φ))))))......(C5)

Where g(Φ)=sin(Φ); h is the tooth height coefficient, and the minimum value of the range is 0, and the maximum value is defined by the following equation:

The tooth height coefficient is between 0 and the maximum value of the above formula; Φ is the input parameter; i is an arbitrary number, variable circumference on the tooth shape, affecting the tooth shape; m is the modulus; z1 is the rigidity The number of teeth of the ring gear; for example, a set of data examples, for example: modulus m = 0.3, input parameter Φ = (2π) x number of teeth; i = m / 2 = 1.5; and the tooth height coefficient h is about 0.3. In this example, the number of teeth of the rigid ring gear in the outer ring is 82 teeth, and the number of teeth of the flexible planet gear in the inner ring is 80 teeth.

[b] Rigid Ring Gear Manufacturing Step 12: The rigid ring gear to be machined is cut by the aforementioned hobbing cutter using a conventional generating method to form a rigid ring gear 21 of a harmonic reducer 20.

When the foregoing steps are completed, the rigid ring gear 21 of the harmonic reducer 20 is fabricated.

Thereafter, the following steps (as shown in FIG. 4B) can also be performed: [c] flexible planetary gear manufacturing step 13: the tooth shape of the rigid ring gear 21 of the harmonic reducer 20, using a conventional meshing equation, A flexible circular to-be-processed component is machined to form the flexible planet gear 22 of the harmonic reducer 20.

When this step is completed, the flexible planetary gear of the harmonic reducer 20 is made. twenty two.

When the manufactured rigid ring gear 21 and the flexible planetary gear 22 are assembled with a conventional harmonic generator 23, the harmonic reducer 20 is obtained. Referring to the fifth, sixth, seventh and eighth figures, respectively, a perspective view, a front view, a side view and an exploded perspective view of the harmonic reducer 20 are shown.

In more detail, the equation (L1) of the rigid ring gear tooth profile of the aforementioned harmonic reducer 20 is: L ₁ = [ x 1 y 1 0] ^T

among them:

Secondly, the equation of the tooth profile of the flexible planetary gear of the aforementioned harmonic reducer is: L ₂ =[ x 2 y 2 0] ^T

Where: z2 is the number of teeth of the flexible planet wheel;

Since the curve equation of the created gear cutter of the present invention is defined by one of the aforementioned mathematical formulas (C1) to (C5). When h=1 and i=1, the tooth shapes defined by the equations (C1) to (C5) are as shown by the curves S1, S2, S3, S4, and S5 of the tenth figure.

If Equation (C5) is selected and control i = 1 is unchanged, and the tooth height coefficients h = 0.5, 1 and 1.5 are changed, the resulting tooth profile is as shown by the curves S6, S7, S8 of the eleventh figure.

If equation (C5) is selected and the tooth height coefficient h = 1 is unchanged, and i = 0.5, 1 and 1.5 are changed, the resulting tooth profile is as shown by the curve S9, S10, S11 of the twelfth figure.

Since the present invention creates a full-closed continuous curved gear, such as a rigid ring gear tooth shape, via a hobbing cutter having a continuous function curve, thereby obtaining a flexible planetary gear tooth shape, thereby obtaining a continuous rotation of the entire circle. Conjugate gear train.

For the analysis of the "sliding coefficient", please refer to the thirteenth figure, wherein the present invention is the case where the equation (C5) is selected (indicated by the curve S12), and the conventional involute tooth profile (with the curve S13). Comparing, from the thirteenth figure, the sliding coefficient of the present invention is maintained at around zero (about plus or minus 0.1). Within) almost pure scrolling. However, the slip coefficient of the conventional involute tooth profile has a large variation, which represents a relatively large relative sliding between the tooth and the tooth. It makes the invention have the advantages of low relative sliding ratio, low wear, low temperature rise, and low contact stress.

Please refer to Fig. 14, in which the equations (C1), (C3) and (C5) of the present invention are compared, and the results (represented by curves S14, S15 and S16, respectively) are only slightly different, and all three are maintained at Near 0, and (C5) is slightly better than (C3), (C3) is better than (C1), but both are excellent. Since (C2) and (C4) have the same properties as the equations (C1), (C3), and (C5), it can be inferred that (C2) and (C4) also have the advantages described in the previous paragraph.

Furthermore, for the analysis of "Relative Radius of Curvature", please refer to the fifteenth figure, in which the equations (C1), (C3) and (C5) of the present invention are compared, and the results are respectively Curves S17, S18 and S19 indicate that all three are maintained between 0.01m and 0.06m, and there is no dramatic change. In other words, the contact stress at the time of contact is low, which also has the advantages of low wear and low temperature rise. In addition, since (C2) and (C4) have the same properties as the equations (C1), (C3), and (C5), it can be inferred that (C2) and (C4) also have the advantages described in the previous paragraph.

In addition, the harmonic reducer originally has the advantages of high reduction ratio, high efficiency and low energy consumption.

Moreover, referring to the sixteenth and seventeenth embodiments, the inner surface of the rigid ring gear 21 of the present invention may also be changed to a concave curved surface or an inner convex curved surface, of course, corresponding to the flexible planetary gear 22. The surface should also be changed to a convex or concave curved surface. That is, the value of the z direction in the two equations ( L ₁ =[ x 1 y 1 0] ^T and L ₂ =[ x 2 y 2 0] ^T ) is modified (not 0). At this time, the two are less likely to produce side sliding or falling off (z-axis direction). Moreover, these two types are also within the scope of protection of the present invention.

Of course, the above method can be achieved by using a hobbing cutter, and can also be achieved by wire cutting. Therefore, the present invention is a rigid ring gear and a flexible planetary gear of a harmonic reducer, which includes a rigid ring gear 21 and A flexible planet gear 22, wherein the equation of the tooth profile of one of the rigid ring gear 21 and the flexible planet gear 22 is: L ₁ =[ x 1 y 1 0] ^T

The other equation of the tooth profile is: L ₂ =[ x 2 y 2 0] ^T

Since x1, y1, x2, and y2 of the above two equations have been previously defined, they will not be described here.

Therefore, the invention has the advantages and effects of low relative sliding ratio, low wear, low temperature rise, low contact stress, high reduction ratio, high efficiency and low energy consumption.

11‧‧‧Preparation steps

12‧‧‧Rigid ring gear manufacturing steps

13‧‧‧Flexible planetary wheel manufacturing steps

20‧‧‧Harmonic reducer

21‧‧‧Rigid ring gear

22‧‧‧Flexible planetary gear

23‧‧‧Harmonic generator

91‧‧‧Rigid ring gear tooth line

92‧‧‧Flexible planetary gear line

93‧‧‧ round curve

94‧‧‧Tooth crown

95‧‧‧ tooth root circle

A1, a3, b1, b3‧‧‧ arc lines

A2, b2‧‧‧ straight line

a, b, c, S1, S2, S3, S4, S5, S6, S7, S8, S9, S10, S11, S12, S13, S14, S15, S16, S17, S18, S19‧‧

The first picture is a schematic diagram of a conventional harmonic reducer with an involute profile.

The second figure is a schematic diagram of the first type of discontinuous tooth harmonic reducer.

The third figure is a schematic diagram of a second type of discontinuous tooth harmonic reducer.

The fourth A picture is a method for manufacturing the rigid ring gear of the harmonic reducer of the present invention

The fourth B diagram is a method for manufacturing the flexible planetary gear of the harmonic reducer of the present invention

The fifth figure is a perspective view of the harmonic reducer of the present invention

Figure 6 is a front view of the harmonic reducer of the present invention

The seventh figure is a side view of the harmonic reducer of the present invention

The eighth figure is an exploded perspective view of the harmonic reducer of the present invention

The ninth diagram is a schematic view of the curve of the hob cutter of the present invention

Figure 10 is a schematic view showing the tooth profile of the curve equations (C1) to (C5) of the indented cutter of the present invention.

The eleventh figure is a schematic diagram of the tooth profile produced by the invention with different tooth height coefficients h

The twelfth figure is a schematic diagram of the tooth form produced by the invention using different arbitrary numbers i

The thirteenth diagram is a schematic diagram of the sliding coefficient of the equation (C5) of the present invention and the conventional involute profile

Figure 14 is a schematic view showing the sliding coefficients of the equations (C1), (C3) and (C5) of the present invention.

The fifteenth diagram is a schematic diagram of the relative curvature radii of the equations (C1), (C3) and (C5) of the present invention.

Figure 16 is a perspective view showing a variation of the rigid ring gear and the flexible planetary gear of the present invention.

Figure 17 is a perspective view showing a variation of the rigid ring gear and the flexible planetary gear of the present invention.

20‧‧‧Harmonic reducer

21‧‧‧Rigid ring gear

22‧‧‧Flexible planetary gear

23‧‧‧Harmonic generator

Claims (5)

A method for manufacturing a rigid ring gear of a harmonic reducer, comprising: [a] preparing step: preparing a hobbing cutter and a rigid annular component to be processed, the hobbing cutter being a long strip cutter having a gear The longitudinal surface of the surface of the gear cutter forms a curve of a hobbing cutter. The curve equation of the hobbing cutter is defined by one of the following mathematical formulas (1) to (5): f(Φ ) = h . g(i.Φ).........(C1) f(Φ)= h . g(g(i.Φ)).........(C2) f(Φ)= h . g(g(g(i.Φ)))............(C3) f(Φ)= h . g(g(g(i.Φ)))))......(C4) f(Φ)= h . g(g(g(g(i.Φ))))))(C5) where g(Φ)=sin(Φ) h is the tooth height coefficient, and the minimum value of the range is 0. Its maximum value is defined by the following equation: The tooth height coefficient is between 0 and the maximum value of the above formula; Φ is the input parameter; i is an arbitrary number; m is the modulus; z1 is the number of teeth of the rigid ring gear; [b] rigid ring gear manufacturing steps: The aforementioned hobbing cutter cuts the rigid annular component to be processed by a conventional creation method to form a rigid ring gear of a harmonic reducer. The method for manufacturing a rigid ring gear of a harmonic reducer according to claim 1, wherein the equation of the tooth profile of the finally formed rigid ring gear is: L ₁ =[ x 1 y 1 0] ^T wherein: A method for manufacturing a flexible planetary gear of a harmonic reducer, comprising: [a] preparing step: preparing a hobbing cutter and a rigid annular processing component, the hobbing cutter being a long strip cutter having a The surface of the gear knives, the longitudinal section of the surface of the gear knives forms a curve of a hobbing cutter, and the curve equation of the hobbing cutter is defined by one of the following mathematical formulas (1) to (5): f ( Φ)= h . g(i.Φ).........(C1) f(Φ)= h . g(g(i.Φ)).........(C2) f(Φ)= h . g(g(g(i.Φ)))............(C3) f(Φ)= h . g(g(g(i.Φ)))))......(C4) f(Φ)= h . g(g(g(g(i.Φ))))))(C5) where g(Φ)=sin(Φ) h is the tooth height coefficient, and the minimum value of the range is 0. Its maximum value is defined by the following equation: The tooth height coefficient is between 0 and the maximum value of the above formula; Φ is the input parameter; i is an arbitrary number; m is the modulus; z1 is the number of teeth of the rigid ring gear; [b] rigid ring gear manufacturing steps: The hobbing cutter cuts the rigid annular component to be processed by a conventional creation method to form a rigid ring gear of a harmonic reducer; [c] a flexible planetary gear manufacturing step: a rigid ring of the harmonic reducer The tooth shape of the gear is cut by a flexible circular workpiece to be processed by a conventional meshing equation to form a flexible planetary gear of a harmonic reducer. The method for manufacturing a flexible planetary gear of a harmonic reducer according to claim 3, wherein the equation of the tooth profile of the finally formed flexible planetary gear is: L ₂ =[ x 2 y 2 0] ^T Where: z2 is the number of teeth of the flexible planet wheel; A rigid ring gear and a flexible planetary gear of a harmonic reducer include a rigid ring gear and a flexible planetary gear, wherein the rigid ring gear and the tooth profile of one of the flexible planetary wheels are : L ₁ =[ x 1 y 1 0] ^T and the equation of the other tooth profile is: L ₂ =[ x 2 y 2 0] ^T where: also Where: h is the tooth height coefficient, the minimum value of the range of values is 0, and the maximum value is defined by the following equation: The tooth height coefficient is between 0 and the maximum value of the above formula; Φ is an input parameter; i is an arbitrary number; m is a modulus; z1, z2 are one of the rigid ring gear and the flexible planetary gear The other number of teeth.