JP2009024841A - Trochoid gear and reduction gear - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a trochoid gear easy to design, by eliminating inconvenience such as abrasion without limiting material, while adopting an internal gear integrated with a pin and a holder. <P>SOLUTION: This trochoid gear 1 is provided by meshing an external gear 2 and the internal gear 3 having the tooth number more by one than its external gear. The external gear 2 has a tooth shape having an addendum part of a circular arc curve, having a deddendum part of an epitrochoid curve and smoothly connecting these two curves by a common tangent. The internal gear 3 has a tooth shape having an addendum part of a circular arc curve, having a deddendum part of a hypotrochoid curve and smoothly connecting these two curves by a common tangent. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The invention according to the claims relates to a trochoid gear used as an intermeshing planetary gear in a reduction gear, a gear pump, and the like, and a reduction gear using the same.

In an internally meshing planetary gear, an internal gear (external gear) having an epitrochoidal tooth shape and a plurality of cylindrical pins (or rollers) attached to a holder so as to be able to rotate (rotate) ( Internal gearing is achieved with an internal gear (pin separation type). In a reduction gear having such a planetary gear, the external gear has one fewer teeth than the internal gear, and the reduction ratio corresponds to the number of pins used as the internal gear. Examples of trochoidal gears having such pins and reduction gears using the same are shown in, for example, Patent Documents 1 and 2 below.
The “epitrochoid” refers to a locus drawn by a point on a circle that rolls without slipping outside the base circle as shown in FIG. 7 (upper part). Further, “hypotrochoid” described later refers to a locus drawn by a point on a circle that rolls without slipping inside the base circle as shown in FIG. 7 (lower part).

  In order to obtain a large reduction ratio in the reducer as described above, it is necessary to attach a large number of pins to the holder of the internal gear, and the number of parts increases and the assembly becomes complicated and the manufacturing cost increases. More and more examples have adopted internal gears that are integrated with the holder. However, since the trochoid gear has a large relative slip when meshed, if the same torque as before (torque that could be transmitted by the pin-separated internal gear) is applied to the internal gear with the pin integrated in the holder In addition, the wear tends to increase, the transmission efficiency decreases, or seizure occurs.

The following Patent Documents 3 to 5 propose gears that can partially eliminate such problems.
JP-A-61-136041 Japanese Patent Laid-Open No. 4-28047 Japanese Examined Patent Publication No. 63-4056 JP-A-6-50394 JP-A-4-29645

  The techniques described in Patent Documents 3 and 4 relate to the trochoidal gear as shown in FIG. 8B used in the section of the bb cross section in the planetary gear speed reducer shown in FIG. This is an example in which a pin and a holder are integrated. The external gear 2 'employs a conventional epitrochoid tooth profile, the internal gear 3' has a tooth tip portion formed in an arc, and the tooth root portion is formed by an envelope curve of the external gear tooth shape. According to this, in an important region that greatly contributes to torque transmission, each tooth in each of the inner and outer gears 2 'and 3' comes into contact with the mating gear at both the tooth tip portion and the tooth root portion. A decrease in surface pressure at a point can be expected, and some of the above problems can be solved.

  However, it is not easy to design an envelope curve of an external gear tooth profile (epitrochoid curve) that moves in a planetary motion. For the design, for example, on CAD, the locus of the tip of the tooth tip (convex point of the trochoid curve) during planetary movement is obtained, and further, the locus of the point on the tooth root side is obtained from it, and this is repeated. Thus, it is necessary to take out only the outermost area of all the trajectories. In that case, the design based on the meshing theory cannot be developed, and the time and labor required for the design become enormous.

  The technique described in Patent Document 5 impregnates one or both of an external gear and an internal gear with oil in advance. This technology can also partially eliminate the above-mentioned problems such as wear, but in this case, it is necessary to use a porous material such as a metal powder sintered material, and the gear material is extremely limited. It becomes like.

  The invention according to the claims was made in consideration of the above points, and while adopting an internal gear in which a pin and a holder are integrated, problems such as wear can be solved without specially limiting the material, In addition, the present invention provides a trochoid gear that is easy to design.

The trochoidal gear according to the present invention is a trochoidal gear in which an external gear and an internal gear (for example, one having 1 more teeth than the external gear) mesh with each other,
B) The external gear has a tooth profile in which the tooth tip portion is an arc curve and the tooth root portion is an epitrochoid curve, and these two curves are smoothly connected by a common tangent line, and
B) The internal gear is characterized in that the tooth tip portion is an arc curve and the tooth root portion is a hypotrochoid curve, and these two curves have a tooth profile smoothly connected by a common tangent line. .

FIG. 6A shows the meshing of the epitrochoid curve external gear and the separation-type internal gear, and FIG. 6B shows the meshing of the hypotrochoid curve internal gear and the separation-type external gear. In both cases, the external gear that performs planetary motion in the center of the internal gear is depicted as being eccentric to the right. In such a state, it can be said that the meshing of teeth that greatly contributes to torque transmission is concentrated in the right half.
By the way, in both gears (a) and (b), all teeth are engaged with the mating gear. Here, when the state of meshing is observed in detail, the following can be understood.
○ The external gear of (a) meshes with the mating gear on the right side and the tooth tip on the left side.
○ In the internal gear of (a), the tooth tip part meshes with the counterpart gear over the entire circumference.
○ In the external gear of (b), the tooth tip part meshes with the mating gear over the entire circumference.
○ In the internal gear of (b), the tooth bottom portion meshes with the mating gear on the right side and the tooth tip portion on the left side.
For this reason, if the tooth bottom part is an epitrochoid curve, the tooth tip part is an arcuate curve external gear, and the tooth bottom part is a hypotrochoid curve and the tooth tip part is an arcuate curve internal gear, it greatly contributes to torque transmission. In the range (substantially right side in the figure), both the tooth bottom part and the tooth tip part mesh with the mating gear, and in the range (substantially left side in the figure) that does not contribute much to torque transmission, it is considered that a gear that does not engage is established.
Therefore, FIG. 1 shows a picture in which the internal and external gears formed as in the above (a) and b) are engaged. As shown in this figure, in the region where both gears mesh with each other, the tooth base part of the external gear (the epitrochoid curve part) and the tooth tip part of the internal gear (the arc curve part) are in contact (small in the figure). In addition to the contact portion 4a) indicated by a circle, the tooth tip portion (arc curve portion) of the external gear and the tooth root portion (hypotrochoid curve portion) of the internal gear contact (contact portion 4b indicated by a large circle in the figure). ). In addition, the external gear and the internal gear mesh with each other only in a region where the sliding speed is small (such as a portion surrounded by an ellipse in the figure) that greatly contributes to torque transmission. From these points, it can be said that this gear has advantages in various points, such as a small surface pressure during torque transmission, and tooth surface wear and transmission efficiency, troubles such as seizure.
Compared with the gears of Patent Documents 3 and 4 described above, the difference is that the tooth profile of the external gear is not an epitrochoid curve in the entire region, but the tooth tip portion is an arc curve. When the external gear is an arc curve, the envelope curve is a hypotrochoid curve. Therefore, according to this invention, each tooth form of an internal gear and an external gear can be formulated mathematically, and tooth form design becomes easy. Both epitrochoid meshing and hypotrochoid meshing are well-known facts that the gear theory has been established, and a more devised design is possible. The trochoid gear of the invention is used in the planetary gear reducer (part of the bb cross section) shown in FIG. 8 (a), the gear pump main body (not shown), etc., like the gears of the cited documents 3 and 4. can do.

In the external gear and the internal gear, the connecting parts of the above two curves (the external gear indicates the arc curve and the epitrochoid curve, and the internal gear indicates the arc curve and the hypotrochoid curve) The epitrochoid curve or the hypotrochoid curve preferably matches the vicinity of the maximum point of torque transmission efficiency. Specifically, it is preferable that the amount of eccentricity between the external gear and the internal gear is appropriately determined so that the connecting portion matches the maximum point of torque transmission efficiency.
When the two gears mesh with each other, the contact point between the trochoid curve and the arc changes by the meshing movement, and when the contact point is farthest from the tooth tip point, the torque transmission efficiency between the internal and external gears is maximized. That is, the contact point (portion X in FIG. 1) at the end in the region where the inner and outer gears mesh with each other is the maximum point of torque transmission efficiency. When the connecting part of each of the two curves is matched with the epitrochoid curve or the hypotrochoid curve in the vicinity of the maximum torque transmission efficiency point, the contact point of the counter gear stays only within the range of the arc curve, It does not move to the range of the hypotrochoid curve or epitrochoid curve. Therefore, according to this gear, an effect that the meshing between the external gear and the internal gear becomes particularly stable can be obtained.

In the gear configured as described above, it is particularly preferable that the convex points of the external gear and the internal gear are in contact with each other at a portion 180 ° away from the central portion of the region where the external gear and the internal gear mesh.
That is, as shown in FIG. 1, in addition to a region that greatly contributes to torque transmission (portion surrounded by an ellipse in the drawing), a portion that is 180 ° away from the central portion of the region (portion Y in the drawing) However, the amount of eccentricity between the internal and external gears, the PCD of the internal and external gears, the arc diameter, and the number of teeth are determined so that the convex points of the external gear and the internal gear are in contact with each other. The external gear and the internal gear are in contact with each other only at the above-mentioned region that contributes to torque transmission and at one point indicated by the symbol Y. This is advantageous in that the design and production of the tooth profile is particularly simplified and easy.

On the other hand, the dimensions and the number of teeth are determined as described above (that is, the convex points of the external gear and the internal gear are in contact with each other at a portion 180 ° away from the central portion of the region where the external gear and the internal gear mesh). In addition, the convex points may not be in contact with each other by chamfering the tooth tips.
If it does so, the interference of a tooth tip can be avoided in parts other than said area | region which contributes to torque transmission. Since it is possible to avoid meshing of the convex points that do not contribute to torque transmission at all, wasteful wear and loss of transmission efficiency can be reduced. FIG. 5 shows an example.

Furthermore, it is also meaningful that at least one of the external gear and the internal gear is formed of ductile cast iron impregnated with lubricating oil, or a diamond-like carbon film is formed on the surface.
When such a feature is added to the above-described trochoid gear, the above-described problems such as tooth surface wear and reduced transmission efficiency are further eliminated. Each tooth in the inner and outer gears is brought into contact with the mating gear at both the tooth root part and the tooth tip part to reduce the surface pressure at the time of meshing, and the surface of each gear thus has a self-lubricating property to thereby provide friction. This is because the degree of wear decreases synergistically when reduced.
The trochoidal gear shown above is preferably used by being incorporated in a reduction gear.

According to the trochoid gear of the claimed invention, in an important region that greatly contributes to torque transmission, one tooth in each of the inner and outer gears contacts the mating gear at both the root portion and the tip portion. The surface pressure during torque transmission is small, and there are advantages in various respects such as tooth surface wear and transmission efficiency, troubles such as seizure. In addition, each tooth profile of the internal gear and the external gear can be mathematically formulated, and the tooth profile design becomes easy, and a more thoughtful design becomes possible.
In the external gear and the internal gear, the engagement between the external gear and the internal gear is particularly stable when the connecting portions of the two curves are made to coincide with each other in the vicinity of the maximum point of the torque transmission efficiency.

Also, if the convex points of the external gear and the internal gear are in contact with each other at a portion 180 ° away from the central portion of the region where the external gear and the internal gear mesh, the design and production of the tooth profile is particularly simplified and easy. Become.
In addition, if it is configured so that the convex points do not touch each other due to negative dislocation of the tooth tip or chamfering of the tooth tip, the tooth profile can be easily designed and manufactured and interference of the tooth tip can be avoided by a simple method. Therefore, useless wear and loss of transmission efficiency can be reduced.
If at least one of the external gear and the internal gear is made of ductile cast iron impregnated with a lubricating oil, or if a diamond-like carbon film is formed on the surface, the above-mentioned problems such as wear on the tooth surface and reduction in transmission efficiency may occur. Furthermore, it becomes easy to be eliminated.
The speed reducer incorporating the trochoidal gear also provides advantages based on the above features.

  Embodiments of the invention will be described with reference to the drawings. A trochoid gear (gear pair) 1 shown in FIGS. 1 to 5 is one in which an external gear 2 and an internal gear 3 that both include a trochoid curve mesh with each other, and the internal gear 3 and the external gear having one fewer teeth than that. 2 is used by being incorporated in, for example, the planetary gear speed reducer 10 (part of the bb cross section) shown in FIG. When used in the illustrated speed reducer 10, an eccentric body 12 is first attached to the input shaft 11, and a plurality of external gears 2 are provided so as to be able to rotate eccentrically via the eccentric body 12. The internal gear 3 is provided and fixedly arranged so as to be in mesh with the external gear 2, and the output shaft 14 is attached so as to transmit only the rotation component of the external gear 2 through the support shaft 13. In this way, a reduction ratio equal to the number of teeth of the internal gear is obtained between the input shaft 11 and the output shaft 14.

  A trochoid gear (hybrid trochoid gear) 1 shown in FIGS. 1A and 1B has a tooth profile shown in FIG. That is, in the external gear 2 (right side in the figure), the tooth tip portion is an arc curve 2a and the tooth root portion is an epitrochoid curve 2b, and these two curves are smoothly connected by a common tangent to form a tooth profile. Has been. On the other hand, the internal gear 3 (left side in the figure) has a tooth tip portion of an arc curve 3a and a tooth root portion of a hypotrochoid curve 3b, and these two curves are smoothly connected by a common tangent.

  The pair of external gear 2 and internal gear 3 form a preferable mesh shown in FIG. 1 when meshed with each other being appropriately eccentric. In other words, in an important region that greatly contributes to torque transmission (engagement region, such as a portion b surrounded by an ellipse as shown in the figure), one tooth in each of the inner and outer gears 2 and 3 is formed between the root portion and the tip portion. Both contact the mating gear. The tooth base part of the external gear 2 (the epitrochoid curve part) and the tooth tip part of the internal gear 3 (arc curve part) are in contact with each other at the small round part 4a in FIG. The tooth tip portion (arc curve portion) and the tooth root portion of the internal gear 3 (hypotrochoid curve portion) come into contact with each other at a large circular portion 4b in FIG. Considering the elastic deformation at the time of meshing, it is expected that the external gear 2 and the internal gear 3 are in contact with each other on a macroscopic basis. From these points, the trochoid gear 1 has the effect that the surface pressure during torque transmission is reduced and the tooth surface wear is reduced.

  In the trochoid gear 1 of FIG. 1, the external gear 2 and the internal gear 3 are generally not in contact with each other in the portion other than the meshing region described above. If the two gears are in contact with each other in a region other than the meshing region, the sliding speed is high at the contact portion and the progress of wear is significant, and such contact hardly contributes to torque transmission. Therefore, it can be said that the gear 1 of FIG. 1 is rather advantageous in that transmission efficiency is improved and seizure is prevented.

For the trochoid gear 1, the trochoid coefficient α is calculated from α = ec · n1 / ae from the center eccentricity ec of the external gear 2, the number of teeth n 1 of the internal gear 3, and ae which is the PCD of the internal gear arc center. . When the trochoid coefficient α is close to 1, the trochoid curve is close to a cycloid curve, and when α is less than 1, the trochoid curve is a curve away from the cycloid curve.
If this trochoid coefficient α is large, the sliding speed of the tooth root portion will be small and efficient torque transmission will be possible, but if the coefficient α is too large, the connecting point of the two curves will overtake the torque transmission efficiency maximum point. As a result, the meshing of both teeth becomes unstable. Further, as shown in FIGS. 3A and 3B and FIGS. 4A and 4B, the trochoid coefficient is 0.96 in the example of FIG. 3, and the coefficient is 0.74 in the example of FIG. The number of teeth is 80) When the coefficient α is large, the meshing area becomes narrow (in the example of FIG. 3, the area is 8 °, which is considerably narrower than 35 ° in the example of FIG. 4). For this reason, it is preferable to set the trochoid coefficient α and the eccentricity ec so as to have an appropriate meshing region and the connecting point exactly coincides with the maximum torque transmission efficiency point.

  The external gear 2 and the internal gear 3 have the dimensions and the number of teeth so that the convex points of the two portions are in contact with each other even at a portion 180 ° away from the center portion of the meshing region (the portion indicated by Y in FIG. 1). If defined, there is an advantage that the design and production can be simplified. However, it is preferable to prevent tooth tip interference in the sense of reducing tooth tip wear and improving transmission efficiency. FIGS. 5A, 5 </ b> B, 5 </ b> C, and 5 </ b> D are examples in which chamfered portions 2 c and 3 c are provided at the tooth tips of the external gear 2 and the internal gear 3 to avoid the interference of the tooth tips. .

  In the trochoid gear 1 shown above, since the envelope curve of the external gear tooth profile is a hypotrochoid curve, each tooth profile of the external gear 2 and the internal gear 3 can be mathematically formulated, and the tooth profile design is easy. is there. That is, for example, the tooth profile curve can be formulated as follows.

The equation for the epitrochoid center curve is as follows:
cev = {cex, cey};
Here, cex is the x coordinate of the epitrochoid center curve, and cey is its y coordinate.
cex = ec Cos [q] + ae Cos [q / n1]; cey = ec Sin [q] + ae Sin [q / n1];
ae: PCD at the center of the internal tooth arc, ec: Center eccentricity of the external gear, re: Radius of the internal tooth arc, q: Parameter (q = 2Pin1 is one cycle). Pi represents π.
n0: Number of external teeth, n1: Number of internal teeth (here, n1 = n0 + 1)
If this curve is offset in the center direction by an inner tooth arc diameter in order to mesh with the internal gear, a tooth profile curve of the external gear is established.
sev = {sex, sey};
Here, sex is the x coordinate of the parallel curve, and sey is its y coordinate.
sev = cev + re * {{Cos [Pi / 2],-Sin [Pi / 2]}, {Sin [Pi / 2], Cos [Pi / 2]}}. {dex, dey} / der;
der = Sqrt [dex ^ 2 + dey ^ 2]; dex = D [cex, q]; dey = D [cey, q];
The coordinates of the initial point (tooth tip convex point) are sev (0) = {ae + ec-re, 0}.
Note that D [f (q), q] represents the differentiation of f (q) by q.

Similarly, the hypotrochoid central curve chv and the hypotrochoid parallel curve shv are as follows.
chv = {chx, chy};
Here, chx is the x coordinate of the hypotrochoid center curve, and chy is its y coordinate.
chx = -ec Cos [q] + ah Cos [q / n1]; chy = + ec Sin [q] + ah Sin [q / n1];
ah: PCD at the center of the external tooth arc, ec: Center eccentricity of the external gear, rh: Radius of the external tooth arc, q: Parameter (q = 2Pin1 for one cycle)
n1: Number of external teeth, n2: Number of internal teeth (here n2 = n0 + 2)
shv = {shx, shy};
Here, shx is the x coordinate of the parallel curve, and shy is its y coordinate.
shv = chv + rh * {{Cos [Pi / 2], Sin [Pi / 2]}, {-Sin [Pi / 2], Cos [Pi / 2]}}. {dhx, dhy} / dhr;
dhr = Sqrt [dhx ^ 2 + dhy ^ 2]; dhx = D [chx, q]; dhy = D [chy, q];

The contact point of the arc that meshes with the trochoid curve changes with the meshing motion. When the contact point is farthest from the tooth tip point, the torque transmission efficiency between the internal and external gears is maximized. The point on the trochoid curve that meshes with this point is called the maximum torque transmission efficiency point and can be formulated as follows.
Epitrochoid torque transmission efficiency maximum point: qem = Pi n1 / n0-n1 / n0 ArcCos [(ec n1) / aa];
Maximum torque transmission efficiency of hypotrochoid: qhm = Pi n1 / n2-n1 / n2 ArcCos [(ec n1) / aa];
ArcCos [x] is the inverse cosine function of x.

Consider replacing the tooth tip of the external gear with a circular arc and smoothly connecting it with the epitrochoid parallel curve.
When the arc radius is rh and the arc center position is (ae + ec-re + dela-rh, 0), the deviation length delre between the epi curve and the arc curve is obtained as follows.
delre = (sex- (ae + ec-re + dela-rh)) ^ 2 + sey ^ 2-rh ^ 2
Since the two curves touch at the connection point qc of the two curves, from the two equations {delre (qc) = 0, D [delre, q] (qc) = 0} Conditions qc and rh are obtained.
Here, when de1a = 0, the arc touches the convex point of the epicurve. In order to prevent the outer teeth and the inner teeth from interfering over the entire circumference, there is a condition of de1a ≧ 0. de1a corresponds to the clearance between the external and internal tooth tips.
Further, since the arc rh and the epi parallel curve sev are in contact with each other in qc, delre can be rewritten with the epi center curve only in qc.
delre = (cex- (ae + ec + de1a-re-rh)) ^ 2 + cey ^ 2- (re + rh) ^ 2
= (cex- (ae + ec + dela-rw)) ^ 2 + cey ^ 2-rw ^ 2 where rw = re + rh
It is more advantageous to reduce calculation load if this is used for solving equations.
From the obtained rw, the external tooth arc diameter of the hypo curve is determined by rh = rw-re. Also, ah = ae + ec-rw-de1a determines the PCD of the external tooth arc center. That is, if the epicurve tooth profile parameters ae, ec, re, n0 and the inter-tooth clearance de1a are determined, the hypocurve tooth profile parameters ah, ec, rh, and no which mesh with the epicurve are automatically obtained.

α = ec n1 / ae is called a trochoid coefficient. When α = 1, the two trochoid curves are both cycloid curves. In this case, the tooth base part is also an arc.
卜 If the locoid coefficient is large, the sliding speed of the tooth root portion is reduced, and efficient torque transmission can be performed.
However, when the trochoid coefficient increases, the connecting point of the two curves overtakes the maximum torque transmission efficiency point, and the meshing of both teeth becomes unstable. Further, the meshing area is also narrowed.
For this reason, it is effective to design the eccentricity ec so that the connection point exactly matches the maximum torque transmission efficiency point.
In addition, the two arc diameters re and rh have a degree of freedom in their distribution according to the conditional expression rw = re + rh. Therefore, rather than the design where either one is extremely small, the design that both are set to almost the same value, that is, when the epi tooth surface deteriorates due to excessive surface pressure, the hypo tooth surface also deteriorates at the same time. However, it is peculiar.

It is a figure which shows mesh | engagement with the external gear 2 and the internal gear 3 about the trochoid gear 1 which concerns on implementation of invention. A detailed view of the portion b in the gear 1 of FIG. 1A is shown in FIG. It is a figure explaining the tooth profile curve of the external gear 2 and the internal gear 3. FIG. It is a figure which shows the relationship between the trochoid coefficient (alpha), the meshing area | region of the external gear 2 and the internal gear 3, etc. FIG. A detailed view of a portion b in the gear 1 of FIG. 1A is shown in FIG. It is a figure which shows the relationship between the trochoid coefficient (alpha), the meshing area | region of the external gear 2 and the internal gear 3, etc. FIG. A detailed view of a portion b in the gear 1 of FIG. 1A is shown in FIG. FIGS. 5A and 5B show an example in which a chamfered portion is provided on the tooth tip in order to prevent interference of the tooth tip. 5 (c) and 5 (d) are detailed views of the c and d portions in FIGS. 5 (a) and 5 (b), respectively. FIG. 6A shows the meshing of the epitrochoid curve external gear and the separation-type internal gear, and FIG. 6B shows the meshing of the hypotrochoid curve internal gear and the separation-type external gear. It is a conceptual diagram which shows an epitrochoid and a hypotrochoid. FIG. 8A is a cross-sectional view showing the planetary gear speed reducer 10, and FIG. 8B is a view showing a conventional trochoidal gear used in such a speed reducer, with the bb cross section in FIG. FIG. In addition, both (a) and (b) are figures described in Patent Document 3.

Explanation of symbols

1 Trochoid gear 2 External gear 3 Internal gear 10 Planetary gear reducer

Claims (6)

A trochoid gear in which an external gear and an internal gear mesh with each other,
The external gear has a tooth profile in which the tooth tip is an arc curve and the tooth root is an epitrochoid curve, and these two curves are smoothly connected by a common tangent line,
The internal gear has a tooth profile in which the tooth tip portion is an arc curve and the tooth root portion is a hypotrochoid curve, and these two curves have a tooth profile smoothly connected by a common tangent line. .   2. The trochoid gear according to claim 1, wherein, in the external gear and the internal gear, a connecting portion of each of the two curves coincides with the vicinity of the maximum point of the torque transmission efficiency of the epitrochoid curve or the hypotrochoid curve.   The dimension and the number of teeth are determined so that convex points of the external gear and the internal gear are in contact with each other at a portion 180 ° away from a central portion of a region where the external gear and the internal gear mesh with each other. The trochoid gear according to 1 or 2.   The dimension and the number of teeth are determined so that the convex points of the external gear and the internal gear are in contact with each other at a portion 180 ° away from the central portion of the region where the external gear and the internal gear mesh with each other. The trochoid gear according to claim 3, wherein the convex points are not in contact with each other.   At least one of the external gear and the internal gear is formed of ductile cast iron impregnated with a lubricating oil, or a diamond-like carbon film is formed on the surface thereof. The trochoid gear described in 1.   A speed reducer comprising the trochoidal gear according to claim 1.

Images