Crown gear reduction mechanism, design support system and method for crown gear reduction mechanism

Abstract

To improve the alignment of the contact points between the rotor teeth and stator teeth. [Solution] A crown gear reduction mechanism comprising a stator 1 having an annular stator gear row 11, a rotor 2 having an annular rotor gear row 21 and positioned at an angle to the stator 1, and an output shaft 3 to which the rotation of the rotor 2 is transmitted, wherein the stator gear row 11 and the rotor gear row precesse at multiple locations on both the left and right sides of the tilt center line of the rotor 2, wherein the tooth profile of each stator tooth 41 in the stator gear row 21 is such that at the contact portion with each rotor tooth 42 in the rotor gear row 21, the number of teeth M of the stator gear row 41 S In this case, the central angle of one tooth is 2π / M S In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as the tooth width direction, with the top of the stator tooth 41 as the x-axis reference position, the tooth width direction as coordinate x, and the tooth height direction as coordinate z, then z is defined by a sixth-degree polynomial with respect to x. u With a limit of z l This is the lower limit.

Description

[Technical Field]

[0001] The present invention relates to a design method for a crown gear reduction mechanism, and more particularly to a design method that improves the meshing accuracy of rotor teeth and stator teeth and optimizes load distribution to achieve durability and extended lifespan under high-load environments, and to a crown gear reduction mechanism having a tooth profile of stator teeth or rotor teeth based on this design concept. [Background technology]

[0002] A crown gear reduction mechanism is a reduction mechanism that achieves reduction by having a fixed crown gear, which is the stator gear row, and a movable crown gear, which is the rotor gear row, positioned at an angle to the stator gear row. By causing the rotor teeth of the rotor gear row to precesse while being tilted at a predetermined angle relative to the stator teeth of the stator gear row, it converts input rotation into output rotation with a high reduction ratio. This crown gear reduction mechanism has excellent features such as achieving a high reduction ratio in a single stage, extremely low backlash, and the ability to be made small and lightweight, so it is attracting attention in a wide range of applications that require high precision and high torque, such as robot arm joint drives, machine tool spindle drives, electric vehicle drive systems, industrial robots, precision positioning devices, and housing equipment.

[0003] Compared to conventional reduction mechanisms, the crown gear reduction mechanism has the following significant advantages. Firstly, it employs a configuration where the difference in the number of teeth between the rotor and stator is 1. For example, if the stator has 49 teeth and the rotor has 50 teeth, a high reduction ratio of 50:1 can be achieved. Secondly, the structure maintains constant meshing at two points on either side of the tilt centerline, resulting in extremely small backlash and enabling highly accurate positioning. Thirdly, approximately 25% of the total number of teeth are meshed simultaneously, and theoretically, the load is distributed across a large number of teeth, so high torque transmission capability can be expected.

[0004] Conventional crown gear reduction mechanisms include a stator made of a crown gear and a rotor made of a crown gear with one different number of teeth, and transmits rotation by pressing the rotor against the stator and causing it to precess (see, for example, Patent Document 1). According to the technology disclosed in Patent Document 1, the rotor meshes with the stator in an inclined state, and the teeth mesh at two points on the left and right sides of the tilt centerline, thereby reducing backlash and reducing the diameter. Furthermore, a flexible spoke structure is provided between the rotor and the output shaft, which is characterized by absorbing displacement due to precession while transmitting rotation to the output shaft.

[0005] However, according to the technology disclosed in Patent Document 1, since essentially only about one tooth engages at each of the two locations on either side of the tilt centerline, it is not easy to distribute the load across the entire tooth, and the problem of stress concentration due to tooth contact and local contact conditions is not adequately addressed.

[0006] For this reason, a crown gear reduction mechanism has been disclosed in which the shape of the rotor teeth and stator teeth are configured based on the trajectory of the teeth when the rotor performs a predetermined precessional motion, so that multiple teeth are always meshing and contributing to the drive (see, for example, Patent Document 2). According to the technology disclosed in Patent Document 2, the strength and durability of the entire reduction mechanism can be improved by forming the stator tooth row along the trajectory of the rotor teeth and increasing the number of teeth that mesh simultaneously.

[0007] In the crown gear reduction mechanism disclosed in Patent Document 2, approximately 25% of the total number of teeth mesh simultaneously. For example, if the rotor has 50 teeth, approximately 12 teeth on each side of the tilt centerline, totaling approximately 24 to 25 teeth (approximately 48 to 50% of the total number of teeth), are located in the region where they contact the stator teeth, and of these, approximately 25% of the teeth effectively contribute to the drive.

[0008] This characteristic theoretically distributes the load across multiple teeth, reducing the stress on individual teeth and resulting in higher torque transmission and a longer lifespan. Considering that typical spur gears have only 1-2 teeth meshing simultaneously, the 25% simultaneous meshing rate of the crown gear reduction mechanism is extremely high, making it one of its most distinctive features.

[0009] However, the structural characteristic of such crown gear reduction mechanisms, in which approximately 25% of the total number of teeth mesh simultaneously, creates a new concern, as described below. If there is even a slight mismatch in the tooth profile design or tooth contact design, the load may not be ideally evenly distributed among multiple teeth, and excessive stress may be concentrated on some of the contacting teeth. As a result, fatigue due to repeated loading is accelerated at the stress-concentrated area, making it impossible to achieve a long lifespan.

[0010] In other words, if there is a small mismatch in the initial design of the rotor teeth and stator teeth, the effect will expand over time with use, eventually leading to a vicious cycle where only certain teeth bear the load. As a result, the performance of the crown gear reduction mechanism deteriorates rapidly with use. [Prior art documents] [Patent Documents]

[0011] [Patent Document 1] Patent No. 4511635 [Patent Document 2] Patent No. 5860549 [Overview of the Initiative] [Problems that the invention aims to solve]

[0012] Therefore, the present invention has been devised in view of the above-described problems, and its object is, in view of the characteristics of a crown gear reduction mechanism having an extremely high simultaneous engagement ratio, to improve the alignment at the contact portions between the rotor teeth and the stator teeth, thereby distributing the load over the entire teeth, minimizing stress concentration caused by tooth contact or local contact conditions, and enabling the maintenance of the intended performance over a long period and achieving a long service life. The present invention also provides a crown gear reduction mechanism, as well as a design support system and method for the crown gear reduction mechanism.

Means for Solving the Problems

[0013] The crown gear reduction mechanism according to the present invention includes a stator having an annular stator tooth row, a rotor having an annular rotor tooth row and positioned inclined with respect to the stator, and an output shaft to which the rotation of the rotor is transmitted. The rotor is configured to perform a precession motion while engaging the stator tooth row and the rotor tooth row at a plurality of locations on both the left and right sides sandwiching the tilt center line of the rotor. In the crown gear reduction mechanism, the tooth profile of each stator tooth in the stator tooth row is defined in a plane coordinate system with the circumferential direction normalized to 1 with a central angle of 2π / M per tooth as the reference length and the tooth width direction, where M is the number of teeth in the stator tooth row. When the end portion on the bottom side of the contact portion of the stator tooth is the z-axis reference position and the top portion of the stator tooth is the x-axis reference position, and the tooth width direction is the coordinate x and the tooth height direction is the coordinate z, z is bounded by z defined by Equation (1) as the upper limit and z defined by Equation (2) as the lower limit. S When taken as M, the circumferential direction normalized to 1 with a central angle of 2π / M per tooth as the reference length S is defined in a plane coordinate system with the tooth width direction, and when the end portion on the bottom side of the contact portion of the stator tooth is the z-axis reference position and the top portion of the stator tooth is the x-axis reference position, with the tooth width direction as the coordinate x and the tooth height direction as the coordinate z, z is u bounded by z defined by Equation (1) as the upper limit and z defined by Equation (2) as the lower limit, l and The tooth profile of each rotor tooth in the rotor gear row described above is such that, at least at the contact point with each stator tooth in the stator gear row, the number of teeth M in the rotor gear row R In this case, the central angle of one tooth is 2π / M R In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the rotor tooth is the z-axis reference position, the top of the rotor tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (4). u With the upper limit being z defined by equation (5) l Set the lower limit is characterized by the above. z u =d / 200(a6x 6 +a4x 4 +a2x 2 +a0+C u)····(1) z l =d / 200(a6x 6 +a4x 4 +a2x 2 +a0+C l )····(2) Here, d is the diameter of the stator, C u =2.0, C l =-2.0 Also, a6, a4, a2, and a0 have a tooth count M, which can be determined from equation (3). S It is calculated from this.

number

number

[0014] The design support system for a crown gear reduction mechanism according to the present invention comprises a stator having an annular stator tooth row, a rotor having an annular rotor tooth row and positioned at an angle to the stator, and an output shaft to which the rotation of the rotor is transmitted, wherein the rotor is configured to perform precession motion by meshing the stator tooth row and the rotor tooth row at multiple locations on both the left and right sides of the rotor's tilt centerline, and the design support system for a crown gear reduction mechanism comprises the tooth profile data of each stator tooth in the designed stator tooth row. and data on the tooth profile of each rotor tooth in the designed rotor gear array. A data acquisition means for obtaining the tooth profile data of each stator tooth obtained by the data acquisition means, at least at the contact portion with each rotor tooth in the rotor tooth array, the number of teeth M in the stator tooth array. S In this case, the central angle of one tooth is 2π / M S In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the stator tooth is the z-axis reference position, the apex of the stator tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (1). u The upper threshold curve S is below the curve of . u And z defined by equation (2) l Lower threshold curve S is greater than or equal to the curve. l Determine whether or not it is included between and The tooth profile data of each rotor tooth obtained by the above data acquisition means is, at least at the contact portion with each stator tooth in the stator tooth array, the number of teeth M in the rotor tooth array. R In this case, the central angle of one tooth is 2π / M R In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the rotor tooth is the z-axis reference position, the top of the rotor tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (4). u The upper threshold curve T is below the curve of . u And z defined by equation (5) l The lower threshold curve T is greater than or equal to the curve of . l Determine whether or not it is included between them. The system is characterized by comprising a determination means and an output means for outputting the determination result obtained by the determination means. z u =d / 200(a6x 6 +a4x 4 +a2x 2 +a0+C u )····(1) z l =d / 200(a6x 6 +a4x 4+a2x 2 +a0+C l )····(2) Here, d is the diameter of the stator, C u =2.0, C l =-2.0 Also, a6, a4, a2, and a0 have a tooth count M, which can be determined from equation (3). S It is calculated from this.

number

number

[0015] The present invention relates to a design support method for a crown gear reduction mechanism comprising a stator having an annular stator tooth row, a rotor having an annular rotor tooth row and positioned at an angle to the stator, and an output shaft to which the rotation of the rotor is transmitted, wherein the rotor is configured to perform precession motion by meshing the stator tooth row and the rotor tooth row at multiple locations on both the left and right sides of the rotor's tilt centerline, and the method relates to the tooth profile data of each stator tooth in the designed stator tooth row. and data on the tooth profile of each rotor tooth in the designed rotor gear array. A data acquisition step to obtain the tooth profile data of each stator tooth obtained in the above data acquisition step, and at least at the contact portion with each rotor tooth in the rotor tooth array, the number of teeth M in the stator tooth array. S In this case, the central angle of one tooth is 2π / M S In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the stator tooth is the z-axis reference position, the apex of the stator tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (1). u The upper threshold curve S is below the curve of . u And z defined by equation (2) l Lower threshold curve S is greater than or equal to the curve. l Determine whether or not it is included between and The tooth profile data of each rotor tooth acquired in the above data acquisition step is, at least at the contact portion with each stator tooth in the stator tooth array, the number of teeth M in the rotor tooth array. R In this case, the central angle of one tooth is 2π / M R In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the rotor tooth is the z-axis reference position, the top of the rotor tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (4). u The upper threshold curve T is below the curve of . u And z defined by equation (5) l The lower threshold curve T is greater than or equal to the curve of . l Determine whether or not it is included between the two. The invention is characterized by having a computer perform a determination step and an output step that outputs the determination result from the determination step. z u =d / 200(a6x 6 +a4x 4 +a2x 2 +a0+C u )····(1) z l =d / 200(a6x 6 +a4x4 +a2x 2 +a0 + C l )····(2) Here, d is the diameter of the stator, C u = 2.0, C l = -2.0 Also, a6, a4, a2, a0 are calculated from the number of teeth M in Equation (3). S as follows.

Number

Number

Advantages of the Invention

[0019] It should be noted that there may be some incorrect or unclear notations in the original text (such as "<着 ", "<照40>", "<着6>" which seem to be incorrect tags). This translation is based on the best understanding of the text with the given rules.According to the present invention, which has the above-described configuration, in view of the characteristics of a crown gear reduction mechanism with an extremely high simultaneous meshing rate, the alignment of the rotor teeth and stator teeth at their contact points is improved, thereby distributing the load across the entire tooth, minimizing stress concentration caused by tooth contact and localized contact conditions, and enabling the maintenance of the intended performance over a long period of time and extending the lifespan. [Brief explanation of the drawing]

[0020] [Figure 1] Figure 1 is a perspective view of a crown gear reduction mechanism to which the present invention is applied. [Figure 2] Figure 2(a) shows the configuration in which the rotor teeth and stator teeth mesh with each other, and Figure 2(b) is a plan view of the stator teeth. [Figure 3] Figure 3 is a three-dimensional diagram showing the stator tooth arrangement in the stator. [Figure 4] Figure 4 shows the state of one stator tooth in the xz coordinate system, which is a planar coordinate system, as represented by the reference equation (A). [Figure 5] Figure 5 shows the relationship between a6, a4, a2, and a0 in relation to the number of teeth MS in the stator tooth array. [Figure 6] Figure 6 shows the shapes of the curves zu and zl defined by equations (1) and (2). [Figure 7] Figure 7 shows the shapes of the curves zu and zl defined by equations (4) and (5). [Figure 8] Figure 8 is a block diagram of the design support system for a crown gear reduction mechanism. [Figure 9] Figure 9 is a flowchart of the design support system and its software program. [Modes for carrying out the invention]

[0021] The crown gear reduction mechanism to which the present invention is applied will be described in detail below with reference to the drawings.

[0022] Figure 1 is a perspective view of a crown gear reduction mechanism 10 to which the present invention is applied. The crown gear reduction mechanism 10 is mounted within a cylindrical housing 8 that forms its outer shell and comprises a stator 1 which is a fixed crown gear, a movable rotor 2 which performs precessional motion while meshing with the stator 1 at multiple points, an output shaft 3 which is connected to the rotor 2 so as to be able to transmit power, and a press rotor 4 which presses against the rotor 2.

[0023] The stator 1 and rotor 2 are entirely housed within the housing 8. The stator 1 is mounted within the housing 8, and the rotor 2 is positioned within the housing 8 opposite the stator 1.

[0024] The stator 1 has an annular stator tooth row 11 that protrudes from the rotor 2. The stator tooth row 11 has a large number of stator teeth 41 arranged in an annular shape.

[0025] On the rotor 2, on the surface 23 facing the stator 1, an annular rotor gear row 21 and a second rotor gear row 22 located inside the rotor gear row 21 are formed. The rotor gear row 21 and the second rotor gear row 22 are arranged concentrically with respect to each other on the opposing surface 23 of the rotor 2. The rotor gear row 21 has a large number of rotor teeth 42 arranged in an annular shape.

[0026] The output shaft 3 has a cylindrical shaft portion 31 and a gear portion 32 provided at the end of the shaft portion 31. The gear portion 32 is mounted inside the housing 8. The gear portion 32 consists of a crown gear in which an annular output tooth row 321 is formed. The end of the shaft portion 31 protrudes outside the housing 8, but is not limited to this, and a structure in which it is housed without protruding from the housing 8 may also be adopted.

[0027] On the rotor 2, the press rotor 4 is pressed against the opposing surface 24 that is opposite to the surface 23 facing the stator 1. The press rotor 4 is rotatably housed within the housing 8 via the bearing portion 5.

[0028] In the crown gear reduction mechanism 10, the rotor 2, which is pressed against the stator 1 via the press rotor 4, meshes with the stator 1 in a tilted position in one direction and also meshes with the gear portion 32 of the output shaft 3. In this position, when the press rotor 4 is rotated around the central axis C by an external power source such as an external motor (not shown), the rotor 2 performs a precessional motion due to the meshing of the rotor teeth 21 and the stator teeth 11.

[0029] Figure 2(a) shows the configuration in which the rotor teeth 21 of rotor 2 and the stator teeth 11 of stator 1 mesh with each other. The rotor teeth 42 of rotor teeth 21 contact and mesh with the stator teeth 41 of stator teeth 11, rotating around the central axis C. Figure 2(b) is a plan view of the stator teeth 41. The stator teeth 41 are arranged circumferentially in a concentric pattern.

[0030] It is preferable that the rotor 2 performs precession motion while the rotor teeth 21 mesh with the stator teeth 11 at multiple locations on both the left and right sides of the rotor 2's tilt centerline.

[0031] When rotor 2 precesses, the second rotor gear row 22 and the output gear row 321 of rotor 2 mesh, transmitting the rotational component of rotor 2 to the output shaft 3. As a result, the output shaft 3 rotates around the central axis C. Incidentally, the press rotor 4, stator 1, and output shaft 3 share a common central axis C.

[0032] In the crown gear reduction mechanism 10, the difference in the number of teeth between the stator 1 and the rotor 2, in other words, the difference between the number of stator teeth 41 and the number of rotor teeth 42, is 1, but is not limited to this.

[0033] If the external power source (not shown) that rotates the press rotor 4 is a motor, then the motor and the crown gear reduction mechanism 10 that transmits that power constitute a power unit.

[0034] In the crown gear reduction mechanism 10 having the configuration described above, the rotor 2 has a rotor tooth row 21 and a second rotor tooth row 22 on the surface 23 facing the stator 1, and is pressed by the press rotor 4 on the opposite surface 24 from the surface 23. As a result, the rotor 2 is positioned in an inclined position tilted in one direction relative to the stator 1, the rotor tooth row 21 meshes with the stator tooth row 11 at multiple points, and the second rotor tooth row 22 meshes with the output tooth row 321 formed on the gear portion 32 of the output shaft 3.

[0035] In this state, when the press rotor 4 is rotated around the central axis C by an external power source (not shown), rotational force is applied from the press rotor 4 to the rotor 2 while maintaining a pressing state. Because the rotor 2's stator gear row 11 and rotor gear row 21 are meshed in an inclined position, the rotor 2's simple rotation is constrained, and due to the meshing relationship between the rotor gear row 21 and the stator gear row 11, it performs precession around the central axis C.

[0036] As rotor 2 precesses, the meshing position between the second rotor gear row 22 on rotor 2 and the output gear row 321 on output shaft 3 sequentially moves in the circumferential direction. As a result, the rotational component included in the precession of rotor 2 is transmitted to output shaft 3, causing output shaft 3 to rotate around the central axis C. In other words, the rotational input of press rotor 4 is extracted as the rotational output of output shaft 3 via the precession of rotor 2.

[0037] In this case, the amount of precession (phase shift) of the rotor 2 is determined based on the difference in the number of teeth between the stator 1 and the rotor 2, in other words, the difference between the number of teeth in the stator gear row 11 and the number of teeth in the rotor gear row 21. The rotational speed of the output shaft 3 decreases relative to the input rotational speed according to this shift. For example, if the difference in the number of teeth between the stator gear row 11 and the rotor gear row 21 is 1, the rotor 2 precesses with a small relative advance per input revolution, and this relative advance is transmitted to the output shaft 3 via the meshing of the second rotor gear row 22 and the output gear row 321, thereby obtaining a large reduction ratio. Note that the difference in the number of teeth is not limited to 1, and may be set appropriately according to design requirements such as the desired reduction ratio, load capacity, efficiency, and vibration.

[0038] Furthermore, if the external power source is a motor, the motor and the crown gear reduction mechanism 10 constitute a power unit, and the rotation of the motor can be reduced and output from the output shaft 3.

[0039] In the crown gear reduction mechanism 10 to which the present invention is applied, the alignment of the contact points between the stator teeth 41 and rotor teeth 42 is improved in the stator 1 and rotor 2 in order to further improve the simultaneous meshing rate of the tooth rows of each other. The optimal tooth profile required to improve the alignment of the stator teeth 41 and rotor teeth 42 during meshing will be described.

[0040] Figure 3 shows the stator gear row 11 in stator 1 in three dimensions. A single stator tooth 41 in this stator gear row 11 is defined in a planar coordinate system. The tooth profile of each stator tooth 41 is such that at least the contact portion C with each rotor tooth 42 in the rotor gear row 21 has a number of teeth M in the stator gear row 11. S In this case, the central angle of one tooth located at the outermost radial circumference of stator 1 is 2π / M S Normalize to 1 using as the base length.

[0041] As shown in Figures 4(a) and (b), one stator tooth 41 can be represented by the following reference equation (A) in the xz coordinate system as a planar coordinate system. Focusing on one stator tooth 41, the top of the stator tooth 41 is set as the x-axis reference position, the root end of the contact portion C of the stator tooth 41 is set as the z-axis reference position, the tooth width direction extending in the circumferential direction is set as coordinate x, and the tooth height direction is set as coordinate z to form an xz coordinate system. In the x coordinate system, this x-axis reference position is set as 0. In coordinate x, the reference lengths of one tooth are set to x1 to x2.

[0042] z=d / 200(a6x 6 +a4x 4 +a2x 2 +a0)····(A) Here, d is the diameter of the disc-shaped stator 1.

[0043] In this standard formula (A), a6, a4, a2, and a0 are the number of teeth M of the stator tooth arrangement 11 according to the following formula (3). S It is calculated from.

[0044]

number

[0045] Number of teeth in stator dentition 11: M S Based on this, a6, a4, a2, and a0 can be calculated based on the matrix in equation (3). By pre-setting the calculated a6, a4, a2, and a0 as coefficients in equation (A) and substituting the diameter d of stator 1, the reference equation (A) can be expressed as a sixth-degree polynomial where z is expressed as a function of x. By substituting a value of x between reference lengths x1 and x2 into the reference equation (A), the corresponding value of z can be obtained, and consequently, a plot with specified x and z coordinates can be obtained. By gradually shifting the value of x, plots based on the corresponding z values ​​can be obtained sequentially, and the set of these plots will depend on the curve embodied by the sixth-degree polynomial.

[0046] Note that a6, a4, a2, and a0 represent the number of teeth M in the stator tooth arrangement 11. S It changes depending on the value of . Figure 5 shows the number of teeth M of the stator tooth row 11. S This shows the relationship between a6, a4, a2, and a0. S As the value of increases, the values ​​of a6, a4, a2, and a0 tend to approach each other, and a new rate of change has been discovered. These relationships are embodied through the determinant shown in equation (3).

[0047] In the crown gear reduction mechanism 10 to which the present invention is applied, with respect to the tooth profile of the stator teeth 41 in the stator tooth array 11 as defined by the reference formula (A), z is defined by formula (1) with respect to x. u With the upper limit being z defined by equation (2), l This is the lower limit.

[0048] z u =d / 200(a6x 6 +a4x 4 +a2x 2 +a0+C u )····(1) z l =d / 200(a6x 6 +a4x 4 +a2x 2 +a0+C l )····(2) C u =2.0, C l =-2.0

[0049] Figure 6 shows z defined by equations (1) and (2). u , z l This shows the shape of the curve. The tooth profile defined by the standard formula (A) of the stator tooth 41 is defined by the z defined in this formula (2). l The curve is greater than or equal to the curve defined by equation (1) z u It is assumed that the curve is below the curve shown in equation (2). By ensuring that the tooth profile of the stator teeth 41 is greater than or equal to the curve shown in equation (2) and less than or equal to the curve shown in equation (1), it is possible to minimize the occurrence of small initial mismatches at the contact area C between the rotor teeth 42 and the stator teeth 41, thereby improving the mutual alignment at the time of contact. As a result, the crown gear reduction mechanism 10 to which the present invention is applied can improve the meshing accuracy between the rotor teeth 42 and the stator teeth 41 and optimize load distribution, thereby achieving durability and a longer lifespan under high-load environments.

[0050] On the other hand, if the tooth profile of the stator teeth 41, as defined by standard formula (A), deviates at the contact area C from the region enclosed by the curves of formulas (1) and (2), that is, if the tooth profile of the stator teeth 41 is less than the curve of formula (2) or greater than the curve of formula (1), the meshing accuracy between the rotor teeth 42 and the stator teeth 41 will decrease. The effects of this mismatch will expand over time with usage, ultimately leading to a vicious cycle where only certain teeth bear the load. As a result, durability and extended lifespan under high-load environments cannot be achieved.

[0051] Therefore, the tooth profile defined by the standard formula (A) of the stator tooth 41 is the z of this formula (2). l The curve is greater than or equal to z in equation (1), and u The curve should be less than or equal to the specified value.

[0052] Note that C in equations (1) and (2) u , C l This is not limited to the range described above, and in order to further improve meshing accuracy and optimize load distribution, C u =1.2, C l It is desirable that the value be -1.2. The tooth profile defined by the standard formula (A) of the stator teeth 41 is such that the contact portion C is such that u =1.2, C l By being within the range defined by equations (1) and (2) = -1.2, the meshing accuracy can be further improved and load distribution can be optimized.

[0053] Furthermore, in order to further improve accuracy, C u =0.85, C l It is desirable that the value be -0.85. The tooth profile defined by the standard formula (A) of the stator teeth 41 is such that the contact portion C is such that u =0.85, C l By falling within the range defined by equations (1) and (2) = -0.85, the meshing accuracy can be further improved and load distribution can be more optimized.

[0054] The contact portion C in the stator teeth 41 of stator 1, as shown in Figure 4, is given by equation (7) via the x-axis reference position. 1L ~x 1H , x 2L ~x 2H It is sufficient if it is within that range.

[0055]

number

[0056] At least the contact portion C of the stator teeth 41, within the range described above, has a tooth profile defined by standard formula (A) that is z in formula (2). l The curve is greater than or equal to z in equation (1), and u It is sufficient that it is below the curve. And in this equation (7), x 1L ~x 1H , x 2L ~x 2H In all cases, the number of teeth in the stator tooth arrangement 11 is M. S It is given as a function of .

[0057] The rotor teeth 21 of the rotor 2 that meshes with the stator teeth 11 of the stator 1 may also be optimized in terms of the tooth profile of the rotor teeth 42, as described below, in order to improve the consistency during meshing.

[0058] Similarly, for the rotor teeth 42, they are defined in a plane coordinate system, and at least at the contact portion C with the stator tooth row 11, the number of teeth of the rotor tooth row 21 is M R In this case, the central angle of one tooth is 2π / M R The length is normalized to 1, with the reference length set to 1. The top of the rotor tooth 42 is set as the x-axis reference position, and the root end of the contact portion C of the rotor tooth 42 is set as the z-axis reference position. In the x-coordinate system, this x-axis reference position is set to 0.

[0059] In this case, when focusing on one rotor tooth 42, we define the xz coordinate system as the tooth width direction extending in the circumferential direction as coordinate x, and the tooth height direction as coordinate z. In coordinate x, the reference lengths of one tooth are defined as x1 to x2. As a result, as shown in Figure 7, the tooth profile of the rotor tooth 42 can be expressed in the xz coordinate system as a planar coordinate system by the following reference equation (B).

[0060] z=d / 200(a4x 4 +a2x 2 +a0)···(B) Here, d is the diameter of the disc-shaped rotor 2.

[0061] In this standard formula (B), a4, a2, and a0 are the number of teeth M of the rotor tooth arrangement 21 according to formula (6). R It is calculated from.

[0062]

number

[0063] Rotor tooth arrangement 21, number of teeth M R Based on this, a4, a2, and a0 can be calculated from the matrix in equation (6). By pre-setting the calculated a4, a2, and a0 as coefficients in equation (B) and substituting the diameter d of rotor 2, the reference equation (B) can be expressed as a quartic equation with respect to z, where only x is the variable. By substituting a value of x between reference lengths x1 and x2 into the reference equation (B), the corresponding value of z can be obtained, and consequently, a plot with specified x and z coordinates can be obtained. By gradually shifting the value of x, plots based on the corresponding z values ​​can be obtained sequentially, and the set of these plots will depend on a curve embodied by a quartic equation.

[0064] Note that a4, a2, and a0 represent the number of teeth M in the rotor tooth arrangement 21. R It changes depending on the value of M. R As the value of increases, we have newly discovered a tendency for the values ​​of a4, a2, and a0 to approach each other, as well as the rate of change, and we have embodied these relationships through the determinant shown in equation (6).

[0065] In the crown gear reduction mechanism 10 to which the present invention is applied, with respect to the tooth profile of the rotor teeth 42 in the rotor tooth row 21 as defined by the reference formula (B), z is defined by formula (4) with respect to x. u With the upper limit being z defined by equation (5) l This is the lower limit.

[0066] z u =d / 200(a4x 4 +a2x 2 +a0+C u )····(4) z l =d / 200(a4x 4 +a2x 2 +a0+C l )····(5) C u =2.0, C l =-2.0

[0067] Figures 7(a) and (b) show z defined by equations (4) and (5). u , z l This shows the shape of the curve. The tooth profile defined by the standard formula (B) of the rotor teeth 42 is defined by the z defined in this formula (5). l The curve is greater than or equal to the curve defined by equation (4) z u It is assumed that the curve is below this value. By having the tooth profile of the rotor teeth 42 be greater than or equal to the curve of equation (5) and less than or equal to the curve of equation (4), it is possible to minimize the occurrence of small initial mismatches at the contact portion C between the rotor teeth 42 and the stator teeth 41, thereby improving the mutual alignment at the time of contact. As a result, the crown gear reduction mechanism 10 to which the present invention is applied can improve the meshing accuracy between the rotor teeth 42 and the stator teeth 41 and optimize load distribution, thereby achieving durability and a longer lifespan under high-load environments.

[0068] On the other hand, if the tooth profile of the rotor teeth 42, as defined by standard formula (B), deviates at the contact area C from the region enclosed by the curves of formulas (4) and (5), that is, if the tooth profile of the rotor teeth 42 is less than the curve of formula (5) or exceeds the curve of formula (4), the meshing accuracy between the rotor teeth 42 and the stator teeth 41 will decrease. The effects of this mismatch will expand over time with usage, ultimately leading to a vicious cycle where only certain teeth bear the load. As a result, durability and extended lifespan under high-load environments cannot be achieved.

[0069] Therefore, the tooth profile defined by the standard formula (B) for rotor teeth 42 is the z of this formula (5). l The curve is greater than or equal to z in equation (4), and u The curve should be less than or equal to the specified value.

[0070] Note that C in equations (4) and (5) u , C l This is not limited to the range described above, and in order to further improve meshing accuracy and optimize load distribution, C u =1.2, C l It is desirable that it be set to =-1.2, and furthermore, C u =0.85, C l It is desirable that the value be set to -0.85. This will further improve meshing accuracy and optimize load distribution.

[0071] The contact portion C in the rotor teeth 42 of rotor 2 is given by the x-axis reference position shown in equation (8) 1L ~x 1H , x 2L ~x 2H It is sufficient if it is within that range.

[0072]

number

[0073] At least the contact portion C of the rotor teeth 42 has a tooth profile defined by standard formula (B) within the range described above, which is z in formula (5). l The curve is greater than or equal to z in equation (4), and u It is sufficient that it is below the curve. And in this equation (8), x 1L ~x 1H , x 2L ~x 2H In all cases, the rotor tooth arrangement 21 has a number of teeth M. R It is given as a function of .

[0074] In this invention, in addition to cases where either the stator teeth 41 or the rotor teeth 42 are within the range of the curve described above, both the stator teeth 41 and the rotor teeth 42 may be within the range of the curve described above. At the contact portion C between them, the tooth profile of the stator teeth 41 as defined by the reference formula (A) is as z in formula (2) l Above the curve, z in equation (1) u The curve is less than or equal to the z of this equation (5), and the tooth profile defined by the standard equation (B) of the rotor teeth 42 is such that the z of this equation (5) l Above the curve, z in equation (4) u By keeping the curve below this value, the meshing accuracy between the gears can be further improved, thereby extending the lifespan of the crown gear reduction mechanism 10.

[0075] The present invention is not limited to the embodiments described above. For example, it may be embodied as a design support system for a crown gear reduction mechanism. Figure 8 is a block diagram of the design support system 50 for a crown gear reduction mechanism. The design support system 50 is provided via a software program installed on a personal computer (PC) 51. After the design support system 50 actually designs the tooth profiles of the stator teeth 41 and rotor teeth 42, the design data is input to the PC 51. The PC 51, via the software program, determines that the designed tooth profile of the stator teeth 41 is z in equation (2) l Above the curve, z in equation (1) u Whether or not it is included below the curve, and whether the tooth profile of the designed rotor teeth 42 is in equation (5) z l Above the curve, z in equation (4) u The system determines whether the curve is below a certain point. PC51 outputs the result of this determination.

[0076] Figure 9 shows a flowchart of the design support system 50 and its software program.

[0077] First, in step S11, the data of the tooth profile of the designed stator teeth 41 is input. This tooth profile data is provided by the user and can take any form, such as actual design drawings, image data of the tooth profile, xz coordinate axis point sequence data, or curve data. Also in step S11, the number of teeth M of the stator tooth array 11 is input as data necessary for identification. S The system also acquires data on the diameter d of stator 1. This data may be directly input by the user to the PC51 via a user interface, or it may be read from input design drawings, image data, etc., via a software program.

[0078] Next, in step S12, the input tooth profile data is converted to a planar coordinate system of xz coordinate axes under the control of the software program. In step S12, if the input data is already on the xz coordinate axis, this step may be skipped. If the tooth profile data is 3D CAD data, then the number of teeth M of the stator tooth row 11 is... S In this case, the central angle of one tooth is 2π / M S The process normalizes the length to 1 using the given length as the base length.

[0079] Next, the process moves to step S13, where the acquired tooth profile data of the stator tooth 41 is such that, with the top of the stator tooth 41 as the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, z is defined by equation (1) with respect to x. u The upper threshold curve S is below the curve of . u And z defined by equation (2) l Lower threshold curve S is greater than or equal to the curve. l Determine whether or not it is included between these two.

[0080] The upper threshold curve S referred to here is the upper threshold curve S. u z is defined by equation (1). u It may be itself, but is not limited to this, and z as defined in equation (1) u If the curve is below this value, the meshing accuracy can be improved as described above. Therefore, the upper threshold curve Su z is defined by equation (1). u This is considered to be below the curve S. u This may be something that is set in advance on the system side.

[0081] Similarly, the lower threshold curve S l z is defined by equation (2). l The curve itself may be used, but is not limited to this, and is defined by z as defined in equation (2). l If the curve is greater than or equal to the curve, the meshing accuracy can be improved as described above. Therefore, the lower threshold curve S l z is defined by equation (2). l This is considered to be above the curve S. l This may be something that is set in advance on the system side.

[0082] Next, the process moves to step S14, where the judgment result from step S13 is output. In the simplest case, the judgment result is that the tooth profile data of the stator teeth 41 obtained is bounded by the upper threshold curve S u and the lower threshold curve S l If the data is included between the two, it may indicate that the design is appropriate; conversely, if it is not included, it may indicate that there is room for improvement in the design. In addition, the acquired tooth profile data of the stator teeth 41 may be shown as the upper threshold curve S u and the lower threshold curve S l If not included between, the data of the tooth profile of the stator tooth 41 specifically falls within the upper threshold curve S u and the lower threshold curve S l It may also be indicated which part of the upper threshold curve S is deviating. u and the lower threshold curve S l Along with pointing out the part, the upper threshold curve S u and the lower threshold curve S l You may also want to indicate design improvement guidelines to include them between the two.

[0083] In Figure 9 above, we explained the case of determining whether the tooth profile of the designed stator teeth 41 is appropriate, but the rotor teeth 42 are realized using a similar flow, and the explanation can be given by substituting rotor teeth 42 for stator teeth 41. In such a case, in step S11, the data of the tooth profile of the designed rotor teeth 42 is input. Also in step S11, the number of teeth M of the rotor tooth array 21 is input. R The data for the diameter d of rotor 2 is also obtained.

[0084] Next, in step S12, the input tooth profile data is converted to a planar coordinate system with the zx coordinate axis under the control of the software program. The number of teeth in the rotor tooth row 21 is M. R In this case, the central angle of one tooth is 2π / M R The process normalizes the length to 1 using the given length as the base length.

[0085] Next, the process moves to step S13, where the acquired tooth profile data of the rotor tooth 42 is defined as follows: with respect to x, z is defined by equation (4), where the top of the rotor tooth 42 is the x-axis reference position, the tooth width direction is the coordinate x, and the tooth height direction is the coordinate z. u The upper threshold curve T is below the curve of . u And z defined by equation (5) l The lower threshold curve T is greater than or equal to the curve of . l It is determined whether or not it is included between the two. Next, the process moves to step S14 and outputs the result of the determination in step S13.

[0086] This allows us to similarly determine whether the tooth profile data for the rotor teeth 42 is appropriate or not. [Explanation of symbols]

[0087] 1 stater 2 rotors 3 Output shaft 4 Press Rotor 5 Bearing section 8 Housing 10 Crown gear reduction mechanism 11 Stator dentition 21 Rotor teeth 22 Second Rotor Teeth 23 Opposing surfaces 24 Opposing surfaces 31 Shaft 32 Gear section 41 stator teeth 42 rotor teeth 50 Design support systems 51 PC 321 Output dentition

Claims

1. A stator having an annular stator tooth arrangement, A rotor having an annular rotor tooth arrangement and positioned at an angle to the stator, The system comprises an output shaft through which the rotation of the rotor is transmitted, The above rotor is configured to perform precession motion by meshing the stator teeth and the rotor teeth at multiple locations on both the left and right sides of the rotor's tilt centerline, The tooth profile of each stator tooth in the stator gear row described above is such that, at least at the contact point with each rotor tooth in the rotor gear row described above, the number of teeth M in the stator gear row described above is S In this case, the central angle of one tooth is 2π / M S In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the stator tooth is the z-axis reference position, the top of the stator tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (1). u With the upper limit being z defined by equation (2), l With the lower limit, The tooth profile of each rotor tooth in the rotor gear row described above is defined in a planar coordinate system where the circumferential direction is normalized to 1 with a central angle of 2π / MR for one tooth as the reference length, at least at the contact portion with each stator tooth in the stator gear row described above, and the number of teeth in the rotor gear row is MR, and the root end of the contact portion of the rotor tooth is the z-axis reference position, the top of the rotor tooth is the x-axis reference position, the tooth width direction is the coordinate x, and the tooth height direction is the coordinate z, and z is limited to zu as defined by equation (4) and lower bound by zl as defined by equation (5) with respect to x. A crown gear reduction mechanism characterized by the following. z u =d / 200(a 6 x 6 +a 4 x 4 +a 2 x 2 +a 0 +C u )・・・・(1) z l =d / 200(a 6 x 6 +a 4 x 4 +a 2 x 2 +a 0 +C l )・・・・(2) Here, d is the diameter of the stator, C u = 2.0, C l = -2.0 Also a 6 a 4 a 2 a 0 From equation (3), the number of teeth M S It is calculated from this. [Math 1] ・・・・・・・・（３） z u =d / 200(a 4 x 4 +a 2 x 2 +a 0 +C u )...(4) z l = d / 200 (a 4 x 4 + a 2 x 2 + a 0 + C l )...(5) Here, d is the diameter of the rotor, Cu = 2.0, Cl = -2.0 Furthermore, a4, a2, and a0 are calculated from the number of teeth MR using equation (6). [Math 2] ・・・・・・・（６）

2. Furthermore, in equation (1), C u = 0.85, and in equation (2), C l = -0.85 The crown gear reduction mechanism according to claim 1, characterized by the following:

3. In equation (4), C u = 0.85, and in equation (5), C l = -0.85 A crown gear reduction mechanism according to claim 1 or 2, characterized by the above.

4. The contact portion of the stator teeth described above is connected via the x-axis reference position as shown in equation (7) 1L ~x 1H , x 2L ~x 2H It is considered to be within the scope of The crown gear reduction mechanism according to claim 1, characterized by the following: [Math 3] ・・・・・・・・（７） Also, x 2L = -x 1H , x 2H = -x 1L

5. The contact portion of the rotor teeth described above is connected via the x-axis reference position as shown in equation (8) 1L ~x 1H , x 2L ~x 2H It is considered to be within the scope of The crown gear reduction mechanism according to claim 1, characterized by the following: [Math 4] ・・・・・・・・（８） Also, x 2L = -x 1H , x 2H = -x 1L

6. A design support system for a crown gear reduction mechanism comprising a stator having an annular stator gear row, a rotor having an annular rotor gear row and positioned at an angle to the stator, and an output shaft to which the rotation of the rotor is transmitted, wherein the rotor is configured to perform precession motion by meshing the stator gear row and the rotor gear row at multiple locations on both the left and right sides of the rotor's tilt centerline, A data acquisition means for acquiring data on the tooth profile of each stator tooth in the designed stator tooth array and data on the tooth profile of each rotor tooth in the designed rotor tooth array, The tooth profile data of each stator tooth obtained by the above data acquisition means is, at least at the contact portion with each rotor tooth in the rotor tooth array, the number of teeth M in the stator tooth array. S In this case, the central angle of one tooth is 2π / M S In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the stator tooth is the z-axis reference position, the top of the stator tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (1). u The upper threshold curve S is below the curve of . u And z defined by equation (2) l The lower threshold curve S is greater than or equal to the curve. l Determine whether or not it is included between and The data of the tooth profile of each rotor tooth acquired by the above data acquisition means is defined in a planar coordinate system in which the circumferential direction is normalized to 1 with the central angle of one tooth, 2π / MR, as the reference length, at least at the contact portion with each stator tooth in the stator tooth row, and when the number of teeth in the rotor tooth row is MR, the circumferential direction is the tooth width direction, and when the end on the tooth root side of the contact portion of the rotor tooth is the z-axis reference position, and the top of the rotor tooth is the x-axis reference position, and the tooth width direction is the coordinate x, and the tooth height direction is the coordinate z, then the determination means determines whether z is contained between the upper threshold curve T u, which is less than or equal to the curve z u defined by equation (4), and the lower threshold curve T l, which is greater than or equal to the curve z l defined by equation (5), with respect to x. The system includes an output means for outputting the determination result obtained by the above determination means. A design support system for crown gear reduction mechanisms featuring the following characteristics. z u =d / 200(a 6 x 6 +a 4 x 4 +a 2 x 2 +a 0 +C u )・・・・(1) z l =d / 200(a 6 x 6 +a 4 x 4 +a 2 x 2 +a 0 +C l )・・・・(2) Here, d is the diameter of the stator, C u = 2.0, C l = -2.0 Also a 6 a 4 a 2 a 0 From equation (3), the number of teeth M S It is calculated from this. [Math 1] ・・・・・・・・（３） z u =d / 200(a 4 x 4 +a 2 x 2 +a 0 +C u )...(4) z l = d / 200 (a 4 x 4 + a 2 x 2 + a 0 + C l )...(5) Here, d is the diameter of the rotor, Cu = 2.0, Cl = -2.0 Furthermore, a4, a2, and a0 are calculated from the number of teeth MR using equation (6). [Math 2] ・・・・・・・（６）

7. A method for designing a crown gear reduction mechanism comprising a stator having an annular stator gear row, a rotor having an annular rotor gear row and positioned at an angle to the stator, and an output shaft to which the rotation of the rotor is transmitted, wherein the rotor is configured to perform precession motion by meshing the stator gear row and the rotor gear row at multiple locations on both the left and right sides of the rotor's tilt centerline, A data acquisition step to acquire data on the tooth profile of each stator tooth in the designed stator tooth array and data on the tooth profile of each rotor tooth in the designed rotor tooth array, The tooth profile data of each stator tooth acquired in the above data acquisition step is, at least at the contact portion with each rotor tooth in the rotor tooth array, the number of teeth M in the stator tooth array. S In this case, the central angle of one tooth is 2π / M S In a planar coordinate system where the circumferential direction is normalized to 1 with a reference length of , and the tooth width direction is defined as follows: the root end of the contact portion of the stator tooth is the z-axis reference position, the top of the stator tooth is the x-axis reference position, the tooth width direction is coordinate x, and the tooth height direction is coordinate z, then z is defined with respect to x by equation (1). u The upper threshold curve S is below the curve of . u And z defined by equation (2) l The lower threshold curve S is greater than or equal to the curve. l Determine whether or not it is included between and The data of the tooth profile of each rotor tooth acquired in the above data acquisition step is defined in a planar coordinate system in which the circumferential direction is normalized to 1 with the central angle of one tooth, 2π / MR, as the reference length, at least at the contact portion with each stator tooth in the stator tooth row, and the number of teeth in the rotor tooth row is MR, and the tooth width direction is normalized to 1, with the root end of the contact portion of the rotor tooth as the z-axis reference position and the top of the rotor tooth as the x-axis reference position, with the tooth width direction as coordinate x and the tooth height direction as coordinate z, and the determination step determines whether z is included between the upper threshold curve T u, which is less than or equal to the curve z u defined by equation (4), and the lower threshold curve T l, which is greater than or equal to the curve z l defined by equation (5), with respect to x. The computer is to perform the following steps: the determination step described above and the output step which outputs the determination result. A design support method for a crown gear reduction mechanism characterized by the following. z u =d / 200(a 6 x 6 +a 4 x 4 +a 2 x 2 +a 0 +C u )・・・・(1) z l =d / 200(a 6 x 6 +a 4 x 4 +a 2 x 2 +a 0 +C l )・・・・(2) Here, d is the diameter of the stator, C u = 2.0, C l = -2.0 Also a 6 a 4 a 2 a 0 From equation (3), the number of teeth M S It is calculated from this. [Math 1] ・・・・・・・・（３） z u =d / 200(a 4 x 4 +a 2 x 2 +a 0 +C u )...(4) z l = d / 200 (a 4 x 4 + a 2 x 2 + a 0 + C l )...(5) Here, d is the diameter of the rotor, Cu = 2.0, Cl = -2.0 Furthermore, a4, a2, and a0 are calculated from the number of teeth MR using equation (6). [Math 2] ・・・・・・・（６）

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