Work careers and methods for designing work careers

Abstract

To provide a work carrier that can suppress wear on the external teeth and drive pins. [Solution] A work carrier 1 has external teeth 2 formed that mesh with a sun gear pin and an internal gear pin, wherein the diameter of the carrier tip circle is set to a value greater than or equal to the diameter of the pitch circle R2, and less than or equal to the sum of the diameter of the pitch circle R2 and the diameters of the sun gear pin and the internal gear pin, and the tip angle A formed by a first line B connecting the carrier center O2 and the root center point 4b, a second line D passing through the first line B and perpendicular to the pitch circle R2, and a third line F passing through the first intersection C and inclined toward the carrier center O2 than the second line D, is set to the larger of the optimal angle on the sun gear side and the optimal angle on the internal gear side.

Description

[Technical Field]

[0001] This disclosure relates to an invention concerning a work carrier and a method for designing a work carrier. [Background technology]

[0002] Conventionally, work carriers are known that have external teeth that mesh with a sun gear having multiple sun gear pins located inside the surface plate and a multiple internal gear pins located outside the surface plate (see, for example, Patent Documents 1 and 2). [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Application Publication No. 10-315123 [Patent Document 2] Japanese Patent Application Publication No. 9-193009 [Overview of the project] [Problems that the invention aims to solve]

[0004] Incidentally, while a workpiece is being polished by a polishing device, the external teeth of the workpiece carrier repeatedly come into contact with the sun gear pins and internal gear pins (hereinafter collectively referred to as "drive pins"), causing wear on both the external teeth and drive pins. As a result of the wear on the workpiece carrier and drive pins, wear particles are generated, and if these particles mix with the polishing fluid, it can degrade the machining quality of the workpiece. Furthermore, worn workpiece carriers and drive pins need to be replaced, but to reduce the burden of maintenance, it is desirable to extend the replacement period. Moreover, depending on the wear condition of the workpiece carrier and drive pins, it can also become a factor that hinders stable workpiece machining. Therefore, it is necessary to suppress the wear on the external teeth and drive pins of the workpiece carrier.

[0005] This disclosure addresses the above-mentioned issues and aims to provide a work carrier and a work carrier design method that can suppress wear of external teeth and drive pins. [Means for solving the problem]

[0006] To achieve the above objective, the work carrier of this disclosure is a work carrier having external teeth that mesh with a plurality of sun gear pins of a sun gear located inside the surface platen and a plurality of internal gear pins of an internal gear located outside the surface platen. The external teeth are composed of alternating peaks and valleys, and the valleys have a curved tooth root surface that is recessed toward the carrier center with a constant curvature, and the sun gear pin and the internal gear pin have a cylindrical shape with the same pin radius. Furthermore, when the external tooth is viewed in a frontal tooth profile, the following is defined for each valley: The line connecting the carrier center and the root center point, which is the position that bisects the root surface in the circumferential direction, is defined as the first line; the intersection of the first line and the pitch circle, which is the circle connecting the pitch points where the sun gear pin and the internal gear pin touch the external tooth, is defined as the first intersection; the line passing through the first intersection and perpendicular to the first line is defined as the second line; the circle with the same radius as the pin radius and centered at the first intersection is defined as the first circle; the line passing through the first intersection and inclined toward the carrier center more than the second line is defined as the third line; the angle between the second line and the third line is defined as the tip angle; and the first circle and the first circle are defined as The line tangent to the sun gear pin that meshes with a defined groove is defined as the fourth line, the angle between the first line and the fourth line is defined as the first angle, the line tangent to the first circle and the internal gear pin that the first circle meshes with a defined groove is defined as the fifth line, the angle between the first line and the fifth line is defined as the second angle, the point of contact between the fourth line and the sun gear pin to which the fourth line is tangent is defined as the first contact point, the distance from the carrier center to the first contact point is defined as the first distance, the point of contact between the fifth line and the internal gear pin to which the fifth line is tangent is defined as the second contact point, and the distance from the carrier center to the second contact point is defined as the second distance. Furthermore, the first angle at the groove where the sun gear pin meshes, which provides the first distance that satisfies the condition that the diameter of the carrier tip circle < first distance × 2, is defined as the optimal angle on the sun gear side. Furthermore, the second angle at the groove where the internal gear pin engages, which is necessary to obtain the second distance that satisfies the condition that the diameter of the carrier tooth tip circle < second distance × 2, is defined as the optimal angle on the internal gear side. Furthermore, the diameter of the carrier tip circle, which is a circle connecting the tips of the teeth of the peaks, is set to be greater than or equal to the diameter of the pitch circle, and less than or equal to the sum of the diameter of the pitch circle and the diameter of the sun gear pin, and less than or equal to the sum of the diameter of the pitch circle and the diameter of the internal gear pin, and the tip angle is set to the larger of the optimal angle on the sun gear side and the optimal angle on the internal gear side.

[0007] To achieve the above objective, the work carrier design method of this disclosure is a method for designing a work carrier having external teeth that mesh with a plurality of sun gear pins having a sun gear arranged inside a surface plate and a plurality of internal gear pins having an internal gear arranged outside the surface plate, wherein the external teeth are composed of alternately formed peaks and valleys, the valleys have a curved tooth root surface that is recessed toward the center of the carrier with a constant curvature, and the sun gear pins and the internal gear pins have a cylindrical shape with the same pin radius. Furthermore, when the external tooth is viewed in a frontal tooth profile, the following is defined for each valley: The line connecting the carrier center and the root center point, which is the position that bisects the root surface in the circumferential direction, is defined as the first line; the intersection of the first line and the pitch circle, which is the circle connecting the pitch points where the sun gear pin and the internal gear pin touch the external tooth, is defined as the first intersection; the line passing through the first intersection and perpendicular to the first line is defined as the second line; the circle with the same radius as the pin radius and centered at the first intersection is defined as the first circle; the line passing through the first intersection and inclined toward the carrier center more than the second line is defined as the third line; the angle between the second line and the third line is defined as the tip angle; and the first circle and the first circle are defined as A straight line tangent to a sun gear pin that engages with a defined groove is defined as the fourth straight line, the angle between the first straight line and the fourth straight line is defined as the first angle, a straight line tangent to the first circle and the internal gear pin that the first circle engages with a defined groove is defined as the fifth straight line, the angle between the first straight line and the fifth straight line is defined as the second angle, the point of contact between the fourth straight line and the sun gear pin to which the fourth straight line is tangent is defined as the first point of contact, the distance from the carrier center to the first point of contact is defined as the first distance, the point of contact between the fifth straight line and the internal gear pin to which the fifth straight line is tangent is defined as the second point of contact, and the distance from the carrier center to the second point of contact is defined as the second distance. At this time, a step of setting the diameter of a carrier tooth tip circle, which is a circle connecting the tooth tips of the crest portions, to a value that is not less than the diameter of the pitch circle and not more than the sum of the diameter of the pitch circle and the diameter of the sun gear pin, and not more than the sum of the diameter of the pitch circle and the diameter of the internal gear pin; a step of selecting, as an optimum angle on the sun gear side, a first angle in a valley portion where a sun gear pin that satisfies carrier tooth tip circle diameter < 2 × first distance obtained from the first angle calculated for each valley portion meshes; a step of selecting, as an optimum angle on the internal gear side, a second angle in a valley portion where an internal gear pin that satisfies carrier tooth tip circle diameter < 2 × second distance obtained from the second angle calculated for each valley portion meshes; and a step of setting the tooth tip angle to the larger value of the optimum angle on the sun gear side and the optimum angle on the internal gear side.

Advantages of the Invention

[0008] In the work carrier and the work carrier design method of the present disclosure, wear of the external teeth and the drive pins can be suppressed.

Brief Description of the Drawings

[0009] [Figure 1] It is a cross-sectional view schematically showing a polishing apparatus in which the work carrier of the present embodiment is used. [Figure 2] It is an explanatory view showing the positional relationship between the work carrier, the sun gear pin, and the internal gear pin. [Figure 3] It is an enlarged view of the main part of the work carrier of the present embodiment. [Figure 4A] It is an enlarged view of part A in FIG. 2. [Figure 4B] It is an enlarged view of part B in FIG. 2. [Figure 5] It is an explanatory view showing a first straight line, a second straight line, a third straight line, a first intersection point, a first circle, and a tooth tip angle defined for each valley portion. [Figure 6A] It is an explanatory view showing a first angle, a fourth straight line, and a first contact point defined for each valley portion. [Figure 6B] This is an explanatory diagram showing the first straight line defined for each valley. [Figure 7A] This is an explanatory diagram showing the second angle, fifth line, and second point of tangency defined for each valley. [Figure 7B] This is an explanatory diagram showing the second straight line defined for each valley. [Figure 8A] This is an explanatory diagram showing the first design coordinate system. [Figure 8B] This is an explanatory diagram showing the second design coordinate system. [Figure 9] This is a flowchart showing the basic flow of the design method for the external teeth of a work carrier. [Figure 10A] This flowchart shows the flow for determining the optimal angle on the sun gear side in the design method for the external teeth of a work carrier. [Figure 10B] This table shows specific examples of the first angle and first distance calculated for each location in the valley. [Figure 11A] This flowchart shows the flow for determining the optimal angle on the internal gear side in the design method for the external teeth of a work carrier. [Figure 11B] This table shows specific examples of the second angle and second distance calculated for each location in the valley. [Figure 12] This is a flowchart showing the design flow of the external tooth shape in the design method for the external teeth of a work carrier. [Figure 13A] This is an explanatory diagram showing the settings for the carrier center and pitch circle. [Figure 13B] This is an explanatory diagram showing the settings for the first straight line. [Figure 13C] This is an explanatory diagram showing the settings of the virtual first yen. [Figure 13D] This is an explanatory diagram showing the settings for the second straight line. [Figure 13E] This is an explanatory diagram showing the settings for the third straight line. [Figure 13F] This is an explanatory diagram showing the setting state of the second intersection and the specified state of the tooth root surface. [Figure 13G] This is an explanatory diagram showing the setting of the tooth tip line. [Figure 13H]This is an explanatory diagram showing the setting of the carrier tooth tip line and the third intersection, as well as the specified state of the tooth root surface. [Figure 13I] This is an explanatory diagram showing the specified state of the tooth tip surface. [Figure 13J] This is an explanatory diagram showing the final designed external tooth. [Figure 14] This table shows the relationship between the tooth tip angle and the contact ratio of the external teeth with the sun gear pin and internal gear pin. [Modes for carrying out the invention]

[0010] The forms for implementing the work carrier and work carrier design method of this disclosure are described below with reference to the drawings.

[0011] The work carrier 1 in this embodiment is used to hold a thin, disc-shaped workpiece W to be polished by the polishing device 100. Here, the polishing device 100 is a double-sided polishing device capable of simultaneously polishing the front and back surfaces of the workpiece W, as shown in Figure 1. The polishing device 100 comprises an upper platen 101 (platen), a lower platen 102 (platen), a sun gear 103, and an internal gear 104.

[0012] The upper platen 101 and the lower platen 102 each have a ring-shaped (donut-shaped) form with a through hole in the center. The upper platen 101 and the lower platen 102 are arranged concentrically around axis O1. The sun gear 103 is located inside the lower platen 102 (in the central part of the lower platen 102). The internal gear 104 is located outside the lower platen 102 (surrounding the outer circumference of the lower platen 102).

[0013] The upper platen 101 is attached to the rod 116 of the lifting cylinder via a platen suspension 115. The upper platen 101 is raised and lowered by the lifting cylinder. The upper platen 101 is lowered when the workpiece W is being polished. When the upper platen 101 is lowered, a hook 117 attached to the upper platen 101 engages with a driver 111a formed at the upper end of the first drive shaft 111. Here, the first drive shaft 111 is connected to a motor (not shown). Therefore, the upper platen 101 rotates when the first drive shaft 111 rotates due to the motor, and rotational power is transmitted from the driver 111a to the hook 117. Note that the mechanism for supporting and raising / lowering the upper platen 101 is not limited to this.

[0014] The lower platen 102 is connected to a motor (not shown) via a second drive shaft 112. The sun gear 103 is connected to a motor (not shown) via a third drive shaft 113. The internal gear 104 is connected to a motor (not shown) via a fourth drive shaft 114. The upper platen 101, lower platen 102, sun gear 103, and internal gear 104 are each individually rotated around axis O1 in the required direction and at the required speed. Note that the sun gear 103 or the internal gear 104 may be fixed.

[0015] The sun gear 103 and the internal gear 104 each have the form of pin gears.

[0016] In other words, the sun gear 103 has a sun gear body 103A and a plurality of sun gear pins 105 attached to the sun gear body 103A. The sun gear body 103A is a disc member centered on axis O1. The third drive shaft 113 is fixed to the sun gear body 103A. The plurality of sun gear pins 105 are mounted on the outer circumference of the sun gear body 103A at regular intervals, standing upright along axis O1. That is, the plurality of sun gear pins 105 form an annular row of pins that will become the external teeth of the sun gear 103 (see Figure 2). In addition, each sun gear pin 105 is constructed by detachably attaching a cylindrical collar to a cylindrical pin body fixed to the sun gear body 103A. The sun gear pin 105 as a whole has a cylindrical shape.

[0017] The internal gear 104 comprises an internal gear body 104A and a plurality of internal gear pins 106 attached to the internal gear body 104A. The internal gear body 104A is an annular member centered on axis O1. The fourth drive shaft 114 is fixed to the internal gear body 104A. The plurality of internal gear pins 106 are mounted on the inner circumference of the internal gear body 104A at regular intervals, standing upright along axis O1. That is, the plurality of internal gear pins 106 form an annular row of pins that become the internal teeth of the internal gear 104 (see Figure 2). Each internal gear pin 106 is constructed by detachably attaching a cylindrical collar to a cylindrical pin body fixed to the internal gear body 104A. The internal gear pins 106 as a whole have a cylindrical shape.

[0018] Furthermore, the sun gear pin 105 and the internal gear pin 106 are set to have the same diameter. In the following, the radius dimension of the sun gear pin 105 and the radius dimension of the internal gear pin 106 will be referred to as "pin radius Rp".

[0019] The work carrier 1 is a circular, thin plate member. As shown in Figure 2, the work carrier 1 has a workpiece holding hole 1a and external teeth 2.

[0020] The workpiece holding hole 1a is a hole that penetrates the workpiece carrier 1. The workpiece W is held by the workpiece carrier 1 by being positioned inside the workpiece holding hole 1a. The external teeth 2 are formed on the outer periphery of the workpiece carrier 1. As shown in an enlarged view in Figure 2, the external teeth 2 consist of a plurality of peaks 3 and a plurality of valleys 4 that are alternately formed along the outer periphery of the workpiece carrier 1.

[0021] As shown in Figure 3, the ridge portion 3 has a tooth tip surface 3a that constitutes the tooth tip, tooth root surfaces 3b located on both sides of the tooth tip surface 3a, and a connecting surface 3c that connects the tooth tip surface 3a and the tooth root surface 3b. Here, the tooth tip surface 3a is curved along the carrier tooth tip circle R1 when the external tooth 2 is viewed from the front. The "carrier tooth tip circle R1" is the circle that connects the tooth tips, which are the tips of the ridge portion 3. The tooth root surface 3b is formed on a plane that follows the tooth tip line H, which will be described later, when the external tooth 2 is viewed from the front. The connecting surface 3c is curved with a predetermined curvature when the external tooth 2 is viewed from the front.

[0022] The valley portion 4 has a root surface 4a. Both ends of the root surface 4a are smoothly continuous with the abutment surface 3b. When the external tooth 2 is viewed from the front, the root surface 4a is formed as a curved surface that is concave with a constant curvature toward the center of the work carrier 1 (hereinafter referred to as "carrier center O2"). Furthermore, the position that bisects the root surface 4a in the circumferential direction when the external tooth 2 is viewed from the front is defined as the "root center point 4b".

[0023] Furthermore, the work carrier 1 is set so that the diameter φ1 of the carrier tooth tip circle R1 satisfies any value that satisfies the following equation (1). φ2≦φ1≦φ2+(Rp×2) ···(1) Here, φ1 is the diameter of the carrier tooth tip circle R1. φ2: Diameter of the pitch circle R2 of work carrier 1 Rp is the pin radius. In other words, the diameter φ1 of the carrier tooth tip circle R1 is greater than or equal to the diameter φ2 of the pitch circle R2. Also, the diameter φ1 of the carrier tooth tip circle R1 is less than or equal to the sum of the diameter φ2 of the pitch circle R2 and twice the pin radius Rp.

[0024] The "pitch circle R2" is the circle connecting the pitch points P, as shown in Figures 4A and 4B. The "pitch point P" is the position where the sun gear pin 105 and the internal gear pin 106 contact the external teeth 2 of the work carrier 1. Hereafter, the sun gear pin 105 and the internal gear pin 106 will be collectively referred to as the "drive pin". The pitch point P where the sun gear pin 105 contacts the external teeth 2 coincides with the pitch point P where the internal gear pin 106 contacts the external teeth 2. Also, the centers of the carrier tip circle R1 and the pitch circle R2 coincide with the carrier center O2. Furthermore, the circle indicated as "R3" in Figures 4A and 4B is a circle centered at the carrier center O2 with a diameter of φ2 + (Rp × 2). In other words, the carrier tip circle R1, the pitch circle R2, and the circle R3 are concentric circles.

[0025] Furthermore, "twice the pin radius Rp" refers to the diameter of the sun gear pin 105 and the diameter of the internal gear pin 106. Therefore, the diameter φ1 of the carrier tip circle R1 is less than or equal to the sum of the diameter φ2 of the pitch circle R2 and the diameter of the sun gear pin 105, and less than or equal to the sum of the diameter φ2 of the pitch circle R2 and the diameter of the internal gear pin 106. However, in this embodiment, the diameter of the sun gear pin 105 and the diameter of the internal gear pin 106 are the same.

[0026] Furthermore, the work carrier 1 is defined as follows for each valley 4 when the external tooth 2 is viewed in the frontal tooth profile (see Figure 5). Let the first straight line B be the line passing through the carrier center O2 and the midpoint 4b of the tooth root. Let the intersection point of the first line B and the pitch circle R2 be the first intersection point C. Let the second line D be the line that passes through the first intersection point C and is perpendicular to the first line B. Let the first circle E be a circle with the same radius as the pin radius Rp and centered at the first intersection C. Let the third line F be a line that passes through the first intersection C and is inclined more toward the carrier center O2 than the second line D. The third line F is defined symmetrically across the first line B. Let the angle between the second line D and the third line F be the tooth tip angle A. The tooth tip angle A is defined symmetrically across the first line B.

[0027] Furthermore, when the work carrier 1 engages with the sun gear pin 105, the external teeth 2 are defined as follows for each valley 4 when viewed from the front tooth profile (see Figures 6A and 6B). The fourth straight line S is defined as the line tangent to the first circle E and the sun gear pin 105 that engages with the defined valley 4 of the first circle E. The fourth straight line S is defined on the side where the sun gear pin 105 presses against the work carrier 1. The side where the sun gear pin 105 presses against the work carrier 1 is the upstream side in the rotation direction W1 of the sun gear 103. The first angle SA is defined as the angle between the first straight line B, which is defined for each valley section 4, and the fourth straight line S, which is also defined for each valley section 4. As shown in Figure 6B, the first angle SA increases as the position n of valley section 4 moves away from the first reference valley section 4α. The "position n of valley section 4" will be explained later. The point of contact between the fourth straight line S and the sun gear pin 105 that is in contact with the fourth straight line S is defined as the first contact point SG. The distance from the carrier center O2 to the first contact point SG is defined as the first distance L1. Note that in Figure 6B, only the first distance L1 defined for the valley 4 at position n "4" is shown. However, the first distance L1 is defined for each of the valleys 4 located downstream of the first reference valley 4α in the rotational direction W1 of the sun gear 103.

[0028] The fourth straight line S, the first angle SA, the first contact point SG, and the first distance L1 are defined in the valley 4 located downstream of the first reference valley 4α in the rotational direction W1 of the sun gear 103. Here, "first reference valley 4α" refers to the valley 4 through which the first straight line B passes the center OS of the meshing sun gear pin 105.

[0029] Furthermore, when the work carrier 1 is meshed with the internal gear 104, the external teeth 2 are defined as follows for each valley 4 when viewed from the front tooth profile (see Figures 7A and 7B). The fifth straight line I is defined as the line tangent to the first circle E and the internal gear pin 106 that engages with the defined valley 4 of the first circle E. The fifth straight line I is defined on the side where the internal gear pin 106 presses against the work carrier 1. The side where the internal gear pin 106 presses against the work carrier 1 is the upstream side in the rotation direction W2 of the internal gear 104. The second angle IA is defined as the angle between the first straight line B, which is defined for each valley 4, and the fifth straight line I, which is also defined for each valley 4. As shown in Figure 7B, the second angle IA increases as the position n' of valley 4 moves away from the second reference valley 4α'. The "position n' of valley 4" will be explained later. The point of contact between the fifth straight line I and the internal gear pin 106 to which the fifth straight line I is in contact is defined as the second contact point IG. The distance from the carrier center O2 to the second contact IG is defined as the second distance L2. Note that in Figure 7B, only the second distance L2 defined for the valley 4 at position n' is shown. However, the second distance L2 is defined for each valley 4 located downstream of the second reference valley 4α' in the rotational direction W2 of the internal gear 104.

[0030] The fifth straight line I, the second angle IA, the second contact point IG, and the second distance L2 are defined in the valley 4 located downstream of the second reference valley 4α' in the rotational direction W2 of the internal gear 104. Here, "second reference valley 4α'" is the valley 4 through which the first straight line B passes the center OI of the meshing internal gear pin 106.

[0031] Furthermore, the tip angle A of the work carrier 1 is set to the larger of the two values: Asun, the optimal angle on the sun gear side selected from the first angle SA calculated for each of the four valleys, and Aint, the optimal angle on the internal gear side selected from the second angle IA calculated for each of the four valleys.

[0032] The optimal angle Asun on the sun gear side is the smallest first angle SA among the first angles SA calculated for each valley 4 located downstream of the first reference valley 4α in the rotation direction W1 of the sun gear 103, which is the first angle SA at the valley 4 that gives the first distance L1 that satisfies the following equation (2). φ1 <L1×2 ···(2) Here, φ1 is the diameter of the carrier tooth tip circle R1. L1: This is the first distance.

[0033] Here, the first angle SA is calculated based on the Sun Gear pin coordinates (Xs, Ys) and the first intersection coordinates (Xc, Yc) on the first design coordinate system CO1 shown in Figure 8A. The first distance L1 is calculated based on the first junction coordinates (Xp, Yp) on the first design coordinate system CO1.

[0034] The "First Design Coordinate System CO1" is a virtual coordinate system in which the Y-axis is a line passing through the centers (axis O1) of the sun gear 103 and internal gear 104 and the carrier center O2, and the X-axis is a line passing through the carrier center O2 and perpendicular to the Y-axis. In the First Design Coordinate System CO1, the carrier center O2 is the origin. Also, in the First Design Coordinate System CO1, the sun gear 103 side is in the positive direction of the Y-axis, and the internal gear 104 side is in the negative direction of the Y-axis.

[0035] The "Sun Gear Pin Coordinates (Xs, Ys)" indicate the position of the center OS of the Sun Gear pin 105. The "First Intersection Coordinates (Xc, Yc)" indicate the position of the first intersection C. The "First Contact Point Coordinates (Xp, Yp)" indicate the position of the first contact point SG. Furthermore, the Sun Gear Pin Coordinates (Xs, Ys), First Intersection Coordinates (Xc, Yc), and First Contact Point Coordinates (Xp, Yp) are determined for each position n of the valley 4.

[0036] Here, the position n of valley 4 is determined by the number of valleys 4 relative to the position n of the first reference valley 4α. That is, the position n of valley 4 is set to "zero" for the position n of the first reference valley 4α. Then, the position n of valley 4 increases by one each time it moves downstream in the rotational direction W1 of the sun gear 103 from the first reference valley 4α. Specifically, as shown in Figure 6A, the position n of valley 4β adjacent to the first reference valley 4α is "1". Also, the position n of valley 4γ adjacent to valley 4β at position n=1 is "2".

[0037] The sun gear pin coordinates (Xs, Ys) that engage with the valley 4 at any position n can be determined by the following equations (3) and (4). Xs=Rsun·sin((360 / Gsun·n)·π / 180) ···(3) Ys=(Rsun+Rc)-Rsun·cos((360 / Gsun·n)·π / 180) ···(4) Here, Xs is the X-coordinate of the center OS of the sun gear pin 105 that engages with the valley 4 at position n. Ys: Y coordinate of the center OS of the sun gear pin 105 that engages with the valley 4 at position n. Rsun: Radius of the circle connecting the center OS of the Sun Gear pin 105 Gsun: Number of Sun Gear pins 105 Rc: Radius of pitch circle R2 (=φ2 / 2) π: Pi n: This is the location of valley 4.

[0038] Furthermore, the coordinates (Xc, Yc) of the first intersection point in the valley 4 at any position n can be determined by the following equations (5) and (6). Xc=Rc·sin((360 / Gc·n)·π / 180) ···(5) Yc=Rc·cos((360 / Gc·n)·π / 180) ···(6) Here, Xc is the X-coordinate of the first intersection C in the valley 4 at position n. Yc: Y coordinate of the first intersection C in the valley 4 at position n. Rc: Radius of pitch circle R2 (=φ2 / 2) Gc: Total number of teeth in the valley section 4 of work carrier 1 (carrier teeth) π: Pi n: It is the position of groove 4.

[0039] And the first angle SA at the groove 4 at an arbitrary position n is obtained by the following formula (7). Note that when the result of formula (7) is a value of zero or less, it is set to "zero". SA = (360 / Gc · n) + tan -1 (t / s) / π · 180 ···(7) Here, SA: The first angle at the groove 4 at position n Gc: The total number of grooves 4 of the work carrier 1 (number of carrier teeth) π: Pi n: The position of groove 4 s: Formula (8) t: It is formula (9).

[0040] Note that formula (8) and formula (9) are as follows. s = -SQRT(((Rp 2 ·(Ys - Yc) 2 )) / ((Xs - Xc) 2 +(Ys - Yc) 2 )) ···(8) t = (-s · (Xs - Xc)) / (Ys - Yc) ···(9) Here, Xs: The X coordinate of the center OS of the sun gear pin 105 meshing with the groove 4 at position n Ys: The Y coordinate of the center OS of the sun gear pin 105 meshing with the groove 4 at position n Xc: The X coordinate of the first intersection point C at the groove 4 at position n Yc: The Y coordinate of the first intersection point C at the groove 4 at position n Rp: It is the pin radius.

[0041] Furthermore, the first contact point coordinates (Xp, Yp) at the groove 4 at an arbitrary position n are obtained by the following formulas (10) and (11). Xp = Xs - SQRT(s 2 · Rp 2 / (s 2 + t 2 )) ···(10) Yp = Ys - t / s · SQRT(s 2 ·Rp 2 / (s 2 +t 2 )) ···(11) Here, Xs is the X-coordinate of the center OS of the sun gear pin 105 that engages with the valley 4 at position n. Ys: Y coordinate of the center OS of the sun gear pin 105 that engages with the valley 4 at position n. s: Formula (8) t: Formula (9) Rp is the pin radius.

[0042] Then, the first distance L1 in the valley 4 at any position n can be calculated by the following equation (12). L1=SQRT(Xp 2 +Yp 2 ) ···(12) Here, L1 is the first distance in the valley 4 at position n. Xp: X coordinate of the first contact point SG at the valley 4 at position n Yp: Y coordinate of the first contact point SG at the valley 4 at position n.

[0043] The optimal angle Aint on the internal gear side is the smallest second angle IA among the second angles IA calculated for each valley 4 located downstream of the second reference valley 4α' in the rotational direction W2 of the internal gear 104, which is the second angle IA at the valley 4 that gives the second distance L2 satisfying the following equation (13). φ1 <L2×2 ···(13) Here, φ1 is the diameter of the carrier tooth tip circle R1. L2: This is the second distance.

[0044] Here, the second angle IA is calculated based on the internal gear pin coordinates (Xi, Yi) and the first intersection coordinates (Xc', Yc') on the second design coordinate system CO2 shown in Figure 8B. The second distance L2 is calculated based on the first contact point coordinates (Xp', Yp') on the second design coordinate system CO2.

[0045] The "Second Design Coordinate System CO2" is a hypothetical coordinate system in which the Y-axis is a line passing through the centers (axis O1) of the sun gear 103 and internal gear 104 and the carrier center O2, and the X-axis is a line passing through the carrier center O2 and perpendicular to the Y-axis. In the Second Design Coordinate System CO2, the carrier center O2 is the origin. Also, in the Second Design Coordinate System CO2, the internal gear 104 side is in the positive direction of the Y-axis, and the sun gear 103 side is in the negative direction of the Y-axis.

[0046] The "internal gear pin coordinates (Xi,Yi)" indicate the position of the center OI of the internal gear pin 106. The "first intersection coordinates (Xc',Yc')" indicate the position of the first intersection C. The "second contact point coordinates (Xq,Yq)" indicate the position of the second contact point IG. In addition, the internal gear pin coordinates (Xi,Yi), the first intersection coordinates (Xc',Yc'), and the second contact point coordinates (Xq,Yq) are calculated for each position n' of the valley 4.

[0047] Here, the position n' of valley 4 is determined by the number of valleys 4 relative to the position n' of the second reference valley 4α'. That is, the position n' of valley 4 is set to "zero" for the position n' of the second reference valley 4α'. Then, the position n' of valley 4 increases by one for each time it moves downstream of the second reference valley 4α' in the rotational direction W2 of the internal gear 104. Specifically, as shown in Figure 7A, the position n' of valley 4β' next to the second reference valley 4α' is "1". Also, the position n' of valley 4γ' next to valley 4β' with position n'=1 is "2".

[0048] The coordinates (Xi,Yi) of the internal gear pin that engages with the valley 4 at any position n' can be determined by the following equations (14) and (15). Xi= Rint·sin((360 / Gint·n´)·π / 180) ...(14) Yi= Rint·cos((360 / Gint·n´)·π / 180)-(Rint-Rc) ···(15) Here, Xi is the X-coordinate of the center OI of the internal gear pin 106 that engages with the valley 4 at position n'. Yi: The Y coordinate of the center OI of the internal gear pin 106 that engages with the valley 4 at position n'. Rint: The radius of the circle connecting the center OI of the internal gear pin 106. Gint: Number of internal gear pins (106) Rc: Radius of pitch circle R2 (=φ2 / 2) π: Pi n': This is the location of valley 4.

[0049] Furthermore, the coordinates (Xc', Yc') of the first intersection point in the valley 4 at any position n' can be determined by the following equations (16) and (17). Xc´=Rc·sin((360 / Gc·n´)·π / 180) ···(16) Yc´=Rc·cos((360 / Gc·n´)·π / 180) ···(17) Here, Xc': the X-coordinate of the first intersection C in the valley 4 at position n'. Yc': Y coordinate of the first intersection C in the valley 4 at position n'. Rc: Radius of pitch circle R2 (=φ2 / 2) Gc: Total number of teeth in the valley section 4 of work carrier 1 (carrier teeth) π: Pi n': This is the location of valley 4.

[0050] The second angle IA at the valley 4 at any position n' is calculated by the following equation (18). Note that if the result of equation (16) is less than or equal to zero, the second angle IA is set to "zero". IA = (360 / Gc·n') + tan -1 (t´ / s´) / π·180 ...(18) Here, IA: second angle at the valley 4 at position n' Gc: Total number of teeth in the valley section 4 of work carrier 1 (carrier teeth) π: Pi n': Position of Valley 4 s´: Formula (19) t': Equation (20).

[0051] Equations (19) and (20) are as follows. s'=-SQRT(((Rp 2 ·(Yi-Yc´) 2 )) / ((Xi-Xc´) 2 +(Yi-Yc´) 2 )) ···(19) t´=(-s´·(Xi-Xc´)) / (Yi-Yc´) ···(20) Here, Xi is the X-coordinate of the center OI of the internal gear pin 106 that engages with the valley 4 at position n'. Yi: The Y coordinate of the center OI of the internal gear pin 106 that engages with the valley 4 at position n'. Xc': X-coordinate of the first intersection C in the valley 4 at position n'. Yc': Y coordinate of the first intersection C in the valley 4 at position n'. Rp is the pin radius.

[0052] Furthermore, the coordinates (Xq,Yq) of the second point of contact at the valley 4 at any position n' can be obtained by the following equations (21) and (22). Xq = Xi - SQRT(s' 2 ·Rp 2 / (s' 2 +t' 2 )) ···(twenty one) Yq = Yi - t' / s' · SQRT(s' 2 ·Rp 2 / (s' 2 +t' 2 )) ···(twenty two) Here, Xi is the X-coordinate of the center OI of the internal gear pin 106 that engages with the valley 4 at position n'. Yi: The Y coordinate of the center OI of the internal gear pin 106 that engages with the valley 4 at position n'. s´: Formula (19) t´: Formula (20) Rp is the pin radius.

[0053] Then, the second distance L2 at the valley 4 at any position n' can be calculated by the following equation (23). L2 = SQRT(Xq 2+Yq 2 ) ···(twenty three) Here, L1 is the first distance in the valley 4 at position n. Xq: X-coordinate of the second contact point IG at the valley 4 at position n'. Yq: Y coordinate of the second point of contact IG at valley 4 at position n'.

[0054] The design method for the external teeth 2 of the work carrier 1 is shown in the flowcharts in Figures 9, 10, 11A, and 12A. In this embodiment, the design method for the work carrier 1 is performed by a computer.

[0055] The following describes the basic procedure for designing Work Carrier 1, based on the basic flow shown in Figure 9.

[0056] In step S1, the computer reads various preconditions necessary to set the tooth tip angle A. Here, the preconditions read into the computer are information on the basic specifications of the polishing machine 100 and the work carrier 1 that have been set in advance. The preconditions read into the computer include at least the pin radius Rp, the number of sun gear pins 105 Gsun, the radius Rsun of the circle connecting the centers OS of the sun gear pins 105, the number of internal gear pins 106 Gint, the radius Rint of the circle connecting the centers OI of the internal gear pins 106, the total number of valleys 4 of the work carrier 1 Gc, and the diameter φ2 of the pitch circle R2 of the work carrier 1. Each precondition is predetermined. Furthermore, each precondition may be entered as appropriate by the computer operator, or it may be read from memory installed in or connected to the computer.

[0057] In step S2, following the reading of the preconditions in step S1, the computer reads the information of the diameter φ1 of the carrier tooth tip circle R1. Here, the diameter φ1 of the carrier tooth tip circle R1 is set to any value that satisfies equation (1) above, based on the preconditions read in step S1.

[0058] In other words, for example, if the diameter φ2 of the pitch circle R2 of work carrier 1 is 720 mm and the pin radius Rp is 6 mm, the diameter φ1 of the carrier tip circle R1 can be set to a value between 720 (=φ2) mm and 732 (=720 + (6 × 2)) mm. Therefore, the diameter φ1 of the carrier tip circle R1 can be set to, for example, 725.0 mm.

[0059] Furthermore, a larger diameter φ1 of the carrier tip circle R1 of the work carrier 1 increases the contact area between the external teeth 2 and the drive pin, thereby distributing the driving force transmitted from the sun gear 103 and internal gear 104. Therefore, a larger diameter φ1 of the carrier tip circle R1 of the work carrier 1 can suppress wear on the work carrier 1 and the drive pin. However, if the diameter φ1 of the carrier tip circle R1 is too large, the external teeth 2 may interfere with the drive pin and not mesh properly. In other words, if the diameter φ1 of the carrier tip circle R1 of the work carrier 1 is small, the risk of interference between the external teeth 2 and the drive pin can be reduced. However, in this case, it is difficult to increase the contact area between the work carrier 1 and the drive pin. That is, it is desirable to set the diameter φ1 of the carrier tip circle R1 considering the size of the contact area between the external teeth 2 and the drive pin of the work carrier 1 and the level of interference risk between the external teeth 2 and the drive pin.

[0060] Furthermore, the diameter φ1 of the carrier tooth tip circle R1 may be set by a computer operator, or by a calculator or other device installed in or connected to the computer.

[0061] In step S3, following the reading of the carrier tooth tip circle R1 diameter φ1 information in step S2, the computer determines the optimal sun gear angle Asun. The optimal sun gear angle Asun is determined according to the optimal sun gear angle determination flow described later (see Figure 10A).

[0062] In step S4, following the determination of the optimal angle Asun on the sun gear side in step S3, the computer determines the optimal angle Aint on the internal gear side. The optimal angle Aint on the internal gear side is determined according to the internal gear side optimal angle determination flow described later (see Figure 11A).

[0063] In step S5, following the determination of the optimal angle Aint on the internal gear side in step S4, the computer determines the tooth tip angle A. The tooth tip angle A is set to the larger of the optimal angle Asun on the sun gear side, which was read in step S3, and the optimal angle Aint on the internal gear side, which was read in step S4.

[0064] In other words, in step S5, the computer compares the optimal angle Asun on the sun gear side with the optimal angle Aint on the internal gear side. The computer then selects the larger of the two values, Asun and Aint, and determines it as the tooth tip angle A.

[0065] For example, if the optimal angle Asun on the sun gear side is 6° and the optimal angle Aint on the internal gear side is 5°, the tooth tip angle A is determined to be the larger value, which is the optimal angle Asun on the sun gear side, "6°", by comparing "6°" and "5°".

[0066] In step S6, following the determination of the tooth tip angle A in step S5, the computer reads the information on the backlash amount J. The "backlash amount J" is the amount of clearance that is intentionally created between the external teeth 2 and the drive pin when the external teeth 2 and the drive pin of the work carrier 1 mesh.

[0067] The backlash amount J is generally around 0.1 mm to 0.2 mm. The backlash amount J may be determined by the computer operator, or it may be pre-stored in memory installed in or connected to the computer.

[0068] In step S7, following the reading of the backlash amount J information in step S6, the computer uses the various information it has read to set the shape of the external teeth 2 of the work carrier 1. Then the flow proceeds to the end. Here, the shape of the external teeth 2 is set according to the external tooth shape setting flow described later (see Figure 12).

[0069] The procedure for determining the optimal angle Asun on the sun gear side will be explained below based on the optimal angle determination flow for the sun gear side shown in Figure 10A.

[0070] In step S11, the computer sets the position n of the valley 4 for which the first angle SA and first distance L1 are to be calculated to "1". In other words, in step S11, using the first reference valley 4α as a reference, the valley 4β adjacent to the first reference valley 4α is set as the valley 4 for which the first angle SA and first distance L1 are to be calculated.

[0071] In step S12, following the setting of the position n of the valley 4 in step S11 or step S15, the computer calculates the first angle SA and the first distance L1 at the set position n of the valley 4. The first angle SA is calculated using the various preconditions read in step S1 and the above-mentioned equations (3), (4), (5), (6), (7), (8), and (9). The first distance L1 is calculated using the above-mentioned equations (8), (9), (10), (11), and (12).

[0072] For example, if the pin radius Rp is 6 mm, the number of sun gear pins 105 Gsun is 126, the radius Rsun of the circle connecting the centers OS of the sun gear pins 105 is 378 mm, the total number of valleys 4 of the work carrier 1 Gc is 120, and the diameter φ2 of the pitch circle R2 of the work carrier 1 is 720 mm, then the first angle SA and the first distance L1 will be the values ​​shown in Figure 10B, depending on the position n of the valleys 4. Note that each value is shown rounded to the third decimal place. Hereafter in this specification, all values ​​obtained by calculation will be treated in the same manner.

[0073] In step S13, following the calculation of the first angle SA and the first distance L1 in step S12, the computer determines whether the first distance L1 calculated in step S12 satisfies equation (2) above. If it is determined that equation (2) is true (YES), the flow proceeds to step S14. If it is determined that equation (2) is not true (NO), the flow proceeds to step S15.

[0074] If equation (2) is found to be true, it indicates that the external teeth 2 of the work carrier 1 are in a position where they do not mesh with the sun gear pin 105. In other words, when equation (2) is true, it is not necessary to calculate the optimal sun gear angle Asun. On the other hand, if equation (2) is found to be false, it indicates that the external teeth 2 of the work carrier 1 are in a position where they may mesh with the sun gear pin 105. Therefore, it is necessary to calculate the angle (optimal sun gear angle Asun) that results in optimal meshing between the external teeth 2 and the sun gear pin 105.

[0075] In step S14, following the determination in step S13 that equation (2) is true, that is, that the first distance L1 satisfies equation (2), the computer selects the first angle SA calculated in step S12 as the optimal angle Asun on the sun gear side. In other words, the optimal angle Asun on the sun gear side is the first angle SA calculated in step S12. Then the flow proceeds to the end.

[0076] In step S15, following the determination in step S13 that equation (2) does not hold, that is, that the first distance L1 does not satisfy equation (2), the position n of the valley 4 that is the subject of calculation for the first angle SA and the first distance L1 is set to "n+1". As a result, the valley 4 adjacent to the valley 4 that was the subject of calculation for the first angle SA and the first distance L1 in step S12 becomes the new subject of calculation for the first angle SA and the first distance L1. Then, the flow returns to step S12, and the calculation of the first angle SA and the first distance L1 is repeated, with the position n of the valley 4 being changed one by one until equation (2) holds.

[0077] For example, let's consider a case where the pin radius Rp is 6 mm, the number of sun gear pins 105 Gsun is 126, the radius Rsun of the circle connecting the centers OS of the sun gear pins 105 is 378 mm, the total number of valleys 4 of the work carrier 1 Gc is 120, the diameter φ2 of the pitch circle R2 of the work carrier 1 is 720 mm, and the diameter φ1 of the carrier tooth tip circle R1 is set to 725.0 mm.

[0078] When the position n of valley 4 is "1", the first distance L1 is 360.70 mm (see Figure 10B), so the value of "L1 × 2" is 721.41 mm. Since 725.0 (=φ1) > 721.41 (=L1 × 2), equation (2) does not hold. As a result, the flow proceeds to step S15, and the position n of valley 4 is set to "2".

[0079] On the other hand, when the position n of the valley 4 is "2", the first distance L1 is 363.27 mm (see Figure 10B), so the value of "L1 × 2" is 726.54 mm. Since 725.0 (=φ1) < 726.54 (=L1 × 2), equation (2) holds. As a result, the flow proceeds to step S14, and the first angle SA (=5.90, see Figure 10B) at the position n of the valley 4 is "2" is selected as the optimal angle Asun on the sun gear side.

[0080] The procedure for determining the optimal angle Aint on the internal gear side will be explained below based on the optimal angle determination flow for the internal gear side shown in Figure 11A.

[0081] In step S21, the computer sets the position n' of the valley 4 for which the second angle IA and second distance L2 are to be calculated to "1". In other words, in step S21, using the second reference valley 4α' as a reference, the valley 4β' adjacent to the second reference valley 4α' is set as the valley 4 for which the second angle IA and second distance L2 are to be calculated.

[0082] In step S22, following the setting of the position n' of the valley 4 in step S21 or step S25, the computer calculates the second angle IA and the second distance L2 at the set position n' of the valley 4. The second angle IA is calculated using the various preconditions read in step S1 and the above-mentioned equations (14), (15), (16), (17), (18), (19), and (20). The second distance L2 is calculated using the above-mentioned equations (19), (20), (21), (22), and (23).

[0083] For example, if the pin radius Rp is 6 mm, the number of internal gear pins 106 Gint is 368, the radius Rint of the circle connecting the centers OI of the internal gear pins 106 is 1104 mm, the total number of valleys 4 Gc of the work carrier 1 is 120, and the diameter φ2 of the pitch circle R2 of the work carrier 1 is 720 mm, then the second angle IA and the second distance L2 will be the values ​​shown in Figure 11B, depending on the position n' of the valleys 4.

[0084] In step S23, following the calculation of the second angle IA and the second distance L2 in step S22, the computer determines whether the second distance L2 calculated in step S22 satisfies equation (13) above. If it is determined that equation (13) is true (YES), the flow proceeds to step S24. If it is determined that equation (13) is false (NO), the flow proceeds to step S25.

[0085] If equation (13) is found to be true, it indicates that the external teeth 2 of the work carrier 1 are in a position where they do not mesh with the internal gear pin 106. In other words, when equation (13) is true, it means that there is no need to calculate the optimal angle Aint on the internal gear side. On the other hand, if equation (13) is found to be false, it indicates that the external teeth 2 of the work carrier 1 are in a position where they may mesh with the internal gear pin 106. Therefore, it is necessary to calculate the angle (optimal angle Aint on the internal gear side) that results in optimal meshing between the external teeth 2 and the internal gear pin 106.

[0086] In step S24, following the determination in step S23 that equation (13) is true, that is, that the second distance L2 satisfies equation (13), the computer selects the second angle IA calculated in step S22 as the optimal angle Aint on the internal gear side. In other words, the optimal angle Aint on the internal gear side is the second angle IA calculated in step S22. Then the flow proceeds to the end.

[0087] In step S25, following the determination in step S23 that equation (13) does not hold, that is, that the second distance L2 does not satisfy equation (13), the position n' of the valley 4 that is the subject of calculation for the second angle IA and second distance L2 is set to "n'+1". As a result, the valley 4 adjacent to the valley 4 that was the subject of calculation for the second angle IA and second distance L2 in step S22 becomes the new subject of calculation for the second angle IA and second distance L2. Then, the calculation of the second angle IA and second distance L2 is repeated, with the position n' of the valley 4 being changed one by one until equation (13) holds.

[0088] For example, let's consider the case where the pin radius Rp is 6 mm, the number of internal gear pins 106 Gint is 368, the radius Rint of the circle connecting the centers OI of the internal gear pins 106 is 1104 mm, the total number of valleys 4 Gc of the work carrier 1 is 120, the diameter φ2 of the pitch circle R2 of the work carrier 1 is 720 mm, and the diameter φ1 of the carrier tooth tip circle R1 is set to 725.0 mm.

[0089] When the position n' of valley 4 is "1", the second distance L2 is 360.21 mm (see Figure 11B), so the value of "L2 × 2" is 720.41 mm. Since 725.0 (=φ1) > 720.41 (=L2 × 2), equation (13) does not hold. As a result, the flow proceeds to step S25, and the position n' of valley 4 is set to "2".

[0090] Furthermore, when the position n' of valley 4 is "2", the second distance L2 is 361.03 mm (see Figure 11B), so the value of "L2 × 2" is 722.06 mm. Since 725.0 (=φ1) > 722.06 (=L2 × 2), equation (13) does not hold in this case either. As a result, the flow proceeds back to step S25, and the position n' of valley 4 is set to "3".

[0091] Then, when the position n' of the valley 4 is "3", the second distance L2 is 362.51 mm (see Figure 11B), so the value of "L2 × 2" is 725.02 mm. Since 725.0 (=φ1) < 725.02 (=L2 × 2), equation (13) holds. As a result, the flow proceeds to step S24, and the second angle IA (=5.02°, see Figure 11B) at the position n' of the valley 4 is "3" is selected as the optimal angle Aint on the internal gear side.

[0092] The following describes the design procedure for the shape of the external teeth 2 of the work carrier 1, based on the external tooth shape design flow shown in Figure 12.

[0093] In step S31, the carrier center O2 and the pitch circle R2 are set (see Figure 13A). Here, the pitch circle R2 is set based on the information of the diameter φ2 of the pitch circle R2 of the work carrier 1, which was read in step S1 of the basic flow.

[0094] In step S32, following the setting of the carrier center O2 and pitch circle R2 in step S31, the first intersection point C is set on the pitch circle R2 (see Figure 13A). The first intersection point C is set based on the information of the total number of valleys 4 Gc of the work carrier 1, which was read in step S1 of the basic flow. That is, as shown in Figure 13A, the first intersection point C is set on the pitch circle R2 at equal intervals, equal to the total number of valleys 4 Gc.

[0095] In step S33, following the setting of the first intersection C in step S32, the first straight line B is set (see Figure 13B). The first straight line B is a straight line connecting the carrier center O2, which is the center of the pitch circle R2, and the first intersection C. Note that when the tooth root surface 4a is set, the first straight line B can pass through the tooth root center point 4b.

[0096] In step S34, following the setting of the first straight line B in step S33, a virtual first circle E' is set (see Figure 13C). The virtual first circle E' is a circle centered at the first intersection C, with a radius dimension set to the sum of the pin radius Rp and the backlash amount J. The backlash amount J is the value read in step S6 of the basic flow.

[0097] In step S35, following the setting of the virtual first circle E' in step S34, the second straight line D is set (see Figure 13D). The second straight line D is a straight line that passes through the first intersection C and is perpendicular to the first straight line B.

[0098] In step S36, following the setting of the second line D in step S35, the third line F is set (see Figure 13E). The third line F is a line that passes through the first intersection C and is inclined toward the carrier center O2 more than the second line D. The inclination angle of the third line F relative to the second line D is set to the value of the tooth tip angle A determined in step S5 of the basic flow. The third line F is also set symmetrically with respect to the first line B. Here, one of the third lines is denoted as "F" and the other as "F'".

[0099] In step S37, following the setting of the third line F in step S36, the second intersection point G is set (see Figure 13F). The second intersection point G is the intersection of the virtual first circle E' and the third line F. The second intersection points G are set symmetrically across the first line B. Here, one second intersection point is denoted as "G" and the other second intersection point as "G'".

[0100] In step S38, following the setting of the second intersection G in step S37, the root surface 4a is defined (see Figure 13F). The root surface 4a is the portion of the virtual first circle E' that curves toward the carrier center O2, and is defined in the section from one second intersection G to the other second intersection G'. The root surface 4a is shown by a thick line in Figure 13F.

[0101] In step S39, following the definition of the tooth root surface 4a in step S38, the tip line H is set (see Figure 13G). The tip line H is the tangent to the virtual first circle E' passing through the second intersection G. The tip lines H are set symmetrically across the first straight line B. Here, one tip line is denoted as "H" and the other tip line as "H'".

[0102] In step S40, following the setting of the tip line H in step S39, the carrier tip circle R1 and the third intersection K are set (see Figure 13H). Here, the carrier tip circle R1 is set based on the information of the diameter φ1 of the carrier tip circle R1 that was read in step S2 of the basic flow. The third intersection K is the intersection of the tip line H and the carrier tip circle R1. The third intersection K is set symmetrically across the first line B. Here, one third intersection is denoted as "K" and the other third intersection is denoted as "K'".

[0103] In step S41, following the setting of the carrier tip circle R1 and the third intersection K in step S40, the root surface 3b is defined (see Figure 13H). The root surface 3b is defined in the portion of the tip line H(H') from the second intersection G(G') to the third intersection K(K'). The root surface 3b is shown as a thick line in Figure 13H.

[0104] In step S42, following the definition of the root surface 3b in step S41, the tip surface 3a is defined (see Figure 13I). The tip surface 3a is defined in the portion of the carrier tip circle R1 between two adjacent first straight lines B, from one third intersection K to the other third intersection K'. The tip surface 3a is shown as a thick line in Figure 13I.

[0105] In step S43, following the definition of the tooth tip surface 3a in step S42, the connecting surface 3c is defined, and the final shape of the external tooth 2 is designed (see Figure 13J). The connecting surface 3c is a curved surface with an arbitrary curvature that connects the tooth root surface 3b and the tooth tip surface 3a. That is, the third intersection K(K') is rounded to form the connecting surface 3c. Then the flow proceeds to the end.

[0106] The operation of the work carrier 1 and the design method for the work carrier 1 in this embodiment is described below.

[0107] When the workpiece W is polished by the polishing device 100, the workpiece carrier 1 meshes with the sun gear 103 and the internal gear 104, and the drive pin contacts the external teeth 2. The workpiece carrier 1 then rotates by receiving a driving force from the drive pin.

[0108] In this case, in a work carrier 1 where the diameter φ1 of the carrier tip circle R1 is set to a value less than the diameter φ2 of the pitch circle R2, the external teeth 2 cannot contact the drive pins (sun gear pin 105 and internal gear pin 106). In other words, a work carrier 1 in which the diameter φ1 of the carrier tip circle R1 is set to a value less than the diameter φ2 of the pitch circle R2 cannot mesh with the sun gear 103 and the internal gear 104, and therefore does not function as a work carrier 1.

[0109] Furthermore, in a work carrier 1 where the diameter φ1 of the carrier tip circle R1 is set to a value greater than the diameter φ2 + (pin radius Rp × 2) of the pitch circle R2, the external teeth 2 interfere with the drive pins (sun gear pin 105 and internal gear pin 106). Therefore, a work carrier 1 in which the diameter φ1 of the carrier tip circle R1 is set to a value greater than the diameter φ2 + (pin radius Rp × 2) of the pitch circle R2 cannot mesh with the sun gear 103 and internal gear 104, and thus does not function as a work carrier 1.

[0110] In contrast, the design method for the work carrier 1 includes a step (step S2) of setting the diameter φ1 of the carrier tip circle R1 to a value that is greater than or equal to the diameter φ2 of the pitch circle R2, and less than or equal to the sum of the diameter φ2 of the pitch circle R2 and the diameter of the drive pin (= pin radius Rp × 2). In other words, the work carrier 1 has the diameter φ1 of the carrier tip circle R1 set to any value that satisfies the above equation (1).

[0111] As a result, the work carrier 1 can properly mesh with the sun gear 103 and the internal gear 104 without causing interference between the external teeth 2 and the drive pin. Furthermore, the work carrier 1 can rotate smoothly by receiving the driving force from the drive pin.

[0112] Furthermore, in the work carrier 1, a larger contact area between the external teeth 2 and the drive pin allows the driving force transmitted from the drive pin to the external teeth 2 to be dispersed, reducing the surface pressure (driving force received per unit area). As a result, the work carrier 1 can suppress wear on the external teeth 2 and the drive pin.

[0113] In other words, the amount of wear on the external teeth 2 and the drive pin is proportional to the surface pressure calculated by the following formula (24). Therefore, for example, if the contact area between the external teeth 2 and the drive pin is doubled, the surface pressure will be halved, making it possible to reduce the amount of wear on the external teeth 2 and the drive pin by approximately half. SP = F / M ... (24) Here, SP: surface pressure F: Driving force received by external tooth 2 M represents the contact area between the external tooth 2 and the drive pin.

[0114] Thus, in order to suppress wear on the external teeth 2 and drive pins of the work carrier 1, it is necessary to increase the contact area between the external teeth 2 and the drive pins.

[0115] Incidentally, when the external teeth 2 of the work carrier 1 and the drive pin engage, as shown in Figures 4A and 4B, the drive pin enters the valley 4 of the external teeth 2 and contacts the root surface 4a and a portion of the tooth root surface 3b that is continuous with the root surface 4a. Here, when the external teeth 2 are designed, the portion of the virtual first circle E' that curves toward the carrier center O2, and the section from one second intersection G to the other second intersection G', is defined as the root surface 4a (see Figure 13F).

[0116] Therefore, a longer distance from one second intersection G to the other second intersection G' allows for a longer tooth root surface 4a, thereby increasing the contact area between the external tooth 2 and the drive pin. In other words, a longer tooth root surface 4a increases the contact ratio of the drive pin with the external tooth 2.

[0117] The second intersection point G(G') is the intersection of the virtual first circle E' and the third straight line F(F'). Furthermore, the third straight line F(F') is set based on the tooth tip angle A. That is, by adjusting the tooth tip angle A, the position of the second intersection point G(G') is changed, and the distance from one second intersection point G to the other second intersection point G' changes. By appropriately setting the tooth tip angle A, it is possible to increase the length of the tooth root surface 4a and increase the contact area between the external tooth 2 and the drive pin.

[0118] Note that the "contact area between the external tooth 2 and the drive pin" includes not only the contact area between the tooth root surface 4a and the drive pin, but also the contact area between the tooth root surface 3b and the drive pin. Furthermore, if multiple drive pins contact the external tooth 2, the sum of the contact areas between the multiple drive pins and the external tooth 2 becomes the "contact area between the external tooth 2 and the drive pin". In either case, the longer the length of the tooth root surface 4a, the larger the contact area between the external tooth 2 and the drive pin.

[0119] In contrast, the design method for the work carrier 1 includes step S3 of selecting the first angle SA in the valley 4 where the sun gear pin 105 meshes, which is calculated from a first angle SA for each valley 4 to obtain a first distance L1 that satisfies equation (2) above, as the optimal sun gear angle Asun; step S4 of selecting the second angle IA in the valley 4 where the internal gear pin 106 meshes, which is calculated from a second angle IA for each valley 4 to obtain a second distance L2 that satisfies equation (13) above, as the optimal internal gear angle Aint; and step S5 of setting the tooth tip angle A to the larger of the optimal sun gear angle Asun and the optimal internal gear angle Aint.

[0120] Furthermore, the tip angle A of the external teeth 2 of the work carrier 1 is set to the larger of the optimal angle Asun on the sun gear side and the optimal angle Aint on the internal gear side.

[0121] Here, the optimal angle Asun on the sun gear side is the smallest value of the first angle SA calculated for each valley 4, which is the first angle SA in the valley 4 that gives the first distance L1 that satisfies the above equation (2).

[0122] For example, in a work carrier 1 where the tip angle A of the external tooth 2 is set to the first angle SA when the first distance L1 is smaller than φ1 / 2, that is, the first angle SA when equation (2) does not hold, interference occurs between the external tooth 2 and the sun gear 103 when meshing with the sun gear 103. Therefore, in this case, the work carrier 1 is not valid. On the other hand, a work carrier 1 where the tip angle A of the external tooth 2 is set to the first angle SA in the valley 4 that obtains the first distance L1 that satisfies equation (2) can mesh with the sun gear 103 without interference.

[0123] Furthermore, as shown in Figure 14, the smaller the tip angle A of the external teeth 2 of the work carrier 1, the higher the contact ratio of the external teeth 2 with the sun gear pin 105. Therefore, assuming that equation (2) holds, a work carrier 1 in which the tip angle A of the external teeth 2 is set to the minimum value of the first angle SA can avoid interference between the sun gear pin 105 and the external teeth 2 while maximizing the contact area between the external teeth 2 and the sun gear pin 105.

[0124] As a result, a work carrier 1 with the tooth tip angle A set to the optimal angle Asun on the sun gear side can maximize the contact area between the external teeth 2 and the sun gear pin 105 without causing interference between the sun gear 103 and the external teeth 2.

[0125] Furthermore, the optimal angle Aint on the internal gear side is the smallest value of the second angle IA calculated for each valley 4, which is the second angle IA in the valley 4 that gives the second distance L2 satisfying equation (13) above.

[0126] For example, in a work carrier 1 where the tip angle A of the external teeth 2 is set to the second angle IA when the second distance L2 is smaller than φ1 / 2, that is, the second angle IA when equation (13) does not hold, interference occurs between the external teeth 2 and the internal gear 104 when meshing with the internal gear 104. Therefore, in this case, the work carrier 1 is not valid. On the other hand, a work carrier 1 where the tip angle A of the external teeth 2 is set to the second angle IA in the valley 4 that obtains the second distance L2 that satisfies equation (13) can mesh with the internal gear 104 without interference.

[0127] Furthermore, as shown in Figure 14, the smaller the tip angle A of the external teeth 2 of the work carrier 1, the higher the contact ratio of the external teeth 2 with the internal gear pin 106. Therefore, assuming that equation (13) holds, a work carrier 1 in which the tip angle A of the external teeth 2 is set to the minimum value of the second angle IA can avoid interference between the internal gear pin 106 and the external teeth 2 while maximizing the contact area between the external teeth 2 and the internal gear pin 106.

[0128] As a result, a work carrier 1 with the tooth tip angle A set to the optimal angle Aint on the internal gear side can maximize the contact area between the external teeth 2 and the internal gear pin 106 without interfering with the internal gear 104 and the external teeth 2.

[0129] Furthermore, in the work carrier 1, the tooth tip angle A is set to the larger of the optimal angle Asun on the sun gear side and the optimal angle Aint on the internal gear side. As a result, the contact area between the external teeth 2 and the drive pin can be maximized without the external teeth 2 interfering with both the sun gear 103 and the internal gear 104. Therefore, the work carrier 1 can suppress wear on the external teeth 2 and the drive pin.

[0130] Furthermore, in work carrier 1, the first angle SA is calculated based on the coordinates of the center OS of the sun gear pin 105 (sun gear pin coordinates (Xs, Ys)) and the coordinates of the first intersection C (first intersection coordinates (Xc, Yc)) in the first design coordinate system CO1, where the Y-axis is a straight line passing through the axis O1, which is the center of the sun gear 103 and the internal gear 104, and the X-axis is a straight line passing through the carrier center O2 and perpendicular to the Y-axis. The first distance L1 is calculated based on the coordinates of the first contact point SG (first contact point coordinates (Xp, Yp)) in the first design coordinate system CO1.

[0131] Furthermore, in work carrier 1, the second angle IA is calculated based on the coordinates of the center OI of the internal gear pin 106 (internal gear pin coordinates (Xi, Yi)) and the coordinates of the first intersection C (first intersection coordinates (Xc', Yc')) in the second design coordinate system CO2, where the Y-axis is a straight line passing through the axis O1, which is the center of the sun gear 103 and the internal gear 104, and the carrier center O2, and the X-axis is a straight line passing through the carrier center O2 and perpendicular to the Y-axis. The second distance L2 is calculated based on the coordinates of the second contact point IG (second contact point coordinates (Xq, Yq)) in the second design coordinate system CO2.

[0132] This allows for the appropriate determination of the first angle SA, first distance L1, second angle IA, and second distance L2 when designing the work carrier 1. As a result, a work carrier 1 can be obtained that suppresses wear on the external teeth 2 and drive pins.

[0133] Furthermore, in work carrier 1, the coordinates of the center OS of the sun gear pin 105 (sun gear pin coordinates (Xs, Ys)) are calculated using equations (3) and (4) above. The coordinates of the center OI of the internal gear pin 106 (internal gear pin coordinates (Xi, Yi)) are calculated using equations (14) and (15) above. The coordinates of the first intersection C (first intersection coordinates (Xc, Yc), first intersection coordinates (Xc', Yc')) are calculated using equations (5) and (6) or equations (16) and (17) above. The coordinates of the first contact SG (first contact coordinates (Xp, Yp)) are calculated using equations (10) and (11) above. The coordinates of the second contact IG (second contact coordinates (Xq, Yq)) are calculated using equations (21) and (22) above.

[0134] Then, the first angle SA is calculated using equations (7), (8), and (9) above. The first distance L1 is calculated using equation (12) above. The second angle IA is calculated using equations (18), (19), and (20) above. The second distance L2 is calculated using equation (23) above.

[0135] This allows for easy calculation of various values ​​necessary for designing Work Carrier 1. Therefore, it becomes possible to easily design Work Carrier 1.

[0136] The work carrier and work carrier design method described above have been explained, but the specific configuration is not limited to this embodiment. Modifications and additions to the design of the work carrier and work carrier design method described here are permitted as long as they do not depart from the gist of the invention.

[0137] In this embodiment, an example was shown in which the position n of the valley 4 when determining the sun gear pin coordinates (Xs, Ys) and the first intersection coordinates (Xc, Yc) necessary for calculating the first angle SA and the first distance L1 is determined by the number of valleys 4 relative to the position n of the first reference valley 4α. However, it is sufficient if the first angle SA and the first distance L1 can be calculated for each valley 4. Therefore, the position n of the valley 4 does not need to be based on the position n of the first reference valley 4α.

[0138] Furthermore, in this embodiment, an example was shown in which the position n' of the valley 4 when determining the internal gear pin coordinates (Xi, Yi) and the first intersection coordinates (Xc', Yc') necessary for calculating the second angle IA and the second distance L2 is determined by the number of valleys 4 relative to the position n' of the second reference valley 4α'. However, it is sufficient if the second angle IA and the second distance L2 can be calculated for each valley 4. Therefore, the position n' of the valley 4 does not need to be based on the position n' of the second reference valley 4α'.

[0139] Furthermore, in this embodiment, an example is shown in which the sun gear pin coordinates (Xs, Ys) indicate the position of the center OS of the sun gear pin 105 on the first design coordinate system CO1, the first intersection coordinates (Xc, Yc) indicate the position of the first intersection C on the first design coordinate system CO1, the internal gear pin coordinates (Xi, Yi) indicate the position of the center OI of the internal gear pin 106 on the second design coordinate system CO2, and the first intersection coordinates (Xc', Yc') indicate the position of the first intersection C on the second design coordinate system CO2. However, for example, the sun gear pin coordinates (Xs, Ys) and the internal gear pin coordinates (Xi, Yi) may indicate the positions of the sun gear pin center and the internal gear center, respectively, in the same coordinate system. In other words, when calculating the first angle SA, the second angle IA, etc., it is not necessary to separate the data into the first design coordinate system CO1 and the second design coordinate system CO2.

[0140] Furthermore, the formulas used to calculate the first angle SA and the second angle IA, etc., are not limited to the examples above and can be set as appropriate. [Explanation of Symbols]

[0141] 1. Work Career 2. External teeth 3 Yamabe 3a Tooth tip surface 3b Root surface 3c connection side 4 Tanibe 4a. Root surface 4b Root center point

Claims

1. A workpiece carrier having external teeth formed that mesh with a plurality of sun gear pins on a sun gear located inside the surface plate and a plurality of internal gear pins on an internal gear located outside the surface plate, The aforementioned external teeth are composed of alternating peaks and valleys, The aforementioned valley portion has a tooth root surface that is curved and recesses toward the carrier center with a constant curvature. The sun gear pin and the internal gear pin have a cylindrical shape with the same pin radius. With the aforementioned external teeth viewed in a frontal tooth profile, for each of the valleys, The first straight line is defined as the line connecting the carrier center and the root center point, which is the position that bisects the root surface in the circumferential direction. The intersection of the first straight line and the pitch circle, which is a circle connecting the pitch points where the sun gear pin and the internal gear pin touch the external teeth, is defined as the first intersection point. Let the line passing through the first intersection and perpendicular to the first line be the second line. A circle with the same radius as the pin radius and centered at the first intersection is defined as the first circle. A line passing through the first intersection and sloping more toward the carrier center than the second line is defined as the third line. The angle between the second line and the third line is defined as the tooth tip angle. The straight line tangent to the first circle and the sun gear pin that engages with the defined valley of the first circle is defined as the fourth straight line. The angle between the first line and the fourth line is taken as the first angle. The fifth straight line is defined as the line tangent to the first circle and the internal gear pin that engages with the defined valley of the first circle. The angle between the first line and the fifth line is defined as the second angle. The point of contact between the aforementioned four straight lines and the sun gear pin to which the aforementioned four straight lines are tangent is defined as the first contact point. The distance from the carrier center to the first contact point is defined as the first distance. The point of contact between the fifth straight line and the internal gear pin to which the fifth straight line is tangent is defined as the second contact point. The distance from the carrier center to the second contact point is defined as the second distance. The first angle at the valley where the sun gear pins engage, which gives the first distance that satisfies equation 1 below, is defined as the optimal angle on the sun gear side. Diameter of carrier tooth tip circle < 1st distance × 2 ... Equation 1 When the second angle at the groove where the internal gear pin engages, which gives the second distance that satisfies equation 2 below, is defined as the optimal angle on the internal gear side, Diameter of carrier tooth tip circle < Second distance × 2 ... Equation 2 The diameter of the carrier tip circle, which is the circle connecting the tips of the teeth of the aforementioned peaks, is set to be greater than or equal to the diameter of the pitch circle, and less than or equal to the sum of the diameter of the pitch circle and the diameter of the sun gear pin, and less than or equal to the sum of the diameter of the pitch circle and the diameter of the internal gear pin. The tooth tip angle is set to the larger of the optimal angle on the sun gear side and the optimal angle on the internal gear side. A work career characterized by the following features.

2. In the work carrier described in claim 1, The first angle and the first distance are calculated based on the coordinates of the center of the sun gear pin and the coordinates of the first intersection point in a coordinate system in which the Y-axis is a line passing through the centers of the sun gear and the internal gear and the center of the carrier, and the X-axis is a line passing through the center of the carrier and perpendicular to the Y-axis. The second angle and the second distance are calculated based on the coordinates of the center of the internal gear pin and the coordinates of the first intersection in the coordinate system. A work career characterized by the following features.

3. In the work carrier described in claim 2, The coordinates of the center of the aforementioned sun gear pin are calculated using the following equations 3 and 4. The coordinates of the center of the internal gear pin are calculated using the following equations 5 and 6: The coordinates of the first intersection are calculated using the following equations 7 and 8. The first angle is calculated using the following equations 9, 10, and 11. The coordinates of the first contact point are calculated using the following equations 10, 11, 12, and 13. The first distance is calculated using the following equation 14: The second angle is calculated using the following equations 15, 16, and 17. The coordinates of the second contact point are calculated using the following equations 16, 17, 18, and 19. The second distance is calculated using the following equation 20. A work career characterized by the following features. Xs=Rsun・sin((360 / Gsun・n)・π / 180) ・・Formula 3 Ys=(Rsun+Rc)-Rsun・cos((360 / Gsun・n)・π / 180) ・・Formula 4 Xi=Rint・sin((360 / Gint・n)・π / 180) ・・Formula 5 Yi= Rint・cos((360 / Gint・n)・π / 180)−(Rint−Rc) ・・Formula 6 Xc=Rc・sin((360 / Gc・n)・π / 180) ・・Formula 7 Yc=Rc・cos((360 / Gc・n)・π / 180)...Formula 8 SA = (360 / Gc·n) + tan －１ (t / s) / π·180 ··· Equation 9 s = -SQRT(((Rp ２ ·(Ys - Yc) ２ )) / ((Xs - Xc) ２ + (Ys - Yc) ２ )) ··· Equation 10 t=(-s・(Xs-Xc)) / (Ys-Yc)...Formula 11 Xp = Xs - SQRT(s ２ · Rp ２ / (s ２ + t ２ )) ··· Equation 12 Yp = Ys - t / s · SQRT(s ２ · Rp ２ / (s ２ + t ２ )) · · Equation 13 L1 = SQRT(Xp ２ + Yp ２ ) ··· Equation 14 IA = (360 / Gc·n) + tan －１ (t' / s') / π·180 ··· Equation 15 s' = - SQRT(((Rp ２ ·(Yi - Yc) ２ )) / ((Xi - Xc) ２ + (Yi - Yc) ２ ) ··· Equation 16 t'=(-s'・(Xi-Xc)) / (Yi-Yc)...Formula 17 Xq=Xi-SQRT(s' ２ Rp ２ / (s' ２ +t' ２ )) ...Formula 18 Yq=Yi-t´ / s´・SQRT(s´ ２ ・Rp ２ / (s´ ２ +t´ ２ )) ...Formula 19 L2 = SQRT(Xq ２ + Yq ２ ) ··· Equation 20 Here, Xs is the X-coordinate of the center of the sun gear pin that engages with the valley at position n. Ys: Y coordinate of the center of the sun gear pin that engages with the valley at position n. Rsun: The radius of the circle formed by connecting the centers of the sun gear pins. Gsun: Number of sun gear pins π: pi Rc: Radius of the pitch circle n: Location of the valley Xi: X coordinate of the center of the internal gear pin that engages with the valley at position n. Yi: Y coordinate of the center of the internal gear pin that engages with the valley at position n. Rint: The radius of the circle formed by connecting the centers of the internal gear pins. Gint: Number of internal gear pins Xc: X-coordinate of the first intersection point in the valley at position n Yc: Y-coordinate of the first intersection point in the valley at position n Gc: Total number of valleys in the work career SA: First angle at the valley at position n Rp: Pin radius Xp: X-coordinate of the first point of contact in the valley at position n Yp: Y coordinate of the first point of contact in the valley at position n. L1: First distance in the valley at position n IA: Second angle at the valley at position n Xq: X-coordinate of the second point of contact in the valley at position n. Yq: Y coordinate of the second point of contact in the valley at position n. L2 is the second distance at position n in the valley.

4. A method for designing a work carrier having external teeth that mesh with a plurality of sun gear pins on a sun gear located inside the surface platen and a plurality of internal gear pins on an internal gear located outside the surface platen, The aforementioned external teeth are composed of alternating peaks and valleys, The aforementioned valley portion has a tooth root surface that is curved and recesses toward the carrier center with a constant curvature. The sun gear pin and the internal gear pin have a cylindrical shape with the same pin radius. With the aforementioned external teeth viewed in a frontal tooth profile, for each of the valleys, The first straight line is defined as the line connecting the carrier center and the root center point, which is the position that bisects the root surface in the circumferential direction. The intersection of the first straight line and the pitch circle, which is a circle connecting the pitch points where the sun gear pin and the internal gear pin touch the external teeth, is defined as the first intersection point. Let the line passing through the first intersection and perpendicular to the first line be the second line. A circle with the same radius as the pin radius and centered at the first intersection is defined as the first circle. A line passing through the first intersection and sloping more toward the carrier center than the second line is defined as the third line. The angle between the second line and the third line is defined as the tooth tip angle. The straight line tangent to the first circle and the sun gear pin that engages with the defined valley of the first circle is defined as the fourth straight line. The angle between the first line and the fourth line is taken as the first angle. The fifth straight line is defined as the line tangent to the first circle and the internal gear pin that engages with the defined valley of the first circle. The angle between the first line and the fifth line is defined as the second angle. The point of contact between the aforementioned four straight lines and the sun gear pin to which the aforementioned four straight lines are tangent is defined as the first contact point. The distance from the carrier center to the first contact point is defined as the first distance. The point of contact between the fifth straight line and the internal gear pin to which the fifth straight line is tangent is defined as the second contact point. When the distance from the carrier center to the second contact point is defined as the second distance, The steps include setting the diameter of the carrier tip circle, which is the circle connecting the tips of the teeth of the peaks, to a value greater than or equal to the diameter of the pitch circle and less than or equal to the sum of the diameter of the pitch circle and the diameter of the sun gear pin, and less than or equal to the sum of the diameter of the pitch circle and the diameter of the internal gear pin, From the first angle calculated for each valley, the first angle in the valley where the sun gear pin engages, which satisfies the following equation 21, is selected as the optimal angle for the sun gear side. Diameter of carrier tooth tip circle < 1st distance × 2 ... Equation 21 From the second angles calculated for each of the aforementioned valleys, the second angle in the valley where the internal gear pin engages, which satisfies the following equation 22, is selected as the optimal angle for the internal gear. Diameter of carrier tooth tip circle < Second distance × 2 ... Equation 22 The steps include setting the tooth tip angle to the larger of the optimal angle on the sun gear side and the optimal angle on the internal gear side, A method for designing a work career, characterized by including the following:

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