Planetary reducer with small tooth difference and design method thereof

Abstract

The invention relates to a small-tooth-difference planetary reducer and a design method thereof, and the small-tooth-difference planetary reducer comprises a planet wheel, an inner gear ring, a shell, an input shaft and an output shaft; the planet wheel is installed on the planet carrier, and the planet carrier is installed in the center of the inner gear ring and rotates around the center of the inner gear ring to drive the planet wheel to rotate eccentrically. The outer surface of the planet wheel is provided with a cylindrical surface, a plurality of tooth profiles are machined on the cylindrical surface of the outer surface of the planet wheel, the planet wheel is meshed with the inner gear ring, the planet wheel rotates at a low speed through small tooth difference transmission, and the output shaft outputs the rotating speed. The transmission mechanism has the following advantages and effects that precise transmission can be realized, the number of tooth pairs participating in meshing is large, the bearing capacity is high, the transmission efficiency is high, and miniaturization is easy.

Description

Technical Field

[0001] The invention belongs to the field of precision gear transmission mechanisms, and in particular relates to a design method for a planetary reducer with a small tooth difference and a designed planetary reducer with a small tooth difference. Background Art

[0002] Gear transmission technology is mainly composed of gears and is an important part of mechanical transmission. At present, gear transmission technology is widely used in industrial production, but the high-load and large-transmission-ratio gear transmission has a complex structure, high manufacturing difficulty, large volume, and tooth side backlash that affects transmission accuracy. Therefore, it is of great significance to develop a planetary reducer with optimized structure and high transmission accuracy. Summary of the invention

[0003] The present invention aims to provide a planetary precision gear transmission mechanism with small tooth difference, which solves the above-mentioned problems existing in the prior art, realizes precision transmission, improves load-bearing capacity and transmission efficiency, and is easy to miniaturize.

[0004] The technical solution adopted by the patent of the present invention is: a small-tooth-difference planetary precision gear transmission mechanism includes a housing, bolts I, bearings I, end covers, baffles I, bolts II, output shafts, bearings I, planetary gears, inner gear rings, baffles II, bolts III, bearings III, and input shafts; the characteristic is that the actual tooth profile is obtained by equidistant offset of the motion trajectory of a certain point on a fixed coordinate system, the conjugate tooth profile is obtained by solving the conjugate equation, and Z is uniformly processed on the circumferential direction of the outer cylindrical surface of the planetary gear. c The inner cylindrical surface of the inner gear ring is uniformly processed with Z g The planetary gear is installed on the input shaft, which is installed in the center of the inner gear ring. The input shaft drives the planetary gear to revolve and mesh with the inner gear ring. Under the joint action of the inner gear ring and the input shaft, the planetary gear rotates and outputs the speed through the end cover.

[0005] The present invention provides the following technical solution: a planetary reducer with a small tooth difference, comprising:

[0006] The planetary gear has a cylindrical surface on its outer surface, and a plurality of teeth are processed on the cylindrical surface of the outer surface of the planetary gear. The planetary gear is mounted on a planetary carrier, and the planetary carrier is mounted on the center of the inner gear ring and rotates around the center of the inner gear ring, driving the planetary gear to rotate eccentrically;

[0007] The inner gear ring meshes with the planetary gear, and the inner gear ring is evenly distributed on the circumference. g teeth;

[0008] A housing having a cylindrical surface and having teeth on the inner surface of the housing that mesh with the planetary gear teeth;

[0009] The input shaft is installed at the center of the inner gear ring and is used to drive the planetary gear to revolve;

[0010] An output shaft, which is used to output a rotational speed;

[0011] Among them, take a point (x1, y1) on the reducer housing coordinate system, which is at a radius of kr 0 The center of the shell circle coincides with the origin of the coordinate system; the radius is r 0 The center of the base circle coincides with the center of the shell circle, and the spatial positions of the base circle and the shell circle are relatively fixed; there is a running circle with a radius of R on the reducer planetary gear, which is inscribed in the base circle. The two circles roll relative to each other, and the point (x1, y1) forms a point motion trajectory on the running circle, forming the theoretical tooth profile of the planetary gear. The planetary gear is evenly distributed Z in the circumferential direction. c The theoretical tooth profile equation of the i-th planetary gear tooth is:

[0012]

[0013] in, is the tooth profile generation angle, k is the fraction coefficient, and the number of planetary gear teeth Z c and the number of teeth of the inner ring gear Z g The relationship between Z g R=Z c r 0 , Z 1 =R / r 0 , r 0 is the distance from the point to the center of the circle, R is the radius of the base circle, Z 1 is a positive real number with a finite decimal part; the theoretical tooth profile of the planetary gear is equidistantly offset to obtain the actual tooth profile of the i-th planetary gear tooth:

[0014]

[0015] Where r is the equidistant offset distance,

[0016] The actual tooth shape of the planetary gear is transformed by coordinates, and the transformation matrix is:

[0017]

[0018] The conjugate tooth profile of the actual tooth shape of the planetary gear is obtained. The conjugate tooth profile is the tooth profile of the inner gear ring of the housing. The tooth profile equation of the partial tooth profile of the inner teeth of the i-th inner gear ring is:

[0019]

[0020] Among them, φ 1 is the planetary gear angular position coordinate, φ 2 is the angular position coordinate of the inner gear ring, a 0 is the eccentricity,

[0021] φ 1 and The relationship is solved according to the following conjugate equation;

[0022]

[0023] The present invention also provides a planetary reducer with a small tooth difference, which comprises:

[0024] The planetary gear has a cylindrical surface on its outer surface, and a plurality of teeth are processed on the cylindrical surface of the outer surface of the planetary gear. The planetary gear is mounted on a planetary carrier, and the planetary carrier is mounted on the center of the inner gear ring and rotates around the center of the inner gear ring, driving the planetary gear to rotate eccentrically;

[0025] The inner gear ring meshes with the planetary gear, and the inner gear ring is evenly distributed in the circumference. g teeth;

[0026] A housing having a cylindrical surface and having teeth on the inner surface of the housing that mesh with the planetary gear teeth;

[0027] The input shaft is installed at the center of the inner gear ring and is used to drive the planetary gear to revolve;

[0028] An output shaft, which is used to output a rotational speed;

[0029] Among them, take a point (x21, y21) on the reducer planetary gear coordinate system, which is at a radius of kr 1 The center of the circle coincides with the origin of the coordinate system, and the center of the base circle with a radius of r1 coincides with the center of the circle. The base circle and the circle are relatively fixed in space. There is a circle with a radius of R on the reducer housing. The circle is inscribed in the base circle. The two circles roll relative to each other. The point (x21, y21) forms a point motion trajectory on the shell circle, forming the theoretical tooth profile of the shell. The theoretical tooth profile of the inner ring is equidistantly offset to obtain the actual tooth profile of the i-th inner ring tooth:

[0030]

[0031] Among them, Z 2 is the wave number, r 1 is the distance from the point to the center of the circle, is the tooth profile generating angle, k is the fraction coefficient; the theoretical tooth profile of the inner gear ring is equidistantly offset to obtain the actual tooth profile of the i-th inner gear ring tooth: the coordinate transformation of the inter-tooth profile is performed, and the transformation matrix is:

[0032]

[0033] The conjugate tooth profile of the actual tooth shape of the inner gear ring is obtained. The conjugate tooth profile is the planetary gear tooth profile. The tooth profile equation of the i-th planetary gear tooth is:

[0034]

[0035] Among them, φ3 is the angular position coordinate of the inner gear ring, φ 4 is the angular position coordinate of the planetary gear, a 1 Eccentricity

[0036] φ 3 with The relationship is solved by the following conjugate equation:

[0037]

[0038] Preferably, Zc circles with a radius of r are evenly distributed on the planetary wheel circle, wherein the center of the first circle is (x21, y21), and the partial arc of the i-th circle and the partial tooth profile of the planetary wheel outer tooth constitute a complete tooth of the planetary wheel.

[0039] Preferably, the inner teeth of the housing are in conjugate meshing with the outer teeth of the planetary gear, and the transmission ratio is constant.

[0040] Preferably, Zg circles with radius r are evenly distributed on the shell circle, wherein the center of the first circle is (x1, y1), and the partial arc of the ith circle and the partial tooth profile of the inner teeth of the inner gear ring form a complete tooth of the inner gear ring.

[0041]

[0042] Where r is the equidistant offset distance, Internal gear ring

[0043] The present invention also provides a design method for a planetary reducer with a small tooth difference, comprising the steps of tooth profile design based on a housing coordinate system:

[0044] Determine the basic parameters of the planetary gear and the internal gear ring, including the number of planetary gear teeth Z c 、Number of teeth of inner ring gear Z g , base circle radius R, shell circle radius kr 0 , the distance r from the point to the center of the circle 0 , division coefficient k;

[0045] According to the formula Z 1 =R / r 0 Calculate Z 1 , and according to Z g R=Z c r 0 Determine the relationship between parameters;

[0046] For the i-th planet gear tooth, the angle is generated by the tooth shape. Using the theoretical tooth profile equation

[0047]

[0048] Calculate theoretical tooth profile coordinates;

[0049] Calculate the offset distance r according to

[0050] Determine φ i Then use the actual tooth profile equation:

[0051]

[0052] Get the actual tooth profile coordinates;

[0053] According to φ 1 and The conjugate equation of Determine φ 1 , and then use the transformation matrix Perform coordinate transformation on the actual tooth shape to obtain the tooth profile equation of the inner gear ring of the housing

[0054] in and are the planetary gear angular position coordinates, Angular position coordinate of the inner gear ring, a 0 is the eccentricity.

[0055] Or include the gear design steps based on the planetary gear coordinate system:

[0056] Determine the basic parameters of the planetary gear and the internal gear ring, including the number of planetary gear teeth Z c 、Number of teeth of inner ring gear Z g , base circle radius R, travel circle radius kr 1 The distance r from the point to the center of the circle 1 , coefficient k, wave number Z 2 ;

[0057] For the i-th internal gear ring tooth, the angle is generated by the tooth shape Using the theoretical tooth profile equation

[0058] Calculate theoretical tooth profile coordinates;

[0059] Calculate the equidistant offset distance r, according to Sure Then, using the actual tooth profile equation

[0060]

[0061] Get the actual tooth profile coordinates;

[0062] according to and The conjugate equation of Sure Reusing the transformation matrix

[0063]

[0064] By performing coordinate transformation on the actual tooth shape, we can obtain the planetary gear tooth profile equation:

[0065] where φ 3 is the angular position coordinate of the inner gear ring, φ 4 is the angular position coordinate of the planetary gear, a 1 is the eccentricity.

[0066] The tooth profile design of the present invention is to design a new tooth profile based on the trajectory generation principle, and the actual tooth profile is obtained by equidistantly offsetting the motion trajectory of a certain point on a fixed coordinate system, and then the conjugate tooth profile is calculated by the conjugate equation to achieve efficient meshing transmission of gears.

[0067] The structural features of the planetary reducer with small tooth difference of the present invention include: a housing, an input shaft, an output shaft, planetary gears, an inner gear ring and other components. The planetary gears are mounted on the input shaft and mesh with the inner gear ring to produce rotation and revolution, thereby realizing efficient transmission. By changing the input end, the transmission mechanism can be used as a reducer and a speed increaser, and the transmission ratio is a fixed value; the tooth surface is pure rolling, the transmission efficiency is high, the wear is small, and the service life of the transmission mechanism is long; the number of teeth involved in the meshing is large, and the transmission is stable; the mechanism has no tooth side backlash, and the transmission accuracy is high; and the processing and manufacturing are simple.

[0068] Compared with the prior art, the planetary reducer with small tooth difference and the design method thereof of the present invention have at least the following beneficial effects:

[0069] 1. Precision transmission

[0070] Through the unique tooth profile design, the actual tooth profile is obtained according to the trajectory generation principle, and then the conjugate tooth profile is calculated by the conjugate equation, which ensures the efficient meshing transmission of the gears and improves the transmission accuracy.

[0071] 2. Strong carrying capacity

[0072] A large number of tooth pairs involved in meshing can effectively share the load, thereby enhancing the load-bearing capacity of the reducer.

[0073] 3. High transmission efficiency

[0074] The tooth surface is pure rolling, which reduces friction loss, improves transmission efficiency, reduces wear, and extends the life of the transmission mechanism.

[0075] 4. Easy to miniaturize

[0076] Reasonable structural design and tooth shape design make it easier to miniaturize the reducer while ensuring performance, meeting the needs of different application scenarios.

[0077] The technical solution of the present invention is further specifically described below through embodiments and in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 A coordinate diagram of a design method for a planetary reducer with a small tooth difference according to the present invention;

[0079] Figure 2 A schematic structural diagram of a planetary reducer with a small tooth difference and a design method thereof according to the present invention;

[0080] Figure 3 This is a schematic diagram of the coordination of a planetary reducer with a small tooth difference according to the present invention.

[0081] 1-housing, 2-bolt Ⅰ, 3-bearing Ⅰ, 4-end cover, 5-baffle Ⅰ, 6-bolt Ⅱ, 7-output shaft, 8-bearing Ⅰ, 9-planetary gear, 10-inner ring gear, 11-baffle Ⅱ, 12-bolt Ⅲ, 13-bearing Ⅲ, 14-input shaft. DETAILED DESCRIPTION

[0082] The present invention achieves the goals of precise transmission, improved load-bearing capacity, transmission efficiency and easy miniaturization through two tooth profile design methods based on the outer shell coordinate system and the planetary gear coordinate system. Although the two design methods are based on different coordinate systems, they both focus on the core goal of optimizing the tooth profile and improving the transmission performance of the planetary reducer with small tooth difference. For example, the tooth profile design based on the outer shell coordinate system optimizes the meshing of the planetary gear and the inner gear ring in this coordinate system, while the design based on the planetary gear coordinate system can improve the tooth profile matching accuracy from another perspective, thereby jointly achieving an improvement in the overall transmission performance.

[0083] like Figure 1 and Figure 3 As shown, a schematic diagram of a design method of a planetary reducer with a small tooth difference and a schematic diagram of the coordination of a planetary reducer with a small tooth difference of the present invention.

[0084] 1. Tooth profile design of a planetary reducer with small tooth difference according to the present invention (1)

[0085] Take a point on the circle in the inner gear ring coordinate system and perform pure rolling around the planetary gear. The motion trajectory of this point forms a tooth shape, which constitutes the theoretical tooth profile of the planetary gear.

[0086] The planetary gears are evenly distributed Z c The theoretical tooth profile equation of the i-th planetary gear tooth is

[0087]

[0088] in, r 2 is the distance from the point to the center of the circle, is the tooth profile generating angle, k is the coefficient.

[0089] After equidistant offset, the actual tooth profile equation of the i-th tooth of the planetary gear is:

[0090]

[0091] Where r is the offset distance,

[0092] The coordinate transformation of the actual tooth profile of the planetary gear is performed, and the transformation matrix is:

[0093]

[0094] Among them, φ 5 is the planet gear tooth angular position coordinate, φ 6 is the tooth angle position coordinate of the inner gear ring, a 2 Eccentricity

[0095] The conjugate tooth shape on the inner ring is obtained.

[0096] The inner gear ring is evenly distributed on the circumference. g teeth, the tooth profile equation of the i-th internal gear ring tooth is

[0097]

[0098] φ 5 with The relationship can be solved by the following conjugate equation.

[0099]

[0100] 2. Structural design of a planetary reducer with small tooth difference according to the present invention

[0101] See also Figure 2 As shown, a planetary reducer with a small tooth difference of the present invention includes a housing (1), bolts I (2), bearings I (3), end covers (4), baffles I (5), bolts II (6), an output shaft (7), bearings I (8), planetary gears (9), an inner gear ring (10), baffles II (11), bolts III (12), bearings III (13), and an input shaft (14).

[0102] The planetary gear (9) is mounted on the input shaft (14), the input shaft (14) is mounted at the center of the inner gear ring (10), the output shaft (7) is mounted at the center of the end cover (4), the end cover (4) is mounted inside the housing (1), the housing (1) is fixed to the end face of the inner gear ring (10) by bolts I (2), the inner surface of the inner gear ring (10) has a cylindrical surface, and a Z g The planetary gear (9) has a cylindrical surface on its outer surface, and a Z c The actual teeth are meshed with the teeth on the inner ring gear (10) and the teeth on the planetary gear (9).

[0103] The input shaft (14) rotates, driving the planetary gear (9) to revolve and mesh with the inner gear ring (10). The inner gear ring (10) reacts to the planetary gear (9). The planetary gear (9) generates low-speed rotation under the push of the input shaft (14) and the restriction of the inner gear ring (10). The influence of the revolution is eliminated through the short shaft on the end cover (4) and the circular hole on the planetary gear (9). At the same time, the end cover (4) is driven to rotate, and the output shaft power is realized to realize the deceleration movement of the reducer.

[0104] 3. Specific application examples of the present invention (1)

[0105] Design tooth shape

[0106] Radius of base circle of inner gear ring r 2 is 40.5mm, the planetary gear base circle radius R is 40mm, the circular diameter of the circular holes on the planetary gear is 40mm, the number of distributions is 3, the circular hole diameter is 10mm, the short axis circular diameter on the end cover is 40mm, the offset distance r is 0.25, and the number of planetary gear teeth Z c is 160, the tooth shape is obtained according to the derivation formula of this article, and the number of teeth of the inner gear ring is Z g It is 162, the tooth shape is obtained according to the derivation formula in this article, the tooth width is 20mm, the coefficient k is 1, and the transmission ratio is -80.

[0107] Through the above design, the planetary gear tooth profile equation is obtained by utilizing the transformation matrix.

[0108] 4. Tooth profile design of a planetary reducer with small tooth difference according to the present invention (2)

[0109] Take a point on the circle in the planetary gear coordinate system and perform pure rolling around the inner gear ring. The motion trajectory of this point forms a tooth shape, which constitutes the theoretical tooth profile of the inner gear ring.

[0110] The inner gear ring is evenly distributed on the circumference. g teeth, the theoretical tooth profile equation of the i-th internal gear ring tooth is

[0111]

[0112] in, r 3 is the distance from the point to the center of the circle, is the tooth profile generating angle, k is the coefficient.

[0113] After equidistant offset, the actual tooth profile equation of the i-th tooth of the inner gear ring is:

[0114]

[0115] Where r is the offset distance,

[0116] The actual tooth profile of the inner gear ring is transformed by coordinates, and the transformation matrix is:

[0117]

[0118] Among them, φ 7 is the angular position coordinate of the inner gear ring, φ 8 is the angular position coordinate of the planetary gear, a 3 Eccentricity

[0119] Get the conjugate tooth shape on the planetary gear

[0120] The planetary gears are evenly distributed Z c teeth, the tooth profile equation of the i-th planetary gear tooth is

[0121]

[0122] φ 7 with The relationship can be solved by the following conjugate equation.

[0123]

[0124] Where R is the base circle radius.

[0125] 5. Specific application examples of the present invention (2)

[0126] Design tooth shape

[0127] In a specific embodiment, the base circle radius r of the inner gear ring 3 The diameter of the circular hole distribution circle on the planetary gear is 40mm, the number of distribution is 3, the diameter of the circular hole is 10mm, the diameter of the distribution circle of the short axis on the end cover is 40mm, the offset distance r is 0.25, and the number of planetary gear teeth Z is 40.5mm. c is 160, the tooth shape is obtained according to the derivation formula of this article, and the number of teeth of the inner gear ring is Z gIt is 162, the tooth shape is obtained according to the derivation formula in this article, the tooth width is 20mm, the coefficient k is 1, and the transmission ratio is -80.

[0128] Through the above design, the planetary gear tooth profile equation is obtained by utilizing the transformation matrix.

[0129] 6. Specific application examples of the present invention (3)

[0130] In a specific embodiment, the base circle radius r of the inner gear ring 3 The radius of the planetary gear base circle R is 40.5 mm. For example, based on the combination of part of the known arc line and part of the tooth profile, the intersection of the part of the arc line and the part of the inner ring tooth profile is The value is 0.01403π, the diameter of the circular hole distribution circle on the planetary gear is 40mm, the number of distribution is 3, the diameter of the circular hole is 10mm, the diameter of the short shaft distribution circle on the end cover is 40mm, the offset distance r is 0.3, and the number of planetary gear teeth Z c is 160, the tooth shape is obtained according to the derivation formula of this article, the number of teeth of the inner ring gear is Z g It is 162, the tooth shape is obtained according to the derivation formula in this article, the tooth width is 20mm, the coefficient k is 1, and the transmission ratio is -80.

[0131] 7. Structural implementation of specific embodiments

[0132] The outer casing, planetary gears, inner gear ring and other components are processed according to the design requirements, teeth are processed on the cylindrical surface of the outer surface of the planetary gear, and conjugate teeth are processed on the cylindrical surface of the inner surface of the inner gear ring.

[0133] Install the planetary gear on the input shaft, the input shaft is installed at the center of the inner gear ring, the output shaft is installed at the center of the end cover, the end cover is installed inside the shell, and the shell is fixed to the end face of the inner gear ring by bolts I to ensure that each component is installed accurately and the clearance is reasonable.

[0134] The input shaft rotates, driving the planetary gears to revolve. The planetary gears mesh with the inner gear ring, and the inner gear ring reacts to the planetary gears, causing the planetary gears to rotate at a low speed under the push of the input shaft and the restriction of the inner gear ring.

[0135] The influence of revolution is eliminated by the cooperation between the end cover and the planetary gear (such as the short shaft on the end cover and the round hole on the planetary gear), and the end cover is driven to rotate, so that the output shaft outputs power and realizes the deceleration movement of the reducer. During operation, the transmission ratio, transmission accuracy, load-bearing capacity and other performance indicators can be tested and verified to ensure that the reducer meets the design requirements. For example, under the above parameters, the transmission ratio is, which can be verified by actually measuring the ratio of the output speed to the input speed.

[0136] The embodiments described above are merely descriptions of preferred implementation modes of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A planetary reducer with small tooth difference, characterized in that: include: The planetary gear has a cylindrical surface on its outer surface, and a plurality of teeth are processed on the cylindrical surface of the outer surface of the planetary gear. The planetary gear is mounted on a planetary carrier, and the planetary carrier is mounted on the center of the inner gear ring and rotates around the center of the inner gear ring, driving the planetary gear to rotate eccentrically; The inner gear ring meshes with the planetary gear, and the inner gear ring is evenly distributed in the circumference. g teeth; A housing having a cylindrical surface and having teeth on the inner surface of the housing that mesh with the planetary gear teeth; The input shaft is installed at the center of the inner gear ring and is used to drive the planetary gear to revolve; An output shaft, which is used to output a rotational speed; Among them, take a point (x1, y1) on the reducer housing coordinate system, which is on the shell circle with a radius of kr0, and the center of the shell circle coincides with the origin of the coordinate system; the center of the base circle with a radius of r0 coincides with the center of the shell circle, and the base circle and the shell circle are relatively fixed in space; there is a running circle with a radius of R on the reducer planetary gear, and the running circle is inscribed in the base circle, and the two circles roll relatively purely, and the point (x1, y1) forms a point motion trajectory on the running circle, forming the theoretical tooth profile of the planetary gear, and the planetary gear is uniformly distributed Z in the circumferential direction. c The theoretical tooth profile equation of the i-th planetary gear tooth is: in, is the tooth profile generation angle, k is the fraction coefficient, and the number of planetary gear teeth Z c and the number of teeth of the inner ring gear Z g The relationship between Z g R=Z c r0, Z1 = R / r0, r0 is the distance from the point to the center of the circle, R is the radius of the base circle, and Z1 is a positive real number with a finite decimal part; the theoretical tooth profile of the planetary gear is offset equidistantly to obtain the actual tooth profile of the i-th planetary gear tooth: Where r is the equidistant offset distance, The actual tooth shape of the planetary gear is transformed by coordinates, and the transformation matrix is: The conjugate tooth profile of the actual tooth shape of the planetary gear is obtained. The conjugate tooth profile is the tooth profile of the inner gear ring of the housing. The tooth profile equation of the partial tooth profile of the inner teeth of the i-th inner gear ring is: Among them, φ1 is the angular position coordinate of the planetary gear, φ2 is the angular position coordinate of the inner gear ring, a0 is the eccentricity, φ1 and The relationship is solved according to the following conjugate equation; 2. A planetary reducer with small tooth difference according to claim 1, characterized in that: Zg circles with radius r are evenly distributed on the shell circle, wherein the center of the first circle is (x1, y1), and the partial arc of the ith circle and the partial tooth profile of the inner teeth of the inner gear ring form a complete tooth of the inner gear ring.

3. A planetary reducer with small tooth difference according to claim 2, characterized in that: The inner teeth of the housing are conjugately meshed with the outer teeth of the planetary gear, and the transmission ratio is constant.

4. A planetary reducer with small tooth difference, characterized in that: include: The planetary gear has a cylindrical surface on its outer surface, and a plurality of teeth are processed on the cylindrical surface of the outer surface of the planetary gear. The planetary gear is mounted on a planetary carrier, and the planetary carrier is mounted on the center of the inner gear ring and rotates around the center of the inner gear ring, driving the planetary gear to rotate eccentrically; The inner gear ring meshes with the planetary gear, and the inner gear ring is evenly distributed in the circumference. g teeth; A housing having a cylindrical surface and having teeth on the inner surface of the housing that mesh with the planetary gear teeth; The input shaft is installed at the center of the inner gear ring and is used to drive the planetary gear to revolve; An output shaft, which is used to output a rotational speed; Among them, take a point (x21, y21) on the reducer planetary gear coordinate system. This point is on a circle with a radius of kr1. The center of the circle coincides with the origin of the coordinate system. The center of the base circle with a radius of r1 coincides with the center of the circle. The base circle and the circle are relatively fixed in space. There is a circle with a radius of R on the reducer housing. The circle is inscribed in the base circle. The two circles roll relatively. The point (x21, y21) forms a point motion trajectory on the shell circle, which constitutes the theoretical tooth profile of the shell. The theoretical tooth profile of the inner ring is equidistantly offset to obtain the actual tooth profile of the i-th inner ring tooth: Among them, Z2 is the wave number, r1 is the distance from the point to the center of the circle, is the tooth profile generating angle, k is the fraction coefficient; the theoretical tooth profile of the inner gear ring is equidistantly offset to obtain the actual tooth profile of the i-th inner gear ring tooth: Where r is the equidistant offset distance, The actual tooth shape of the inner gear ring is transformed by coordinates, and the transformation matrix is: The conjugate tooth profile of the actual tooth shape of the inner gear ring is obtained. The conjugate tooth profile is the planetary gear tooth profile. The tooth profile equation of the i-th planetary gear tooth is: Among them, φ3 is the angular position coordinate of the inner gear ring, φ4 is the angular position coordinate of the planetary gear, and a1 is the eccentricity φ3 and The relationship is solved by the following conjugate equation:

5. The planetary reducer with small tooth difference according to claim 4, characterized in that: Zc circles with a radius of r are evenly distributed on the planetary wheel circle, wherein the center of the first circle is (x21, y21), and the partial arc of the i-th circle and the partial tooth profile of the planetary wheel outer tooth constitute a complete tooth of the planetary wheel.

6. A planetary reducer with small tooth difference according to claim 5, characterized in that: The inner teeth of the housing are conjugately meshed with the outer teeth of the planetary gear, and the transmission ratio is constant.

7. A design method for a planetary reducer with a small tooth difference, characterized in that: Including the gear design steps based on the shell coordinate system: Determine the basic parameters of the planetary gear and the internal gear ring, including the number of planetary gear teeth Z c 、Number of teeth of inner ring gear Z g , base circle radius R, shell circle radius kr0, distance from the point to the center of the circle r0, and fractional coefficient k; Calculate Z1 according to the formula Z1=R / r0, and g R=Z c r0 determines the relationship between the parameters; For the i-th planet gear tooth, the angle is generated by the tooth shape. Using the theoretical tooth profile equation Calculate theoretical tooth profile coordinates; Calculate the offset distance r according to Determine φ i Then use the actual tooth profile equation: Get the actual tooth profile coordinates; According to φ1 and The conjugate equation of Determine φ1 and then use the transformation matrix Perform coordinate transformation on the actual tooth shape to obtain the tooth profile equation of the inner gear ring of the housing in and are the planetary gear angular position coordinates, The internal gear ring angular position coordinates, a0 is the eccentricity.

8. A design method for a planetary reducer with a small tooth difference, characterized in that: Including the tooth shape design steps based on the planetary gear coordinate system: Determine the basic parameters of the planetary gear and the internal gear ring, including the number of planetary gear teeth Z c 、Number of teeth of inner ring gear Z g , base circle radius R, travel circle radius kr1, the distance from the point to the center of the circle r1, the coefficient k, and the wave number Z2; For the i-th internal gear ring tooth, the angle is generated by the tooth shape Using the theoretical tooth profile equation Calculate theoretical tooth profile coordinates; Calculate the equidistant offset distance r, according to Sure Then, using the actual tooth profile equation Get the actual tooth profile coordinates; according to and The conjugate equation of Sure Reusing the transformation matrix By performing coordinate transformation on the actual tooth shape, we can obtain the planetary gear tooth profile equation: Among them, φ3 is the angular position coordinate of the inner gear ring, φ4 is the angular position coordinate of the planetary gear, and a1 is the eccentricity.

9. A design method for a planetary reducer with a small tooth difference, characterized in that: The tooth profile design steps include: Shell circle There are Zg circles with radius r evenly distributed on the shell circle, and the center of the i-th circle is (x 11i ,y 11i ), the arc line of the upper part of the circle Take a point on the inner gear ring coordinate system and perform pure rolling around the planetary gear. The motion trajectory of this point forms a tooth shape, which constitutes the theoretical tooth profile of the planetary gear. The planetary gears are evenly distributed in the circumference. c The theoretical tooth profile equation of the i-th planetary gear tooth is in, r4 is the distance from the point to the center of the circle, is the tooth profile generating angle, k is the factor coefficient; The theoretical tooth profile of the planetary gear is offset equidistantly to obtain the actual tooth profile of the i-th planetary gear tooth. Where r is the equidistant offset distance, The coordinate transformation of the actual tooth profile of the planetary gear is performed, and the transformation matrix is: Among them, φ9 is the planetary gear tooth angle position coordinate, φ 10 is the tooth angle position coordinate of the inner gear ring, a4 is the eccentricity, and the partial conjugate tooth shape on the inner gear ring is obtained. The inner gear ring is evenly distributed on the circumference. g The tooth profile equation of the partial tooth profile of the inner tooth of the i-th inner gear ring is: φ9 and The relationship is solved by the following conjugate equation: The complete tooth profile can be obtained by connecting the partial tooth profile of the inner gear ring with the known arc line. Among them, θ1 is solved according to the following equation:

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