Method for reducing maximum deformation stress of harmonic reducer flexible gear

Abstract

The invention relates to a method for reducing the maximum deformation stress of a harmonic reducer flexible gear, which comprises the following specific steps of: establishing a geometrical relationship equation of the flexible gear and a flexible bearing, then establishing an equation according to pitch circle fitting conditions of a rigid-flexible gear, and establishing a modulus equation of the rigid-flexible gear according to correct meshing conditions. When the transmission ratio, the wall thickness of the gear ring and the outer diameter of the flexible bearing are given, the displacement coefficients of the flexible gear and the rigid gear can be determined through the three equations, and the theoretical radial maximum deformation of the flexible gear during theoretical accurate transmission of the rigid-flexible gear can be met; the maximum radial deformation of the flexible gear can be taken as the reference circle modulus of the rigid-flexible gear, at the moment, the maximum radial deformation of the flexible gear can be reduced by about 10% relative to the theoretical maximum radial deformation of the flexible gear, after modulus displacement is continuously adopted, the maximum radial deformation of the flexible gear can be further reduced by 5%, and the meshing performance can be basically kept unchanged; the double-point meshing can be ensured, and the backlash and the number of meshing tooth pairs are not reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of harmonic reducers, and in particular to a method for effectively reducing the maximum deformation stress of a harmonic reducer flexspline and increasing the service life of the harmonic reducer by using large displacement gears and module displacement. Background Art

[0002] The harmonic reducer was first proposed by American inventor Musser in the 1950s. Initially, a triangular serrated tooth profile was used. However, due to the neglect of the tooth profile deflection caused by the curvature change due to the deformation of the flexspline, there was severe meshing interference. The service life and reliability of the harmonic reducer were very low, and it also caused great trouble for processing, manufacturing, and tool design. Subsequently, a 30° pressure angle involute tooth profile appeared. Although it was better than a straight tooth profile, the flexspline tooth profile had a small envelope area when unloaded, and was prone to sharp point meshing when loaded. In the 1980s and 1990s, Japan's Harmonack successively launched the IH tooth profile and the S tooth profile, which greatly improved the service life and torque capacity of the harmonic reducer.

[0003] A harmonic reducer typically consists of a rigid wheel with an internal gear, a flexspline with an external gear, and a wave generator. The flexspline's thin-walled structure causes the wave generator to deform periodically as it rotates within the flexspline's inner bore. This causes the pitch circle of the flexspline's outer teeth to align with the pitch circle of the rigid wheel's inner teeth, resulting in a pure rolling motion without slipping. In front of the wave generator's rotation, the rigid-flex spline teeth engage; in back of the wave generator's rotation, they engage.

[0004] The maximum radial deformation of the flexspline during assembly of a harmonic reducer is typically equal to or very slightly different from the modulus m of the rigid-flex spline. For harmonic reducers of the same specification, once the flexible bearing size is selected, the modulus m has very little adjustable range and is essentially fixed. Consequently, the maximum radial deformation of the flexspline is also fixed and cannot be reduced to a value smaller than m. The specification number of the harmonic reducer is its size code. For example, the pitch circle diameter of the 17-size harmonic reducer is d = 1.7 inches. The outer ring of the flexible bearing is tightly fitted with the inner hole of the flexible wheel of the harmonic reducer, that is, the two diameters are equal. Flexible bearings are basically standard parts. There are only a few models that can be adapted to a certain specification of harmonic reducer, and the size difference is very small. For standard non-displacement gear d = m*z, in the harmonic reducer, the z value is generally larger, and the transmission ratio of the harmonic reducer is generally greater than 50, and the minimum will not be less than 30. The z value of the flexible wheel of the harmonic reducer with a transmission ratio of 50 is 100, and the z value of the rigid wheel is 102. Therefore, the deviation of the m value calculated by using flexible bearings of different sizes is very small.

[0005] According to the results of finite element simulation analysis, for a 17-size flexible spline, the modulus is 0.40mm, the ring gear wall thickness is 0.30mm, the maximum radial deformation of the flexible spline is 0.40mm, and the maximum deformation stress of the pure ring gear can reach nearly 400MPa. The maximum deformation stress after adding the cylinder and side structure will exceed 700MPa.

[0006] Although reducing the wall thickness of the ring gear can effectively reduce the maximum deformation stress of the flexible wheel, the reduction in wall thickness leads to a significant decrease in the transmission load capacity, as well as a significant decrease in torsional stiffness and transmission accuracy, resulting in a shortened service life of the harmonic reducer.

[0007] Reducing the maximum radial deformation of the flexspline becomes a factor in not reducing the transmission load capacity and ensuring the transmission accuracy. At the same time, it can greatly reduce the maximum deformation stress of the flexspline. However, if a value less than m is directly taken, it will lead to a change in the transmission ratio and it will not be the nominal value, and it may even cause the rigid-flex spline to not engage normally.

[0008] The present invention proposes a method for reducing the maximum stress of the flexspline assembly deformation by appropriately reducing the maximum radial deformation of the flexspline while ensuring transmission performance (such as side clearance, double-point meshing, etc.). Summary of the Invention

[0009] The object of the present invention is to provide a method for reducing the maximum deformation stress of a flexspline of a harmonic reducer, so as to solve the problems encountered in the above-mentioned background technology.

[0010] To achieve the above object, the technical solution of the present invention is as follows:

[0011] A method for reducing the maximum deformation stress of a flexspline of a harmonic reducer, the method comprising the following steps:

[0012] Step 1: Establish equations based on the geometric relationship between the flexspline and the flexible bearing

[0013] m2*Z2+2*x2*m2=Db+2*hf2+2*δ (1)

[0014] Where m2 is the flexspline modulus, Z2 is the number of flexspline teeth, x2 is the displacement coefficient of the flexspline, hf2 is the flexspline tooth valley height, Db is the outer diameter of the flexible bearing, and δ is the wall thickness of the flexspline gear ring;

[0015] Step 2: Establish equations based on the pitch circle fit conditions of the flexible wheel and the rigid wheel

[0016] m2*Z2+2*x2*m2+2*W0=m1*Z1+2*x1*m1 (2)

[0017] Where W0 is the maximum radial deformation of the flexspline, m1 is the module of the flexspline, Z1 is the number of teeth of the flexspline, and x1 is the displacement coefficient of the flexspline.

[0018] Step 3: Establish the equation based on the conditions that the flexible wheel and the rigid wheel are correctly engaged after the displacement and the transmission ratio remains unchanged

[0019] m1*(1+2*x1 / Z1)=m2*(1+2*x2 / Z2)=m (3)

[0020] Step 4: For equations (1), (2) and (3), take m1 = m2 = m0 to obtain:

[0021] x1 / Z1=x2 / Z2 (4)

[0022] W0=m0*(Z1-Z2) / 2+m0*(x1-x2) (5)

[0023] Step 5: Substitute (4) into (5) to obtain:

[0024] W0=m0*(Z1-Z2) / 2+m0*(Z1-Z2)*x2 / Z2 (6)

[0025] Step 6: Substitute (3) into (6) to obtain:

[0026] W0=m*(Z1-Z2) / 2 (7)

[0027] For dual-wave harmonic drive, take Z1-Z2=2, and Equation (7) is simplified to:

[0028] W0=m (8)

[0029] In the above formula, m is the pitch circle module, and m0 is the pitch circle module. Formula (8) is the necessary and sufficient condition for the rigid-flexible gear pitch circle to be tangent and the transmission ratio to be constant.

[0030] Step 7: Take W0'=m0 as the actual maximum radial deformation of the flexspline and substitute it into the double-arc tooth harmonic reducer simulation program to verify the meshing performance indicators of the rigid-flexspline. For example, under conditions such as side clearance and double-point meshing, it is proved that the meshing performance indicators all meet the requirements.

[0031] Since W0' / W0 = m0 / m = 1 / (1+2*x2 / Z2), x2 takes a positive value, and the larger x2 is, the smaller the W0' / W0 value is, the greater the reduction in the maximum radial stress of the flexspline. For example, for a 17-gauge harmonic reducer, Db = 41.722, δ = 0.3, m0 = 0.40, and Z2 = 100, we obtain x2 = 3.9025. By adopting large displacement, the maximum radial deformation of the flexspline can be reduced by approximately 10% without compromising the meshing performance of the rigid-flex spline.

[0032] If W0' is smaller than m0, the meshing performance of the rigid-flex gear will deteriorate, the meshing clearance will increase significantly, and the meshing will change from double-point meshing to single-point meshing.

[0033] Step 8: Use modular displacement to ensure the meshing performance of the rigid-flex gear while making W0' smaller than m0.

[0034] First, change the rigid wheel module:

[0035] m2*Z2+2*x2*m2+2*W0"=m1'*Z1+2*x1'*m1' (9)

[0036] m1'*(1+2*x1 / Z1)=m' (10)

[0037] From equations (9), (10) and (2), we can get:

[0038] Δm=m-m'=2*ΔW / Z1 (11)

[0039] Where ΔW=W0'-W0";

[0040] Then change the flexspline modulus:

[0041] m2'*Z2+2*x2'*m2'=Db+2*hf2'+2*δ (12)

[0042] m2'*(1+2*x2 / Z2)=m' (13)

[0043] From equations (12), (13) and (1), we can get:

[0044] Δhf2=hf2-hf2'=ΔW*Z2 / Z1 (14)

[0045] m1'=m2'=m0-2ΔW / (Z1+2*x1) (15)

[0046] In the above formula, W0" is the maximum radial deformation of the flexspline after the module is changed, Δm is the change of the module, Δhf2 is the change of the flexspline tooth valley height, ΔW is the change or reduction of the maximum radial deformation of the flexspline, m is the pitch circle module before the module is changed, m' is the pitch circle module after the module is changed, m1' is the pitch circle module of the rigid pulley after the module is changed, and m2' is the pitch circle module of the flexspline after the module is changed;

[0047] The above parameters are substituted back into the double-arc tooth harmonic reducer simulation program, and the meshing performance indicators of the rigid wheel and the flexible wheel are verified under conditions such as side clearance and double-point meshing.

[0048] In the above solution, as a preferred solution, under the premise of ensuring the meshing performance, the minimum value of W0" is W0"=0.95W0'=0.95m0.

[0049] Compared with the prior art, the present invention has the following beneficial effects: the present invention achieves the purpose of reducing the maximum radial deformation of the flexspline while ensuring the meshing performance of the rigid-flex spline through the large displacement gear, and further reduces the maximum radial deformation of the flexspline through the modular displacement. After the large displacement and modular displacement are achieved, the meshing side clearance of the rigid-flex spline remains basically unchanged, and the original two-point meshing also remains basically unchanged, ensuring the constant transmission ratio and meshing accuracy. Without reducing the transmission stiffness and transmission accuracy of the harmonic reducer and reducing the transmission load capacity by reducing the wall thickness of the flexspline gear ring, the large displacement gear and modular displacement can reduce the maximum radial deformation stress of the flexspline while ensuring the meshing performance, thereby ensuring the high stiffness, high precision and high transmission load capacity of the harmonic reducer, while reducing the maximum deformation stress of the flexspline and increasing the service life of the harmonic reducer. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The disclosure of the present invention is illustrated with reference to the accompanying drawings. It should be understood that the drawings are for illustrative purposes only and are not intended to limit the scope of protection of the present invention. In the accompanying drawings, the same reference numerals are used to refer to the same components. Among them:

[0051] Figure 1 This is the meshing diagram of the double arc tooth harmonic reducer with the rigid-flexible gear in deformation state;

[0052] Figure 2 The geometric parameter diagram of the double arc tooth harmonic reducer flexspline;

[0053] Figure 3 The double arc tooth harmonic reducer adopts the rigid-flexible gear tooth curve when W0=m;

[0054] Figure 4 The tooth curves and envelope curves of the flex-flex gear when the double arc tooth harmonic reducer adopts W0'=0.95m0 and does not adopt the modulus change;

[0055] Figure 5 The tooth profile curve and envelope curve family of the flexspline are for the double arc tooth harmonic reducer when W0'=0.95m0 and module displacement are adopted. DETAILED DESCRIPTION

[0056] In order to make the technical means, creative features, objectives and effects of the present invention easier to understand, the present invention will now be further described in detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the relevant components of the present invention.

[0057] According to the technical solution of the present invention, without changing the essential spirit of the present invention, a person skilled in the art may propose a variety of interchangeable structural modes and implementation modes. Therefore, the following specific embodiments and drawings are merely illustrative of the technical solution of the present invention and should not be regarded as the entire invention or as a limitation or restriction of the technical solution of the present invention.

[0058] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and embodiments.

[0059] like Figure 1 As shown, a method for reducing the maximum deformation stress of the flexspline of a harmonic reducer comprises the following steps:

[0060] Step 1: Establish equations based on the geometric relationship between the flexspline and the flexible bearing

[0061] m2*Z2+2*x2*m2=Db+2*hf2+2*δ (1)

[0062] Where m2 is the flexspline modulus, Z2 is the number of flexspline teeth, x2 is the displacement coefficient of the flexspline, hf2 is the flexspline tooth valley height, Db is the outer diameter of the flexible bearing, and δ is the flexspline gear ring wall thickness. Figure 1 shown.

[0063] Step 2: Establish equations based on the pitch circle fit conditions of the flexible wheel and the rigid wheel

[0064] m2*Z2+2*x2*m2+2*W0=m1*Z1+2*x1*m1 (2)

[0065] Where W0 is the maximum radial deformation of the flexspline, m1 is the module of the flexspline, Z1 is the number of teeth of the flexspline, and x1 is the displacement coefficient of the flexspline.

[0066] Step 3: Establish the equation based on the conditions that the flexible wheel and the rigid wheel are correctly engaged after the displacement and the transmission ratio remains unchanged

[0067] m1*(1+2*x1 / Z1)=m2*(1+2*x2 / Z2)=m (3)

[0068] Formulas 1 to 3 are necessary and sufficient conditions to ensure normal and accurate transmission of the harmonic reducer. For a dual-wave harmonic reducer, if the maximum deformation is not equal to the pitch modulus, it means that the pitch of the flexspline and the pitch of the rigid pulley are not equal. From a strict theoretical point of view, this cannot be properly transmitted. However, in reality, there are certain errors in processing and manufacturing. As long as the error is controlled within a certain allowable range, normal transmission can be achieved. However, if the maximum deformation of the flexspline deviates too much from the pitch modulus, it will cause increased slip during the meshing of the rigid and flexsplines, increasing wear and heat at the same time. In severe cases, it will cause the teeth to jam and fail to transmit.

[0069] Step 4: For equations (1), (2) and (3), take m1 = m2 = m0 to obtain:

[0070] x1 / Z1=x2 / Z2 (4)

[0071] W0=m0*(Z1-Z2) / 2+m0*(x1-x2) (5)

[0072] Step 5: Substitute (4) into (5) to obtain:

[0073] W0=m0*(Z1-Z2) / 2+m0*(Z1-Z2)*x2 / Z2 (6)

[0074] Step 6: Substitute (3) into (6) to obtain:

[0075] W0=m*(Z1-Z2) / 2 (7)

[0076] For dual-wave harmonic drive, take Z1-Z2=2, and Equation (7) is simplified to:

[0077] W0=m (8)

[0078] In the above formula, m is the pitch circle modulus, m0 is the pitch circle modulus; Formula (8) is the necessary and sufficient condition for the rigid-flexible wheel pitch circle to be tangent and the transmission ratio to be constant. Figure 2 shown.

[0079] Step 7: Take W0'=m0 as the actual maximum radial deformation of the flexible wheel, and substitute it into the double arc tooth harmonic reducer simulation program to verify the meshing performance indicators of the rigid-flexible wheel. For example, under conditions such as backlash and double-point meshing, it is proved that the meshing performance indicators meet the requirements. Figure 3 It is the family of the flex spline tooth profile curve and flex spline envelope curve when W0'=m0.

[0080] Since W0' / W0 = m0 / m = 1 / (1+2*x2 / Z2), x2 takes a positive value, and the larger x2 is, the smaller the W0' / W0 value is, the greater the reduction in the maximum radial stress of the flexspline. For example, for a 17-gauge harmonic reducer, Db = 41.722, δ = 0.3, m0 = 0.40, and Z2 = 100, we obtain x2 = 3.9025. By adopting large displacement, the maximum radial deformation of the flexspline can be reduced by approximately 10% without compromising the meshing performance of the rigid-flex spline.

[0081] If W0' is smaller than m0, the meshing performance of the rigid-flex gear will deteriorate, the meshing clearance will increase significantly, and the meshing will change from double-point meshing to single-point meshing. Figure 4The tooth profile curve and envelope curve family of the rigid-flexible gear when W0'=0.95m0 and no module modification is used. It can be seen from the figure that the meshing performance of the rigid-flexible gear is significantly deteriorated.

[0082] The ability of the harmonic reducer to transfer loads mainly depends on the maximum radial deformation of the flexspline. When the harmonic reducer transfers loads, the stress generated by the maximum radial deformation of the flexspline generally exceeds more than half of the total maximum stress. Therefore, from a design perspective, it is hoped to reduce the maximum radial deformation of the flexspline. This can increase the service life of the harmonic reducer or its ability to transfer loads, because the greater the working stress of the flexspline, the shorter its life.

[0083] Formulas 1 to 8 show that for a dual-wave harmonic reducer (i.e., a two-tooth-difference harmonic reducer), the maximum deformation of the flexspline is equal to the pitch module of the flexspline or rigid pulley. The equality of the pitch modules of the rigid pulley and flexspline is a necessary and sufficient condition for proper gear transmission. This also applies to any other type of two-gear transmission. In Formula 1, flexspline hf2 = (0.5-0.8)*m2. For a 17-gauge harmonic reducer with a transmission ratio of 50, the flexspline Z2 is 100, the flexible bearing outer diameter Db is generally 41.722, the maximum radial deformation W0 of the flexspline is generally m2, and the flexspline wall thickness δ is generally 0.1-2 mm. The larger the harmonic reducer size, the thicker the wall, but generally does not exceed m2. Given m2, δ, Db, Z2, and hf2, x1 and x2 can be solved.

[0084] In practice, for a harmonic reducer of a given size and transmission ratio, given design specifications such as transmission accuracy and load capacity, the wall thickness δ is essentially fixed. Harmonic reducers typically have short tooth profiles. A standard tooth height results in sharp tooth tips, which degrades meshing and reduces service life. Too short a tooth height dramatically reduces the meshing area, reducing the contact area between the rigid-flex drive and the flex drive, increasing contact stress and increasing the likelihood of tooth slippage and tooth skipping. Therefore, the hf2 value is generally taken to its optimal value, which is also essentially fixed. Furthermore, for a harmonic reducer of a given size, the outer diameter Db of the flexible bearing is also essentially fixed, with minimal variation. Most dimensions of a harmonic reducer, especially those of the mounting interface, must adhere to standardization. A harmonic reducer of the same size cannot be used simply by replacing it with another manufacturer's. Furthermore, some dimensions are constrained by structural design and cannot be significantly changed. Therefore, the sum of the right-hand side of Formula 1 is essentially fixed. Dividing this sum by z2 gives the flex drive pitch modulus, which is also the maximum radial deformation of the flex drive in a dual-wave harmonic reducer.

[0085] Step 8: Use modular displacement to ensure the meshing performance of the rigid-flex gear while making W0' smaller than m0.

[0086] First, change the rigid wheel module:

[0087] m2*Z2+2*x2*m2+2*W0"=m1'*Z1+2*x1'*m1' (9)

[0088] m1'*(1+2*x1 / Z1)=m' (10)

[0089] From equations (9), (10) and (2), we can get:

[0090] Δm=m-m'=2*ΔW / Z1 (11)

[0091] Where ΔW=W0'-W0";

[0092] Then change the flexspline modulus:

[0093] m2'*Z2+2*x2'*m2'=Db+2*hf2'+2*δ (12)

[0094] m2'*(1+2*x2 / Z2)=m' (13)

[0095] From equations (12), (13) and (1), we can get:

[0096] Δhf2=hf2-hf2'=ΔW*Z2 / Z1 (14)

[0097] m1'=m2'=m0-2ΔW / (Z1+2*x1) (15)

[0098] In the above formula, W0" is the maximum radial deformation of the flexspline after the module is changed, Δm is the change of the module, Δhf2 is the change of the flexspline tooth valley height, ΔW is the change or reduction of the maximum radial deformation of the flexspline, m is the pitch circle module before the module is changed, m' is the pitch circle module after the module is changed, m1' is the pitch circle module of the rigid pulley after the module is changed, and m2' is the pitch circle module of the flexspline after the module is changed.

[0099] Finally, the above parameters are substituted back into the double-arc tooth harmonic reducer simulation program to verify the meshing performance indicators of the rigid wheel and the flexible wheel under conditions such as side clearance and double-point meshing.

[0100] In the above scheme, under the premise of ensuring meshing performance, the minimum value of W0" is W0" = 0.95W0' = 0.95m0. The reason for giving 0.95 is to adopt the method proposed in this article. While ensuring double-point meshing, the lower limit coefficient of the maximum radial deformation is obtained using the double-arc harmonic reducer tooth profile design software HarmonicGearDesignV1.0. If the value is less than 0.95, the rigid-flexible wheel will be in single-point meshing and the meshing state will deteriorate. If the only goal is to reduce the maximum radial deformation of the flexible wheel, the transmission accuracy of the harmonic reducer will be greatly reduced, the load transfer capacity will be reduced, and the service life will be shortened. Therefore, it cannot be lower than this value.

[0101] in, Figure 5 When W0'=0.95m0 and the modular displacement is adopted, the tooth profile curve and the envelope curve family of the rigid-flexible gear are shown. It can be seen from the figure that the meshing performance of the rigid-flexible gear is good.

[0102] From the above, it can be concluded that after adopting W0'=m0, the pitch circle of the rigid wheel changes, and the pitch circle modulus change of the new pitch circle is Δm=2ΔW / Z1.

[0103] For m0 = 0.40, Z1 = 102, ΔW = m-m0 = 0.03122 mm, and Δm is approximately 0.61 μm. Due to the inherent errors in the manufacturing process, W0' = m0 can meet the transmission performance requirements.

[0104] Through the implementation of the above scheme, the present invention achieves the positive effect of reducing the maximum radial deformation of the flexspline by adopting a large displacement gear while ensuring that the meshing performance is not reduced. This ensures the constancy of the transmission ratio and the accuracy of the meshing. Without reducing the wall thickness of the flexspline gear ring, which would result in a decrease in the transmission stiffness, transmission accuracy, and transmission load capacity of the harmonic reducer, the large displacement gear and the smaller maximum radial deformation of the flexspline can effectively reduce the maximum radial deformation stress of the flexspline of the harmonic reducer, thereby ensuring the high stiffness, high precision, and high transmission load capacity of the harmonic reducer while also extending the service life of the harmonic reducer.

[0105] In summary, the specific steps of this method include establishing a geometric relationship equation between the flexspline and the flexible bearing, then establishing an equation based on the rigid-flexspline pitch circle fit condition, and finally establishing the rigid-flexspline module equation based on the correct meshing condition. Given the transmission ratio, ring gear wall thickness, and flexible bearing outer diameter, the above three equations can determine the displacement coefficients of the flexspline and rigid-flexspline, as well as the theoretical maximum radial deformation of the flexspline when the rigid-flexspline meets the theoretically precise transmission requirement. When the rigid-flexspline uses a large displacement gear, the maximum radial deformation of the flexspline can be taken as the pitch circle module of the rigid-flexspline. In this case, the maximum radial deformation of the flexspline can be reduced by approximately 10% relative to the theoretical maximum radial deformation of the flexspline. Further modular displacement can be used to further reduce the maximum radial deformation of the flexspline by 5%, while essentially maintaining the same meshing performance, ensuring two-point meshing while maintaining side clearance and meshing tooth pair count. Because the maximum deformation stress of the flexspline increases nonlinearly and rapidly with the maximum radial deformation of the flexspline, the method proposed in this invention reduces the maximum deformation stress of the flexspline by more than 15%.

[0106] This method uses large displacement gears and module displacement to effectively reduce the maximum deformation stress of the harmonic reducer flexspline and increase the service life of the harmonic reducer. This method is not only applicable to double-arc tooth harmonic reducers, but also to harmonic reducers with involute tooth profiles and other tooth profiles.

[0107] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for reducing the maximum deformation stress of a flexspline of a harmonic reducer, characterized in that: The method comprises the following steps: Step 1: Establish equations based on the geometric relationship between the flexspline and the flexible bearing m2*Z2+2*x2*m2=Db+2*hf2+2*δ (1) Where m2 is the flexspline modulus, Z2 is the number of flexspline teeth, x2 is the displacement coefficient of the flexspline, hf2 is the flexspline tooth valley height, Db is the outer diameter of the flexible bearing, and δ is the wall thickness of the flexspline gear ring; Step 2: Establish equations based on the pitch circle fit conditions of the flexible wheel and the rigid wheel m2*Z2+2*x2*m2+2*W0=m1*Z1+2*x1*m1 (2) Where W0 is the maximum radial deformation of the flexspline, m1 is the module of the flexspline, Z1 is the number of teeth of the flexspline, and x1 is the displacement coefficient of the flexspline. Step 3: Establish the equation based on the conditions that the flexible wheel and the rigid wheel are correctly engaged after the displacement and the transmission ratio remains unchanged m1*(1+2*x1 / Z1)=m2*(1+2*x2 / Z2)=m (3) Step 4: For equations (1), (2) and (3), take m1 = m2 = m0 to obtain: x1 / Z1=x2 / Z2 (4) W0=m0*(Z1-Z2) / 2+m0*(x1-x2) (5) Step 5: Substitute (4) into (5) to obtain: W0=m0*(Z1-Z2) / 2+m0*(Z1-Z2)*x2 / Z2 (6) Step 6: Substitute (3) into (6) to obtain: W0=m*(Z1-Z2) / 2 (7) For dual-wave harmonic drive, take Z1-Z2=2, and Equation (7) is simplified to: W0=m (8) In the above formula, m is the pitch circle module, and m0 is the reference circle module; Step 7: Take W0'=m0 as the actual maximum radial deformation of the flexspline, and substitute it into the double-arc tooth harmonic reducer simulation program to verify the meshing performance indicators of the rigid-flexspline, proving that the meshing performance indicators all meet the requirements.

2. The method for reducing the maximum deformation stress of a flexspline of a harmonic reducer according to claim 1, characterized in that: The method further includes step eight: using modular displacement to ensure the meshing performance of the rigid-flex gear while making W0' smaller than m0.

3. The method for reducing the maximum deformation stress of a flexspline of a harmonic reducer according to claim 2, characterized in that: The specific calculation method of step eight is as follows: First, change the rigid wheel module: m2*Z2+2*x2*m2+2*W0"=m1'*Z1+2*x1'*m1' (9) m1'*(1+2*x1 / Z1)=m' (10) From equations (9), (10) and (2), we can get: Δm=m-m'=2*ΔW / Z1 (11) Where ΔW=W0'-W0"; Then change the flexspline modulus: m2'*Z2+2*x2'*m2'=Db+2*hf2'+2*δ (12) m2'*(1+2*x2 / Z2)=m' (13) From equations (12), (13) and (1), we can get: Δhf2=hf2-hf2'=ΔW*Z2 / Z1 (14) m1'=m2'=m0-2ΔW / (Z1+2*x1) (15) In the above formula, W0" is the maximum radial deformation of the flexspline after the module is changed, Δm is the change of the module, Δhf2 is the change of the flexspline tooth valley height, ΔW is the change or reduction of the maximum radial deformation of the flexspline, m is the pitch circle module before the module is changed, m' is the pitch circle module after the module is changed, m1' is the pitch circle module of the rigid pulley after the module is changed, and m2' is the pitch circle module of the flexspline after the module is changed; The above parameters are substituted back into the double arc tooth harmonic reducer simulation program to verify the meshing performance indicators of the rigid wheel and the flexible wheel.

4. The method for reducing the maximum deformation stress of a flexspline of a harmonic reducer according to claim 3, characterized in that: On the premise of ensuring meshing performance, the minimum value of W0" is W0"=0.95W0'=0.95m0.

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