Impact resistance design method for harmonic gear transmission mechanism

Abstract

The invention relates to the technical field of precision transmission, and discloses an impact resistance design method for a harmonic gear transmission mechanism, which is used for constructing an impact performance evaluation model by analyzing an impact force change rule in an engaging impact process. The method comprises the following steps: firstly, establishing a harmonic gear transmission impact model based on an improved kinematics method, calculating a contact force when a flexible gear is engaged with a rigid gear based on a Hertz contact theory and an elastic thin plate theory, solving a hysteresis damping coefficient in a collision process by combining a Hunt-Crossley hysteresis model with a damping coefficient and an energy conservation law, and calculating a harmonic gear transmission impact model according to the hysteresis damping coefficient. According to the method, a harmonic gear transmission collision process impact force model is established, an engaging-in impact force and impact duration conforming to a Hunt-Crossley hysteresis loop are obtained, an impact slow release index (IRI) is constructed, and the impact resistance of a harmonic gear transmission mechanism is evaluated. Through a transient dynamics analysis method, the accuracy of a theoretical impact model calculation method is verified. The method can effectively predict the shock resistance of the harmonic reducer, and provides a theoretical basis for the flexible gear profile design of the harmonic reducer.

Description

Technical Field

[0001] This invention relates to the field of harmonic reducer transmission technology, and in particular to a method for shock-resistant design calculation of a harmonic gear transmission mechanism suitable for humanoid robot joints. Background Technology

[0002] Humanoid robots are intelligent devices that integrate cutting-edge technologies such as artificial intelligence and robotics, possessing a human-like appearance, bipedal walking ability, and voice interaction capabilities. In humanoid robots, the impact resistance of joint reducers is crucial. As a key component of motion control, reducers need to precisely control joint angles, forces, and speeds. Under complex working conditions (such as frequent starts and stops, and collision-risk scenarios), reducers may experience decreased impact resistance or insufficient impact performance. This can lead to accelerated gear wear, reduced precision, and other malfunctions, directly affecting the robot's lifespan and operational reliability.

[0003] To address the impact risk of joint reducers in humanoid robots, researchers both domestically and internationally have proposed several solutions: ABDULLAH et al. studied the fatigue failure of flexures in harmonic gear drives due to alternating stress in robot joint applications. They introduced a correction factor and experimentally determined its impact on the load-bearing capacity of the flexure. Zhang et al. considered the static and dynamic errors of harmonic gear drives and derived the dynamic response of the excitation in a multi-degree-of-freedom system. Qiu Shiyun et al. designed a fracture-resistant flexure with a buffer arc segment to prevent collision with internal components during deformation. Li et al. proposed a reliability analysis method for harmonic reducers that considers multi-source uncertainties and wear.

[0004] The invention patent application "Built-in Cycloidal Reducer and Joint Module with Integrated Disc Output Structure for Humanoid Robot Joints" solves the problems of large size, insufficient transmission accuracy, and insufficient load-bearing capacity of robot joint modules through the integrated design of the cycloidal reducer and motor with an integrated disc output structure and a parabolic shaping method. This results in a compact, high-performance robot joint module, reducing manufacturing costs and improving transmission accuracy and impact resistance. The invention patent application "A Harmonic Reducer Flexible Wheel Structure and Processing Technology" solves the problem of insufficient strength of the flexible wheel by designing stamped and encapsulated parts on it, and setting grooves and bolt holes on them. This achieves high strength and efficient assembly of the flexible wheel, extending its service life.

[0005] Currently, research on harmonic reducers for humanoid robot joints focuses on flexure stress and system dynamics, as well as the overall load-bearing capacity analysis of the flexure. However, it lacks a systematic study on the precise calculation of the meshing impact force of each tooth profile of the flexure. Furthermore, existing impact force calculations rely on a single finite element analysis method, or a combination of meshing stiffness matrix, TCA, and LTCA, making the accuracy of the results uncertain. These methods also have high requirements for computer hardware, making them difficult to meet the needs of precise and rapid analysis in engineering design. In addition, existing research does not clarify the relationship between the magnitude and duration of the impact force between the flexure and rigid wheel during meshing under load, failing to provide direct guidance for the impact resistance performance of harmonic reducers and the optimization design of the flexure tooth profile.

[0006] Therefore, how to accurately and quickly calculate the magnitude of the impact force during the meshing process of the flexible wheel and the rigid wheel, and how to analyze and optimize the impact characteristics of the transmission mechanism by establishing an impact response model and impact resistance performance evaluation index, so as to improve the impact resistance performance of the harmonic reducer and optimize the design of the flexible wheel tooth profile, is a research topic of harmonic reducers. Summary of the Invention

[0007] The purpose of this invention is to provide a shock-resistant design and calculation method for harmonic gear transmission mechanisms suitable for humanoid robot joints, in order to solve the problem that the existing humanoid robot joint reducers have insufficient shock resistance and are difficult to adapt to complex working conditions.

[0008] The innovations of this technology are mainly reflected in the following aspects: Based on the Hertz contact theory model, multiple meshing impact points of a loaded harmonic gear transmission are accurately calculated to determine the relative contact velocity under tooth flank clearance. Furthermore, combined with the Hunt-Crossley hysteresis model with damping coefficients, the relationship between impact force and impact duration during the harmonic transmission collision process is calculated, and an Impact Relief Index (IRI) is constructed to characterize the impact resistance of the harmonic gear transmission mechanism. Transient dynamics is used to verify the theoretical impact force model.

[0009] To achieve the above objectives, this invention provides a shock-resistant design and calculation method for harmonic gear transmission mechanisms suitable for humanoid robot joints, comprising four parts: "determining the actual meshing impact point of the gear teeth, establishing an impact force model with a hysteresis damping coefficient, constructing an impact mitigation index evaluation model, and verifying the transient dynamics module," as detailed below: S1: Establish an initial assembly transmission model of the flexible wheel and rigid wheel based on the improved kinematics method; S2: The intersection of the flexible pitch ellipse and the rigid pitch circle is the initial node. The meshing point of the flexible gear theory is The theoretical meshing point of the rigid wheel is ; Formula 1 for the theoretical meshing common normal of a flexible wheel and a rigid wheel (1) Establish the first i Formula 2 of the equation for the point of engagement (2) Formulas 1 and 2 provide the theoretical engagement point coordinates of the same engagement point of each pair of gear teeth at two different engagement angles, as well as the theoretical engagement point coordinates of two engagement points on the same flexible gear tooth engaging at the same angle. S3: The maximum contact deformation is obtained based on the half-width of the contact area according to Hertz contact theory. When the wave generator and flex wheel transmit torque T At that time, the first [time] is established by torque balance. i The maximum meshing force of the meshing tooth profiles at the contact point of the gear teeth Formula 3: (3) In the formula: m The gear number at which meshing begins. n The tooth number that marks the end of engagement; Combining deformation compatibility equation formula 4 and the first i Formula 5, which is the equation for the elastic torsion angle of the meshing tooth profile pair at the tooth contact point, yields the actual meshing point coordinates for each meshing tooth profile pair. (4) (5) In the formula: This is the amount of elastic deformation. The distance between the meshing points, For the maximum contact deformation, The meshing lever arm for each tooth profile pair, For the maximum contact engagement lever arm, For maximum meshing force, The radius of the flexible pitch ellipse; S4: Based on the laws of conservation of energy and momentum, the dissipated energy between the flexible wheel and the rigid wheel during the impact process is obtained. for: (6) In the formula, m 1, m 2 represents the mass of the flexible wheel and the rigid wheel, respectively. u 1, u 2 represents the velocity of the flexible wheel and the rigid wheel before the impact. v 1, v 2 represents the velocity after the flexible wheel and the rigid wheel collide. The coefficient of recovery; When the flexible gear teeth and the rigid gear teeth are compressed to the maximum deformation stage, the coefficient of restitution is zero, the kinetic energy loss is maximum, mechanical energy is not conserved, but momentum is conserved. Therefore, the maximum elastic potential energy is: (7) Formula 8 is established based on the work done by the maximum elastic potential energy, and Formula 9 is established based on the work done by the energy lost due to hysteresis damping. (8) (9) In the formula, The contact force between the flexible wheel and the rigid wheel. It is the hysteresis damping factor. The initial relative contact velocity, For contact deformation, For contact depth; Simplifying the contact between the flexible wheel and the rigid wheel to the contact between two cylinders, and combining this with the theory of elastic thin plates, the contact force between the flexible wheel and the rigid wheel is: (10) Based on the Hunt-Crossley hysteresis model with damping coefficient in Formula 11, Formula 12 is established as a nonlinear contact impact force model. (11) (12) In the formula, l Let be the axial width of the flexible wheel and the rigid wheel. To measure the overall elastic modulus, , For fitting the tooth profile of the flexible gear, For the elastic modulus of the flexible wheel, t For the tooth root wall thickness, h For the full tooth height of the flexible gear, a The radius of the major axis of the wave generator. b The minor axis radius of the wave generator. The curve radius of the neutral layer in the initial state of the flexible wheel; The maximum impact force of each tooth profile is obtained based on the trapezoidal area of ​​the energy hysteresis loop. F ; Based on the meshing impact force F and duration of impact t An Impact Relief Index (IRI) was constructed to characterize the impact resistance of harmonic gear transmission mechanisms. The IRI is defined as the ratio of the area enclosed by the hysteresis loop to the peak value of the meshing impact force. Impact duration and maximum impact speed The ratio of the products: (13) The larger the impact mitigation index (IRI), the stronger the harmonic gear's ability to regulate and mitigate impact energy under transient impact loads, and the better its impact resistance.

[0010] S5: Import the tooth profile into 3D software and use the Abaqus transient dynamics simulation method to verify the correctness of the impact resistance method in both directions for the harmonic gear transmission mechanism.

[0011] The designed tooth profile is imported into 3D software to perform transient dynamics simulation on the harmonic gear transmission mechanism. The impact force and impact duration under the finite element method are obtained and compared with the theoretical calculation results. The steps of transient dynamics simulation are as follows: S1: The wave generator adopts a double roller contact type wave generator, which consists of two bearings and a connecting rod. The flexible wheel and rigid wheel adopt a three-dimensional tooth profile model established by theoretical analysis model. S2: Enter the Property module, create a material section, and assign the section to the flexible wheel, rigid wheel, and wave generator; S3: Enter the Assembly module to assemble the flexible wheel, rigid wheel, and wave generator; S4: Enter the analysis step module. In analysis step 1, the wave generator is inserted along the direction of the cylinder. In analysis step 2, the wave generator rotates, causing the flexible wheel and rigid wheel to mesh. S5: Enter the Interaction module. In the analysis step (Step 1), create a surface-to-surface contact between the outer surface of the bearing and the inner surface of the flexure. In the analysis step (Step 2), create a surface-to-surface contact between the tooth surface of the flexure and the tooth surface of the rigid wheel. Then, create a revolute joint between the bearing and the connecting rod, a revolute joint between the connecting rod and the flexure, and a revolute joint between the flexure and the rigid wheel. Bind the connecting rod and the bearing and set them as a rigid body. Bind the connecting rod reference point to the lower surface of the flexure cylinder through coupling. Bind the upper reference point of the flexure to the lower surface of the flexure cylinder through coupling. Bind the lower reference point of the flexure to the outer surface of the rigid wheel through coupling. S6: Enter the Load module, fix the outer surface of the rigid wheel in analysis step 1 and analysis step 2, apply the displacement of the wave generator along the cylinder direction in analysis step 1, and apply the rotational angular velocity to the wave generator in analysis step 2. S7: Enter the Mesh module. The wave generator uses a tetrahedral mesh (C3D4H) for its mesh elements, while the flexible and rigid wheels use a hexahedral mesh (C3D8R). The mesh size is specified as flexible wheel > rigid wheel > wave generator for easy and rapid model analysis.

[0012] By adopting the above technical solution, the present invention has the following beneficial effects: Compared to existing single transient dynamics methods, this invention proposes a theoretical impact force calculation method combining Hertz contact theory and the Hunt-Crossley hysteresis model with damping coefficients. Based on an improved kinematic method, an impact model of harmonic gear transmission is established. The impact points of each meshing point of the harmonic gear transmission under load are calculated, and the relative contact velocity under tooth backlash is determined. Based on Hertz contact theory and elastic thin plate theory, the contact force when the flexible gear meshes with the rigid gear is calculated. Furthermore, combining the Hunt-Crossley hysteresis model with damping coefficients and the law of conservation of energy, the hysteresis damping coefficient in the collision process is solved, establishing an impact force model for the harmonic gear transmission collision process. This yields a meshing impact process that conforms to the hysteresis loop in Hunt-Crossley theory. An Impact Relief Index (IRI) is constructed; a larger IRI indicates a stronger ability of the harmonic gear to regulate and relieve impact energy under impact, resulting in better impact resistance. The accuracy of the theoretical impact force calculation method is verified through transient dynamics analysis. This invention combines theoretical calculation with finite element simulation, enabling accurate and rapid calculation of the relationship between meshing impact force and impact time in harmonic gear transmission. By establishing an impact response model and an impact resistance performance evaluation index (IRI), it achieves the analysis and optimization design of the impact characteristics of the transmission mechanism. Attached Figure Description

[0013] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0014] Figure 1 A schematic diagram of the flexible gear tooth profile curve in a harmonic gear transmission mechanism provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the meshing principle of the harmonic gear transmission mechanism of the present invention; Figure 3 This is a schematic diagram of the meshing impact velocity of the harmonic gear transmission mechanism of the present invention; Figure 4This is a graph showing the relationship between impact force and contact deformation calculated for the harmonic gear transmission mechanism of this invention. Figure 5 This is a graph showing the relationship between impact force and impact time calculated for the harmonic gear transmission mechanism of this invention. Figure 6 This is a graph showing the variation of the impact mitigation index and maximum impact force for different tooth profiles of the harmonic gear transmission mechanism of the present invention; Figure 7 This is the three-dimensional digital model of the present invention; Figure 8 A comparison of the theoretical and simulated impact forces calculated for the harmonic gear transmission mechanism of this invention; Figure 9 This is a flowchart of the impact-resistant design method for the harmonic gear transmission mechanism of the present invention. Detailed Implementation

[0015] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] The present invention will be further explained below with reference to specific embodiments.

[0017] like Figure 9 As shown in the figure, this embodiment discloses a harmonic gear transmission mechanism suitable for humanoid robot joints and its impact resistance design calculation method, which is carried out according to the following steps: S1: Write piecewise function code in MATLAB programming software, and substitute it into the formulas (14) for the convex tooth profile segment AB, (15) for the common tangent tooth profile segment BC, and (16) for the concave tooth profile segment CD: (14) (15) (16) In the formula: ; ; ; arc length ; ; ; Tooth tip pressure angle Tooth root pressure angle ; ; ; ; ; Substitute the flexible gear tooth profile parameters of the harmonic gear transmission mechanism in Table 1 into the piecewise function formula to generate the flexible gear tooth profile coordinate data (e.g., Figure 1 As shown in the image, importing the data into 3D software can generate a 3D model.

[0018] Table 1 Basic parameters of harmonic gear transmission

[0019] S2: Based on the improved kinematics method, construct the relationship that the arc length remains unchanged before and after the deformation of the flexible wheel: (17) In the formula: The curve radius of the neutral layer in the initial state of the flexible wheel. The radius vector of the deformed flexible wheel. For the output angle of the flexible wheel, The radius vector of the flexure after deformation is the angle between the radius and the rotation angle of the wave generator.

[0020] A transmission model with wave generator input, fixed rigid wheel, and flexible wheel output is used. By combining the coordinate transformation matrix to solve for the curve of arc length versus meshing angle, the coordinates of the conjugate tooth profile of the rigid wheel are obtained. This coordinate is then imported into 3D software to generate a 3D model, ensuring that the meshing clearance between the rigid wheel and the flexible wheel meets the design requirements (e.g., ...). Figure 2 (As shown).

[0021] The intersection of the flexible pitch ellipse and the rigid pitch circle is the initial node. The meshing point of the flexible gear theory is The theoretical meshing point of the rigid wheel is ; Formula 1 for the theoretical meshing common normal of a flexible wheel and a rigid wheel: (1) Establish the first i Formula 2 for the equation of the engagement point: (2) Formulas 1 and 2 provide the theoretical engagement point coordinates of the same engagement point of each pair of gear teeth at two different engagement angles, as well as the theoretical engagement point coordinates of two engagement points on the same flexible gear tooth engaging at the same angle. S3: According to the torque balance principle, let the torque on the wave generator be... T The actual power transmission teeth of the flexible gear are numbered as follows: m to n Then, the torque equation formula 18 is established: (18) In the formula: For the contact force between the tooth profile and the tooth profile, For contact lever arm; The maximum contact deformation is obtained based on the half-width of the contact region according to Hertz contact theory. When the wave generator and flex wheel transmit torque T At that time, the first equation is established from the torque balance formula 18. i The maximum meshing force of the meshing tooth profiles at the contact point of the gear teeth Formula 3: (3) In the formula: m The gear number at which meshing begins. n The tooth number that marks the end of engagement. This is the amount of elastic deformation. The distance between the meshing points, For the maximum contact deformation, The meshing lever arm for each tooth profile pair; Combining deformation compatibility equation formula 4 and the first i Formula 5, which is the equation for the elastic torsion angle of the meshing tooth profile pair at the tooth contact point, yields the actual meshing point coordinates for each meshing tooth profile pair. (4) (5) In the formula: For the maximum contact engagement lever arm, The radius of the flexible pitch ellipse; When the harmonic reducer is under load, the impact on a single tooth profile causes elastic deformation of the flexure tooth profile, shifting the theoretical meshing point to the actual meshing point. The maximum contact deformation is then: (19) In the formula: For the maximum initial meshing force, b The width of the tooth profile contact area is half the width. , Poisson's ratios for flexible and rigid wheel materials, respectively. , These are the elastic moduli of the flexible and rigid wheel materials, respectively. These are the radii of curvature of the contact area between the flexible wheel and the rigid wheel, respectively.

[0022] Write computational code in MATLAB with the following loop condition for iterative calculation: (20) In the formula: The maximum contact force in the previous iteration. This represents the maximum contact force in the next iteration; Finally, the coordinates of each tooth profile relative to the actual meshing point during the meshing process of the flexible wheel and the rigid wheel are obtained; according to Figure 3The geometric relationship shown allows us to derive the engagement impact velocity as follows: (twenty one) In the formula: The common velocity when the wave generator and the flexspline mesh. This is the common velocity when the flexible wheel and the rigid wheel mesh. The angle between the engagement impact velocity and the transverse axis of the rigid wheel. The angle between the engagement impact velocity and the deformed radius vector; S4: Based on the law of conservation of energy (Equation 22) and the law of conservation of momentum (Equation 23), the energy dissipated between the flexible wheel and the rigid wheel during the impact process is obtained. Formula 6; (twenty two) (twenty three) (6) In the formula, m 1, m 2 represents the mass of the flexible wheel and the rigid wheel, respectively. u 1, u 2 represents the velocity of the flexible wheel and the rigid wheel before the impact. v 1, v 2 represents the velocity after the flexible wheel and the rigid wheel collide. The coefficient of recovery; When the flexible gear teeth and rigid gear teeth are compressed to the maximum deformation stage, the coefficient of restitution is zero, the kinetic energy loss is the maximum, mechanical energy is not conserved, but momentum is conserved. Formula 7 for maximum elastic potential energy is established. (7) Formula 8 is established based on the work done by the maximum elastic potential energy: (8) Formula 9 is established based on the work done by the energy lost due to hysteresis damping: (9) In the formula, The contact force between the flexible wheel and the rigid wheel. It is the hysteresis damping factor. The initial relative contact velocity, For contact deformation, For contact depth; Combining Equations 7 and 8, we obtain the initial contact velocity as follows: (twenty four) In the formula, l Let be the axial width of the flexible wheel and the rigid wheel. To measure the overall elastic modulus, , For fitting the tooth profile of the flexible gear; The contact between the flexible wheel and the rigid wheel is simplified to the contact between two cylinders. Using the theory of elastic thin plates, we obtain formula 10 for the contact force between the flexible wheel and the rigid wheel: (10) Based on the Hunt-Crossley hysteresis model with damping coefficient formula 11, the nonlinear contact impact force model formula 12 is obtained. (11) (12) In the formula, l Let be the axial width of the flexible wheel and the rigid wheel. To measure the overall elastic modulus, , For fitting the tooth profile of the flexible gear, For the elastic modulus of the flexible wheel, t For the tooth root wall thickness, h For the full tooth height of the flexible gear, a The radius of the major axis of the wave generator. b The minor axis radius of the wave generator. The curve radius of the neutral layer in the initial state of the flexible wheel; Substituting the initial meshing impact velocity obtained in step S3 into the equation and using the trapezoidal area of ​​the energy hysteresis loop, the maximum impact force of each tooth profile is obtained. F When the deformation reaches its maximum, the relationship between the maximum impact force of the gear pair and the contact compression deformation can be derived (e.g., Figure 4 As shown), by extracting the time interval from 0 to peak value and then from peak value to 0, the relationship between impact force and impact duration can be obtained (e.g., Figure 5 (as shown) Based on the relationship between impact force, impact duration, and compression deformation, an Impact Relief Index (IRI) is constructed to characterize the impact resistance of harmonic gear transmission mechanisms. The Impact Relief Index IRI is defined as the ratio of the area enclosed by the hysteresis loop to the peak value of the meshing impact force. Impact duration and maximum impact speed The ratio of the products, i.e., Formula 13: (13) The impact mitigation index (IRI) was calculated for teeth 1 to 11 (e.g., Figure 6 As shown in the figure, with the increase of tooth number, the peak impact force of the tooth profile pair is larger and the impact mitigation index (IRI) is larger. Although the tooth profile pair bears a larger transient impact load under impact, its ability to regulate and mitigate impact energy through damping effect is also stronger, so the impact resistance performance is better.

[0023] Next, the results were verified using the finite element method, using the harmonic gear model established by the 3D software (such as...). Figure 7 (As shown) Import the data into Abaqus software, and the steps for transient dynamic simulation are as follows: S1: The wave generator adopts a double roller contact type wave generator, which consists of two bearings and a connecting rod. The flexible wheel and rigid wheel adopt a three-dimensional tooth profile model established by theoretical analysis model. S2: Enter the Property module, create a material section, set the flexible wheel material to 30CrMnSiA, and the rigid wheel and wave generator material to 45 steel. The material property settings are shown in Table 2. Assign the section to the flexible wheel, rigid wheel and wave generator. Table 2 Material Properties of Harmonic Gear Transmission

[0024] S3: Enter the Assembly module to assemble the flexible wheel, rigid wheel, and wave generator; S4: Enter the analysis step module. In analysis step 1, the wave generator is inserted 16mm along the cylinder direction. Select dynamic display analysis for analysis step type, mass amplification factor of 1e5, and enable geometric nonlinear mode. In analysis step 2, the wave generator rotates, causing the flexible wheel and rigid wheel to mesh. Select dynamic display analysis for analysis step type, mass amplification factor of 1e5, and enable geometric nonlinear mode. S5: Enter the Interaction module. In Analysis Step 1, create a surface-to-surface contact between the outer surface of the bearing and the inner surface of the flexspline, selecting the Penalty contact method with a friction coefficient of 0.15. In Analysis Step 2, create a surface-to-surface contact between the flexspline tooth surface and the rigid wheel tooth surface, selecting the Penalty contact method with a friction coefficient of 0.15. Then create a revolute joint between the bearing and the connecting rod, setting the connector property to Hinge. Create another revolute joint between the connecting rod and the flexspline, again setting the connector property to Hinge. Create yet another revolute joint between the flexspline and the rigid wheel, again setting the connector property to Hinge. Bind the connecting rod to the bearing and set it to Rigid. Body), without considering the deformation and force of the wave generator, the reference point of the connecting rod is bound to the lower surface of the flexible wheel cylinder through coupling, the reference point of the upper flexible wheel is bound to the lower surface of the flexible wheel cylinder through coupling, and the reference point of the lower flexible wheel is bound to the outer surface of the rigid wheel through coupling. S6: Enter the Load module, fix the outer surface of the rigid wheel in analysis step 1 and analysis step 2, apply a displacement of 16mm along the cylinder direction to the wave generator in analysis step 1, and apply a rotational angular velocity of 376.99 rad / s to the wave generator in analysis step 2. S7: Enter the Mesh module. The wave generator uses a tetrahedral mesh C3D4H, the flexible wheel and rigid wheel use a hexahedral mesh C3D8R, the flexible wheel mesh size is 0.7, the rigid wheel mesh size is 2.5, and the wave generator mesh size is 6. The impact force curves of teeth 8 and 11 were extracted and compared with the theoretical results (e.g., Figure 8 As shown in the figure, the finite element verification error is ≤10%.

[0025] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for shock-resistant design of a harmonic gear transmission mechanism, characterized in that, include: S1: Establish an initial assembly transmission model of the flexible wheel and rigid wheel based on the improved kinematics method; S2: The intersection of the flexible pitch ellipse and the rigid pitch circle is the initial node. The meshing point of the flexible gear theory is The theoretical meshing point of the rigid wheel is ; Formula 1 for the theoretical meshing common normal of a flexible wheel and a rigid wheel (1) Establish the first i Formula 2 of the equation for the point of engagement (2) Formulas 1 and 2 provide the theoretical engagement point coordinates of the same engagement point of each pair of gear teeth at two different engagement angles, as well as the theoretical engagement point coordinates of two engagement points on the same flexible gear tooth engaging at the same angle. S3: The maximum contact deformation is obtained based on the half-width of the contact area according to Hertz contact theory. When the wave generator and flex wheel transmit torque T At that time, the first [time] is established by torque balance. i The maximum meshing force of the meshing tooth profiles at the contact point of the gear teeth Formula 3: (3) In the formula: m The gear number at which meshing begins. n The tooth number that marks the end of engagement; Combining deformation compatibility equation formula 4 and the first i Formula 5, which is the equation for the elastic torsion angle of the meshing tooth profile pair at the tooth contact point, yields the actual meshing point coordinates for each meshing tooth profile pair. (4) (5) In the formula: This is the amount of elastic deformation. The distance between the meshing points, For the maximum contact deformation, The meshing lever arm for each tooth profile pair, For the maximum contact engagement lever arm, For maximum meshing force, The radius of the flexible pitch ellipse; S4: Based on the laws of conservation of energy and momentum, the dissipated energy between the flexible wheel and the rigid wheel during the impact process is obtained. for: (6) In the formula, m 1, m 2 represents the mass of the flexible wheel and the rigid wheel, respectively. u 1, u 2 represents the velocity of the flexible wheel and the rigid wheel before the impact. v 1, v 2 represents the velocity after the flexible wheel and the rigid wheel collide. The coefficient of recovery; When the flexible gear teeth and the rigid gear teeth are compressed to the maximum deformation stage, the coefficient of restitution is zero, the kinetic energy loss is maximum, mechanical energy is not conserved, but momentum is conserved. Therefore, the maximum elastic potential energy is: (7) Formula 8 is established based on the work done by the maximum elastic potential energy, and Formula 9 is established based on the work done by the energy lost due to hysteresis damping. (8) (9) In the formula, The contact force between the flexible wheel and the rigid wheel. It is the hysteresis damping factor. The initial relative contact velocity, For contact deformation, For contact depth; Simplifying the contact between the flexible wheel and the rigid wheel to the contact between two cylinders, and combining this with the theory of elastic thin plates, the contact force between the flexible wheel and the rigid wheel is: (10) Based on the Hunt-Crossley hysteresis model with damping coefficient in Formula 11, Formula 12 is established as a nonlinear contact impact force model. (11) (12) In the formula, l Let be the axial width of the flexible wheel and the rigid wheel. To measure the overall elastic modulus, , For fitting the tooth profile of the flexible gear, For the elastic modulus of the flexible wheel, t For the tooth root wall thickness, h For the full tooth height of the flexible gear, a The radius of the major axis of the wave generator. b The minor axis radius of the wave generator. The curve radius of the neutral layer in the initial state of the flexible wheel; The maximum impact force of each tooth profile is obtained based on the trapezoidal area of ​​the energy hysteresis loop. F ; Based on the meshing impact force F and duration of impact t An Impact Relief Index (IRI) was constructed to characterize the impact resistance of harmonic gear transmission mechanisms. S5: Import the tooth profile into 3D software and use the Abaqus transient dynamics simulation method to verify the correctness of the impact resistance method in both directions for the harmonic gear transmission mechanism.

2. The method according to claim 1, characterized in that: The impact mitigation index (IRI) is defined as the area enclosed by the hysteresis loop and the peak value of the meshing impact force during the collision. Impact duration and maximum impact speed The ratio of the products, i.e. (13) The larger the impact mitigation index (IRI), the stronger the harmonic gear's ability to regulate and mitigate impact energy under transient impact loads, and the better its impact resistance.

3. The method according to claim 1, characterized in that: In step S5, the theoretical model is verified using the Abaqus transient dynamics simulation method, including: S1: The wave generator adopts a double roller contact type wave generator, which consists of two bearings and a connecting rod. The flexible wheel and rigid wheel adopt a three-dimensional tooth profile model established by theoretical analysis model. S2: Create a material section and assign it to a flexible wheel, a rigid wheel, and a wave generator; assemble the flexible wheel, the rigid wheel, and the wave generator; S3: Step 1 of analysis is the insertion of the wave generator along the direction of the cylinder; Step 2 of analysis is the rotation of the wave generator, which drives the flexible wheel and the rigid wheel to mesh. S4: In analysis step 1, create a face-to-face display contact between the outer surface of the bearing and the inner surface of the flexure. In analysis step 2, create a face-to-face display contact between the tooth surface of the flexure and the tooth surface of the rigid wheel. Create a rotating pair between the bearing and the connecting rod, a rotating pair between the connecting rod and the flexure, and a rotating pair between the flexure and the rigid wheel. Bind the connecting rod to the bearing. Couple the connecting rod reference point to the lower surface of the flexure cylinder. Couple the upper reference point of the flexure to the lower surface of the flexure cylinder. Couple the lower reference point of the flexure to the outer surface of the rigid wheel. S5: Fix the outer surface of the rigid wheel in analysis step 1 and analysis step 2, apply the displacement of the wave generator along the direction of the cylinder in analysis step 1, and apply the rotational angular velocity to the wave generator in analysis step 2. S6: Grid the grid and submit it to the analyzer for solution.

4. The method according to claim 1, characterized in that: In step S5, the mesh size of the Abaqus transient dynamics simulation method should satisfy the following order: flexible wheel > rigid wheel > wave generator; the wave generator mesh element type is tetrahedral C3D4H, and the flexible wheel and rigid wheel mesh element type is hexahedral C3D8R.

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