A gear design method for three-wave harmonic reducer

Abstract

The present invention discloses a gear design method for a three-wave harmonic reducer, which belongs to the technical field of harmonic reducer design. The method is used for the design and calculation simulation of the cam profile of the three-wave harmonic reducer. The method is designed according to the requirements for improving the frequency response and dynamic response of the servo product, and adopts the harmonic transmission principle to select the involute tooth profile as the basic tooth profile of the three-wave meshing gear. MATLAB and CAD are used to perform curve calculation and drawing simulation to obtain the simulated cam linear shape, and the model is imported into the numerical control processing software using a three-dimensional modeling method to complete the processing of the rigid wheel. After the processing, the principle prototype is preliminarily assembled and manually operated, and the rotation is stable and the speed ratio is correct. The technical process inspection determines that the design and processing technology is feasible and can meet the user requirements, and can guide the production after drawing calculation. The correctness of the method is verified through actual processing. The processed three-wave harmonic reducer gear has the characteristics of large load-bearing capacity and high precision, thereby achieving the purpose of improving the load-bearing capacity of the rigid wheel.

Description

Technical Field

[0001] The present invention relates to the technical field of harmonic reducer design and manufacturing, and is used for the design and calculation simulation of cam profiles of three-wave harmonic reducers, in particular to a gear design method for three-wave harmonic reducers. Background Art

[0002] Harmonic reducers are often required in the drive systems of industrial robots. Harmonic reducers are mainly composed of a rigid wheel, a flexspline and a wave generator. The wave generator is generally elliptical. The flexspline produces elastic deformation under the action of the wave generator. The flexspline teeth at the long axis end mesh with the rigid wheel teeth. Because the number of flexspline teeth is less than that of the rigid wheel, relative rotation occurs between the two wheels, thereby transmitting motion and power. The deformation process of the flexspline is a basically symmetrical and harmonic wave. Different flexspline deformation shapes have different working capabilities. The deformation shape of the flexspline depends on the shape of the wave generator. Prior art includes a method for manufacturing a flexible wheel for a harmonic reducer, a method for designing a cam for a multi-cylinder engine, and a multi-cylinder engine, with patent numbers (CN109014803B and CN113389608A). These methods aim to improve product quality and reduce overall engine fuel consumption. However, in actual use, these prior art methods all modify the gear tooth profile, lacking corresponding theoretical calculations. This means that the cam has two high points per revolution, and the load-bearing capacity of a three-wave harmonic reducer is calculated based on theoretical calculations. This results in insufficient load-bearing capacity for the modified gear tooth profile. Therefore, a gear design method for a three-wave harmonic reducer is needed to address the problems presented in the prior art. Summary of the Invention

[0003] The purpose of the present invention is to provide a gear design method for a three-wave harmonic reducer to solve the problem of insufficient bearing capacity in the prior art.

[0004] To solve the above technical problems, the present invention adopts a technical solution: a method for designing gears for a three-wave harmonic reducer, the method comprising the following steps:

[0005] Step 1: Design according to the requirements for improving the frequency response and dynamic response of the servo product;

[0006] Step 2: Using the principle of harmonic drive, the involute tooth profile is selected as the basic tooth profile of the three-wave meshing gear. The three-wave meshing requirement can be achieved by designing a three-wave cam. The basic curve of the cam expansion profile is designed based on Fourier transform.

[0007] Step 3: Use drawing software to calculate the curve and draw a simulation to obtain the simulated cam line shape;

[0008] The Fourier transform is designed as:

[0009] Σ=a*sin(3*x)+b*sin(6*x)+k

[0010] x value range [0, 2*π]

[0011] In the equation, a is the deformation coefficient, b is the profile engagement modification coefficient, and k is the flexible bearing deformation correction coefficient;

[0012] Envelope the cam's unfolded outline onto the inner diameter circle r of the flexible bearing, and the cam polar coordinate system equation is obtained as follows:

[0013] R1=r+a*sin(3*x)+b*sin(6*x)+k;

[0014] r is the inner radius of the flexible bearing;

[0015] Transforming the polar coordinate equation into a rectangular coordinate system equation is:

[0016] Y=r*sin(t)+a*sin(3*t)*sin(t)+b*sin(6*x)*sin(t)+k*sin(t)

[0017] X=r*cos(t)+a*sin(3*t)*cos(t)+b*sin(6*x)*cos(t)+k*cos(t)

[0018] The value range of t is [0, 2*π].

[0019] Import the design parameters of the flexspline teeth into the cam polar coordinate system equation and perform calculations.

[0020] The number of teeth of the flex spline is designed to be z1=201, the number of teeth of the rigid spline is designed to be z2=204, the deformation coefficient a is selected to be 0.30, the modification b is selected to be 0.02, and k is selected to be 0.012;

[0021] Substituting the numerical values ​​into the cam profile equation yields the following equation;

[0022] Y=25*sin(t)+0.3*sin(3*t)*sin(t)+0.03*sin(6*x)*sin(t)+0.012

[0023] *sin(t):

[0024] X=25*cos(t)+0.3*sin(3*t)*cos(t)+0.03*sin(6*x)*cos(t)+0.012*cos(t):

[0025] The value range of t is [0, 2*π].

[0026] The drawing software includes any one of MATLAB and CAD. The basic curve of the cam expansion profile in step 2 is input into the software to obtain the simulated cam linear shape. The model is imported into the CNC machining software using a three-dimensional modeling method, and the disc-shaped cam profile is machined using a milling machine.

[0027] The drawing simulation comprises the following steps:

[0028] Step 1: Calculate the flexspline wall thickness; Based on the maximum design torque of 20 N.M, the flexspline wall thickness parameter is selected as 0.01 to 0.0125 times the diameter. The flexspline material is 30CrMnSiA, and σ0.2 is 830 MPa, which makes the reducer no-load current small. The flexspline wall thickness coefficient is selected as 0.01, that is, the wall thickness s is 0.32 mm. Use the simulation in SolidWorks to perform a force analysis on the flexspline strength, in which the boundary condition is set as one end fixed and the other end loaded with a torque of 20 N.M. The analysis data shows that the maximum torque is 660 MPa < σ0.2, which is sufficient strength.

[0029] Step 2: Simulate the meshing of the flexible spline and the rigid spline under the cam profile;

[0030] The meshing of the flex spline and the rigid spline under the cam profile in step 2 includes:

[0031] Step 2.1: Determine the flexspline tooth profile parameters based on the transmission ratio and the flexible bearing diameter;

[0032] Step 2.2: Determine the tooth profile parameters of the rigid wheel based on the transmission ratio and the flexible wheel;

[0033] Step 2.3: Perform deformation simulation of the flexspline according to the cam profile, and arrange the calculated flexspline tooth shape along the normal direction of the cam curve to obtain the deformed flexspline profile;

[0034] Step 2.4: Simulate and verify the meshing of the flexible gear and the rigid gear under the action of the cam.

[0035] The module of the flexspline is selected to be 0.16m, the diameter of the flexible bearing is d=32mm, the three-wave reducer is a multiple of 3, the number of teeth of the flexspline is 201, the tooth height coefficient is selected to be 0.7, and the flexspline with involute tooth shape is produced using CAD drawing software.

[0036] The module of the rigid wheel is selected to be 0.16m. The number of teeth of the rigid wheel of the three-wave reducer is 3 more than that of the flexible wheel, so the number of teeth of the rigid wheel is 204. The tooth height coefficient is selected to be 0.7. The involute toothed rigid wheel is made using CAD drawing software.

[0037] The deformed flexspline and the rigid wheel contour line are superimposed to obtain a static simulation diagram of the meshing. The flexspline meshing has three meshing areas with an intersection angle of 120 degrees in one circle. As the cam contour deforms, the flexspline completes meshing and disengagement with the rigid wheel within a range of 60 degrees, and an appropriate tooth profile clearance is reserved.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] The three-wave harmonic reducer gear design method provided by the present invention is designed according to the requirements for improving the frequency response and dynamic response of the servo product, and adopts the harmonic transmission principle to select the involute tooth profile as the basic tooth profile of the three-wave meshing gear, adopts MATLAB and CAD to perform curve calculation and drawing simulation to obtain the simulated cam line shape, and uses a three-dimensional modeling method to import the model into the numerical control processing software, and determines the meshing flexible wheel tooth profile parameters by drawing according to the cam profile, and uses a standard 0.16 die gear hobbing cutter to complete the flexible wheel processing, and determines the meshing rigid wheel tooth profile parameters by drawing according to the cam profile, and uses a standard 0.16 die gear shaping cutter to complete the rigid wheel processing. After the processing, the principle prototype is preliminarily assembled and manually operated, and the rotation is smooth and the speed ratio is correct. The technical process inspection determines that the design and processing technology is feasible and can meet user requirements, and can guide production after drawing calculation. The correctness of the method is verified through actual processing. The processed three-wave harmonic reducer gear has the characteristics of large load capacity and high precision, thereby achieving the purpose of improving the load capacity of the rigid wheel. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the process of the present invention;

[0041] Figure 2 A schematic diagram of a flexible pulley for a 32-type machine according to the present invention;

[0042] Figure 3 A schematic diagram of the cam used in the 32-machine wave generator of the present invention;

[0043] Figure 4 Schematic diagram of the rigid wheel used in the 32-machine wave generator of the present invention;

[0044] Figure 5 It is a static simulation diagram of the 32-type parts of the present invention;

[0045] Figure 6 Schematic diagram of the tooth profile parameters of the meshing flexspline of the present invention;

[0046] Figure 7 Schematic diagram of the deformed flexible pulley profile of the present invention;

[0047] Figure 8 It is a schematic diagram of the meshing simulation diagram of the present invention;

[0048] Figure 9Schematic diagram of tooth top clearance inspection according to the present invention. DETAILED DESCRIPTION

[0049] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0050] like Figure 1 As shown, a design method for a three-wave harmonic reducer gear comprises the following steps: step 1: designing according to the requirements for improving the frequency response and dynamic response of the servo product; step 2: adopting the principle of harmonic transmission, selecting the involute tooth profile as the basic tooth profile of the three-wave meshing gear, and achieving the three-wave meshing requirement by designing a three-wave cam, wherein the basic curve of the cam expansion profile is designed based on Fourier transform; step 3: using drawing software to calculate the curve, using MATLAB and CAD to perform curve calculation and drawing simulation to obtain the simulated cam linear shape, and using 3D modeling to import the model into the CNC machining software, and according to the cam The contour line is determined by drawing the meshing flexible wheel tooth profile parameters, and the standard 0.16 die gear hobbing cutter is used to complete the flexible wheel processing, and the meshing rigid wheel tooth profile parameters are determined by drawing according to the cam contour line, and the rigid wheel processing is completed using a standard 0.16 die gear shaping cutter. After the processing, the principle prototype is initially assembled and manually operated, and the rotation is stable and the speed ratio is correct. The technical process inspection shows that the design and processing technology is feasible and can meet the user requirements. It can guide production after drawing calculations, and the correctness of the method is verified after actual processing. The processed three-wave harmonic reducer gear has the characteristics of large load-bearing capacity and high precision, achieving the purpose of improving the load-bearing capacity of the rigid wheel.

[0051] like Figure 1 The three-wave harmonic reducer gear design method shown in the figure requires a harmonic reducer with greater torsional stiffness than the double-wave torsional stiffness according to the requirements of improving the frequency response and dynamic response of the servo product. According to the principle of harmonic transmission, the involute tooth profile is selected as the basic tooth profile of the three-wave meshing gear. The three-wave meshing requirements can be achieved by designing a three-wave cam. The basic curve of the cam expansion profile can be designed based on Fourier transform as follows:

[0052] Σ=a*sin(3*x)+b*sin(6*x)+k

[0053] x value range [0, 2*π]

[0054] In the equation, a is the deformation coefficient, b is the profile engagement modification coefficient, and k is the flexible bearing deformation correction coefficient. The cam expansion profile is enveloping the flexible bearing inner diameter circle r, and the cam polar coordinate system equation is obtained as follows:

[0055] R1=r+a*sin(3*x)+b*sin(6*x)+k;

[0056] Note: r is the inner radius of the flexible bearing

[0057] Transform the polar coordinate equation into the rectangular coordinate system equation:

[0058] Y=r*sin(t)+a*sin(3*t)*sin(t)+b*sin(6*x)*sin(t)+k*sin(t)

[0059] X=r*cos(t)+a*sin(3*t)*cos(t)+b*sin(6*x)*cos(t)+k*cos(t)

[0060] The value range of t is [0, 2*π];

[0061] The present invention uses a 32-type flexible bearing to study the three-wave harmonic reducer. The number of flexspline teeth is designed to be z1=201, the number of rigid spline teeth is designed to be z2=204, the deformation coefficient a is selected to be 0.30, the modification b is selected to be 0.02, and k is selected to be 0.012 (this group of parameters is determined based on simulation drawing); the numerical values ​​are substituted into the cam profile equation to obtain the following equation:

[0062] Y=25*sin(t)+0.3*sin(3*t)*sin(t)+0.03*sin(6*x)*sin(t)+0.012

[0063] *sin(t):

[0064] X=25*cos(t)+0.3*sin(3*t)*cos(t)+0.03*sin(6*x)*cos(t)+0.012*cos(t);

[0065] Wherein, the value range of t is [0, 2*π];

[0066] Use MATLAB and CAD to calculate and simulate the curve to obtain the simulated cam line shape, use the 3D modeling method to import the model into the CNC processing software, and use the engraving and milling machine to process the disc-shaped cam contour line;

[0067] like Figure 2 -- Figure 9As shown, the drawing simulation verification: the meshing flexspline tooth profile parameters are determined by drawing according to the cam profile, and the flexspline processing is completed using a standard 0.16 die involute gear hobbing cutter; the flexspline wall thickness is calculated. According to the maximum design torque of 20N.M, the flexspline wall thickness parameter is selected as 0.01 to 0.0125 times the diameter. The flexspline material is 30CrMnSiA, σ0.2 is 830MPa, and in order to make the reducer no-load current small, the flexspline wall thickness coefficient is selected as 0.01, that is, the wall thickness s is 0.32mm. Using SolidW In orks, simulation is used to analyze the strength of the flexible wheel. The boundary conditions are set as follows: one end is fixed and the other end is loaded with a torque of 20N.M. The analysis data shows that the maximum torque is 660MPa<σ0.2, which means the strength is sufficient. The meshing of the flexible wheel and the rigid wheel under the cam profile is simulated. The flexible wheel tooth profile parameters are determined according to the transmission ratio and the diameter of the flexible bearing. The flexible wheel module is selected as 0.16m and the flexible bearing diameter is d=32mm. Since the three-wave reducer is a multiple of 3, the number of flexible wheel teeth is 201 and the tooth height coefficient is selected as The value is selected as 0.7, and the CAD drawing software is used to make the involute toothed flexible wheel; the tooth profile parameters of the rigid wheel are determined according to the transmission ratio and the flexible wheel, and the rigid wheel module is selected as 0.16m. Since the number of teeth of the rigid wheel of the three-wave reducer is 3 more than that of the flexible wheel, the number of teeth of the rigid wheel is 204, and the tooth height coefficient is selected as 0.7. The CAD drawing software is used to make the involute toothed flexible wheel; the deformation simulation of the flexible wheel is carried out according to the cam profile, and the calculated flexible wheel tooth profile is arranged along the normal direction of the cam curve to obtain the deformed flexible wheel profile; the meshing simulation of the flexible wheel and the rigid wheel under the action of the cam and the Verification was performed by superimposing the deformed flexspline with the rigid profile to obtain a static simulation diagram of the meshing. The static simulation diagram shows that the flexspline meshes in three meshing areas with a 120-degree angle around the circumference. As the cam profile deforms, the flexspline engages and disengages with the rigid gear within a 60-degree range, with appropriate tooth clearance reserved. The meshing diagram shows that the flexspline deforms along the cam profile, producing three evenly distributed meshing areas around the circumference, meeting the design requirements. After processing, the prototype was initially assembled and manually operated, and the rotation was smooth with the correct speed ratio. Technical process inspection determined that the design and processing technology was feasible and could meet user requirements. Drawing calculations guided production, and physical processing verified the correctness of the method.

[0068] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A gear design method for a three-wave harmonic reducer, characterized in that: The method comprises the following steps: Step 1: Design according to the requirements for improving the frequency response and dynamic response of the servo product; Step 2: Using the principle of harmonic drive, the involute tooth profile is selected as the basic tooth profile of the three-wave meshing gear. The three-wave meshing requirement can be achieved by designing a three-wave cam. The basic curve of the cam expansion profile is designed based on Fourier transform. The Fourier transform is designed as follows: Σ=a*sin(3*x)+b*sin(6*x)+k; x ranges from [0 to 2*π]; In the equation, a is the deformation coefficient, b is the profile engagement modification coefficient, and k is the flexible bearing deformation correction coefficient; Envelope the cam's unfolded outline onto the inner diameter circle r of the flexible bearing, and the cam polar coordinate system equation is obtained as follows: R1=r+a*sin(3*x)+b*sin(6*x)+k; r is the inner radius of the flexible bearing; Transforming the polar coordinate equation into a rectangular coordinate system equation is: Y=r*sin(t)+a*sin(3*t)*sin(t)+b*sin(6*x)*sin(t)+k*sin(t); X=r*cos(t)+a*sin(3*t)*cos(t)+b*sin(6*x)*cos(t)+k*cos(t); The value range of t is [0, 2*π]; Import the parameters of the flexspline tooth number design into the cam polar coordinate system equation and perform calculations; Step 3: Use drawing software to calculate the curve and draw a simulation to obtain the simulated cam line shape.

2. The gear design method for a three-wave harmonic reducer according to claim 1, characterized in that: The number of teeth of the flex spline is designed to be z1=201, the number of teeth of the rigid spline is designed to be z2=204, the deformation coefficient a is selected to be 0.30, the modification b is selected to be 0.02, and k is selected to be 0.012; Substituting the numerical values ​​into the cam profile equation yields the following equation; Y=25*sin(t)+0.3*sin(3*t)*sin(t)+0.03*sin(6*x)*sin(t)+0.012*sin(t); X=25*cos(t)+0.3*sin(3*t)*cos(t)+0.03*sin(6*x)*cos(t)+0.012*cos(t); The value range of t is [0, 2*π].

3. The gear design method for a three-wave harmonic reducer according to claim 1, characterized in that: The drawing software includes any one of MATLAB and CAD. The basic curve of the cam expansion profile in step 2 is input into the software to obtain the simulated cam linear shape. The model is imported into the CNC machining software using a three-dimensional modeling method, and the disc-shaped cam profile is machined using a milling machine.

4. The gear design method for a three-wave harmonic reducer according to claim 1, characterized in that: The drawing simulation comprises the following steps: Step 1: Calculate the flexspline wall thickness; Based on the maximum design torque of 20 N.M, the flexspline wall thickness parameter is selected as 0.01 to 0.0125 times the diameter. The flexspline material is 30CrMnSiA, and σ0.2 is 830 MPa, which makes the reducer no-load current small. The flexspline wall thickness coefficient is selected as 0.01, that is, the wall thickness s is 0.32 mm. Use the simulation in SolidWorks to perform a force analysis on the flexspline strength, in which the boundary condition is set as one end fixed and the other end loaded with a torque of 20 N.M. The analysis data shows that the maximum torque is 660 MPa < σ0.2, which is sufficient strength. Step 2: Simulate the meshing of the flexible spline and the rigid spline under the cam profile.

5. The gear design method for a three-wave harmonic reducer according to claim 2, characterized in that: The meshing of the flex spline and the rigid spline under the cam profile in step 2 includes: Step 2.1: Determine the flexspline tooth profile parameters based on the transmission ratio and the flexible bearing diameter; Step 2.2: Determine the tooth profile parameters of the rigid wheel based on the transmission ratio and the flexible wheel; Step 2.3: Perform deformation simulation of the flexspline according to the cam profile, and arrange the calculated flexspline tooth shape along the normal direction of the cam curve to obtain the deformed flexspline profile; Step 2.4: Simulate and verify the meshing of the flexible gear and the rigid gear under the action of the cam.

6. The gear design method for a three-wave harmonic reducer according to claim 5, characterized in that: The module of the flexspline is selected to be 0.16m, the diameter of the flexible bearing is d=32mm, the three-wave reducer is a multiple of 3, the number of teeth of the flexspline is 201, the tooth height coefficient is selected to be 0.7, and the flexspline with involute tooth shape is produced using CAD drawing software.

7. The gear design method for a three-wave harmonic reducer according to claim 5, characterized in that: The module of the rigid wheel is selected to be 0.16m. The number of teeth of the rigid wheel of the three-wave reducer is 3 more than that of the flexible wheel, so the number of teeth of the rigid wheel is 204. The tooth height coefficient is selected to be 0.

7. The involute toothed rigid wheel is made using CAD drawing software.

8. The gear design method for a three-wave harmonic reducer according to claim 5, characterized in that: The deformed flexspline and the rigid wheel contour line are superimposed to obtain a static simulation diagram of the meshing. The flexspline meshing has three meshing areas with an intersection angle of 120 degrees in one circle. As the cam contour deforms, the flexspline completes meshing and disengagement with the rigid wheel within a range of 60 degrees, and an appropriate tooth profile clearance is reserved.

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