A method for modifying the tooth profile of cycloid gear of RV reducer based on temperature effect

Abstract

The present invention provides a cycloidal wheel tooth profile modification method for an RV reducer based on temperature effect, comprising the following steps: S1, obtaining a surface roughness value, and establishing a three-dimensional microscopic model of the surface of a pin tooth; S2, modifying the cycloidal wheel tooth profile using a second-order parabola method, and determining the modification amount of the cycloidal wheel tooth profile in a high temperature environment; S3, by measuring the surface roughness of the modified cycloidal wheel tooth surface, using Matlab to establish a three-dimensional microscopic model of the surface of the cycloidal wheel tooth in a high temperature environment; S4, calculating the actual contact stiffness of the rough surface of the cycloidal wheel and the pin wheel in a high temperature environment; S5, optimizing the cycloidal wheel tooth profile modification coefficient. The present invention fully considers the influencing factors such as the actual working temperature, the high temperature performance of the material, the surface roughness of the tooth profile, the friction coefficient, etc., takes the maximum contact stiffness as the modification target, and establishes a mathematical model of actual contact mechanics in a high temperature environment, achieving the modification target of both maintaining conjugate meshing and improving meshing stiffness in a high temperature environment.

Description

Technical Field

[0001] The invention relates to the technical field of design and manufacturing of cycloid wheels, and in particular to a method for modifying tooth profile of a cycloid wheel of an RV reducer based on temperature effect. Background Art

[0002] The precision RV reducer for industrial robots is a precision transmission device developed on the basis of cycloidal pinwheel transmission. It has the advantages of strong load-bearing capacity, small size, and high hardness. It directly affects the working efficiency and working accuracy of industrial robots. Due to the inevitable manufacturing and installation errors of the cycloidal wheel in the production process, the cycloidal pinwheel will be in a state of premature or late meshing in the working condition. In addition, the thermal deformation caused by temperature changes will also cause problems such as meshing interference and excessive contact stress. The above situations all cause serious deformation of the two rough tooth surfaces of the cycloidal pinwheel, shortening its working cycle. At present, a large number of studies have been conducted on the modification of the cycloidal wheel tooth profile from the aspects of lubrication, conjugate meshing, meshing stiffness, torsional stiffness and Hertz theory. However, the premise of the above studies is that the contact model is established with the ambient temperature as the normal temperature, and the dynamic parameters and material properties are considered from a macroscopic perspective, and the influence of temperature on the meshing of gear teeth is not considered. Summary of the invention

[0003] In order to solve the technical problems existing in the prior art, the present invention provides a cycloidal gear tooth profile modification method for an RV reducer based on temperature effect. By establishing a contact mechanics mathematical model of thermal deformation of the tooth profile caused by temperature, the actual contact state between the contact surfaces is reflected, thereby achieving the modification goal of maintaining conjugate meshing and improving meshing stiffness.

[0004] The present invention is implemented by the following technical scheme: A method for modifying the tooth profile of a cycloid gear of an RV reducer based on temperature effect, comprising the following steps:

[0005] S1. Measure the surface roughness of the needle teeth to obtain the surface roughness value, and use MATlab to establish a three-dimensional microscopic model of the needle teeth in a high temperature environment based on the surface roughness value and the two-dimensional cross-section formula;

[0006] S2. Modify the cycloid gear tooth profile using the second-order parabola method to determine the modification amount of the cycloid gear tooth profile in a high temperature environment;

[0007] S3. By measuring the surface roughness of the modified cycloid gear tooth surface, a three-dimensional microscopic model of the cycloid gear tooth surface in a high temperature environment is established using Matlab;

[0008] S4. Calculate the actual contact stiffness of the rough surface of the cycloid wheel and the pin wheel in a high temperature environment;

[0009] S5. Optimize the modification coefficient of the cycloid gear tooth profile; optimize the modification coefficient using the contact stiffness as an evaluation index, measure the surface roughness of the cycloid gear tooth profile again after the cycloid gear is modified, repeat steps S2 to S4, obtain the maximum contact stiffness, and determine the final modification coefficient.

[0010] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0011] 1. The present invention fully considers the influencing factors such as the actual working temperature, high-temperature performance of materials, surface roughness of tooth profile, friction coefficient, etc., takes the maximum contact stiffness as the modification target, establishes a mathematical model of actual contact mechanics in a high-temperature environment, reflects the real contact state, and achieves the modification target of maintaining conjugate meshing and improving meshing stiffness in a high-temperature environment.

[0012] 2. The present invention is beneficial to improving the meshing efficiency and transmission accuracy of the reducer in a high temperature environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the method of the present invention;

[0014] Figure 2 a is a profile diagram of the needle teeth of the present invention;

[0015] Figure 2 b is a partial enlarged view of the outline of the needle teeth of the present invention;

[0016] Figure 3 It is a tooth profile modification diagram of the cycloid wheel of the present invention;

[0017] Figure 4 a is a tooth profile diagram of the cycloid wheel after modification of the present invention;

[0018] Figure 4 b is a partial enlarged view of the tooth profile of the cycloid wheel after the modification of the present invention;

[0019] Figure 5 It is the rough surface contact model of the pin wheel and the cycloid wheel of the present invention;

[0020] Figure 6 Schematic diagram of the influence of the modification coefficient on the contact stiffness of the present invention;

[0021] In the figure, 51 is the rough surface of the pin wheel, and 52 is the rough surface of the cycloid wheel. DETAILED DESCRIPTION

[0022] The present invention is further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0023] Example

[0024] like Figure 1As shown, in this embodiment, a method for modifying the cycloid gear tooth profile of an RV reducer based on temperature effect comprises the following steps:

[0025] S1. Measure the surface roughness of the needle teeth to obtain the surface roughness value, and use MATlab to establish a three-dimensional microscopic model of the needle teeth in a high temperature environment based on the surface roughness value and the two-dimensional cross-section formula;

[0026] S2. Modify the cycloid gear tooth profile using the second-order parabola method to determine the modification amount of the cycloid gear tooth profile in a high temperature environment;

[0027] S3. By measuring the surface roughness of the modified cycloid gear tooth surface, a three-dimensional microscopic model of the cycloid gear tooth surface in a high temperature environment is established using Matlab;

[0028] S4. Calculate the actual contact stiffness of the rough surface of the cycloid wheel and the pin wheel in a high temperature environment;

[0029] S5. Optimize the modification coefficient of the cycloid gear tooth profile; optimize the modification coefficient using the contact stiffness as an evaluation index, measure the surface roughness of the cycloid gear tooth profile again after the cycloid gear is modified, repeat steps S2 to S4, obtain the maximum contact stiffness, and determine the final modification coefficient.

[0030] In this embodiment, the specific process of step S1 is as follows:

[0031] S11. Through measurement, the radius of the needle tooth r = 3mm, its surface roughness value Ra = 0.8mm, the small segment range of the needle tooth circle θ∈[1.2π, 1.4π], and the sample length N = 10 -6 mm, cut-off length Ns = 5 × 10 -6 , spatial frequency γ = 1.5, fractal dimension B = 1.56, characteristic scale G = 4.9, temperature difference ΔT is 200 °C, α is 12.5×10 -6 .

[0032] S12. Based on the surface roughness value and the two-dimensional cross-section formula, Matlab was used to establish Figure 1 The microscopic mathematical model of the needle tooth surface is shown in the figure; the two-dimensional cross-section formula is as follows:

[0033] L * =[L(θ)±w(s)·k]·(1+ΔT·α)

[0034] Where L(θ) is a one-dimensional vector function; (θ) is an arbitrary rotation angle; w(s) represents the height of the micro-protrusion on the surface; s is the arc length of the curve; k is the unit normal vector at a certain point on the curve; L * is the cross-sectional profile curve of each rough surface, ΔT is the temperature difference, and α is the linear expansion coefficient.

[0035] Specifically,

[0036] Where w(s) represents the height of the micro-protrusion on the surface; x is the coordinate of the profile displacement; γ n is the spatial frequency of the rough surface; fractal dimension n is the frequency index; characteristic scale

[0037] Specifically, L(θ)=x(θ)i+y(θ)j, L(θ)∈C 0 ,

[0038] In the formula, i is a unit vector in any direction, j is a vector orthogonal to i; C 0 represents a continuous parameterized function; L(θ) is a one-dimensional vector function; x(θ) is the coordinate value in the x direction in the rectangular coordinate system; y(θ) is the coordinate value in the y direction in the rectangular coordinate system.

[0039] Specifically, the calculation formula of the unit normal vector k at a point on the curve is as follows:

[0040]

[0041] In the formula, is the first-order derivative of L(θ); is the second-order derivative of L(θ).

[0042] In this embodiment, the specific process of step S2 is as follows:

[0043] S21. Through measurement, the number of teeth of the cycloid wheel is Za=39, the number of needle teeth is Rz=40, the eccentricity a=1.25mm, the pitch circle radius of the needle teeth is 64, and the rotation arc around the pitch circle of the cycloid wheel is The modification coefficient a1 is -0.0001 and -0.00005 respectively.

[0044] S22. Use the second-order parabola method to modify the cycloid gear profile and obtain the following Figure 2 The modification diagram of the cycloid wheel is shown in the figure, where the modification equation of the second-order parabola method is:

[0045]

[0046] Wherein, x1 is the coordinate value of the x direction in the rectangular coordinate system; y1 is the coordinate value of the y direction in the rectangular coordinate system; Rz is the distribution circle radius of the needle teeth; is the rotation arc around the pitch circle of the cycloid wheel; a is the eccentricity; θ a is the absolute rotation angle of the rolling circle; r is the radius of the needle tooth; Δr is the modification amount of any point on the cycloid gear tooth profile in the normal direction; M is the short amplitude coefficient; Z b is the number of teeth on the pin wheel; Za is the number of teeth of the cycloid wheel.

[0047] Specifically, Δr = a1·(OL-OL0) 2

[0048] Where a1 is the modification coefficient, OL0 is the distance from the meshing point to the cycloid wheel node after the cycloid wheel rotates around the center point, and OL is the distance from any meshing point to the cycloid wheel node.

[0049] In this embodiment, the specific process of step S3 is as follows:

[0050] S31. Measure the surface roughness of the cycloid gear tooth surface after modification, taking the value Ra = 0.8 mm, and use the unit normal vector calculation formula to obtain the unit normal vector m of the cycloid gear tooth profile. c , the vector The arc of rotation of the module around the pitch circle of the cycloid wheel Integrate within the range to obtain the arc length s of the curve;

[0051] S32, when a1 = -0.00003, the microscopic mathematical model of the needle tooth surface is established using Matlab, and the following is obtained: Figure 3 The tooth profile diagram and partial enlarged diagram of the cycloid wheel after modification are shown.

[0052] In this embodiment, the specific process of step S4 is as follows:

[0053] S41, the material of the cycloid wheel and the needle teeth is GCr15, the elastic modulus is 206GPa, the Poisson's ratio is 0.3, the fractal dimension B=1.555, the characteristic scale G=4.73×10 -6 mm; Take the maximum contact area a when the meshing force F = 15N L 0.8×10 - 11 mm 2 , surface contact coefficient λ B is 0.0034, and the critical contact area when the friction factor is 0.4 0.5×10-16mm 2 ;

[0054] S42. Calculate the contact stiffness of the rough surface between the cycloid wheel and the pin wheel. The specific formula is as follows:

[0055]

[0056] In the formula, λ B is the surface contact coefficient, E is the comprehensive elastic modulus of the cycloid wheel and the pin wheel, B is the fractal dimension, a L is the maximum contact area among the contact points, is the critical contact area.

[0057] Specifically, the surface contact coefficient λ B The calculation formula is as follows:

[0058]

[0059] Where R1 and R2 are the curvature radii of the pin wheel and the modified cycloid wheel respectively;

[0060] Specifically, the calculation formula of the comprehensive elastic modulus of the cycloid wheel and the pin wheel is as follows:

[0061]

[0062] Where E1 and E2 are elastic moduli, and V1 and V2 are Poisson's ratios.

[0063] In this embodiment, Figure 4 The figure shows the contact surface diagram of the cycloid wheel and the pin wheel. The contact stiffness K is calculated. n =2×10 5 N·mm -1 .

[0064] In this embodiment, the specific process of step S5 is: optimize the modification coefficient with contact stiffness as the evaluation index, measure the surface roughness of the cycloid gear tooth profile again after the cycloid gear is modified, and repeat steps S2 to S4; when the friction factor μ=0 and the surface roughness value R a = 0.2, taking different values ​​of the modification coefficient a1, we get Figure 5 The variation law of the modification amount and contact stiffness is shown.

[0065] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A method for modifying the tooth profile of a cycloid gear of an RV reducer based on temperature effect, characterized in that: The following steps are involved: S1. Measure the surface roughness of the needle teeth to obtain the surface roughness value, and use MATlab to establish a three-dimensional microscopic model of the needle teeth in a high temperature environment based on the surface roughness value and the two-dimensional cross-section formula; S2. Modify the cycloid gear tooth profile using the second-order parabola method to determine the modification amount of the cycloid gear tooth profile in a high temperature environment; S3. By measuring the surface roughness of the modified cycloid gear tooth surface, a three-dimensional microscopic model of the cycloid gear tooth surface in a high temperature environment is established using Matlab; S4. Calculate the actual contact stiffness of the rough surface of the cycloid wheel and the pin wheel in a high temperature environment; S5. Optimize the modification coefficient of the cycloid gear tooth profile; optimize the modification coefficient using the contact stiffness as an evaluation index, measure the surface roughness of the cycloid gear tooth profile again after the cycloid gear is modified, repeat steps S2 to S4, obtain the maximum contact stiffness, and determine the final modification coefficient; The two-dimensional cross-section formula in step S1 is as follows: L * =[L(θ)±w(s)·k]·(1+ΔT·α) Where L(θ) is a one-dimensional vector function; θ is an arbitrary rotation angle; w(s) represents the height of the micro-convexity on the surface; s is the arc length of the curve; k is the unit normal vector at a point on the curve; L * is the cross-sectional profile curve of each rough surface; ΔT is the temperature difference, α is the linear expansion coefficient; The second-order parabola modification equation in step S2 is: In the formula, x1 is the coordinate value of the x direction in the rectangular coordinate system; y1 is the coordinate value of the y direction in the rectangular coordinate system; R z is the distribution circle radius of the needle teeth; is the rotation arc around the pitch circle of the cycloid wheel; a is the eccentricity; θ a is the absolute rotation angle of the rolling circle; r is the radius of the needle tooth; Δr is the modification amount of any point on the cycloid gear tooth profile in the normal direction; M is the short amplitude coefficient; Z b is the number of teeth on the pin wheel; Z a is the number of teeth of the cycloid wheel; The specific process of step S3 is as follows: S31, by measuring the surface roughness of the modified cycloid gear tooth surface, the surface roughness value Ra is obtained, and the unit normal vector m of the cycloid gear tooth profile is obtained using the unit normal vector calculation formula c , the vector The arc of rotation of the module around the pitch circle of the cycloid wheel Integrate within the range to obtain the arc length s of the curve; S32. Use Matlab to establish a microscopic mathematical model of the pinion tooth surface, and obtain a tooth profile diagram and a local magnified diagram of the gear after the cycloid wheel is modified; The calculation formula of the contact stiffness of the rough surface between the cycloid wheel and the pin wheel in step S4 is as follows: In the formula, λ B is the surface contact coefficient, E is the comprehensive elastic modulus of the cycloid wheel and the pin wheel, B is the fractal dimension, a L is the maximum contact area among the contact points, is the critical contact area.

2. The method for modifying the tooth profile of a cycloid gear of an RV reducer based on temperature effect according to claim 1, characterized in that: The specific calculation formula of the height w(s) of the surface micro-protrusion is as follows: Where w(s) represents the height of the micro-protrusion on the surface; x is the coordinate of the profile displacement; γ n is the spatial frequency of the rough surface; B is the fractal dimension; n is the frequency index; G is the characteristic scale.

3. The method for modifying the cycloid gear profile of an RV reducer based on temperature effect according to claim 1, characterized in that The specific calculation formula of the one-dimensional vector function L(θ) is as follows: L(θ)=c(θ)i+y(θ)j,L(θ)∈C 0 In the formula, i is a unit vector in any direction, j is a vector orthogonal to i; C 0 represents a continuous parameterized function; L(θ) is a one-dimensional vector function; x(θ) is the coordinate value in the x direction in the rectangular coordinate system; y(θ) is the coordinate value in the y direction in the rectangular coordinate system.

4. The method for modifying the tooth profile of a cycloid gear of an RV reducer based on temperature effect according to claim 1, characterized in that: The calculation formula of the unit normal vector k at a point on the curve is as follows: In the formula, is the first-order derivative of L(θ); is the second-order derivative of L(θ).

5. The method for modifying the tooth profile of a cycloid gear of an RV reducer based on temperature effect according to claim 1, characterized in that: The calculation formula for the modification amount Δr of any point on the cycloid gear tooth profile in the normal direction is as follows: Δr=a1·(OL-OL0) 2 Where a1 is the modification coefficient, OL0 is the distance from the meshing point to the cycloid wheel node after the cycloid wheel rotates around the center point, and OL is the distance from any meshing point to the cycloid wheel node.

6. The method for modifying the tooth profile of a cycloid gear of an RV reducer based on temperature effect according to claim 1, characterized in that: Surface contact coefficient λ B The calculation formula is as follows: Where R1 and R2 are the curvature radii of the pin wheel and the modified cycloid wheel respectively; The calculation formula of the comprehensive elastic modulus of the cycloid wheel and the pin wheel is as follows: Where E1 and E2 are elastic moduli, and V1 and V2 are Poisson's ratios.

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