Method for generating virtual code gears for a gear vision measuring instrument

Abstract

The application provides a virtual code special gear generation method for a gear visual measuring instrument. First, a mathematical model of each part of the profile of an involute gear is established by calculating the profile of the involute gear, and then an image edge feature is superimposed on the profile of the involute gear to generate a simulation virtual code special gear template. The profile of the involute gear comprises a root transition fillet, an involute left tooth surface, a tooth top circle, an involute right tooth surface and a base circle. The application provides a virtual code special gear, replaces a physical template to complete a gear visual measuring system and realizes high-precision and ultra-precision measurement of a small-modulus gear.

Description

Technical Field

[0001] This invention belongs to the fields of measurement technology and instruments, mechanical transmission technology and gear measurement technology, and relates to the field of small module gear measurement. More specifically, it relates to a verification simulation method for the measurement and evaluation functions of a gear vision measurement system. Background Technology

[0002] Currently, the most common small module gear measuring equipment on the market includes two types: gear measuring centers based on contact probes and image-based measuring equipment based on vision measurement. Compared to contact measurement, machine vision measurement has the advantages of better accuracy, higher efficiency, lower measuring force, and the ability to measure minute structures, making it a promising application in the field of small module gear vision measurement.

[0003] For gear vision measurement instruments, the correctness, adaptability, and robustness of the measurement system, especially the measurement software system, all require verification using MATE gear templates. Physical templates used for verification of precision measuring instruments are typically manufactured with high precision and require calibration with instruments of even higher precision levels to obtain the nominal values ​​of the template parameters. To reduce machining difficulty, the working surface of the template should be designed as simply as possible with geometry that is easy to precision machine, such as planes, cylindrical surfaces, or spheres. However, templates composed of simple geometries cannot fully realize the calibration functions of measuring instruments with complex curved surfaces. Templates with high-precision complex curved surfaces are usually indispensable; therefore, high-precision gear templates have always been one of the research focuses in the field of gear measurement.

[0004] In the field of small module gear measurement, especially for micro-module gears with a module of less than 0.3 mm, (1) obtaining high-precision code gear templates has always been a problem, mainly for two reasons: First, small module gears have complex geometry and small size, making it difficult to manufacture high-precision gear templates; Second, there is a lack of ultra-precision measuring instruments for small module gears with high-precision micro-force measuring heads. Even if code gears that meet the accuracy requirements can be manufactured, verification and measurement cannot be achieved. Verification of the software and hardware functions of the small module gear measurement system and calibration of the instruments have become urgent problems to be solved. (2) When the actual visual gear measurement system experiences "software failures" such as repeatability or accuracy deterioration of measurement results or irregular shutdowns during use, it is impossible to distinguish the root cause of the problem.

[0005] Therefore, a virtual code gear generation method is needed for gear vision measurement instruments to replace physical templates in verifying the correctness, adaptability, and robustness of gear vision measurement systems, especially measurement software algorithms. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a method for generating virtual code gears for gear vision measurement instruments. By establishing virtual code gears, the correctness, adaptability, and robustness of the gear vision measurement system, especially the measurement software algorithm, can be verified to replace the physical template.

[0007] This invention is achieved through the following technical solution: A method for generating virtual code gears for gear vision measurement instruments, comprising the following steps: Step 1: Calculate the profile of the involute gear. The profile of the involute gear includes the root fillet, the left involute tooth surface, the addendum circle, the right involute tooth surface, and the base circle. The profiles of internal and external gears are basically the same, only the names of the addendum circle and the root circle are interchanged. The mathematical model and establishment process of each part of the profile of the involute gear are as follows: Step 1.1: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)-ρ f Draw the root fillet at the left tooth face of the involute cylindrical gear, θ∈(θ1,θ2], where L Pf =(r f +ρ f )*cos(arc sin(r f / (r f +ρ f ))), ρ f It is the radius of the tooth root transition curve, r f It is the radius of the tooth root circle; Step 1.2: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k ), Y = r b *sin(θ k )-r b *θ k *sin(θ k ), θ k Draw the left tooth surface of the involute cylindrical gear ∈(θ3, θ4), where r b Let θ be the radius of the base circle. k The angle of development of point k on the involute line; Step 1.3: According to the formula X = r a *cos(θ), Y=r a *sin(θ),θ∈(θ5,θ6] plots the tooth tip circle, where r a It is the radius of the tooth tip circle; Step 1.4: According to the formula X = r b*cos(θ k )+r b *θ*sin(θ k Y = -r b *sin(θ k )+r b *θ k *sin(θ k ), θ k Draw the right tooth surface of the involute cylindrical gear ∈(θ7,θ8); Step 1.5: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)+ρ f , θ∈(θ9,θ 10 Draw the root fillet at the right tooth face of the involute cylindrical gear; Step 1.6: According to the formula X = r f *cos(θ), Y=r f *sin(θ), θ∈(θ) 11 ,θ 12 Draw the root circle of the involute cylindrical gear; Step 1.7: After drawing tooth 1 using steps 1.1 to 1.6, rotate and copy tooth 2, tooth 3, etc., one by one according to the angle until a complete gear is drawn; Step 2: Overlay image edge features onto the involute gear contour to generate a simulated virtual gear template; Step 2.1: Extract as much information as possible reflecting the edge features of the photographed object from the image captured by the imaging system, mainly including: a) the width W of the edge, b) the gray values ​​on both sides of the edge, c) the gray gradient law of the edge, and d) the distribution law of random error of gray values; where the width W is in pixels. Step 2.2: Overlay the extracted edge feature information onto the contour established in Step 1; that is, A. Set a region with a width of W at the edge of the contour; B. Set the distribution range of pixel gray values ​​in the width region according to the distribution of gray values ​​on both sides of the edge of the measured image; C. Assign values ​​to the pixels in the width region according to the gray gradient law of the extracted edge; D. Assign the gray values ​​of the pixels in the non-edge parts on both sides of the extracted edge to the pixels at the same position on the contour of the involute gear.

[0008] Furthermore, in step 1, systematic errors can be superimposed on the calculated profile of the involute gear.

[0009] Furthermore, the system errors superimposed on the virtual gear template are used to simulate and calculate the gear geometry error based on the principle of actual gear hobbing or grinding process error formation; the virtual template can be used for simulation and verification of gear process error analysis functions based on gear measurement.

[0010] Furthermore, another type of virtual code gear template superimposed system error directly specifies arbitrary form of error on the error-free gear profile; among them, the virtual template is mainly used for simulation verification of the measurement and evaluation functions of the gear vision measurement system.

[0011] Furthermore, in step 1, random errors can be superimposed on the calculated profile of the involute gear.

[0012] Furthermore, the magnitude of the superimposed random error is usually no more than 1 / 3 of the maximum magnitude of the systematic error, and should be greater than the minimum resolution of the measurement system being verified. It should be noted that the random errors superimposed on the virtual code gear template are "pseudo-random," and these random errors are recorded and used as known data.

[0013] Furthermore, in step 1, coarse errors can be superimposed on the calculated profile of the involute gear.

[0014] Furthermore, the superimposed gross errors include incorrect tooth count, incorrect module, broken teeth, connected teeth, no inner hole, large displacement, tooth tip reflection, and abnormally large amplitude tooth profile deviation, tooth pitch deviation, and tooth tip circle deviation.

[0015] Furthermore, in step 2, the pixels within a width W region of the involute tooth profile edge can be assigned grayscale values ​​according to the pattern of the arctangent curve in the normal direction.

[0016] Furthermore, the random error distribution law of the grayscale values ​​of the non-edge parts on both sides of the edge in step 2 can also be based on the random error law of the non-edge parts on both sides of the actual image edge or on experience to directly assign values ​​to the pixels at the same position of the virtual code gear.

[0017] The beneficial effects of this invention are as follows: Using the technical solution proposed in this invention avoids two major challenges encountered in obtaining high-precision Coder gear templates: First, small-module gears have complex geometries and tiny dimensions, making it difficult to manufacture high-precision gear templates; second, there is a lack of ultra-precision measuring instruments for small-module gears with high-precision micro-force measuring heads, meaning that even if Coder gears meeting the required precision can be manufactured, verification and measurement are still impossible. Furthermore, when actual visual gear measurement systems experience "software malfunctions" such as repeatability issues, decreased accuracy, or random system crashes, virtual Coder gear templates can be used to differentiate the root causes of the problems. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 It is the mathematical model for calculating the profile of the first tooth of an involute gear; Figure 2 This is a schematic diagram of the virtual code gear creation process; Figure 3 It is a virtual code gear template built according to theoretical formulas; Figure 4 It is a virtual code gear template with actual edge features; Figure 5 It is a feature error curve that can be superimposed on the tooth profile of a virtual gear template; Figure 6 It is a virtual gear template with a set error; Figure 7 Figure a) shows a virtual code gear template with missing teeth; Figure b) shows a virtual code gear template with connected teeth; Figure c) shows a virtual code gear template with fibers; and Figure d) shows a virtual code gear template with reflections. Figure 8 This is a flowchart for creating a virtual code gear template; Figure 9 This is a flowchart of a virtual code gear template with gear errors; Figure 10 This is a flowchart of a verification method for gear vision measurement software based on virtual code gears; Figure 11 This is the measurement effect of the error-free virtual template in the CVGM system. Detailed Implementation

[0020] The advantages, features, and specific embodiments of the present invention will be further described below with reference to the accompanying drawings. These embodiments are given by way of example only with reference to the accompanying drawings and are non-limiting illustrations, diagrams, and explanations of the present invention.

[0021] The virtual code gear generation method for gear vision measuring instruments proposed in this invention (1) can provide gear vision measuring instruments with high-precision virtual code gear templates that have edge features as similar as possible to the images obtained by the vision measuring system from photographing physical templates. This avoids two problems in the process of obtaining high-precision actual code gear templates: first, small module gears have complex geometry and small size, making it difficult to manufacture high-precision gear templates; second, there is a lack of ultra-precision measuring instruments for small module gears with high-precision micro-force measuring heads, so even if code gears that meet the accuracy requirements can be manufactured, verification measurement cannot be achieved. (2) The generated virtual code gear template has a stable edge profile and is not affected by the optical system. Therefore, when the actual vision gear measuring system experiences "software failures" such as measurement result repeatability or accuracy deterioration, or irregular shutdowns during use, the virtual code gear template can be used to distinguish the root cause of the problem.

[0022] Figure 1 This is a mathematical model for calculating the profile of the first tooth of an involute gear. Established as follows... Figure 1 The rectangular coordinate system O-XY shown: 1) ∠COD is the angle corresponding to the tooth root transition arc CD, denoted by γ1. The formula for calculating this angle is γ1=arctan(ρ f / R b The tooth root transition arc CD is tangent to the involute DE at point D and to the tooth root circle at point C. Then the (θ1,θ2] corresponding to the arc CD is (π / 2,π-γ1*π / 180], where γ1 equals γ5. 2) ∠DOE is the angle corresponding to the involute DE. Replace ∠DOE with γ2, and then use r... a =r b From / cos(α) and θ=tan(α)-α, we can obtain γ2=tan[arccos(r b / r a )], and γ2 is equal to the development angle at the intersection of the left tooth surface of the involute and the tooth tip circle, then the (θ3,θ4] corresponding to the left tooth surface of the involute is (0,γ2]; 3) ∠EOF is the angle corresponding to the tooth tip arc EF. Replace ∠DOE with γ3. This is derived from the tooth width formula, tooth pitch formula, and the development angle formula at the pitch circle θ. f =∠DOP=tan(arccos(d b / d)), the formula for the coordinates of the intersection point of the pitch circle and the involute x f =rb*cos(θ) f )+rb*θ f *sin(θ f ), y f =rb*cos(θ) f )-rb*θ f*sin(θ f Formula for calculating the angle γ at the intersection of the pitch circle and the involute. f =∠DOE=arctan(x) f / y f Formula for the coordinates of the intersection point of the tooth tip circle and the involute: x a =r b *cos(θ a )+r b *θ a *sin(θ a ), ya = r b *cos(θ a )-r b *θ a *sin(θ a The formula for calculating the angle between the tip circle and the involute is γ2 = arctan(x). a / y a Combining these equations, we can derive ∠EOF=γ³=π*m / d+2*γ f -γ2, where the angle (θ5,θ6] corresponding to the tooth tip circle formula can be obtained as (γ2,γ2+γ3); 4) The (θ7,θ8] corresponding to the right tooth surface of the involute is the same as (θ3,θ4), but the right tooth surface of the involute needs to be rotated clockwise by (γ2+γ3+γ4)*180 / π degrees, where γ4 is equal to γ2. The tooth profile at the corresponding angle of the right tooth surface of the involute can be obtained by using the coordinate transformation matrix. 5) The tooth root transition arc GH corresponds to (θ9, θ) 10 Similar to (θ1,θ2), it also requires rotation (γ2+γ3+γ). 4) * 180 / π degrees; 6) ∠HOK is the angle corresponding to the root transition circle arc HK, denoted by γ6. The formula for calculating this angle is γ6=(π*m / d-γ5). The root circle arc HK is tangent to the root transition circle arc at points H and K respectively. Therefore, the angle corresponding to arc HK is (θ... 11 ,θ 12 ]for: (γ2+γ3+γ4+γ5,γ2+γ3+γ4+γ5+γ6]; Where, d b d is the base circle diameter, d is the pitch circle diameter, and x is the base circle diameter. f Let y be the x-coordinate of the intersection point of the pitch circle and the left tooth surface of the involute. f Let x be the ordinate of the intersection point of the pitch circle and the left tooth surface of the involute. a Let y be the x-coordinate of the intersection point of the addendum circle and the left involute tooth surface. a is the ordinate of the intersection point of the addendum circle and the left involute tooth surface, and m is the module.

[0023] Figure 2 This is a schematic diagram of the process of creating the virtual code gear profile. Figure 3 It is a virtual gear template built according to theoretical formulas. This template does not have edge features similar to those obtained by the actual visual measurement system from the image of the physical template, and the tooth profile is affected by pixel density and presents a "sawtooth" shape.

[0024] Figure 4 It is a virtual code gear template with actual edge features. The simulated virtual template image has edge features that are as close as possible to the image of the physical template obtained by the actual vision measurement system. These features include: a) the gray values ​​on both sides of the edge, b) the width of the edge, where the edge width is usually in pixels, c) the gray-level gradient of the edge, and d) the distribution of random errors in the gray values.

[0025] Figure 5 It is a feature error curve that can be superimposed on the tooth profile of a virtual gear template. The formula for this feature error curve is: K(ρ)=[1-2*|ρ / ρ a -1 / 2|^1.5]*sin(5π*ρ / ρ a ), In the formula, ρ a The involute development at the tip of the virtual code gear is calculated using the formula ρ. a =r b *tan(α ta The error curve is symmetrical. The horizontal axis represents the normalized span ρ, with a value range of [0,1], corresponding to the involute tooth profile from the base circle to the addendum circle. The vertical axis represents the deviation coefficient K superimposed on the tooth profile. The maximum value of the deviation coefficient K is (0.5,1), and the minimum values ​​are (0.306,-0.825) and (0.694,-0.825), with a peak-to-valley value of 1.825. Figure 6 It is a virtual gear template with a set error.

[0026] Figure 7 There are abnormal virtual code gear templates, from left to right: missing teeth, connected teeth, fibers, and reflections. Figure 8 This is a flowchart for creating a virtual code gear template. Figure 9 This is a flowchart of a virtual code gear template with gear errors. Figure 10 This is a flowchart of a verification method for gear vision measurement software based on virtual code gears. Figure 11 This is the measurement effect of the error-free virtual template in the CVGM system.

[0027] Invention Embodiment 1 When m = 0.5, z = 30, and α = 20°, an error-free virtual code gear template with edge features approximating those obtained from images of the physical template captured by the CVGM measurement system is generated, such as... Figure 4 As shown, the method consists of the following steps: Step 1: Calculate the profile of the involute gear. The profile of the involute gear includes the root fillet, the left involute tooth surface, the addendum circle, the right involute tooth surface, and the base circle. The profiles of internal and external gears are basically the same, only the names of the addendum circle and the root circle are interchanged. The mathematical model and establishment process of each part of the profile of the involute gear are as follows: Step 1.1: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)-ρ f Draw the root fillet at the left tooth face of the involute cylindrical gear, θ∈(θ1,θ2], where L Pf =(r f +ρ f )*cos(arc sin(r f / (r f +ρ f ))), ρ f It is the radius of the tooth root transition curve, r f It is the radius of the tooth root circle; Step 1.2: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k ), Y = r b *sin(θ k )-r b *θ k *sin(θ k ), θ k Draw the left tooth surface of the involute cylindrical gear ∈(θ3, θ4), where r b Let θ be the radius of the base circle. k The angle of development of point k on the involute line; Step 1.3: According to the formula X = r a *cos(θ), Y=r a *sin(θ),θ∈(θ5,θ6] plots the tooth tip circle, where r a It is the radius of the tooth tip circle; Step 1.4: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k Y = -r b *sin(θk )+r b *θ k *sin(θ k ), θ k Draw the right tooth surface of the involute cylindrical gear ∈(θ7,θ8); Step 1.5: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)+ρ f , θ∈(θ9,θ 10 Draw the root fillet at the right tooth face of the involute cylindrical gear; Step 1.6: According to the formula X = r f *cos(θ), Y=r f *sin(θ), θ∈(θ) 11 ,θ 12 Draw the root circle of the involute cylindrical gear; Step 1.7: After drawing tooth 1 using steps 1.1 to 1.6, rotate and copy tooth 2, tooth 3, etc., one by one according to the angle until a complete gear is drawn; Step 2: Overlay image edge features onto the involute gear contour to generate a simulated virtual gear template; Step 2.1: Extract as much information as possible reflecting the edge features of the photographed object from the image captured by the imaging system, mainly including: a) the width W of the edge, b) the gray values ​​on both sides of the edge, c) the gray gradient law of the edge, and d) the distribution law of random error of gray values; where the width W is in pixels. Step 2.2: Overlay the extracted edge feature information onto the contour established in Step 1. Specifically: A. Define a region of width W at the edge of the contour; B. Define the distribution range of pixel gray values ​​within the width region based on the gray value distribution on both sides of the edge in the measured image; C. Assign values ​​to the pixels within the width region according to the gray gradient law of the extracted edge; D. Assign the gray values ​​of the pixels on the non-edge parts on both sides of the extracted edge to the pixels at the same positions on the contour of the involute gear.

[0028] Invention Embodiment 2 When m = 0.5, z = 30, and α = 20°, a virtual code gear template with systematic errors is generated, possessing edge features similar to those obtained from images of physical templates captured by the CVGM system. For example... Figure 6 As shown, the method consists of the following steps: Step 1: Calculate the profile of the involute gear. The profile of the involute gear includes the root fillet, the left involute tooth surface, the addendum circle, the right involute tooth surface, and the base circle. The profiles of internal and external gears are basically the same, only the names of the addendum circle and the root circle are interchanged. The mathematical model and establishment process of each part of the profile of the involute gear are as follows: Step 1.1: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)-ρ f Draw the root fillet at the left tooth face of the involute cylindrical gear, θ∈(θ1,θ2], where L Pf =(r f +ρ f )*cos(arc sin(r f / (r f +ρ f ))), ρ f It is the radius of the tooth root transition curve, r f It is the radius of the tooth root circle; According to the predetermined error law, such as K(ρ)=[1-2*|ρ / ρ a -1 / 2|^1.5]*sin(5π*ρ / ρ a The error is superimposed on the involute tooth profile, where ρ a The involute development length of the virtual code gear is calculated using the formula ρ. a =r b *tan(α ta The error curve is symmetrical. The horizontal axis represents the normalized span ρ, with a value range of [0,1], corresponding to the involute tooth profile from the base circle to the addendum circle. The vertical axis represents the deviation coefficient K superimposed on the tooth profile. The maximum value of the deviation coefficient K is (0.5,1), and the minimum values ​​are (0.306,-0.825) and (0.694,-0.825), with a peak-to-valley value of 1.825. According to the gear accuracy evaluation standard, the error is superimposed along the normal direction of the tooth surface; Step 1.2: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k ), Y = r b *sin(θ k )-r b *θ k *sin(θ k ), θ k Draw the left tooth surface of the involute cylindrical gear ∈(θ3, θ4), where r b Let θ be the radius of the base circle.k The angle of development of point k on the involute line; Step 1.3: According to the formula X = r a *cos(θ), Y=r a *sin(θ),θ∈(θ5,θ6] plots the tooth tip circle, where r a It is the radius of the tooth tip circle; Step 1.4: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k Y = -r b *sin(θ k )+r b *θ k *sin(θ k ), θ k Draw the right tooth surface of the involute cylindrical gear ∈(θ7,θ8); Step 1.5: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)+ρ f , θ∈(θ9,θ 10 Draw the root fillet at the right tooth face of the involute cylindrical gear; Step 1.6: According to the formula X = r f *cos(θ), Y=r f *sin(θ), θ∈(θ) 11 ,θ 12 Draw the root circle of the involute cylindrical gear; Step 1.7: After drawing tooth 1 using steps 1.1 to 1.6, rotate and copy tooth 2, tooth 3, etc., one by one according to the angle until a complete gear is drawn; Step 2: Overlay image edge features onto the involute gear contour to generate a simulated virtual gear template; Step 2.1: Extract as much information as possible reflecting the edge features of the photographed object from the image captured by the imaging system, mainly including: a) the width W of the edge, b) the gray values ​​on both sides of the edge, c) the gray gradient law of the edge, and d) the distribution law of random error of gray values; where the width W is in pixels. Step 2.2: Overlay the extracted edge feature information onto the contour established in Step 1. Specifically: A. Define a region of width W at the edge of the contour; B. Define the distribution range of pixel gray values ​​within the width region based on the gray value distribution on both sides of the edge in the measured image; C. Assign values ​​to the pixels within the width region according to the gray gradient law of the extracted edge; D. Assign the gray values ​​of the pixels on the non-edge parts on both sides of the extracted edge to the pixels at the same positions on the contour of the involute gear.

[0029] Invention Embodiment 3 When m = 0.5, z = 30, and α = 20°, a coarse-error virtual code gear template with edge features similar to those obtained from images of physical templates captured by the CVGM system is generated, such as... Figure 7 As shown, taking fiber error as an example, this method consists of the following steps: Step 1: Calculate the profile of the involute gear. The profile of the involute gear includes the root fillet, the left involute tooth surface, the addendum circle, the right involute tooth surface, and the base circle. The profiles of internal and external gears are basically the same, only the names of the addendum circle and the root circle are interchanged. The mathematical model and establishment process of each part of the profile of the involute gear are as follows: Step 1.1: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)-ρ f Draw the root fillet at the left tooth face of the involute cylindrical gear, θ∈(θ1,θ2], where L Pf =(r f +ρ f )*cos(arc sin(r f / (r f +ρ f ))), ρ f It is the radius of the tooth root transition curve, r f It is the radius of the tooth root circle; Step 1.2: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k ), Y = r b *sin(θ k )-r b *θ k *sin(θ k ), θ k Draw the left tooth surface of the involute cylindrical gear ∈(θ3, θ4), where r b Let θ be the radius of the base circle. k The angle of development of point k on the involute line; Step 1.3: According to the formula X = r a *cos(θ), Y=r a *sin(θ),θ∈(θ5,θ6] plots the tooth tip circle, where r a It is the radius of the tooth tip circle; Step 1.4: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k Y = -r b *sin(θ k )+r b *θ k *sin(θ k ), θ k Draw the right tooth surface of the involute cylindrical gear ∈(θ7,θ8); Step 1.5: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)+ρ f , θ∈(θ9,θ 10 Draw the root fillet at the right tooth face of the involute cylindrical gear; Step 1.6: According to the formula X = r f *cos(θ), Y=r f *sin(θ), θ∈(θ) 11 ,θ 12 Draw the root circle of the involute cylindrical gear; Step 1.7: After drawing tooth 1 using steps 1.1 to 1.6, rotate and copy tooth 2, tooth 3, etc., one by one according to the angle until a complete gear is drawn; Step 1.8: Based on the formulas x=J*r*cos(β) and y=K*r*sin(β)*cos(β), randomly generate N fiber errors with different positions, sizes and shapes around the tooth profile, where N, J and K are pre-defined pseudo-random coefficients, and β∈(0,2π]. Where ρ f =0.19, L pf =7.06244469, r f =6.875, r b =7.04769468, r a =8, r=7.5; Step 2: Overlay image edge features onto the involute gear contour to generate a simulated virtual gear template. Step 2.1: Extract as much information as possible reflecting the edge features of the photographed object from the image captured by the imaging system, mainly including: a) the width W of the edge, b) the gray values ​​on both sides of the edge, c) the gray gradient law of the edge, and d) the distribution law of random error of gray values; where the width W is in pixels. Step 2.2: Overlay the extracted edge feature information onto the contour established in Step 1. Specifically: A. Define a region of width W at the edge of the contour; B. Define the distribution range of pixel gray values ​​within the width region based on the gray value distribution on both sides of the edge in the measured image; C. Assign values ​​to the pixels within the width region according to the gray gradient law of the extracted edge; D. Assign the gray values ​​of the pixels on the non-edge parts on both sides of the extracted edge to the pixels at the same positions on the contour of the involute gear.

[0030] Invention Embodiment 4 When m = 0.5, z = 20, and α = 20°, a virtual gear template with features similar to those in the image captured by the CVGM instrument is generated and input into the CVGM system for measurement and comparison. Step 1: Calculate the profile of the involute gear. The profile of the involute gear includes the root fillet, the left involute tooth surface, the addendum circle, the right involute tooth surface, and the base circle. The profiles of internal and external gears are basically the same, only the names of the addendum circle and the root circle are interchanged. The mathematical model and establishment process of each part of the profile of the involute gear are as follows: Step 1.1: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)-ρ f Draw the root fillet at the left tooth face of the involute cylindrical gear, θ∈(θ1,θ2], where L Pf =(r f +ρ f )*cos(arc sin(r f / (r f +ρ f ))), ρ f It is the radius of the tooth root transition curve, r f It is the radius of the tooth root circle; Step 1.2: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k ), Y = r b *sin(θ k )-r b *θ k *sin(θ k ), θ kDraw the left tooth surface of the involute cylindrical gear ∈(θ3, θ4), where r b Let θ be the radius of the base circle. k The angle of development of point k on the involute line; Step 1.3: According to the formula X = r a *cos(θ), Y=r a *sin(θ),θ∈(θ5,θ6] plots the tooth tip circle, where r a It is the radius of the tooth tip circle; Step 1.4: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k Y = -r b *sin(θ k )+r b *θ k *sin(θ k ), θ k Draw the right tooth surface of the involute cylindrical gear ∈(θ7,θ8); Step 1.5: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)+ρ f , θ∈(θ9,θ 10 Draw the root fillet at the right tooth face of the involute cylindrical gear; Step 1.6: According to the formula X = r f *cos(θ), Y=r f *sin(θ), θ∈(θ) 11 ,θ 12 Draw the root circle of the involute cylindrical gear; Step 1.7: After drawing tooth 1 using steps 1.1 to 1.6, rotate and copy tooth 2, tooth 3, etc., one by one according to the angle until a complete gear is drawn; Step 2: Overlay image edge features onto the involute gear contour to generate a simulated virtual gear template; Step 2.1: Extract as much information as possible reflecting the edge features of the photographed object from the image captured by the imaging system, mainly including: a) the width W of the edge, b) the gray values ​​on both sides of the edge, c) the gray gradient law of the edge, and d) the distribution law of random error of gray values; where the width W is in pixels. Step 2.2: Overlay the extracted edge feature information onto the contour established in Step 1. Specifically: A. Define a region of width W at the edge of the contour; B. Define the distribution range of pixel gray values ​​within the width region based on the gray value distribution on both sides of the edge in the measured image; C. Assign values ​​to the pixels within the width region according to the gray gradient law of the extracted edge; D. Assign the gray values ​​of the pixels on the non-edge parts on both sides of the extracted edge to the pixels at the same positions on the contour of the involute gear. Step 3: Input the generated virtual code gear template, which has similar features to the image captured by the imaging system, into the corresponding imaging system for measurement, and compare the parameters of the virtual code gear with the output parameters of the corresponding measurement system. The maximum total deviation of the tooth profile of the error-free virtual code gear template is 1.9 micrometers. This is due to the quantization error when converting the theoretical tooth profile into gear pixels and the error of the edge extraction algorithm. This is the limit of accuracy that this version of the software algorithm can achieve under the measurement system of the optical instrument of this instrument. According to the gear precision standard (ISO-1328.1:2013), the overall accuracy index of this virtual code gear is level 2. The tolerance ratio between adjacent accuracy levels in the gear accuracy standard is approximately 1.414. According to the principle that the measurement error is 1 / 3 of the tolerance of the gear being measured, this measurement system can meet the gear measurement requirements of level 5-6 accuracy.

[0031] The above four embodiments are preferred solutions and need to be explained. In step 1, using the coordinate transformation matrix to obtain the equations of all the teeth of the complete gear or to calculate the mathematical model of the complete gear can also achieve the same effect as drawing the theoretical gear. These are simple inferences of the present invention, and others should not apply for other patents again.

[0032] Furthermore, in step 1, the equations for the superimposed errors of the virtual gear template cannot be completely enumerated, but they are nothing more than three types: random errors, systematic errors, and gross errors. The locations of the superimposed errors on the virtual gear template contour are also diverse, including at the tooth root fillet, on the left and right tooth surfaces, and on the tooth tip circle or tooth root circle; these are simple deductions of the present invention, and others may not apply them to other patents.

[0033] Furthermore, in step 2, the width of the blurred edge region can also be set directly based on experience. Common widths are 3, 5, and 7, where the width is usually measured in pixels. However, setting the edge blur width of the virtual code gear template based on the actual edge blur width of the image captured by the specific shooting system can better assist the shooting system in identifying the root cause of "software failures" such as measurement result repeatability or accuracy deterioration, or irregular crashes during the use of the visual gear measurement system. These are simple inferences of the present invention, and others may not apply for other patents based on them.

[0034] Furthermore, in step 2, the pixel grayscale gradient pattern within the blurred edge width region can be composed of the arctangent function and other functions, or it can be obtained by polynomial or Fourier fitting; these are simple inferences of the present invention, and others may not apply for other patents based on these inferences.

[0035] In summary, this invention provides a method for generating virtual code gears for gear vision measurement instruments. By superimposing image edge features on the involute gear contour, a virtual code gear is established to replace the physical template for calibrating the gear vision measurement system, thereby achieving high-precision, small-module gear ultra-precision measurement.

[0036] The foregoing has shown and described the main features, basic principles, and advantages of the present invention. The above description of the disclosed embodiments enables those skilled in the art to implement or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, the present invention is not to be limited to the embodiments shown herein. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications may be made to the invention based on actual circumstances without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents. The invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for generating virtual code gears for gear vision measuring instruments, characterized in that, This method consists of the following steps: Step 1: Calculate the profile of the involute gear. The profile of the involute gear includes the root fillet, the left involute tooth surface, the addendum circle, the right involute tooth surface, and the base circle. The profiles of internal and external gears are basically the same, only the names of the addendum circle and the root circle are interchanged. The method for establishing each part of the profile of the involute gear is as follows: Step 1.1: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)-ρ f Draw the root fillet at the left tooth face of the involute cylindrical gear, θ∈(θ1,θ2], where L Pf = (rf+ρf)*cos(arcsin(rf / (rf+ρf))), where ρf is the radius of the tooth root transition curve, r f It is the radius of the tooth root circle; Step 1.2: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k ), Y = r b *sin(θ k )-r b *θ k *sin(θ k ), θ k Draw the left tooth surface of the involute cylindrical gear ∈(θ3, θ4), where r b Let θ be the radius of the base circle. k The angle of development of point k on the involute line; Step 1.3: According to the formula X = r a *cos(θ), Y=r a *sin(θ),θ∈(θ5,θ6] plots the tooth tip circle, where r a It is the radius of the tooth tip circle; Step 1.4: According to the formula X = r b *cos(θ k )+r b *θ*sin(θ k Y = -r b *sin(θ k )+r b *θ k *sin(θ k ), θ k Draw the right tooth surface of the involute cylindrical gear ∈(θ7,θ8); Step 1.5: According to the formula X = ρ f *cos(θ)+L Pf Y = ρ f *sin(θ)+ρ f , θ∈(θ9,θ 10 Draw the root fillet at the right tooth face of the involute cylindrical gear; Step 1.6: According to the formula X = r f *cos(θ), Y=r f *sin(θ), θ∈(θ) 11 ,θ 12 Draw the root circle of the involute cylindrical gear; Step 1.7: After drawing tooth 1 using steps 1.1 to 1.6, rotate and copy tooth 2, tooth 3, etc., one by one according to the angle until a complete gear is drawn; Step 2: Overlay image edge features onto the involute gear contour to generate a simulated virtual gear template; Step 2.1: Extract the object image edge features from the images captured by the imaging system, or specify image edge features based on experience. The image edge features include: a) the width W of the edge, b) the gray values ​​on both sides of the edge, c) the gray gradient law of the edge, and d) the distribution law of random error of gray values; where the width W is in pixels. Step 2.2: Overlay the image edge features onto the contour established in Step 1; that is, A. Set a region with a width of W at the edge of the contour; B. Set the gray values ​​of the corresponding positions on both sides of the width region on the image according to the target gray values ​​on both sides of the edge; C. Assign values ​​to the pixels in the width region according to the gray gradient law of the edge; D. Assign the gray values ​​of the pixels in the non-edge parts on both sides of the edge to the pixels at the corresponding positions in the involute gear image.

2. The virtual code gear generation method for gear vision measurement instruments as described in claim 1, characterized in that, In step 1, the superposition system error of the involute gear profile is calculated.

3. The virtual code gear generation method for gear vision measurement instruments as described in claim 2, characterized in that, The system errors superimposed on the virtual gear template are used to simulate and calculate the gear geometry errors based on the principle of actual gear hobbing or grinding process errors. The virtual template can be used for simulation and verification of gear process error analysis functions based on gear measurement.

4. The virtual code gear generation method for gear vision measurement instruments as described in claim 2, characterized in that, The system error superimposed on the virtual gear template allows for the direct specification of any form of error on the error-free gear profile; the virtual template is mainly used for simulation verification of the measurement and evaluation functions of the gear vision measurement system.

5. The virtual code gear generation method for gear vision measurement instruments as described in claim 1, characterized in that, In step 1, the random error of the involute gear profile superposition is calculated.

6. The virtual code gear generation method for gear vision measuring instruments as described in claim 5, characterized in that, The magnitude of the superimposed random errors is usually no more than 1 / 3 of the maximum magnitude of the systematic error and should be greater than the minimum resolution of the measurement system being verified; among them, the random errors superimposed on the virtual code gear template are "pseudo-random" and these random errors are recorded and used as known data.

7. The virtual code gear generation method for gear vision measurement instruments as described in claim 1, characterized in that, In step 1, the gross error of the involute gear profile superposition is calculated.

8. The virtual code gear generation method for gear vision measuring instruments as described in claim 7, characterized in that, The superimposed gross errors include incorrect tooth count, incorrect module, broken teeth, connected teeth, no inner hole, large displacement, tooth tip reflection, and abnormally large tooth profile deviation, tooth pitch deviation, and tooth tip circle deviation.

9. The virtual code gear generation method for gear vision measurement instruments as described in claim 1, characterized in that, In step 2, the pixels within a width W region of the involute tooth profile edge are assigned grayscale values ​​according to the arctangent curve in the normal direction.

10. The virtual code gear generation method for a gear vision measurement instrument as described in claim 1, characterized in that, In step 2, the random error distribution law of gray values ​​of the non-edge parts on both sides of the edge is as follows: the pixels of the non-edge parts on both sides of the edge are assigned values ​​according to the random error law of the non-edge parts on both sides of the actual image or based on experience, to the pixels at the same position as the virtual code gear.

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