Method for measuring pose of gear by using line structured light and adjustment method thereof

Abstract

A kind of line structured light measurement gear pose quantization and its adjustment method belongs to the field of precision testing technology and instrument, gear detection technology.According to the input of gear parameters, a three-dimensional model of gear is established, and the theoretical calculation of line structured light pose parameters is carried out, the tooth profile is obtained by the theoretical pose parameters, then the second-order center method is used to derive point by point, and the complete tooth profile is extracted by threshold extraction, the tooth profile data inclination ratio is obtained, which is used as the pose quantization index to accurately adjust the line structured light probe pose, which can effectively avoid the influence of shadow effect on the line structured light measurement of gear, and realize stable and reliable gear measurement.The pose quantization and its adjustment method provides a basis for measurement and adjustment of accurate tooth surface, saves the repeated adjustment of traditional method, improves the measurement efficiency and is suitable for different measurement environments.

Description

TECHNICAL FIELD

[0001] The application relates to a method for quantifying and adjusting the pose of a line structured light measuring gear, and belongs to the technical field of precision testing and instruments and non-contact gear testing. BACKGROUND

[0002] Line structured light measurement has the advantages of fast measurement speed, complete information and high repeatability, and is popularized and applied in non-contact gear measurement. Since the shape of the gear is complex, line structured light measurement must be carried out at a suitable position and angle (referred to as pose) to achieve high-precision profile measurement. Therefore, the optimization of the measurement pose of the line structured light probe is the key to accurately measuring the gear profile, and the prerequisite for optimization is to first quantify the pose parameters of the line structured light probe, and then adjust the pose, so as to obtain a complex gear profile that meets the measurement requirements. The essence of quantification and adjustment is the optimal position relationship among the three coordinate systems of the workpiece, the probe and the instrument. The position relationship between the workpiece and the instrument is basically fixed, while the position of the probe can be changed, so the pose quantification of the probe and the gear is the main way to solve the problem.

[0003] So far, the shadow effect and steep tooth surface measurement in pose optimization are the realistic problems in line structured light measurement of gears, that is, according to the circumferential distribution characteristics of the gear teeth, the front gear tooth can easily block the rear tooth profile to produce a shadow effect, or the laser forms multiple reflection phenomena on the steep metal gear tooth root surface, and the line structured light probe needs to be at a proper pose to obtain a relatively "flat" measurement tooth profile. In actual measurement, the pose of the line structured light probe in gear measurement is currently mainly adjusted according to experience, and there is a lack of quantification method and index for the optimal pose of the probe, and there is no relevant specification and standard, and there is no corresponding pose quantification formula from the gear parameters and system parameters, which is not conducive to high-precision measurement of gears with different parameters on the same instrument, and seriously affects the application and popularization of line structured light measurement of gears.

[0004] Since this "flat" tooth profile is realized by biasing the probe pose and rotating the gear, the corresponding inclination degree of the unit tooth profile from the dedendum circle to the addendum circle is taken as the key index for measuring the pose. It is beneficial to the repeatability and accuracy of gears with different parameters on the same instrument, and can provide a theoretical basis for pose quantification in line structured light measurement of gears. Especially when measuring gears with known basic parameters, the position and attitude parameters of the line structured light sensor can be estimated in combination with the theoretical three models of the gear, thereby improving the efficiency and accuracy of gear measurement. SUMMARY

[0005] This invention addresses the shadowing effect and steep tooth surface measurement problems encountered when measuring gears with a line structured optical probe. It provides a method for quantifying the pose of a line structured optical probe in non-contact gear measurement, enabling high-precision measurement of the three-dimensional tooth surface of cylindrical gears. This pose quantization method can be applied to both quadri-axis measuring machines with a single line structured optical probe and multi-axis measuring machines with multiple line structured optical probes.

[0006] The method employed in this invention includes the following steps:

[0007] W1: Create a 3D model of the gear

[0008] Establish the gear coordinate framework according to the right-hand rule. Based on gear design standards The center of rotation is determined, and the base circle of the gear's radial direction is defined. Due to unavoidable manufacturing errors or active topological modifications in actual gears, the theoretical tooth surface normal error... It is difficult to exist; in the gear model, it can be understood as having arbitrary tooth profiles. The theoretical development of points has increased in length. Superimposed normal error For the actual unfolded length Characterized as

[0009]

[0010] In the formula For any p Point on the coordinate frame z Axis parameter values, for p The corresponding unfolding angle of the point. This is the pressure angle.

[0011] Based on the actual unfolded length Characterized arbitrary points on the tooth surface The shape and position of the corresponding helical involute tooth surface are expressed by the general formula:

[0012]

[0013] In the formula, For the tooth surface point relative to the gear coordinate frame The projected angle corresponding to the axis, this angle is determined by the initial angle. Overlay and The physical meaning of the corresponding angle is expressed as

[0014]

[0015] W2: Theoretical Calculation of Pose Parameters for Linear Structured Light

[0016] Gear line structure light measurement is realized by a series of tooth profile unit measurements. Tooth profile unit refers to the profile of the line structure light probe in a single measurement, which contains complete 2D tooth surface information from the dedendum to the addendum. The specific steps are as follows:

[0017] (1) Calibration of coordinate frame. Take the cylindrical mandrel as the calibration piece, extract the central reference point based on the uniqueness of the mandrel axis in the system, and realize the calibration of the position, attitude and coordinate transformation matrix of the coordinate frame.

[0018] (2) Calculation of gear tooth rotation angle In order to realize ordered measurement, the measured gear tooth is calculated according to the initial rotation angle

[0019]

[0020] In the formula, the gear tooth spacing coefficient, the pitch circle radius, the gear modulus.

[0021] (3) Judgment of existence of shielding. Generally, the dedendum area is the first profile to be shielded under line structure light, so measuring the dedendum is the most basic condition for judging the completeness of the tooth profile. According to the corresponding rotation angle , the spatial coordinates of the line structure light capturing the dedendum in the gear frame can be calculated as

[0022]

[0023] And the relative tooth surface of the measured tooth surface can be determined according to the included angle of the left and right tooth surfaces on the dedendum circle. The spatial coordinates of the left tooth surface are

[0024]

[0025] If there is a shadow effect, the adjacent tooth profile will have spatial coordinate interference phenomenon. If the rotation angle continues to increase, the left tooth profile will partially shield the light plane, that is, the coordinates of the dedendum A , shielding leads to the inability of the right tooth profile to collect complete tooth profile units.

[0026] (4) Establishment of line structure light probe parameters. There are theoretically various combinations of different rotation angles and structure light pose offsets . Combined with the shielding judgment condition, the general form of the pose parameters is

[0027]

[0028] In the formula,​ Reference distance of line structured light. Longitudinal distance from the root to the reference line in the line structured light coordinate frame, Transverse distance from the root to the optical axis in the line structured light coordinate frame.

[0029] W3: Threshold extraction of complete tooth profile

[0030] Generally, in gear line structured light measurement, a single tooth surface can measure multiple "steep" profile data, including a small amount of random noise points. First, the tooth profile evaluation unit is used to extract the accurate complete tooth profile from the profile data. Due to the large amount of data of a single tooth surface, which can be up to hundreds of millions, the non-target area data can be reduced by threshold reduction, which can improve the operation efficiency. Secondly, threshold preprocessing can also filter out the influence of noise and interference interval. The second-order center method is used to derive point by point Profile segmentation of line structured light measurement gear.

[0031]

[0032] In the formula, And is the value for calculating the derivative of the first point and the second point, is the physical constant distance parameter between structured light spots. According to this idea, the derivative is calculated point by point

[0033]

[0034] In the formula, is the differential data point output by the (j+1)th calculation, and n represents the number of profile points of a single scan. The differential threshold processing of the measured line structured light optimal pose measurement profile is set to Calculate the start threshold of the effective tooth profile And the end threshold , that is, the intersection position of the involute and the addendum circle, and the intersection position of the transition curve and the dedendum circle can be adaptively calculated and identified. According to the identified position, the complete tooth profile is extracted.

[0035] W4: Tooth profile data tilt ratio

[0036] Tilt ratio of tooth profile data is an important indicator reflecting the "steepness" of the measured tooth profile unit under the pose parameters. The measured tooth surface is adjusted by the initial adjustment angle , is the angle between the expected structured light optical axis and the linearized tooth surface, which takes the default value . In order to solve the angle , first establish the best linear objective function of the sample data point set :

[0037]

[0038] wherein, K is the slope of the linear function, Y and X lower intercept of the probe frame and the tooth profile unit data The tooth profile data fitting constraint is established by the mean square error between the target function and

[0039]

[0040] wherein, n is the actual tooth profile unit point number, is the captured profile data. The included angle is solved by the azimuth angle formula , that is, the included angle of the tilt of the captured tooth profile unit and the optical axis of the probe frame

[0041]

[0042] Note that, due to the positive and negative slope problem of the left and right tooth profile units of the tooth profile, the actual included angle needs to be converted into . Further, the quantitative tooth profile data tilt ratio can be solved:

[0043]

[0044] W5: linear structured light probe pose adjustment

[0045] Adjust the pose of the probe and the rotation of the gear , so as to realize the accurate calibration and adjustment of the linear structured light measurement of the gear pose, and take two indexes as the adjustment standard of the optimal pose.

[0046] (1) The tilt ratio is as small as possible. The tooth profile data tilt ratio is less than 50%, and the linear structured light probe pose bias parameter is unreasonable.

[0047] (2) Avoid shadow effect. By the longitudinal distance of the tooth root to the reference line in the linear structured light coordinate frame and the transverse distance of the tooth root to the optical axis in the linear structured light coordinate frame , combined with the tooth root shielding condition, it is determined whether there is shadow effect.

[0048] Adjust to meet the two conditions, that is, the linear structured light probe pose adjustment is completed.

[0049] The linear structured light measurement of the gear pose quantization and its adjustment method has the following advantages:

[0050] ​​1. The mathematical model corresponding to the physical model can quickly obtain the estimated theoretical parameters of the line structured light probe, save the repeated adjustment of the traditional method, improve the measurement efficiency, and be suitable for different measurement environments;

[0051] 2. The method can adapt to the detection of various types of cylindrical gears. Different types of gears are based on tooth profile characteristics and use the gear coordinate frame as a reference. This pose quantization method is universal;

[0052] 3. The method can effectively avoid the influence of shadow effect on line structured light measurement of gears, and obtain stable and reliable tooth profile data;

[0053] 4. The method first proposes to quantify the pose parameters of line structured light in the form of tilt ratio, providing a basis for measurement and adjustment of accurate tooth surfaces;

[0054] 5. Through gentle tooth profile measurement, the data stability of line structured light measurement of gears is ensured from the perspective of optical measurement. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 Mathematical model of the measured gear's involute helical tooth surface

[0056] Figure 2 Parameters of the line structured light probe relative to the gear coordinate frame

[0057] Figure 3 Tooth root blocking model for judging the light plane of line structured light

[0058] Figure 4 Actual measurement of the gear tooth profile in the light plane

[0059] Figure 5 Point-by-point derivative tooth profile graph

[0060] Figure 6 Tooth profile data fitting to calculate the tilt ratio

[0061] Figure 7 Pose quantization and adjustment of line structured light measurement of gears on a horizontal measuring machine

[0062] Figure 8 Flowchart of pose quantization and adjustment DETAILED DESCRIPTION

[0063] The pose quantization and adjustment method of line structured light measurement of gears will be further described below in combination with the drawings. This method can be applied to both vertical measuring machines and horizontal measuring machines. As shown in Figure 7 , a horizontal measuring machine is used as an example for illustration.

[0064] The horizontal measuring machine comprises a precision rotating unit, a measuring unit and a machine tool bed, the precision rotating unit and the measuring unit being installed on the machine tool bed. The precision rotating unit comprises a precision rotary table, a transmission C spindle and a gear positioning clamp, an axial circle grating being connected with the transmission C spindle, the gear positioning clamp being coaxially installed with the precision rotary table, and the rotation angle of the gear tooth being measured by the axial circle grating The measuring unit comprises a line structured light probe, a probe adjusting platform and a probe holder, one end of the holder being fixed to the x-axis of the machine tool bed, and the other end supporting the probe adjusting platform, the space angle calibration of the line structured light probe being realized through the adjusting platform; the machine tool bed is the machine tool body and x The axial 、y The axial z The axial x The axial 、y The axial z The axial x The axial grating, y The axial grating, z The axial grating, the C axial circle grating and the line structured light probe are connected with the motor of the C axial, so that the pose quantization and the adjustment process are fully automated. The data of the , , , , , , , .

[0065] T1: a three-dimensional mathematical model of the tooth surface of the measured gear is established

[0066] According to the right-hand rule, a gear coordinate frame is established Figure 1 The gear design reference is taken as the center of rotation, and the base circle of the gear in the radial direction is determined . Due to the inevitable manufacturing errors of the actual gear or the active topological modification, the normal error of the theoretical tooth surface is difficult to exist, and on the gear model, it can be understood as the theoretical developed length of any point on the tooth profile plus the normal error , the actual developed length is represented as .

[0067]

[0068] In the formula For any p Point on the coordinate frame z Axis parameter value, The corresponding unwinding angle of the point p, The base circle radius of the gear, The pressure angle.

[0069] According to the actual unwinding length The shape and position of the tooth surface of any point The general expression of the corresponding spiral involute tooth surface is

[0070]

[0071] In the formula, The projection angle of the tooth surface point in the gear coordinate frame with respect to The axis, the angle is superimposed With , the physical meaning of the corresponding angle is expressed as

[0072]

[0073] T2: Determine the line structure light pose parameters

[0074] As Figure 2 , gear line structure light measurement is realized by a series of tooth profile unit measurements. Tooth profile unit refers to the profile of the line structure light probe in a single measurement, which contains complete 2D tooth surface information from the root to the top. The specific steps are:

[0075] Calibration of the coordinate frame. Take the cylindrical mandrel as the calibration part, extract the center reference point based on the uniqueness of the mandrel axis in the system, and realize the calibration of the position, attitude and coordinate transformation matrix of the coordinate frame.

[0076] Calculation of the tooth rotation angle In order to realize the ordered measurement, the measured gear teeth are calculated according to the initial rotation angle

[0077]

[0078] In the formula, Tooth spacing coefficient, The gear modulus, The pitch circle radius of the gear.

[0079] Judgment of existence of shielding. As Figure 3 , usually, the root area is the first profile to be shielded under line structure light, so the root is measured ​​is the most basic condition to judge the tooth profile integrity. According to the corresponding rotation angle , the spatial coordinates of the tooth root captured by the structured light in the gear frame can be calculated as

[0080] , wherein, is the dedendum radius of the gear.

[0081] The opposite tooth surface of the measured tooth surface can be determined according to the included angle of the left and right tooth surfaces on the dedendum circle , and the spatial coordinates of the left tooth surface are

[0082]

[0083] If there is a shadow effect, the adjacent tooth profile will have a spatial coordinate interference phenomenon. If the rotation angle continues to increase, the left tooth profile will partially block the light plane, that is, the coordinates of the tooth root A are , and the blocking causes the right tooth profile to be unable to collect a complete tooth profile unit.

[0084] Establishment of the line structured light probe parameters. At different rotation angles and pose offsets of the structured light probe , there are theoretically multiple combinations. Combined with the blocking judgment condition, the general form of the pose parameters is

[0085]

[0086] , wherein, is the reference distance of the line structured light. is the longitudinal distance from the tooth root to the reference line in the line structured light coordinate frame, is the transverse distance from the tooth root to the optical axis in the line structured light coordinate frame.

[0087] T3: Threshold extraction of complete tooth profile

[0088] As Figure 4 , in the line structured light measurement of a gear, multiple “steep” profile data of a tooth surface can be measured at a time, including a small amount of random noise points. First, the accurate complete tooth profile is extracted from the profile data according to the tooth profile evaluation unit. Since a single tooth surface often has a data amount of tens of millions, the non-target area data can be reduced through threshold reduction, which can improve the operation efficiency. Secondly, the threshold preprocessing can also filter out the influence of noise and interference intervals. Through the second-order center method, the derivative is calculated point by point to segment the profile of the gear measured by the line structured light.

[0089]

[0090] , wherein, and is used to calculate the value of the first point and the second point derivative, is the physical constant distance parameter between the structure light spots. According to this idea, the derivative is calculated point by point

[0091]

[0092] In the formula, is the differential data point output by the (j+1)th calculation, and n represents the number of profile points in a single scan. As Figure 5 , the measured line structure light optimizes the pose measurement profile of the differential threshold value processing, and sets the starting threshold value of the effective profile and the ending threshold value , so that the involute and the intersection point of the addendum circle, and the intersection point of the transition curve and the dedendum circle can be adaptively calculated and identified. Then, the complete profile is extracted according to the identified position.

[0093] T4: Profile data tilt ratio

[0094] As Figure 6 , the tilt ratio of the profile data is an important indicator reflecting the "steepness" degree of the measured profile unit under the pose parameters. The measured tooth surface is determined through the initial adjustment angle , is the angle between the expected structure light axis and the linearized tooth surface, and the default value is taken. In order to solve the angle , first, the best linear objective function of the sampling data point set is established :

[0095]

[0096] Among them, K is the slope of the linear function, Y and X are the intercept and profile unit data under the frame of the probe. Through the mean square error between the objective function and , the fitting constraint of the profile data is established:

[0097]

[0098] In the formula, n is the actual number of profile unit points, is the captured profile data. The angle is solved by the azimuth angle formula, that is, the tilt angle between the captured profile unit and the optical axis of the frame of the probe:

[0099] ​​

[0100] Note that due to the positive and negative slope problem of the tooth profile left and right tooth profile units, the actual included angle needs to be converted into . Further, the quantized tooth profile data slope ratio can be solved:

[0101]

[0102] T5: Adjust the linear structure light probe pose

[0103] Bias the probe pose And gear rotation Adjustment, so as to realize the accurate calibration of the linear structure light measurement gear pose, and take the two indicators as the adjustment standard of the optimal pose.

[0104] The slope ratio is as small as possible. The tooth profile data slope ratio is less than 50%, and the linear structure light probe pose bias parameter is unreasonable. Avoid shadow effect. Through the longitudinal distance from the tooth root to the reference line in the linear structure light coordinate frame And the transverse distance from the tooth root to the optical axis in the linear structure light coordinate frame , combined with the tooth root blocking condition to determine whether there is a shadow effect. Adjust to meet the two conditions, which is the end of the linear structure light probe pose adjustment.

[0105] The detailed measurement process is shown in Figure 8 .

Claims

1. A method for quantizing and adjusting the pose of gears using line structured light measurement, characterized in that: A 3D model of the gear is established based on the input gear parameters, and then the theoretical calculation of the pose parameters of the line structured light is performed. The tooth profile is obtained through the theoretical pose parameters, and then the second-order center method is used to differentiate point by point. The complete tooth profile is then extracted by thresholding, and the tooth profile tilt ratio is obtained. Using this as a pose quantification index, the pose of the line structured light probe is precisely adjusted. The specific steps of this method are as follows. W1: Create a 3D model of the gear Establish the gear coordinate framework according to the right-hand rule. Based on gear design standards Let the center of rotation be determined, and the base circle of the gear's radial direction be defined. Due to unavoidable manufacturing errors or active topological modifications in actual gears, the theoretical tooth surface normal error... It is difficult to exist; in the gear model, it can be understood as having arbitrary tooth profiles. The theoretical development of points Superimposed normal error For the actual unfolded length Characterized as In the formula Let p be the z-axis parameter value of any point on the coordinate frame. Let p be the unfolding angle. For pressure angle, Based on the actual unfolded length Characterized arbitrary points on the tooth surface The shape and position of the corresponding helical involute tooth surface are expressed by the general formula: In the formula, For the tooth surface point relative to the gear coordinate frame The projected angle corresponding to the axis, this angle is determined by the initial angle. Overlay and The physical meaning of the corresponding angle is expressed as: W2: Theoretical Calculation of Pose Parameters for Linear Structured Light Gear line structured light measurement is achieved through a series of tooth profile unit measurements. A tooth profile unit refers to the profile of the line structured light probe in a single measurement, containing complete 2D tooth surface information from the tooth root to the tooth tip. Specific steps include: (1) The coordinate frame is calibrated by using a cylindrical mandrel as the calibration component. The center reference point is extracted based on the uniqueness of the mandrel axis in the system, thereby calibrating the position, attitude and coordinate transformation matrix of the coordinate frame. (2) Gear rotation angle In order to achieve orderly measurement, the measured gear teeth are calculated based on the initial rotation angle. calculate In the formula, For gear module, Tooth spacing coefficient; (3) Judgment of occlusion: Usually, the tooth root region is the first contour to be occluded under line structured light, so measuring the tooth root is important. It is the most basic condition for judging the integrity of the tooth profile, based on the corresponding rotation angle. The spatial coordinates of the structured light capturing the tooth root in the gear frame can be calculated as follows: The tooth surfaces opposite each other that are being tested can be determined by the angle between the left and right tooth surfaces on the root circle. Determine the spatial coordinates, such as the spatial coordinates of the left tooth surface. If a shadowing effect exists, spatial coordinate interference will occur between adjacent tooth profiles. If the rotation angle... If it continues to increase, the left tooth profile will... Partial occlusion of the light plane, i.e., coordinates at the tooth root A. The occlusion prevented the acquisition of complete tooth profile units on the right tooth profile; (4) Establishment of parameters for the line structured optical probe at different rotation angles and structured light probe pose bias Theoretically, there are multiple combinations. Combined with the occlusion judgment condition, the general formula for pose parameters is: In the formula, This is the reference distance for line structured light. This represents the longitudinal distance from the tooth root to the reference line within the coordinate frame of the line structured light. The lateral distance from the tooth root to the optical axis under the linear structured optical coordinate frame; W3: Threshold extraction of complete tooth profile Typically, in gear line structured light measurement, multiple "steep" profile data points on the tooth surface can be measured in a single operation, including a small number of random noise points. First, a precise, complete tooth profile must be extracted from the profile data according to the tooth profile evaluation unit. Since a single tooth surface often involves hundreds of millions of data points, thresholding to remove non-target regions can improve computational efficiency. Second, threshold preprocessing can also filter out the influence of noise and interference intervals. This is achieved by point-by-point differentiation using the second-order center method. The gear measured by line structured light is segmented into profiles; In the formula, and It is used to calculate the derivative values ​​at the first and second points. Let the physical constant distance parameter between structured light spots be used as an example; then, the derivative is calculated point by point according to this approach. In the formula, This refers to the differential data points output in the (j+1)th calculation, where n represents the number of contour points in a single scan. The differential threshold processing of the measured contour for optimal pose measurement using line structured light is set. Calculate the initial threshold for the effective tooth profile and termination threshold It can adaptively calculate and identify the intersection of the involute and the addendum circle, as well as the intersection of the transition curve and the root circle, and then extract the complete tooth profile based on the identified position. W4: Tooth profile data inclination ratio Inclination ratio of tooth profile data It is an important indicator reflecting the "steepness" of the measured tooth profile unit under pose parameters. The measured tooth surface is adjusted through the initial angle. Sure, The angle between the desired structured light optical axis and the linearized tooth surface is set to the default value. In order to solve the included angle First, establish the optimal linear objective function for the sampled data point set. : Where K is the slope of the linear function, and Y and X are the intercepts and tooth profile unit data of the probe frame. Through the objective function and The mean squared error between them is used to establish fitting constraints for the tooth profile data: In the formula, n is the actual number of tooth profile unit points. The included angle is obtained by solving the azimuth formula for the captured contour data. That is, capturing the tooth profile unit and the probe frame Inclination angle of the optical axis: Note that due to the positive and negative slope issues of the inclination of the left and right tooth profile units, the actual included angle needs to be converted into... This allows us to solve for the quantified tooth profile inclination ratio: W5: Line Structured Light Meter Pose Adjustment probe pose offset and gear rotation Adjustments are made to achieve precise calibration of the gear pose measured by line structured light, using two indicators as the adjustment criteria for the optimal pose; (1) The inclination ratio should be as small as possible, and the inclination ratio of the tooth profile data should be as small as possible. If the deviation is less than 50%, the pose offset parameters of the line structured light probe are considered unreasonable. (2) To avoid the shadow effect, the longitudinal distance from the tooth root to the reference line is determined by the coordinate frame of the line structured light. Lateral distance from tooth root to optical axis under the structured optical coordinate frame The presence of a shadow effect is determined by combining the tooth root occlusion conditions; Once these two conditions are met, the pose adjustment of the line structured light probe is complete.

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