A method for calculating the shape deviation of the rotating envelope axis section of a disc milling cutter with rotation axis error

Abstract

The present invention relates to the technical field of tool shape deviation, and in particular to a method for calculating the shape deviation of a rotating envelope axis section of a disc milling cutter containing a rotation axis error. The method is characterized in that, firstly, a tool and workpiece coordinate system is established and a disc milling cutter machining mathematical model is obtained according to the gear meshing principle, a rotation axis error model is established, the envelope section of the disc milling cutter after rotation is calculated, and then fitting processing is performed on the tool rotation envelope deviation points. Finally, the distance from the point on the tool contour line containing the rotation deviation after correction to the theoretical tool curve is calculated to obtain the shape deviation of the tool. The present invention aims to quantitatively calculate the influence of the rotation deviation on the disc cutter shaft section deviation, and uses a segmentation interval comparison peak value algorithm to perform denoising processing on the tool discrete points, thereby obtaining a more accurate disc cutter envelope contour containing a rotation axis error, thereby improving the calculation accuracy of the tool envelope deviation, and laying a foundation for subsequent rotation axis error correction and improving gear machining accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of tool shape deviation, and in particular to a method for calculating the axial section shape deviation of a disc milling cutter, in particular to a method for calculating the axial section shape deviation of a disc milling cutter including a rotation axis error. Background Art

[0002] A milling cutter is a rotating tool used for milling. The milling cutter has one or more teeth. When working, each tooth cuts off the excess of the workpiece intermittently in sequence. Milling cutters are mainly used to process planes, steps, grooves, formed surfaces and cut off workpieces on milling machines. In order to achieve the processing of complex grooves, disc milling cutters are often used, which not only improves the surface quality of the processed grooves, but also greatly improves the processing efficiency. Disc milling cutters can be divided into three types: single-sided blade, double-sided blade and three-sided blade. Among them, three-sided blade is the most common. It is widely used because it has obvious advantages in processing complex or deep grooves with a certain length and step surfaces of various shapes. At the same time, disc milling cutters can also process spur gears and helical gears. When processing spur gears, the axial section tooth shape of the cutter disc is calculated by the profiling method, and the cross-sectional shape of the milling cutter teeth corresponds to the tooth groove shape.

[0003] When the disc milling cutter is milling the workpiece, the gear blank and disc milling cutter are installed on the workbench and spindle respectively according to the processing parameters. However, during the gear milling process, the tool is also rotating. The geometric error of the rotating axis refers to the position and direction error of the axis average line of the rotating axis. This error therefore causes the shape deviation of the tooth profile of the disc milling cutter shaft section, thereby affecting the machining accuracy of the gear. In order to improve the machining accuracy of the disc milling cutter, it is particularly important to analyze and correct the shape deviation of the cutter head shaft surface caused by the rotation error. Summary of the invention

[0004] The purpose of the present invention is to propose a method for calculating the cross-sectional shape deviation of the rotating envelope axis of a disc milling cutter containing a rotation axis error, so as to quantitatively calculate the influence of the rotation deviation on the cross-sectional deviation of the disc cutter axis, and use the algorithm of segmentation interval comparison peak value to denoise the discrete points of the tool, so as to obtain a more accurate disc tool envelope contour containing a rotation axis error, thereby improving the calculation accuracy of the tool envelope deviation, laying a foundation for subsequent rotation axis error correction and improving gear processing accuracy.

[0005] To achieve the above purpose, the technical solution provided by the present invention is as follows:

[0006] A method for calculating the shape deviation of a cutter head shaft section including a rotation error comprises the following steps:

[0007] S1. Establishing a mathematical model of a disc milling cutter;

[0008] S2, establish a disc milling cutter gear milling processing space coordinate system, and calculate the coordinate matrix transformation;

[0009] S3. Establish a rotation axis error model based on the kinematic model of the machine tool rotation axis;

[0010] S4, using a segmentation interval comparison peak value algorithm to perform fitting processing on the tool rotation envelope deviation points generated by the rotation error to obtain a high-precision tool profile;

[0011] S5. The point after data fitting is used as the minimum distance point on the disc milling cutter model with rotation deviation. According to the distance formula from the point to the straight line, the normal distance from the fitting data point to the theoretical tool contour is obtained, that is, the tool truncation error.

[0012] The method of establishing the mathematical model of the disc milling cutter in step S1 mainly includes the following contents:

[0013] Establish tool coordinate system Ox at the rotation center of the disc milling cutter t y t z t , where z t The axis of the axis and the cutter head coincide, and point m is any point on the cutting edge. t y t z t The coordinate equation is:

[0014]

[0015] Where:

[0016] R is the maximum radius of the cone surface of the disc milling cutter, b is the tooth top width, β is the cone bottom angle, m is any point on the cutting edge, R m and φ are both variable parameters, R m is the radius of the corresponding rotating surface formed by the rotation of point m during cutting, φ is O t m in x t Oy t Plane and x t The angle of the axis.

[0017] The normal vector of any point on the disc cutter in the tool coordinate system is:

[0018]

[0019] The step S2 establishes a disc milling cutter gear milling processing space coordinate system, and the method for calculating the coordinate matrix transformation mainly includes the following contents:

[0020] W m {O m -x m ,y m ,z m} is the machine tool coordinate system, W g {O g -xg ,y g ,z g} is the workpiece coordinate system, W t {O t -x t ,y t ,z t} is the tool coordinate system. By using the homogeneous transformation operation of the matrix, the tool coordinate system W can be obtained. t To the workpiece coordinate system W g The homogeneous transformation matrix of the conversion:

[0021]

[0022] Where:

[0023] D is the machine tool coordinate system W m and workpiece coordinate system W g is the distance between the origins of the two coordinate systems, and θ is the angle between the y axes of the two coordinate systems.

[0024] The method of establishing the rotation axis error model according to the kinematic model of the machine tool rotation axis in step S3 mainly includes the following contents:

[0025] When the rotation axis c-axis rotates around the actual rotation axis by an angle C, the c-axis model with rotation error is described as: R′ Z (C) = T(δ C (C))R(ε C (C))R Z (C)

[0026] in:

[0027] T(δ C (C))=T Z (δz c (C))T X (δx c (C))T Y (δy c (C));

[0028] R(ε C (C))=R Z (εz c (C))R X (εx c (C))R Y (εy c (C));

[0029] T P (i) represents the homogeneous translation matrix of the geometric error i along the p-axis;

[0030] R P(i) represents the homogeneous transformation matrix for a rotation of i degrees about the p-axis.

[0031] The method in step S4 uses an algorithm of dividing intervals and comparing peaks to fit the deviation points of the tool rotation envelope caused by the rotation error, so as to obtain a high-precision tool profile, which mainly includes the following contents:

[0032] (1) Perform linear interpolation on the known discrete points, reasonably compensate for the missing data in the discrete points, and lay a foundation for obtaining a more accurate and smooth tool profile subsequently.

[0033] (2) Find the points with peak values in the vertical coordinate direction among all points. The judgment criterion is that when the vertical coordinate value of a certain point is greater than the vertical coordinate values of its two adjacent points, it is marked as a peak. Save the horizontal and vertical coordinates of all peak points as a new point set [xpks, ypks]. Form a sequence with the differences obtained by subtracting the x values of every two peaks, and find the minimum difference in this sequence and return it to dx. Multiply dx by 10 to get thresh.

[0034] (3) For the point set where the distance between two adjacent peaks is greater than thresh, remove the abnormal points: If the latter peak is greater than the former peak, that is, in the point set where ypks(i + 1)>ypks(i), exclude the x values corresponding to the y values smaller than the peak and the x values corresponding to the decreasing y values in the corresponding xpks(i) and xpks(i + 1) intervals, and insert the remaining points into the point set [xpks, ypks];

[0035] If the latter peak is smaller than the former peak, that is, in the point set where ypks(i + 1)<ypks(i), exclude the x values corresponding to the y values smaller than the peak and the x values corresponding to the increasing y values in the corresponding xpks(i) and xpks(i + 1) intervals, and insert the remaining points into the point set [xpks, ypks].

[0036] (4) For the point set showing a monotonic trend, remove the noise points: Smooth the point set outside the first peak and the last peak, and sort the obtained points and the xpks vector together according to the size of x.

[0037] (5) Eliminate the points with abnormal fluctuations: Set a threshold, calculate the difference of the vector ypks and take the absolute value, find the positions where it is greater than the threshold and eliminate them to obtain a new point set.

[0038] (6) Connect the remaining points in sequence to obtain the fitted tool profile.

[0039] The step S5 uses the point after data fitting as the minimum distance point on the disc milling cutter model with rotation deviation, and obtains the normal distance from the fitting data point to the theoretical tool contour, i.e., the tool truncation error, according to the distance formula from the point to the straight line. The method mainly includes the following contents:

[0040] The actual axial section truncation curve of the disc milling cutter is a collection of a series of points after fitting. By comparing the fitted tool curve with the theoretical tool curve, the actual truncation error of the tool can be obtained. Each measured data point after fitting corresponds to the minimum distance point M on the disc milling cutter model. i , the tool section error is the distance from the fitted data point to the theoretical tool profile. According to the distance formula from the point to the straight line, the tool axis section shape error is:

[0041]

[0042] in

[0043] M i (x i ,y i ) is a point on the corrected tool profile, N t (x t ,y t ) is M i The point on the theoretical tool profile where the distance is the smallest.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] When a disc milling cutter processes a workpiece, the position and direction errors of the axis average line of the rotating axis cause large errors in the position and direction of the tool relative to the workpiece, which leads to tooth profile deviation in the processed tooth profile and reduces the machining accuracy of the gear. The present invention quantitatively calculates the influence of the rotation deviation on the disc cutter shaft section deviation, thereby obtaining the tool shape error, and uses the algorithm of segmentation interval comparison peak value to perform denoising on the tool discrete points, thereby obtaining a more accurate disc cutter envelope profile containing the rotation axis error, improving the calculation accuracy of the tool envelope deviation, and laying a foundation for the subsequent correction of the rotation axis error and improving the gear machining accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic diagram of coordinate parameters of a disc milling cutter according to the present invention;

[0047] Figure 2 It is a coordinate schematic diagram of the disc-shaped milling cutter of the present invention enveloping an involute cylindrical spur gear;

[0048] Figure 3 It is a schematic diagram of the rotational geometric error coordinate conversion of the present invention;

[0049] Figure 4It is the algorithm flow chart of the present invention;

[0050] Figure 5 A comparison diagram of the fitted tool profile of the present invention and the theoretical tool profile;

[0051] Figure 6 It is a schematic diagram of the cutter truncation error of the present invention.

[0052] In the figure: 1. workpiece, 2. disc milling cutter. DETAILED DESCRIPTION

[0053] In order to clarify the technical problems, technical solutions, implementation processes and performance demonstrations, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only for explanation. The present invention is not intended to limit the present invention. Various exemplary embodiments, features and aspects of the present disclosure will be described in detail below with reference to the accompanying drawings. The same reference numerals in the drawings represent elements with the same or similar functions. Although various aspects of the embodiments are shown in the drawings, the drawings do not have to be drawn to scale unless otherwise specified.

[0054] The word "exemplary" is used exclusively herein to mean "serving as an example, example, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.

[0055] In addition, in order to better illustrate the present disclosure, numerous specific details are given in the following specific embodiments. It should be understood by those skilled in the art that the present disclosure can also be implemented without certain specific details. In some examples, methods, means, components and circuits well known to those skilled in the art are not described in detail in order to highlight the main purpose of the present disclosure.

[0056] Example 1

[0057] A method for calculating the shape deviation of a cutter head shaft section including a rotation error comprises the following steps:

[0058] S1. Establishing a mathematical model of a disc milling cutter;

[0059] like Figure 1 As shown in the figure, the tool coordinate system Ox is established at the rotation center of the disc milling cutter. t y t z t , where z t The axis of the axis and the cutter head coincide, and point m is any point on the cutting edge. t y t z t The coordinate equation is:

[0060]

[0061] Where:

[0062] R is the maximum radius of the cone surface of the disc milling cutter, b is the tooth top width, β is the cone bottom angle, m is any point on the cutting edge, R m and φ are both variable parameters, R m is the radius of the corresponding rotating surface formed by the rotation of point m during cutting, φ is O t m in x t Oy t Plane and x t The angle of the axis.

[0063] The normal vector of any point on the disc cutter in the tool coordinate system is:

[0064]

[0065] S2, establish a disc milling cutter gear milling processing space coordinate system, and calculate the coordinate matrix transformation;

[0066] like Figure 2 As shown, the disc milling cutter 2 is used for processing the workpiece 1; m {O m -x m ,y m ,z m} is the machine tool coordinate system, W g {O g -x g ,y g ,z g} is the workpiece coordinate system, W t {O t -x t ,y t ,z t} is the tool coordinate system. By using the homogeneous transformation operation of the matrix, the tool coordinate system W can be obtained. t To the workpiece coordinate system W g The homogeneous transformation matrix of the conversion:

[0067]

[0068] Where:

[0069] D is the machine tool coordinate system W m and workpiece coordinate system W g is the distance between the origins of the two coordinate systems, and θ is the angle between the y axes of the two coordinate systems.

[0070] S3. Establish a rotation axis error model based on the kinematic model of the machine tool rotation axis;

[0071] like Figure 3 As shown in the figure, when the rotation axis c-axis rotates around the actual rotation axis by an angle C, the c-axis model with rotation error is described as:

[0072] R′ Z (C) = T(δ C (C))R(ε C (C))R Z (C)

[0073] in:

[0074] T(δ C (C))=T Z (δz c (C))T X (δx c (C))T Y (δy c (C));

[0075] R(ε C (C))=R Z (εz c (C))R X (εx c (C))R Y (εy c (C));

[0076] T P (i) represents the homogeneous translation matrix of the geometric error i along the p-axis;

[0077] R P (i) represents the rotational homogeneous transformation matrix with an angle of i degrees around the p axis.

[0078] S4, using a segmentation interval comparison peak value algorithm to perform fitting processing on the tool rotation envelope deviation points generated by the rotation error to obtain a high-precision tool profile;

[0079] like Figure 4 As shown, the method of fitting the tool rotation envelope deviation points generated by the rotation error by using the algorithm of segmentation interval comparison peak value to obtain the high-precision tool contour mainly includes the following contents:

[0080] (1) Linear interpolation is performed on known discrete points to reasonably compensate for the missing data in the discrete points, while laying the foundation for obtaining a more accurate and smooth tool contour in the future.

[0081] (2) Find the point with a peak value in the ordinate direction among all the points. The judgment standard is that when the ordinate value of a point is greater than the ordinate values ​​of the two points before and after it, it is marked as a peak. The horizontal and vertical coordinates of all peak points are saved as a new point set [xpks, ypks]. The difference obtained by subtracting the x values ​​of every two peaks is formed into a sequence, and the minimum difference is found in this sequence and returned to dx. Multiply dx by 10 to get thresh.

[0082] (3) For the point set where the distance between two adjacent peaks is greater than thresh, remove the outliers: If the next peak value is greater than the previous peak value, i.e., in the point set where ypks(i + 1) > ypks(i), exclude the x values corresponding to the y values smaller than the peak and the x values corresponding to the decreasing y values in the corresponding interval of xpks(i) and xpks(i + 1), and insert the remaining points into the point set [xpks, ypks];

[0083] If the next peak value is less than the previous peak value, i.e., in the point set where ypks(i + 1) < ypks(i), exclude the x values corresponding to the y values smaller than the peak and the x values corresponding to the increasing y values in the corresponding interval of xpks(i) and xpks(i + 1), and insert the remaining points into the point set [xpks, ypks].

[0084] (4) For the point set showing a monotonic trend, remove the noise points: Find the point set outside the first peak and the last peak for smoothing, and sort the obtained points and the xpks vector together according to the magnitude of x.

[0085] (5) Eliminate the points with abnormal fluctuations: Set a threshold, calculate the difference of the vector ypks and take the absolute value, find the positions greater than the threshold and eliminate them to obtain a new point set.

[0086] (6) Connect the remaining points in sequence to obtain the fitted tool profile.

[0087] S5. Take the points after data fitting as the minimum distance points on the disc cutter model with rotational deviation. According to the distance formula from a point to a line, obtain the normal distance from the fitted data points to the theoretical tool profile, that is, the tool section error.

[0088] As Figure 5 and Figure 6 shown, the actual axis section profile curve of the disc cutter is a set of a series of points after fitting. Compare the fitted tool curve with the theoretical tool curve to obtain the actual section error of the tool. Each measured data point after fitting corresponds to the minimum distance point M i on the disc cutter model. The tool section error is the distance from the fitted data point to the theoretical tool profile. According to the distance formula from a point to a line, the tool axis section shape error is:

[0089]

[0090] where

[0091] M i (x i , y i ) is a point on the corrected tool profile, Nt (x t ,y t ) is M i The point on the theoretical tool profile where the distance is the smallest.

[0092] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. The present invention may have various changes and improvements without departing from the spirit and scope of the present invention, and these changes and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for calculating the shape deviation of the cross section of the rotating envelope axis of a disc milling cutter containing a rotation axis error, characterized in that: It includes the following steps: S1. Establish a mathematical model of the face milling cutter; S2. Establish a spatial coordinate system for face milling cutter tooth machining and calculate the coordinate matrix transformation; S3. Establish a rotational axis error model according to the kinematic model of the machine tool's rotating axis; S4. Use an algorithm of dividing intervals and comparing peaks to fit the tool rotation envelope deviation points caused by rotational errors to obtain a high-precision tool profile; S5. Take the points after data fitting as the minimum distance points on the face milling cutter model with rotational deviation. According to the distance formula from a point to a line, obtain the normal distance from the fitted data points to the theoretical tool profile, that is, the tool section error; The method for establishing the mathematical model of the face milling cutter in step S1 includes the following content: Establish tool coordinate system Ox at the rotation center of the disc milling cutter t y t z t , where z t The axis of the axis and the cutter head coincide, and point m is any point on the cutting edge. t y t z t The coordinate equation is: In the formula: R is the maximum radius of the cone surface of the disc milling cutter, b is the tooth top width, β is the cone bottom angle, m is any point on the cutting edge, R m and φ are both variable parameters, R m is the radius of the corresponding rotating surface formed by the rotation of point m during cutting, φ is O t m in x t Oy t Plane and x t The angle of the axes; The normal vector of any point on the disc cutter in the tool coordinate system is: The method for establishing the spatial coordinate system for face milling cutter tooth machining and calculating the coordinate matrix transformation in step S2 includes the following content: W m {O m -x m ,y m ,z m } is the machine tool coordinate system, W g {O g -x g ,y g ,z g } is the workpiece coordinate system, W t {O t -x t ,y t ,z t } is the tool coordinate system. By using the homogeneous transformation operation of the matrix, the tool coordinate system W can be obtained. t To the workpiece coordinate system W g The homogeneous transformation matrix of the conversion: In the formula: D is the machine tool coordinate system W m and workpiece coordinate system W g The distance between the origins of the two coordinate systems, θ is the angle between the y axes of the two coordinate systems; the method of establishing the rotation axis error model according to the kinematic model of the machine tool rotation axis in step S3 includes the following contents: When the rotation axis c-axis rotates around the actual rotation axis by an angle C, the c-axis model with rotation error is described as: R′ Z (C) = T(δ C (C))R(ε C (C))R Z (C) Among them: T(δ C (C))=T Z (δz c (C))T X (δx c (C))T Y (δy c (C)); R(ε C (C))=R Z (εz c (C))R X (εx c (C))R Y (εy c (C)); T P (i) represents the homogeneous translation matrix of the geometric error i along the p-axis; R P (i) represents the rotational homogeneous transformation matrix with an angle of i degrees around the p axis.

2. The method for calculating the shape deviation of the cross section of the rotating envelope axis of a disc milling cutter containing a rotation axis error according to claim 1, characterized in that: The method for using an algorithm of dividing intervals and comparing peaks to fit the tool rotation envelope deviation points caused by rotational errors to obtain a high-precision tool profile in step S4 includes the following content: (1) Perform linear interpolation on the known discrete points, reasonably compensate for the missing data in the discrete points, and lay a foundation for obtaining a more accurate and smooth tool profile subsequently; (2) Find the points with peak values in the vertical coordinate direction among all points. The judgment criterion is that when the vertical coordinate value of a certain point is greater than the vertical coordinate values of its two adjacent points, it is marked as a peak. Save the horizontal and vertical coordinates of all peak points as a new point set [xpks, ypks]. Form a sequence with the differences obtained by subtracting the x values of every two peaks, and find the minimum difference in this sequence and return it to dx. Multiply dx by 10 to get thresh; (3) For the point set where the distance between two adjacent peaks is greater than thresh, remove the abnormal points: If the latter peak is greater than the former peak, that is, in the point set where ypks(i + 1)>ypks(i), exclude the x values corresponding to the y values smaller than the peak and the x values corresponding to the decreasing y values in the corresponding xpks(i) and xpks(i + 1) intervals, and insert the remaining points into the point set [xpks, ypks]; If the latter peak is smaller than the former peak, that is, in the point set where ypks(i + 1)<ypks(i), exclude the x values corresponding to the y values smaller than the peak and the x values corresponding to the increasing y values in the corresponding xpks(i) and xpks(i + 1) intervals, and insert the remaining points into the point set [xpks, ypks]; (4) For the point set showing a monotonic trend, remove the noise points: Find the point set outside the first peak and the last peak for smoothing processing, and sort the obtained points and the xpks vector together according to the size of x; (5)剔除波动起伏异常的点:设定一个阈值,计算向量ypks的差分并取绝对值,找到其中大于阈值的位置并剔除,得到新的点集; (6) Connect the remaining points in sequence to obtain the fitted tool profile.

3. The method for calculating the shape deviation of the cross section of the rotating envelope axis of a disc milling cutter containing a rotation axis error according to claim 1, characterized in that: The step S5 uses the point after data fitting as the minimum distance point on the disc milling cutter model with rotation deviation, and obtains the normal distance from the fitting data point to the theoretical tool contour, i.e., the tool truncation error, according to the distance formula from the point to the straight line, including the following: The actual axial section truncation curve of the disc milling cutter is a collection of a series of points after fitting. By comparing the fitted tool curve with the theoretical tool curve, the actual truncation error of the tool can be obtained; each measured data point after fitting corresponds to the minimum distance point M on the disc milling cutter model. i , the tool section error is the distance from the fitted data point to the theoretical tool profile. According to the distance formula from the point to the straight line, the tool axis section shape error is: in M i (x i ,y i ) is a point on the corrected tool profile, N t (x t ,y t ) is M i The point on the theoretical tool profile where the distance is the smallest.

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