A precision turning method for complex curved surfaces with cutting length of cutting edge

Abstract

This invention discloses a method for precision turning of complex curved surfaces that achieves constant cutting lengths of the cutting edge, relating to the field of turning machining technology. The method includes: planning a turning tool path on the surface to be machined and discretizing trajectory points; calculating the arc length of the turning tool path and the geometric parameters of the trajectory points; calculating the safe tool axis angle range for each trajectory point on the turning tool path; calculating the corresponding cutting edge angle range based on the safe tool axis angle range for each trajectory point; optimizing the initial cutting edge angle spline curve using a genetic algorithm to obtain a new cutting edge angle spline curve; and calculating the tool axis vector for each trajectory point from the cutting edge angle spline curve. This invention achieves constant cutting lengths of the cutting edge by adjusting the actual cutting position of the tool's cutting edge during the turning process, extending tool life, reducing machining errors caused by accelerated tool wear, and improving overall machining efficiency while avoiding the reduction in cutting efficiency due to tool changes or parameter reductions.

Description

Technical Field

[0001] This invention relates to a method for precision turning of complex curved surfaces that can achieve cutting lengths of equal cutting edge, belonging to the field of turning technology. Background Technology

[0002] In modern manufacturing, turning has become the most common machining method for complex curved surface parts. As the application of complex curved surface parts in aerospace and other fields becomes more widespread, the requirements for machining accuracy and surface quality of these parts are becoming increasingly stringent. Therefore, improving turning technology and enhancing the accuracy and surface quality of machined parts has become one of the key research focuses in related fields.

[0003] Controlling tool wear is a key factor in ensuring the surface quality and precision of parts. During turning, machining errors caused by tool wear are unavoidable, especially after a period of cutting and some wear has occurred, at which point the errors become particularly noticeable. Current research on tool wear mainly focuses on optimizing cutting parameters to reduce tool wear and extend tool life. However, optimizing cutting parameters with an excessive emphasis on tool life can lead to reduced cutting efficiency, thus affecting overall machining efficiency. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for precision turning of complex curved surfaces that can achieve equal cutting lengths of the cutting edge. By adjusting the actual cutting position of the cutting edge of the tool during the turning process, equal cutting lengths of the cutting edge can be achieved. This extends the tool's service life, reduces machining errors caused by increased tool wear, and improves overall machining efficiency, avoiding the reduction in cutting efficiency caused by tool changes or parameter reductions.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] This invention provides a method for precision turning of complex curved surfaces that can achieve a cutting length with the same cutting edge, comprising:

[0007] Obtain the surface to be processed and the surface processing parameters;

[0008] Plan the turning tool path on the surface to be machined and discretize the trajectory points;

[0009] Calculate the arc length and geometric parameters of the turning toolpath.

[0010] Using arc length micro-elements as the spacing, the trajectory points are refined by interpolating the trajectory points in the turning tool path, and the geometric parameters of the trajectory points are calculated.

[0011] Calculate the safe tool axis angle range for each trajectory point on the turning tool path based on the surface to be machined and the surface machining parameters;

[0012] The corresponding blade angle range is calculated based on the safe blade axis angle range of each trajectory point.

[0013] The upper and lower limits of the blade angle range of each trajectory point are fitted to obtain curves, and the curves are divided to obtain multiple blade angle intervals.

[0014] An initial cutting edge angle spline curve is constructed, and a genetic algorithm is used to optimize it to maximize the uniformity of the effective cutting path length of the cutting edge, thus obtaining the cutting edge angle spline curve.

[0015] The tool axis vector for each trajectory point is calculated from the spline curve of the cutting edge angle.

[0016] Furthermore, the surface machining parameters include generatrix point set data, number of spiral points per revolution, and tool parameters. The generatrix point set data includes the starting and ending coordinates of the connecting line segments of the generatrix point set, and the tool parameters include the tool arc radius, tool holder width, and tool length.

[0017] Furthermore, the turning toolpath planning adopts the isoparametric method, and the trajectory point discretization is performed using isoangular discretization. The expression for isoangular discretization is:

[0018] ;

[0019] in, Represents the three-dimensional coordinates of the trajectory points. This indicates the height of the trajectory point from the center line of rotation. Represents the first point on the busbar point set points Axis coordinates Represents the first point on the busbar point set points Axis coordinates Represents the first point on the busbar point set The height of each point from the center line of rotation, Represents the first point on the busbar point set The height of each point from the center line of rotation, n = 1,2,…,N-1 This indicates the number of spiral points per revolution.

[0020] Furthermore, the expression for calculating the arc length of the turning toolpath is:

[0021] ;

[0022] in, This represents the arc length of the turning toolpath. Represents the distance between two adjacent trajectory points Axis coordinate difference Represents the distance between two adjacent trajectory points Axis coordinate difference Represents the distance between two adjacent trajectory points Axis coordinate difference;

[0023] The geometric parameters of the trajectory point include the normal vector, the normal vector, and the geometric parameters of the trajectory point. The included angle;

[0024] The expression for calculating the normal vector is:

[0025] ;

[0026] in, Indicates the first The normal vector of each trajectory point Represents the three-dimensional coordinates of the trajectory points. This indicates the height of the trajectory point from the center line of rotation;

[0027] The normal vector and The expression for calculating the included angle is:

[0028] ;

[0029] in, Indicates the first The normal vector of each trajectory point and The included angle, express The unit vector of the axis is [0,0,1].

[0030] Furthermore, the arc length micro-element is the minimum value among the arc length spacings of all adjacent trajectory points.

[0031] Furthermore, the method for determining the range of the safety cutter axis angle includes:

[0032] S1. Select a tool that meets the condition of local non-interference safety tool axis angle range. The expression for the condition of local non-interference safety tool axis angle range is:

[0033] ;

[0034] in, Indicates the radius of the tool arc. Represents the minimum concave surface radius of the surface to be processed;

[0035] S2. Perform normal compensation on the trajectory points, with the compensation distance being the tool arc radius. Calculate the tool center point, and its expression is:

[0036] ;

[0037] in, Indicates the first The three-dimensional coordinates of the tool center point corresponding to each trajectory point Indicates the first The three-dimensional coordinates of the trajectory points , , The first The normal vector of each trajectory point is in axis, axis, Components on the axis;

[0038] The three-dimensional coordinates of the tool center point are simplified to two-dimensional coordinates in the rz plane, and the expression is:

[0039] ;

[0040] in, Indicates the first The two-dimensional x-coordinate of the tool center point corresponding to each trajectory point Indicates the first The two-dimensional ordinate of the tool center point corresponding to each trajectory point;

[0041] The rz plane is obtained by combining the two-dimensional coordinates of the tool center point corresponding to all trajectory points;

[0042] S3. Using a three-stage stepping formula to substitute the tool axis angle, calculate the two-dimensional coordinates of the starting and ending points of the tool boundary. The expression for the three-stage stepping formula of the tool axis angle is as follows:

[0043] ;

[0044] in, Indicates the cutter axis angle. , This indicates the range of safe tool axis angles obtained from the first step. This indicates the range of safe tool axis angles obtained from the second-stage stepping;

[0045] The calculation expressions for the two-dimensional coordinates of the starting and ending points of the tool boundary are as follows:

[0046] ;

[0047] ;

[0048] ;

[0049] ;

[0050] in, Indicates the first The starting point of the tool's right boundary corresponding to each trajectory point Indicates the first The right boundary endpoint of the tool corresponding to each trajectory point Indicates the first The left boundary starting point of the tool corresponding to each trajectory point Indicates the first The left boundary endpoint of the tool corresponding to each trajectory point Indicates the width of the tool holder. Indicates the length of the cutting tool. Indicates the first The two-dimensional coordinates of the starting point of the right boundary of the tool corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's right boundary endpoint corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's left boundary starting point corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's left boundary endpoint corresponding to each trajectory point;

[0051] S4. Based on the coordinates of the starting and ending points of the tool boundary, obtain the left and right boundary segments of the tool. Determine whether the left and right boundary segments of the tool intersect the generatrix of the rz plane. The expression for the determination condition is:

[0052] ;

[0053] ;

[0054] in, Indicates the position of the intersection point within the boundary line segment of the tool holder. This indicates the position of the intersection point within the connecting line segment of the busbar point set. Indicates the starting coordinates of the tool holder boundary line segment. Indicates the coordinates of the endpoint of the tool holder boundary line segment. This represents the starting coordinates of the line segment connecting the set of busbar points. This represents the coordinates of the endpoint of the line segment connecting the set of points on the busbar. It indicates and signifies;

[0055] If at least one of the left boundary line segment and the right boundary line segment of the tool satisfies the judgment condition, it indicates that there is interference between the tool and the surface to be machined; otherwise, there is no interference, and the maximum non-interference continuous angle interval is obtained.

[0056] S5. Repeat steps S3 to S4 until the maximum non-interference continuous angle interval corresponding to the tool axis angle of the third step is obtained.

[0057] S6. Reduce the safety threshold at the end of the maximum non-interference continuous angle interval corresponding to the tool axis angle of the third step to obtain the safe tool axis angle range.

[0058] Furthermore, the corresponding cutting edge angle range calculated based on the safety cutting edge angle range of each trajectory point is obtained through the cutting edge angle-to-cutting edge angle conversion formula, which is:

[0059] ;

[0060] in, Indicates the blade angle. Represents the normal vector of the trajectory point and The included angle, express The unit vector along the axis is [0,0,1]. Indicates the angle of the cutter axis.

[0061] Furthermore, the horizontal axis of the curve represents the arc length of the turning tool path, and the vertical axis represents the cutting edge angle.

[0062] The blade angle interval is divided uniformly, and the maximum and minimum values ​​of the blade angles among all trajectory points are taken as the starting points of the blade angle interval, respectively. The expression is as follows:

[0063] ;

[0064] in, Indicates the range of blade angles. This represents the maximum value of the blade angle among all trajectory points. This represents the minimum blade angle among all trajectory points. Indicates the number of blade angle ranges. This indicates the size of the range of blade angles.

[0065] Furthermore, the construction of the initial cutting edge angle spline curve, and the optimization of it using a genetic algorithm to maximize the uniformity of the effective cutting path length of the cutting edge, to obtain the cutting edge angle spline curve, includes:

[0066] D1. Construct an initial blade angle spline curve, wherein the control points on the initial blade angle spline curve do not exceed 1 / 100 of the number of trajectory points;

[0067] D2. Adjust the positions of the control points so that the initial x-coordinate of each control point is the sum of the x-coordinate of the previous control point and the arc length of the turning toolpath divided by the total number of control points. The x-coordinate of the first control point should be 0, and the y-coordinate should be... ,in, Indicates weight, , This indicates the upper limit of the blade angle of the trajectory point corresponding to the horizontal coordinate of the control point. This indicates the lower limit of the blade angle of the trajectory point corresponding to the x-coordinate of the control point. Indicates the first The blade angle of each control point, i.e., its ordinate;

[0068] D3. Using the minimization of the root mean square error of the total arc length distribution for each blade angle interval as the objective function, a genetic algorithm is used to optimize the weights in the ordinate of the control points, resulting in an optimized blade angle spline curve. The expression for calculating the total arc length of the blade angle interval is as follows:

[0069] ;

[0070] in, Indicates the first The total arc length of each blade angle range Indicates the first The blade angle range where each trajectory point is located Indicates the first The number of trajectory points within a blade angle range Let represent the infinitesimal element representing the arc length of the trajectory between two adjacent points. Indicates the first Index of the blade angle interval where each trajectory point is located;

[0071] D4. Repeat D3 until the root mean square error of the total arc length distribution of each blade angle interval of the blade angle spline curve is less than 10 and the maximum relative arc length deviation is less than 0.1. Use this as the blade angle spline curve.

[0072] Furthermore, the step of calculating the blade axis vector of each trajectory point from the blade angle spline curve includes: discretizing the blade angle spline curve, wherein each point on the blade angle spline curve represents the blade angle of the trajectory point corresponding to the same abscissa;

[0073] Based on the conversion formula between the cutting edge angle and the cutting axis angle, the corresponding cutting axis vector is calculated from the cutting edge angle of each trajectory point.

[0074] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0075] This invention controls the actual cutting position of the cutting edge by changing the axial angle of the turning tool. By combining computer geometry and optimization algorithms, an optimized tool axis angle change curve is obtained, realizing turning with equal effective cutting length. This not only extends the tool's service life and reduces machining errors caused by increased local wear of the tool, but also improves the overall machining efficiency and avoids the reduction in machining efficiency caused by tool changes or changes in cutting parameters. Attached Figure Description

[0076] Figure 1 This is a flowchart illustrating a method for precision turning of complex curved surfaces with equal cutting lengths of cutting edge, as described in one embodiment of the present invention.

[0077] Figure 2 This is a flowchart illustrating the calculation of the tool axis angle in a method for precision turning of complex curved surfaces with equal cutting lengths, as described in one embodiment of the present invention.

[0078] Figure 3 This is a schematic diagram illustrating the relationship between the tool axis angle and the tool cutting edge angle in a precision turning method for complex curved surfaces with equal cutting lengths, as described in one embodiment of the present invention.

[0079] Figure 4 This is a flowchart illustrating the curve for optimizing the cutting edge angle in a precision turning method for complex curved surfaces with equal cutting lengths, as described in one embodiment of the present invention.

[0080] Figure 5 This is a schematic diagram of the parabolic surface of revolution in the precision turning method for complex curved surfaces that can achieve the same cutting length of the cutting edge in Embodiment 2 of the present invention;

[0081] Figure 6 This is a schematic diagram of the generatrix of the parabolic surface in the precision turning method for complex curved surfaces that can achieve the same cutting length of the cutting edge in Embodiment 2 of the present invention;

[0082] Figure 7 This is a schematic diagram of the tool trajectory in the precision turning method for complex curved surfaces with equal cutting lengths in Embodiment 2 of the present invention;

[0083] Figure 8 This is a schematic diagram of the feasible region for the tool axis angle in the precision turning method for complex curved surfaces with equal cutting lengths of the cutting edge in Embodiment 2 of the present invention;

[0084] Figure 9 This is a schematic diagram of the feasible region for the cutting edge angle in the precision turning method for complex curved surfaces with equal cutting edge length in Embodiment 2 of the present invention;

[0085] Figure 10 This is a schematic diagram of the cutting edge angle interval division in the precision turning method for complex curved surfaces with equal cutting edge length in Embodiment 2 of the present invention;

[0086] Figure 11 This is a schematic diagram of the optimized cutting edge angle surface in the precision turning method for complex curved surfaces that can achieve equal cutting lengths of the cutting edge in Embodiment 2 of the present invention;

[0087] Figure 12This is a schematic diagram of the total arc length of the trajectory of each cutting edge angle interval in the precision turning method for complex curved surfaces that can achieve equal cutting length of cutting edge in Embodiment 2 of the present invention;

[0088] Figure 13 This is a partial tool axis vector diagram of the precision turning method for complex curved surfaces with equal cutting lengths in Embodiment 2 of the present invention. Detailed Implementation

[0089] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0090] Example 1:

[0091] like Figure 1 As shown, this embodiment of the invention provides a method for precision turning of complex curved surfaces that can achieve cutting lengths of equal cutting edge, specifically including the following steps:

[0092] Obtain the surface to be processed and the surface processing parameters. The surface processing parameters include the generatrix point set data, the number of spiral points per revolution, and the tool parameters. In this embodiment, the generatrix point set data specifically includes the starting point and ending point coordinates of the connecting line segments of the generatrix point set, and the tool parameters specifically include the tool arc radius, the tool holder width, and the tool length.

[0093] The turning tool path is planned on the surface to be machined, and trajectory points are generated along the turning tool path. In this embodiment, the turning tool path is planned using the isoparametric method, and the discretization method uses equal-angle discretization. Its expression is:

[0094] ;

[0095] in, Represents the three-dimensional coordinates of the trajectory points. This indicates the height of the trajectory point from the center line of rotation. Represents the first point on the busbar point set points Axis coordinates Represents the first point on the busbar point set points Axis coordinates Represents the first point on the busbar point set The height of each point from the center line of rotation, Represents the first point on the busbar point set The height of each point from the center line of rotation, n = 1,2,…,N-1 This indicates the number of spiral points per revolution.

[0096] Calculate the arc length and geometric parameters of the turning toolpath, where the expression for calculating the arc length of the turning toolpath is:

[0097] ;

[0098] in, This represents the arc length of the turning toolpath. Represents the distance between two adjacent trajectory points Axis coordinate difference Represents the distance between two adjacent trajectory points Axis coordinate difference Represents the distance between two adjacent trajectory points The difference between the axis coordinates.

[0099] The geometric parameters of the trajectory points include the normal vector, the normal vector and the normal vector. The angle between the two vectors, where the expression for calculating the normal vector is:

[0100] ;

[0101] in, Indicates the first The normal vector of each trajectory point Represents the three-dimensional coordinates of the trajectory points. This indicates the height of the trajectory point from the center line of rotation.

[0102] Normal vector and The expression for calculating the included angle is:

[0103] ;

[0104] in, Indicates the first The normal vector of each trajectory point and The included angle, express The unit vector of the axis is [0,0,1].

[0105] The trajectory points are re-interpolated using arc length micro-elements as the spacing to refine the trajectory points, resulting in refined trajectory points and their corresponding geometric parameters. In this embodiment, the arc length micro-elements are the minimum value among the arc length spacings of all adjacent trajectory points.

[0106] like Figure 2 As shown, the safe tool axis angle range for each trajectory point on the turning toolpath is calculated based on the surface to be machined and the tool parameters. The safe tool axis angle range includes safe angle intervals for local non-interference and global non-interference, specifically including:

[0107] S1. Select a tool that satisfies the condition of local non-interference safety tool axis angle range. The expression for the condition of local non-interference safety tool axis angle range is:

[0108] ;

[0109] in, Indicates the radius of the tool arc. This represents the minimum concave surface radius of the surface to be processed.

[0110] S2. Next, the safe angle range for global non-interference is calculated. In this embodiment, the method for calculating the safe angle range for global non-interference is the ray method.

[0111] Normal compensation is performed on the trajectory points, with the compensation distance being the tool arc radius. The tool center point is calculated, and its expression is as follows:

[0112] ;

[0113] in, Indicates the first The three-dimensional coordinates of the tool center point corresponding to each trajectory point Indicates the first The three-dimensional coordinates of the trajectory points , , The first The normal vector of each trajectory point is in axis, axis, Components on the axis.

[0114] Due to the rotational symmetry of the surface of revolution, the three-dimensional coordinates of the tool center point are simplified to two-dimensional coordinates, and their expression is:

[0115] ;

[0116] in, Indicates the first The two-dimensional x-coordinate of the tool center point corresponding to each trajectory point Indicates the first The two-dimensional ordinate of the tool center point corresponding to each trajectory point.

[0117] The rz plane is obtained by combining the two-dimensional coordinates of the tool center point corresponding to all trajectory points.

[0118] S3. Using a three-stage stepping formula to substitute the tool axis angle, calculate the two-dimensional coordinates of the starting and ending points of the tool boundary. The expression for the three-stage stepping formula of the tool axis angle is:

[0119] ;

[0120] in, Indicates the cutter axis angle. , This indicates the range of safe tool axis angles obtained from the first step. This indicates the range of safe tool axis angles obtained from the second-stage stepping.

[0121] The meaning of three-level stepping is: when performing a level one stepping, ... (This means taking values ​​from 0° to 180°, in units of 10°) as the tool axis angle and substituting them into subsequent calculations to obtain the safe tool axis angle range for the first step. Then, the second step is performed... (Meaning: from) Left end value -10 to The value at the right end is increased by 10 (in 1° increments) and used as the tool axis angle in subsequent calculations to obtain the safe tool axis angle range for the second-level stepping. Finally, a third-level stepping is performed to... (Meaning: from) Starting from the left end value -1 to The value on the right is incremented by 1, and the value is taken in 0.1° increments as the tool axis angle. This value is then substituted into subsequent calculations to obtain the safe tool axis angle range obtained by the three-level stepping method. The three-level stepping calculation method can effectively reduce computational costs, and the result of each level of calculation is for the purpose of more accurate calculation in the next level.

[0122] The formula for calculating the two-dimensional coordinates of the tool boundary start and end points is as follows:

[0123] ;

[0124] ;

[0125] ;

[0126] ;

[0127] in, Indicates the first The starting point of the tool's right boundary corresponding to each trajectory point Indicates the first The right boundary endpoint of the tool corresponding to each trajectory point Indicates the first The starting point of the tool's left boundary corresponding to each trajectory point. Indicates the first The left boundary endpoint of the tool corresponding to each trajectory point Indicates the width of the tool holder. Indicates the length of the cutting tool. Indicates the first The two-dimensional coordinates of the starting point of the right boundary of the tool corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's right boundary endpoint corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's left boundary starting point corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's left boundary endpoint corresponding to each trajectory point.

[0128] S4. Based on the coordinates of the starting and ending points of the tool boundary, obtain the left and right boundary segments of the tool. Determine whether the left and right boundary segments of the tool intersect the generatrix of the rz plane. The expression for the determination condition is:

[0129] ;

[0130] ;

[0131] in, Indicates the position of the intersection point within the boundary line segment of the tool holder. This indicates the position of the intersection point within the connecting line segment of the busbar point set. Indicates the starting coordinates of the tool holder boundary line segment. Indicates the coordinates of the endpoint of the tool holder boundary line segment. This represents the starting coordinates of the line segment connecting the set of busbar points. This represents the coordinates of the endpoint of the line segment connecting the set of points on the busbar. It indicates and signifies.

[0132] If at least one of the left and right boundary segments of the tool satisfies the judgment condition, it indicates that there is interference between the tool and the surface to be machined; otherwise, there is no interference, and the maximum non-interference continuous angle interval is obtained.

[0133] S5. Repeat steps S3 to S4 until the maximum non-interference continuous angle interval corresponding to the tool axis angle of the third step is obtained.

[0134] S6. The safe tool axis angle range is obtained by reducing the end of the maximum non-interference continuous angle interval corresponding to the tool axis angle of the third step by a safety threshold. In this embodiment, the safety threshold is 2°.

[0135] Combination Figure 3 Based on the conversion formula between cutting edge angle and cutting axis angle, calculate the range of cutting edge angle (the effective cutting angle range) for each trajectory point. The conversion formula between cutting edge angle and cutting axis angle is as follows:

[0136] ;

[0137] in, Indicates the blade angle. Represents the normal vector of the trajectory point and The included angle, express The unit vector along the axis is [0,0,1]. Indicates the angle of the cutter axis.

[0138] Two curves are fitted to the upper and lower limits of the cutting edge angle range for each trajectory point. In this embodiment, the horizontal axis of the curve represents the arc length of the turning tool path, and the vertical axis represents the cutting edge angle. The curves are then uniformly divided to obtain cutting edge angle intervals. The beginning and end of each interval represent the maximum and minimum cutting edge angle values ​​among all trajectory points, respectively, which can be expressed as:

[0139] ;

[0140] in, Indicates the range of blade angles. This represents the maximum value of the blade angle among all trajectory points. This represents the minimum blade angle among all trajectory points. Indicates the number of blade angle ranges. This indicates the size of the range of blade angles.

[0141] like Figure 4 As shown, an initial cutting edge angle spline curve is constructed, and a genetic algorithm is used to optimize it to maximize the uniformity of the effective cutting path length of the cutting edge, resulting in the cutting edge angle spline curve, specifically including:

[0142] D1. Construct an initial blade angle spline curve. Select an appropriate number of control points based on the curve complexity. In order to avoid overfitting, in this embodiment, the number of control points on the initial blade angle spline curve does not exceed 1 / 100 of the number of trajectory points.

[0143] D2. Adjust the positions of the control points so that the initial x-coordinate of each control point is the sum of the x-coordinate of the previous control point and the arc length of the turning toolpath divided by the total number of control points. Note that the x-coordinate of the first control point is 0, and the y-coordinate is... ,in, Indicates weight, , This indicates the upper limit of the blade angle of the trajectory point corresponding to the horizontal coordinate of the control point. This indicates the lower limit of the blade angle of the trajectory point corresponding to the x-coordinate of the control point. Indicates the first The blade angle of each control point, i.e., its ordinate.

[0144] D3. Using the minimization of the root mean square error of the total arc length distribution for each blade angle interval as the objective function, a genetic algorithm is used to optimize the weights in the ordinate of the control points, resulting in an optimized blade angle spline curve. The expression for calculating the total arc length of the blade angle interval is:

[0145] ;

[0146] in, Indicates the first The total arc length of each blade angle range Indicates the first The blade angle range where each trajectory point is located Indicates the first The number of trajectory points within a blade angle range Let represent the infinitesimal element representing the arc length of the trajectory between two adjacent points. Indicates the first Index of the blade angle interval where each trajectory point is located.

[0147] D4. Repeat D3 until the root mean square error of the total arc length distribution of each blade angle interval of the blade angle spline curve is less than 10 and the maximum relative arc length deviation is less than 0.1. Use this as the blade angle spline curve.

[0148] Finally, the blade angle spline curve is discretized, and the points obtained by discretization on the blade angle spline curve represent the blade angles of the trajectory points with the same horizontal coordinate.

[0149] Based on the conversion formula between the cutting edge angle and the cutting axis angle, the cutting edge angle of the trajectory point is converted into its corresponding cutting axis vector.

[0150] Example 2:

[0151] Based on Example 1, Figure 5 The example shown is a finishing machining of a parabolic surface of revolution. The turning tool is a circular arc turning tool with a radius of 3mm, a shank width of 6mm, and a tool length of 100mm. The generatrix of the parabolic surface of revolution is shown below. Figure 6 As shown, 180 trajectory points are discretized at equal angles in each revolution of the busbar point set, generating a total of 17,722 spiral trajectory points.

[0152] It should be noted that all data below are in the International System of Units (SI), with length in mm and angle in °.

[0153] Combination Figure 7 The calculated arc length of the trajectory is 7089.7143, and the arc length of the smallest adjacent trajectory point is 0.0737. This is used as the infinitesimal element of the arc length. Interpolating the arc length of the trajectory yields 762,787 new trajectory points.

[0154] The minimum radius of curvature of the surface is calculated to be 3.1104, and the radius of the tool arc is 3, satisfying the local non-interference condition; the feasible region for the tool axis angle is then calculated using the ray casting method, as shown below. Figure 8 As shown, based on this, the upper and lower limits of the cutter axis angle are reduced inward by 2° as the safe cutter axis angle range.

[0155] Combination Figure 9 The feasible region for the maximum blade angle is obtained through the conversion formula between blade angle and blade axis angle. The upper limit is a maximum of 90.7 and the lower limit is a minimum of -88.6. Dividing each angle interval into 2.0172 intervals, 89 blade angle intervals are obtained, as shown below. Figure 10 As shown.

[0156] A blade angle spline curve is constructed and optimized using a genetic algorithm to obtain the final result. Figure 11 The curve shown has a total arc length for each angular interval as follows: Figure 12 As shown, the deviation between the trajectory arc length and the average arc length of each cutting edge angle interval is less than 0.1, which can ensure that the tool is fully utilized during the turning process and the actual cutting trajectory arc length of the part of the cutting edge participating in the cutting is approximately equal.

[0157] Therefore, by using the conversion formula between the cutting edge angle and the cutting axis angle, the optimized cutting edge angle is converted into the cutting axis angle, and then the cutting axis vector of each trajectory point is obtained. The cutting axis vector drawn by uniform sampling is as follows: Figure 13 As shown.

[0158] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for precision turning of complex curved surfaces with equal cutting lengths of the cutting edge, characterized in that, include: Obtain the surface to be processed and the surface processing parameters; Plan the turning tool path on the surface to be machined and discretize the trajectory points; Calculate the arc length and geometric parameters of the turning toolpath. Using arc length micro-elements as the spacing, the trajectory points are refined by interpolating the trajectory points in the turning tool path, and the geometric parameters of the trajectory points are calculated. Calculate the safe tool axis angle range for each trajectory point on the turning tool path based on the surface to be machined and the surface machining parameters; The corresponding blade angle range is calculated based on the safe blade axis angle range of each trajectory point. The upper and lower limits of the blade angle range of each trajectory point are fitted to obtain curves, and the curves are divided to obtain multiple blade angle intervals. An initial cutting edge angle spline curve is constructed. Based on the cutting edge angle range, a genetic algorithm is used to optimize the initial cutting edge angle spline curve to maximize the uniformity of the effective cutting path length of the cutting edge, thus obtaining the cutting edge angle spline curve. The tool axis vector for each trajectory point is calculated from the spline curve of the cutting edge angle.

2. The method for precision turning of complex curved surfaces with equal cutting lengths as described in claim 1, characterized in that, The surface machining parameters include generatrix point set data, number of spiral points per revolution, and tool parameters. The generatrix point set data includes the starting and ending coordinates of the connecting line segments of the generatrix point set. The tool parameters include the tool arc radius, tool holder width, and tool length.

3. The method for precision turning of complex curved surfaces with equal cutting lengths of the cutting edge as described in claim 1, characterized in that, The turning toolpath is planned using the isoparametric method, and the trajectory points are generated using isoangular discretization. The expression for isoangular discretization is: ； in, Represents the three-dimensional coordinates of the trajectory points. This indicates the height of the trajectory point from the center line of rotation. Represents the first point on the busbar point set points Axis coordinates Represents the first point on the busbar point set points Axis coordinates Represents the first point on the busbar point set The height of each point from the center line of rotation, Represents the first point on the busbar point set The height of each point from the center line of rotation, n = 1,2,…,N-1 This indicates the number of spiral points per revolution.

4. The method for precision turning of complex curved surfaces with equal cutting lengths as described in claim 1, characterized in that, The expression for calculating the arc length of the turning toolpath is: ； in, This represents the arc length of the turning toolpath. Represents the distance between two adjacent trajectory points Axis coordinate difference Represents the distance between two adjacent trajectory points Axis coordinate difference Represents the distance between two adjacent trajectory points Axis coordinate difference; The geometric parameters of the trajectory point include the normal vector, the normal vector, and the geometric parameters of the trajectory point. The included angle; The expression for calculating the normal vector is: ； in, Indicates the first The normal vector of each trajectory point Represents the three-dimensional coordinates of the trajectory points. This indicates the height of the trajectory point from the center line of rotation; The normal vector and The expression for calculating the included angle is: ； in, Indicates the first The normal vector of each trajectory point and The included angle, express The unit vector of the axis is [0,0,1].

5. The method for precision turning of complex curved surfaces with equal cutting lengths of the cutting edge as described in claim 1, characterized in that, The arc length micro-element is the minimum value among the arc length spacings of all adjacent trajectory points.

6. The method for precision turning of complex curved surfaces with equal cutting lengths of the cutting edge as described in claim 1, characterized in that, The method for determining the range of the safety cutter shaft angle includes: S1. Select a tool that meets the condition of local non-interference safety tool axis angle range. The expression for the condition of local non-interference safety tool axis angle range is: ； in, Indicates the radius of the tool arc. Represents the minimum concave surface radius of the surface to be processed; S2. Perform normal compensation on the trajectory points, with the compensation distance being the tool arc radius. Calculate the tool center point, and its expression is: ； in, Indicates the first The three-dimensional coordinates of the tool center point corresponding to each trajectory point Indicates the first The three-dimensional coordinates of the trajectory points , , The first The normal vector of each trajectory point is in axis, axis, Components on the axis; The three-dimensional coordinates of the tool center point are simplified to two-dimensional coordinates in the rz plane, and the expression is: ； in, Indicates the first The two-dimensional x-coordinate of the tool center point corresponding to each trajectory point Indicates the first The two-dimensional ordinate of the tool center point corresponding to each trajectory point; The rz plane is obtained by combining the two-dimensional coordinates of the tool center point corresponding to all trajectory points; S3. Using a three-stage stepping formula to substitute the tool axis angle, calculate the two-dimensional coordinates of the starting and ending points of the tool boundary. The expression for the three-stage stepping formula of the tool axis angle is as follows: ； in, Indicates the cutter axis angle. , This indicates the range of safe tool axis angles obtained from the first step. This indicates the range of safe tool axis angles obtained from the second-stage stepping; The calculation expressions for the two-dimensional coordinates of the starting and ending points of the tool boundary are as follows: ； ； ； ； in, Indicates the first The starting point of the tool's right boundary corresponding to each trajectory point Indicates the first The right boundary endpoint of the tool corresponding to each trajectory point Indicates the first The left boundary starting point of the tool corresponding to each trajectory point Indicates the first The left boundary endpoint of the tool corresponding to each trajectory point Indicates the width of the tool holder. Indicates the length of the cutting tool. Indicates the first The two-dimensional coordinates of the starting point of the right boundary of the tool corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's right boundary endpoint corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's left boundary starting point corresponding to each trajectory point. Indicates the first The two-dimensional coordinates of the tool's left boundary endpoint corresponding to each trajectory point; S4. Based on the coordinates of the starting and ending points of the tool boundary, obtain the left and right boundary segments of the tool. Determine whether the left and right boundary segments of the tool intersect the generatrix of the rz plane. The expression for the determination condition is: ； ； in, Indicates the position of the intersection point within the boundary line segment of the tool holder. This indicates the position of the intersection point within the connecting line segment of the busbar point set. Indicates the starting coordinates of the tool holder boundary line segment. Indicates the coordinates of the endpoint of the tool holder boundary line segment. This represents the starting coordinates of the line segment connecting the set of busbar points. This represents the coordinates of the endpoint of the line segment connecting the set of points on the busbar. It indicates and signifies; If at least one of the left boundary line segment and the right boundary line segment of the tool satisfies the judgment condition, it indicates that there is interference between the tool and the surface to be machined; otherwise, there is no interference, and the maximum non-interference continuous angle interval is obtained. S5. Repeat steps S3 to S4 until the maximum non-interference continuous angle interval corresponding to the tool axis angle of the third step is obtained. S6. Reduce the safety threshold at the end of the maximum non-interference continuous angle interval corresponding to the tool axis angle of the third step to obtain the safe tool axis angle range.

7. The method for precision turning of complex curved surfaces with equal cutting lengths of the cutting edge as described in claim 1, characterized in that, The corresponding cutting edge angle range, calculated based on the safety cutting edge angle range of each trajectory point, is obtained through a cutting edge angle-to-cutting edge angle conversion formula. This conversion formula is as follows: ； in, Indicates the blade angle. Represents the normal vector of the trajectory point and The included angle, express The unit vector along the axis is [0,0,1]. Indicates the angle of the cutter axis.

8. The method for precision turning of complex curved surfaces with equal cutting lengths of the cutting edge as described in claim 1, characterized in that, The horizontal axis of the curve represents the arc length of the turning tool path, and the vertical axis represents the cutting edge angle. The blade angle interval is divided uniformly, and the maximum and minimum values ​​of the blade angles among all trajectory points are taken as the starting points of the blade angle interval, respectively. The expression is as follows: ； in, Indicates the range of blade angles. This represents the maximum value of the blade angle among all trajectory points. This represents the minimum blade angle among all trajectory points. Indicates the number of blade angle ranges. This indicates the size of the range of blade angles.

9. The method for precision turning of complex curved surfaces with equal cutting lengths of the cutting edge as described in claim 1, characterized in that, The initial cutting edge angle spline curve is constructed, and then optimized using a genetic algorithm based on the cutting edge angle range to maximize the uniformity of the effective cutting path length, resulting in the following cutting edge angle spline curve: D1. Construct an initial blade angle spline curve, wherein the control points on the initial blade angle spline curve do not exceed 1 / 100 of the number of trajectory points; D2. Adjust the positions of the control points so that the initial x-coordinate of each control point is the sum of the x-coordinate of the previous control point and the arc length of the turning toolpath divided by the total number of control points. The x-coordinate of the first control point should be 0, and the y-coordinate should be... ,in, Indicates weight, , This indicates the upper limit of the blade angle of the trajectory point corresponding to the horizontal coordinate of the control point. This indicates the lower limit of the blade angle of the trajectory point corresponding to the x-coordinate of the control point. Indicates the first The blade angle of each control point, i.e., its ordinate; D3. Using the minimization of the root mean square error of the total arc length distribution for each blade angle interval as the objective function, a genetic algorithm is used to optimize the weights in the ordinate of the control points, resulting in an optimized blade angle spline curve. The expression for calculating the total arc length of the blade angle interval is as follows: ； in, Indicates the first The total arc length of each blade angle range Indicates the first The blade angle range where each trajectory point is located Indicates the first The number of trajectory points within a blade angle range Let represent the infinitesimal element representing the arc length of the trajectory between two adjacent points. Indicates the first Index of the blade angle interval where each trajectory point is located; D4. Repeat D3 until the root mean square error of the total arc length distribution of each blade angle interval of the blade angle spline curve is less than 10 and the maximum relative arc length deviation is less than 0.

1. Use this as the blade angle spline curve.

10. The method for precision turning of complex curved surfaces with equal cutting lengths as described in claim 1, characterized in that, The process of calculating the tool axis vector for each trajectory point from the tool edge angle spline curve includes: Discretize the blade angle spline curve, where each point on the blade angle spline curve represents the blade angle of the trajectory point corresponding to the same abscissa; Based on the conversion formula between the cutting edge angle and the cutting axis angle, the corresponding cutting axis vector is calculated from the cutting edge angle of each trajectory point.

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