A side milling cutter planning method for weight adjustment of non-developable ruled surfaces

Abstract

The present invention discloses a side milling cutter position planning method for weight adjustment of non-developable ruled surfaces. The method first completes the non-developable ruled surface construction based on the original control points; secondly, the original two-point offset algorithm is used to obtain the initial tool axis vector with equal parameters, and the maximum overcut position of the corresponding side milling area is solved; then the maximum overcut offset position and the initial tool vector are used to form two segmented vectors, and the weight factor is calculated; finally, the side milling cutter axis vector after weight adjustment is obtained. In addition, the method calculates different weight factors for different distortion positions, which can be better adapted to the side milling of non-developable ruled surfaces. The present invention focuses on the side milling processing errors of non-developable ruled surfaces, especially the overcut and individual positioning tool errors, and completes the purpose of outputting the tool axis vector by the weight optimization algorithm with the initial tool axis vector as the starting point, thereby improving the side milling processing accuracy and efficiency, and providing certain technical support for the field of modern mechanical manufacturing and processing.

Description

Technical Field

[0001] The present invention relates to the field of mechanical processing, and in particular to a side milling cutter position planning method for adjusting the weight of a non-developable ruled surface. Background Art

[0002] Non-developable ruled surfaces are widely used in mechanical processing fields such as aerospace, energy and chemical engineering. As the geometric characteristic surfaces of functional key components, such as compressors and turbines, the rapid development of modern mechanical processing industry has put forward higher requirements for the surface accuracy of such parts. In the past 20 years, researchers have been committed to studying and optimizing the tool trajectory of non-developable ruled surfaces to minimize the deviation between the design surface and the machined surface and achieve the goal of high-precision processing. At present, the main popular methods for five-axis CNC machining of non-developable ruled surfaces are point milling with ball-end milling cutters and side milling with cylindrical and conical cutters. Point milling uses a point contact method, which is less efficient than the line contact method of side milling. Due to the characteristics of non-developable ruled surfaces, any tool with a radius other than 0 will produce theoretical errors when side milling them, including overcutting and undercutting errors. Overcutting errors are more difficult to correct, while undercutting can be reduced by error compensation technology to meet the machining accuracy requirements.

[0003] In the tool planning algorithm for side milling on non-developable ruled surfaces, the initial algorithm selected points on the straight generatrix of the non-developable ruled surface for normal offsets to form the tool axis vector. The difference lies in the number of offset points selected. Compared to single-point offsets, which produce overcutting errors at both the blade root and blade tip, two-point offsets ensure errors at the blade root and blade tip, but can produce larger overcutting errors at the blade mid-blade. Three-point and four-point offsets require first establishing a two-point offset model, then calculating the complete tool axis vector using the slip interval. The determination of the slip interval places certain requirements on the density of the wire interpolation, and also increases the number of equations to solve and the number of unknowns. This algorithm is relatively accurate but computationally complex. With the continuous development of tool planning algorithms, envelope theory has been proposed. This theory first obtains the initial tool axis vector based on point normal offsets, then determines the tool axis trajectory surface through principles such as least squares consistent approximation, ultimately improving the fit between the tool envelope surface and the designed surface. The introduction of envelope theory has greatly reduced the overall deviation of the impeller, but this method can only be defined when all tool axis vectors are known. It is difficult to position the tool individually considering the error distribution, and the method and process are relatively complicated, which limits its application in engineering practice.

[0004] In summary, various optimization algorithms currently exist for side milling of non-developable ruled surfaces, but factors such as efficiency, ease of operation, and engineering practicality must also be considered during tool position planning. In this area of fundamental research, Chinese patent application number CN201910294854.8 discloses a tool position correction method for five-axis side milling of non-developable ruled surfaces. This method corrects the tool position based on the actual tool axis swept surface and the offset tool axis curved surface, but does not consider the issues of individual tool positioning and errors in the specific tool axis vector. Summary of the Invention

[0005] The problem solved by the present invention is to provide a method for planning the side milling cutter position with weight adjustment for non-developable ruled surfaces. The method first performs cubic uniform B-spline curve fitting encryption processing based on the original control points to complete the non-developable ruled surface construction; secondly, the original two-point offset algorithm is used to obtain the initial tool axis vector with equal parameters; then, based on the initial tool axis vector, the maximum overcut error position corresponding to the initial tool axis vector is solved; two segmented vectors are formed by the initial tool axis vector and the maximum overcut error position offset point; further, the maximum overcut error value is solved in the side milling area corresponding to the two segmented vectors, and the weight factor is obtained by comparison; finally, the weighted side milling cutter axis vector is obtained with the weight factor, the maximum overcut position offset point and the initial tool axis vector. The above steps are applied to all the initial tool axis vectors obtained with equal parameters to obtain all the tool position information after the non-developable ruled surface weight adjustment. In addition, the method can calculate different weight factors for different distortion positions of the non-developable ruled surface, which is better adapted to the side milling processing of the non-developable ruled surface. The invention focuses on the machining errors generated during the five-axis side milling of non-developable ruled surfaces, especially considering the error distribution of overcutting errors and individually positioned tools. Combined with the structural characteristics of non-developable ruled surfaces, the invention achieves the purpose of outputting the tool axis vector through a weighted optimization algorithm with the initial tool axis vector as the starting point, thereby improving the machining accuracy of five-axis side milling of non-developable ruled surfaces and providing certain technical support for the field of modern mechanical manufacturing and processing.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces comprises the following steps:

[0008] 1) Perform cubic uniform B-spline curve fitting based on the given original control points of the non-developable ruled surface to form a smooth transition surface form;

[0009] 2) Using the original two-point offset algorithm and other parameters to obtain the initial tool axis vector;

[0010] 3) Based on the initial tool axis vector, solve the maximum overcutting error position corresponding to the initial tool axis vector;

[0011] 4) Two segment vectors are formed by the initial tool axis vector and the maximum overcutting error offset point;

[0012] 5) Calculate the maximum overcut error value in the side milling area corresponding to the two segmented vectors respectively, and compare them to obtain the weight factor;

[0013] 6) Obtain the side milling cutter axis vector after weight adjustment using the weight factor, the maximum overcut position offset point, and the initial cutter axis vector, and repeat steps 3)-5) to obtain all weight-adjusted planned cutter vectors;

[0014] 7) Use weight adjustment to plan the tool arrow to complete the side milling of non-developable ruled surface.

[0015] A further improvement of the present invention is that the specific implementation method of step 1) is as follows:

[0016] For the impeller blades, the direction from the inlet to the outlet is defined as U, and the direction from the root to the tip is defined as V. The original control points are fitted and encrypted using the cubic uniform B-spline curve method. The corresponding encrypted points at the root and tip are connected to form a non-developable ruled surface with uniform transition and smoothness. The equation of the non-developable ruled surface is expressed as follows:

[0017] S(u,v)=(1-v)×C1(u)+v×C2(u), 0≤u≤1; 0≤v≤1

[0018] Where S(u,v) represents a non-developable ruled surface, C1(u) and C2(u) are two conductors on the non-developable ruled surface, and both are cubic uniform B-spline curves.

[0019] A further improvement of the present invention is that the specific implementation method of step 2) is as follows:

[0020] The original two-point offset algorithm is used to encrypt the points of the two cubic uniform B-spline curves obtained in step 1). The side milling cutter contacts are selected by advancing forward from the same starting position using the equal parameter method, and the selected cutter contacts are normal-biased to obtain the initial tool axis vector; the original two-point offset algorithm, that is, the two points on the same straight line are connected correspondingly after normal offset to form the tool axis vector; the unit normal vector is obtained by solving the partial derivative of the U-direction cubic uniform B-spline curve equation and the V-direction unit vector, and the cross product of the two is obtained.

[0021] A further improvement of the present invention is that the specific implementation of step 3) is as follows:

[0022] Based on the initial tool axis vector, the position of the maximum overcut error is solved, wherein the solution process involves the step size accuracy; the maximum overcut position generated by the initial tool axis vector is located in the middle of the leaf; to speed up the solution, a preset is first made, and then exploration is carried out from the preset position to both sides until the maximum overcut position is obtained; then, the maximum overcut point is offset along the unit normal vector of the non-developable ruled surface.

[0023] A further improvement of the present invention is that the specific implementation of step 4) is as follows:

[0024] Due to the different characteristics of the unit normal vectors at different positions of the same straight generatrix on the non-developable ruled surface, the maximum overcut offset point is not on the initial tool axis vector, that is, the initial tool vector is not parallel to the corresponding straight generatrix. Therefore, two segmented vectors can be formed by connecting the two points of the initial tool axis vector and the maximum overcut offset point respectively.

[0025] A further improvement of the present invention is that the specific implementation of step 5) is as follows:

[0026] For the two segmented vectors determined in step 4), the maximum overcutting error values are respectively solved in the corresponding side milling areas, and the weight factor is calculated based on the maximum overcutting error values of the two segmented vectors.

[0027] A further improvement of the present invention is that the specific implementation of step 6) is as follows:

[0028] The weighted side milling cutter axis vector is obtained by using the weight factor, the maximum overcut offset point, and the initial tool axis vector. The new two-point offset point position is then calculated, and the tool axis vector that meets the requirements for the non-developable ruled surface is planned. The expressions for calculating the new tool axis vector and the new two-point offset point position are as follows:

[0029]

[0030]

[0031] in, are two segment vectors respectively, t is the weight factor, is the tool axis vector after weight adjustment, and P1' and P2' are the new two-point offset points.

[0032] A further improvement of the present invention is that, in step 7), the tool used for the side milling of the non-developable ruled surface is a rotary tool.

[0033] A further improvement of the present invention is that the rotary tool is a cylindrical tool or a conical tool.

[0034] The present invention has at least the following beneficial technical effects:

[0035] The present invention focuses on the theoretical error in the side milling process of non-developable ruled surfaces, combines the characteristics of non-developable ruled surfaces and machining processes, and innovatively proposes a side milling cutter position planning method for weight adjustment of non-developable ruled surfaces. First, based on the given original control points, the non-developable ruled surface construction is completed by the cubic uniform B-spline method; secondly, the original two-point offset algorithm is adopted to obtain the initial tool axis vector with equal parameters, and the maximum overcut error position of the side milling area corresponding to the vector is solved; then, two segmented vectors are formed with the maximum overcut position offset point and the initial tool axis vector, and the weight factor is calculated by the side milling area corresponding to the two segmented vectors; finally, the side milling cutter axis vector after weight adjustment is obtained. Applying the above steps to all initial tool axes can obtain all tool position information. This method uses the initial tool axis vector as the starting point, solves the maximum overcut position under the initial tool axis vector, and uses this as a parameter to call the weighted adjusted tool axis vector, so the calculated new tool axis vector can greatly reduce the overcut error. At the same time, each initial tool axis vector corresponds to a different side milling area of the non-developable ruled surface, so the maximum overcut values generated are not consistent. Therefore, this method can calculate different weighted tool vectors for different torsion positions on the non-developable ruled surface, and can subsequently better adapt to specific practical operations by fine-tuning the weight factors. In summary, this method can effectively improve the machining accuracy of five-axis side milling of non-developable ruled surfaces, especially for overcutting and the need to individually correct the tool axis vector at a certain position. It has good engineering practicality and provides certain technical support for the field of modern mechanical manufacturing and processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The impeller of the embodiment of the present invention;

[0037] Figure 2 A non-developable ruled surface according to an embodiment of the present invention;

[0038] Figure 3 are the discrete straight generatrix with equal parameters and the initial knife vector;

[0039] Figure 4 A three-dimensional schematic diagram of the tool position planning method for weight adjustment;

[0040] Figure 5 A two-dimensional schematic diagram of the weight-adjusted tool location planning method;

[0041] Figure 6 This is a statistical comparison chart of errors at the same busbar;

[0042] Figure 7 The error distribution diagram of the whole blade processed by the tool vector is adjusted for weight;

[0043] Figure 8 This is the error distribution diagram of the initial tool vector machining the whole blade;

[0044] Figure 9This is a flow chart of the tool position planning method for weight adjustment of the present invention. DETAILED DESCRIPTION

[0045] The exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art. It should be noted that, unless there is a conflict, the embodiments of the present disclosure and the features described in the embodiments can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0046] Figure 1 The present invention includes an impeller with a non-developable ruled surface. The present invention is described in detail using a blade of the impeller, wherein the curved surface of the blade is a non-developable ruled surface. The specific implementation is as follows:

[0047] 1. Based on the given original control points of the non-developable ruled surface, a cubic uniform B-spline curve is fitted to form a smooth transition surface. Based on the given original control points of the blade root and blade tip, a cubic uniform B-spline curve is fitted and encrypted to obtain a smooth transition surface, such as Figure 2 shown.

[0048] In the embodiment, the impeller blade is a non-developable ruled surface. The blade is defined as U-direction from the inlet to the outlet, and V-direction from the blade root to the blade tip. The original control points are fitted with a cubic uniform B-spline curve, and interpolation encryption is performed. The blade root and the blade tip are connected to form a non-developable ruled surface with uniform transition and smoothness. The smooth transition surface form ensures the smoothness of the tool movement to a certain extent, avoiding the deceleration and stopping of the five-axis machining machine. This embodiment gives the blade root and blade tip an equal number of original control points, both n+1, and uses a cubic uniform B-spline curve to represent the adjacent control points, where the equation of the i-th segment curve is expressed as:

[0049]

[0050] Among them, t is the surface parameter, the parameter range is [0,1], and it changes evenly according to the position of the control point, d i To control the vertex, S i (t) is the curve equation, i=0,1,2…n-1.

[0051] After fitting the original control points, an interpolation parameter is selected. In this example, a parameter of 0.2 is selected, meaning that four points are added between two control points after the interpolation process. Based on the specific construction method of the non-developable ruled surface, the corresponding interpolation points at the blade root and blade tip are connected, ultimately resulting in a uniform and smooth transition surface. The equation for the non-developable ruled surface is as follows:

[0052] S(u,v)=(1-v)×C1(u)+v×C2(u), (0≤u≤1; 0≤v≤1)

[0053] Where S(u,v) represents a non-developable ruled surface, C1(u) and C2(u) are two conductors on the non-developable ruled surface, and both are cubic uniform B-spline curves. The cubic uniform B-spline curve is expressed as follows:

[0054]

[0055] Among them, P i are the control points of the cubic uniform B-spline curve, B i,k (u) is the cubic uniform B-spline curve basis function, which is obtained by using the de Boer-Cox recursion, as shown in the following formula:

[0056]

[0057] Where k is the degree of the B-spline curve. When it is a cubic uniform B-spline curve, k=3. It is formed by two quadratic uniform B-spline curve basis functions B i,2 (u), B i+1,2 (u) is obtained recursively.

[0058] 2. Use the original two-point offset algorithm and equal parameters to obtain the initial tool axis vector. The original two-point offset algorithm, that is, the two points on the same straight bus are connected to form a tool axis vector after normal offset. In this embodiment, the two points on the straight bus are selected as the corresponding points of the blade root and the blade top. In the equal parameter method, first select a starting trajectory of a non-developable ruled surface, consider the embodiment, tool parameters and the problem of ensuring processing accuracy, determine the equal parameter values, and then move forward from the initial trajectory to gradually obtain the remaining trajectory positions. All the acquired trajectory points are normal offset with the position of the non-developable ruled surface where the point is located. The offset distance is a tool radius. In this embodiment, the tool selected is a cylindrical tool, and the tool radius r is 5mm.

[0059] The process of calculating the unit normal vector and offset point is as follows:

[0060] 1) Finding the unit vector in the U direction: Taking a point with equal parameters as an example, the unit tangent vector is obtained by taking the partial derivative of the cubic uniform B-spline curve equation at the point. The expression for the unit tangent vector is as follows:

[0061]

[0062] Among them, S u is the tangent vector to U, B i,3 (u) is the U-direction cubic uniform B-spline curve basis function, P i are the coordinates of the control points;

[0063] 2) Finding the unit vector in the V direction: According to the characteristics of non-developable ruled surfaces, the V direction of the surface is a straight line. The unit vector S can be solved directly based on the corresponding positions of the blade root and blade tip. v ;

[0064] 3) The cross product of the U-direction tangent vector and the V-direction unit vector gives the unit normal vector of the non-developable ruled surface, which is expressed as follows:

[0065]

[0066] in, is the unit normal vector, S u 、S v are the unit vectors in the U and V directions respectively;

[0067] 4) Normal offset: offset the equal parameter trajectory point in the direction of the unit normal vector of the point. The offset distance is a tool radius r. The expression is as follows:

[0068]

[0069] Among them, P' is the point position after offset, r is the tool radius;

[0070] By connecting the offset discrete points, we can get the initial tool axis vector. Here we only take one initial tool axis vector as an example. Figure 3 shown.

[0071] 3. Based on the initial tool axis vector, solve the maximum overcut error position under the corresponding initial tool axis vector. By giving a step size parameter, the maximum overcut error position is solved based on the initial tool axis vector. Among them, the step size determines the accuracy of the maximum overcut position selection. Considering the calculation time and solution accuracy, the solution step size is given to 0.05 for the non-developable ruled surface of this embodiment. Generally, the maximum overcut position generated by the initial tool axis vector is located in the middle of the leaf. In order to speed up the solution speed, it can be preset first, and then explored from the preset position to both sides, and the step size is accumulated until the maximum overcut error position is obtained. After the maximum overcut position is obtained, the maximum overcut position point is normal offset along the unit external normal vector of the point to obtain the maximum overcut error offset point.

[0072] The steps for solving the maximum overcut error position are as follows:

[0073] Set the sampling points and perform uniform interpolation on the initial tool vector and the corresponding straight busbar of the embodiment according to the given step size. First, solve the Euclidean distance d between the initial tool vector and the corresponding point of the straight busbar of the embodiment, and then solve the absolute value E of the difference between the Euclidean distance and the tool radius r. In order to speed up the solution, first compare whether the preset is the maximum overcut position. If it is the maximum overcut position, output it directly. If not, it is necessary to accumulate the step size from the preset position to both sides until the maximum error position is output. The expression for solving the Euclidean distance d and the error value E is as follows:

[0074]

[0075] Where E is the overcut error value, (x1, y1, z1) is a point on the straight generatrix of the non-developable ruled surface, (x2, y2, z2) is the corresponding point on the initial tool axis, and r is the tool radius.

[0076] 4. Two segment vectors are formed by the initial tool axis vector and the maximum overcut error offset point. Due to the characteristics of non-developable ruled surfaces, the unit normal vector directions of the same straight generatrix are not the same, such as Figure 4 Unit normal vector of non-developable ruled surface As shown, the maximum overcut offset point P S With the initial sword They are not on the same straight line. Connect the initial two points P1 and P2 of the tool vector with the maximum overcut offset point P S Two segment vectors can be formed. In the figure, P1 and P2 are the two initial points of the knife vector, P S is the maximum overcut offset point, the maximum overcut value corresponding to the initial tool vector E, C1(u), C2(u), C s (u) are three wires at different positions on the non-developable ruled surface, among which C1(u) and C2(u) are wires at given control points on the non-developable ruled surface, and C s (u) is the conductor at the maximum overcut position.

[0077] 5. Calculate the maximum overcut error value in the side milling area corresponding to the two segment vectors, and compare them to obtain the weight factor. The maximum overcut error values t1 and t2 are calculated in the corresponding side milling area. The weight factor is calculated by the maximum overcut error value of the two segment vectors. The expression of the weight factor is shown as follows:

[0078]

[0079] Among them, t is the weight factor, t1 is The maximum overcut error value of the corresponding side milling area, t2 is Corresponding to the maximum overcut error value in the side milling area.

[0080] 6. Obtain the side milling cutter axis vector after weight adjustment by using the weight factor, the maximum overcut position offset point and the initial cutter axis vector. Repeat steps 3-5 to obtain all weight-adjusted planned cutter vectors. S Solving the weight adjustment of the sword arrow And the maximum overcut offset point P S Adjust the sword arrow with weight By summing and subtracting the two new offset points P1' and P2', we can plan the tool axis vector of the non-developable ruled surface that meets the requirements. Repeat steps 3-5, and use the weighted tool position planning algorithm to adjust all the initial tool axis vectors selected in step 2 and other parameters to obtain the full side milling tool vector of the entire blade. In order to facilitate the view analysis, the maximum overcut error E is magnified, as shown in the following figure: Figure 5 The specific expression is shown as follows:

[0081]

[0082]

[0083] in, is a two-segment vector, t is a weight factor, To adjust the weight of the knife arrow, P1' and P2' are the new two offset points.

[0084] Among them, the weight factor t is explained in detail. First, the weight factor changes with the different positions of the non-developable ruled surface, so it can better perform adaptive adjustment according to the distortion of the non-developable ruled surface. Overcutting error relative When it is larger, the weight factor t is larger, so the tool axis vector after weight adjustment should be toward the area with smaller overcut error value. tilt, The relative overcut is reduced, so that the overcut and undercut errors generated by the blade root and blade tip are basically equal, which is better for subsequent error compensation. At this time, the weight adjustment knife vector's inclination angle α relative to the initial knife vector is shown in the following expression:

[0085]

[0086] Particularly, when t = 0.5, it indicates that the overcut error ratios of the two segment vectors are the same, i.e., α = 0°;

[0087] At the same time, the weight adjustment knife arrow two points P1', P2' and the initial knife arrow two points P1, P2 of the distance difference is E1, E2, the expression is as follows:

[0088]

[0089]

[0090] 7. Use weight adjustment to plan the tool arrow to complete the side milling of non-developable ruled surface.

[0091] By using the above-mentioned non-developable ruled surface weight adjustment side milling cutter position planning method, the weight adjustment tool vector is obtained to perform side milling processing on this embodiment, and the error statistical distribution is as follows: Figure 6 、 7 shown. Figure 6 The error statistics of the weighted adjusted tool arrow and the initial tool arrow at the same straight line are compared. To illustrate the superiority of this method, Figure 6 In addition to selecting the blade root and blade apex connected by a normal offset to form the initial blade vector, the error comparison also used the 25% and 75% blade height points to form the blade vector. Compared with the blade root and blade tip, the cumulative error of the present invention was reduced by 46.27%, and the overcutting rate of the blade vector formed at 25% and 75% blade height was reduced by over 40%. Figure 7 The error distribution diagram of the whole blade produced by the weight adjustment tool position planning method is shown in Figure 2. There is a partial undershoot area at the inlet. This is due to the large torsion at the inlet of the blade in this embodiment. Figure 8 The present invention maintains a certain advantage in the machining error of the initial tool arrow for the entire blade in areas with high torsion, including cumulative error and overcut error, with the cumulative error reduced by 48.07%. The above error distribution verifies the technical prominence of the present invention in the side milling process of non-developable ruled surfaces, especially in terms of overcut error, achieving the goal of improving the machining accuracy of non-developable ruled surfaces. This provides certain technical support for the field of modern mechanical manufacturing and processing, and has certain promotion and application value.

[0092] The above description is merely a preferred embodiment of the present invention and does not limit the present invention to any extent. Based on the present invention, modifications and improvements can be made, which is easy for those engaged in this industry. Therefore, any content that does not depart from the technical solution of the present invention and is simply modified, equivalently changed, and modified by the technical essence of the present invention falls within the scope of protection of the technical solution of the present invention.

Claims

1. A side milling cutter position planning method for adjusting weights on non-developable ruled surfaces, characterized in that: The following steps are involved: 1) Perform cubic uniform B-spline curve fitting based on the given original control points of the non-developable ruled surface to form a smooth transition surface form; 2) Using the original two-point offset algorithm and other parameters to obtain the initial tool axis vector; 3) Based on the initial tool axis vector, solve the maximum overcutting error position corresponding to the initial tool axis vector; 4) Two segment vectors are formed by the initial tool axis vector and the maximum overcutting error offset point; 5) Calculate the maximum overcut error value in the side milling area corresponding to the two segmented vectors respectively, and compare them to obtain the weight factor; 6) Obtain the side milling cutter axis vector after weight adjustment using the weight factor, the maximum overcut position offset point, and the initial cutter axis vector, and repeat steps 3)-5) to obtain all weight-adjusted planned cutter vectors; 7) Use weight adjustment to plan the tool arrow to complete the side milling of non-developable ruled surface.

2. A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces according to claim 1, characterized in that: The specific implementation method of step 1) is as follows: For the impeller blades, the direction from the inlet to the outlet is defined as U, and the direction from the root to the tip is defined as V. The original control points are fitted and encrypted using the cubic uniform B-spline curve method. The corresponding encrypted points at the root and tip are connected to form a non-developable ruled surface with uniform transition and smoothness. The equation of the non-developable ruled surface is expressed as follows: S(u,v)=(1-v)×C1(u)+v×C2(u), 0≤u≤1; 0≤v≤1 Where S(u,v) represents a non-developable ruled surface, C1(u) and C2(u) are two conductors on the non-developable ruled surface, and both are cubic uniform B-spline curves.

3. The method for side milling cutter position planning for non-developable ruled surface weight adjustment according to claim 2, characterized in that: The specific implementation method of step 2) is as follows: The original two-point offset algorithm is used to encrypt the points of the two cubic uniform B-spline curves obtained in step 1). The side milling cutter contacts are selected by advancing forward from the same starting position using the equal parameter method, and the selected cutter contacts are normal-biased to obtain the initial tool axis vector; the original two-point offset algorithm, that is, the two points on the same straight line are connected correspondingly after normal offset to form the tool axis vector; the unit normal vector is obtained by solving the partial derivative of the U-direction cubic uniform B-spline curve equation and the V-direction unit vector, and the cross product of the two is obtained.

4. A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces according to claim 3, characterized in that: The specific implementation of step 3) is as follows: Based on the initial tool axis vector, the position of the maximum overcut error is solved, wherein the solution process involves the step size accuracy; the maximum overcut position generated by the initial tool axis vector is located in the middle of the leaf; to speed up the solution, a preset is first made, and then exploration is carried out from the preset position to both sides until the maximum overcut position is obtained; then, the maximum overcut point is offset along the unit normal vector of the non-developable ruled surface.

5. A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces according to claim 4, characterized in that: The specific implementation of step 4) is as follows: Due to the different characteristics of the unit normal vectors at different positions of the same straight generatrix on the non-developable ruled surface, the maximum overcut offset point is not on the initial tool axis vector, that is, the initial tool vector is not parallel to the corresponding straight generatrix. Therefore, two segmented vectors can be formed by connecting the two points of the initial tool axis vector and the maximum overcut offset point respectively.

6. A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces according to claim 5, characterized in that: The specific implementation of step 5) is as follows: For the two segmented vectors determined in step 4), the maximum overcutting error values are respectively solved in the corresponding side milling areas, and the weight factor is calculated based on the maximum overcutting error values of the two segmented vectors.

7. A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces according to claim 6, characterized in that: The specific implementation of step 6) is as follows: The weighted side milling cutter axis vector is obtained by using the weight factor, the maximum overcut offset point, and the initial tool axis vector. The new two-point offset point position is then calculated, and the tool axis vector that meets the requirements for the non-developable ruled surface is planned. The expressions for calculating the new tool axis vector and the new two-point offset point position are as follows: in, are two segment vectors respectively, t is the weight factor, is the tool axis vector after weight adjustment, and P1' and P2' are the new two-point offset points.

8. The method for side milling cutter position planning by adjusting weight of non-developable ruled surface according to claim 1, characterized in that: In step 7), the tool used for the side milling of the non-developable ruled surface is a rotary tool.

9. A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces according to claim 8, characterized in that: Cylindrical tools are used as rotary tools.

10. A side milling cutter position planning method for adjusting weights of non-developable ruled surfaces according to claim 8, characterized in that: The rotary tool is a conical tool.

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