Automatic tool selection method and system for a blisk flow passage

Abstract

The present disclosure provides an automatic tool selection method and system for a blade disc flow channel, and relates to the technical field of computer-aided manufacturing. The method comprises the following steps: based on a three-dimensional geometric model corresponding to the blade disc, determining a hub spline curve and a casing spline curve corresponding to the flow channel, and performing parameterization processing on the two to obtain initial parameters; based on the initial parameters, performing iterative calculation on each hub feature point to obtain a depth range corresponding to the flow channel; based on the three-dimensional geometric model, determining a suction surface curve and a pressure surface curve corresponding to the flow channel; traversing each feature point in the suction surface curve, determining the nearest feature point corresponding to each feature point from the pressure surface curve based on an iterative search algorithm, and based on each feature point and the corresponding nearest feature point, determining a width range corresponding to the flow channel; and based on the depth range and the width range, determining a target tool corresponding to the flow channel. Through the above method, the machining precision and efficiency of the flow channel are improved.

Description

Technical Field

[0001] This disclosure relates to the field of computer-aided manufacturing technology, and in particular to an automatic tool selection method and system for a bladed disk flow channel. Background Technology

[0002] With the development of computer-aided manufacturing (CAD) technology, its application in the processing and manufacturing field is becoming increasingly widespread. The bladed disk, a core component of aero-engines and gas turbines, has a complex flow channel structure and varied curved surfaces, requiring extremely high machining accuracy and surface quality. By introducing algorithms and intelligent decision-making systems, CAD technology can more scientifically select the most suitable cutting tools and precisely adjust cutting parameters, thereby improving flow channel production efficiency, ensuring product quality, and reducing costs.

[0003] Currently, by extracting the critical profile of the flow channel, the maximum applicable tool radius is calculated iteratively using the bisection method, and the flow channel is divided into multiple regions, each using a tool of a different size for distributed roughing. However, this multi-tool partitioning machining method has significant drawbacks: because different tool sizes are used in different regions, residual allowance remains at the region junctions, affecting the machining quality of the flow channel; simultaneously, the bisection method can only reduce the search interval by half each time, requiring multiple iterations to determine the maximum tool radius, resulting in longer solution time and low efficiency of multi-tool partitioning machining; furthermore, frequent tool changes increase machining time and machine tool load, affecting overall production efficiency.

[0004] In summary, improving the machining accuracy and efficiency of the flow channel has become the main problem to be solved. Summary of the Invention

[0005] To overcome the problems existing in related technologies, this disclosure provides an automatic blade selection method and system for impeller flow channels.

[0006] According to a first aspect of the present disclosure, an automatic blade selection method for an impeller flow channel is provided, the method comprising:

[0007] Construct a three-dimensional geometric model corresponding to the bladed disk, and based on the three-dimensional geometric model, determine the hub spline curve and casing spline curve corresponding to the flow channel;

[0008] The hub spline curve and the casing spline curve are parameterized to obtain initial parameters, and the depth range corresponding to the flow channel is obtained by iterative calculation of each hub feature point based on the initial parameters.

[0009] Based on the three-dimensional geometric model, the suction surface curve and pressure surface curve corresponding to the flow channel are determined. Each feature point in the suction surface curve is traversed. The nearest feature point corresponding to each feature point is determined from the pressure surface curve based on an iterative search algorithm. Based on each feature point and its corresponding nearest feature point, the width range corresponding to the flow channel is determined.

[0010] Based on the depth range and the width range, the target tool corresponding to the flow channel is determined.

[0011] In one possible design, determining the hub spline curve and casing spline curve corresponding to the flow channel based on the three-dimensional geometric model includes:

[0012] Extract discrete data point sets of the hub surface and casing surface from the three-dimensional geometric model;

[0013] Along the flow channel direction, extract the hub feature point set corresponding to the hub surface from the discrete data point set, and perform cubic spline interpolation on the hub feature point set to generate the hub spline curve;

[0014] Extract the set of casing feature points corresponding to the casing surface from the discrete data point set, and perform cubic spline interpolation on the set of casing feature points to generate the casing spline curve.

[0015] In one possible design, the parameterization of the hub spline curve and the casing spline curve to obtain initial parameters includes:

[0016] For each hub feature point on the hub spline curve, perform the following operations:

[0017] Connecting adjacent casing feature points in the casing spline curve yields multiple straight line segments;

[0018] Determine the vertical distance from the hub feature point to each straight line segment, and determine the minimum vertical distance, the target straight line segment corresponding to the minimum vertical distance, and the foot of the perpendicular;

[0019] Determine the coordinates of the hub feature point, the coordinates of the perpendicular foot, and the coordinates of the endpoints corresponding to the target straight line segment;

[0020] Based on the coordinates of the hub feature point, the coordinates of the perpendicular foot, and the coordinates of the endpoint, a two-dimensional linear equation system is constructed and solved to obtain the casing curve parameters and minimum distance corresponding to the hub feature point.

[0021] The casing curve parameters and the minimum distance are determined as the initial parameters corresponding to the hub feature points.

[0022] In one possible design, the iterative calculation of each hub feature point based on the initial parameters to obtain the depth range corresponding to the flow channel includes:

[0023] Using the initial parameters as the starting point of the iteration, each hub feature point is determined from the hub spline curve, and each casing feature point is determined from the casing spline curve; the hub feature points and the casing feature points correspond one-to-one.

[0024] The effective distance between each hub feature point and the corresponding casing feature point is determined, and the position of the casing feature point corresponding to the minimum effective distance is determined by iteratively adjusting the parameter position of the casing feature point;

[0025] The depth range of the flow channel is determined based on the location of the casing feature point corresponding to each hub feature point.

[0026] In one possible design, determining the effective distance between each hub feature point and its corresponding casing feature point, and determining the casing feature point position corresponding to the minimum effective distance by iteratively adjusting the parameter positions of the casing feature points, includes:

[0027] Based on the current casing feature point coordinates, unit normal vector, and current hub feature point coordinates, construct axial and radial objective functions;

[0028] Based on the current casing feature points and unit normal vector, the axial objective function is solved to obtain the axial function value, and the radial objective function is solved to obtain the radial function value;

[0029] If the absolute value of the axial function value is less than the axial tolerance threshold, and the absolute value of the radial function value is less than the radial tolerance threshold, then the location of the casing feature point corresponding to the minimum effective spacing is determined.

[0030] If the absolute value of the axial function value is not less than the axial tolerance threshold, or the absolute value of the radial function value is not less than the radial tolerance threshold, then the initial parameters are updated to obtain iterative parameters, and the parameter positions of the casing feature points are adjusted based on the iterative parameters until the position of the casing feature point corresponding to the minimum effective spacing is determined.

[0031] In one possible design, updating the initial parameters to obtain the iterative parameters includes:

[0032] Extract the casing curve parameters and minimum distance from the initial parameters;

[0033] Calculate the partial derivative of the axial objective function with respect to the casing curve parameters to obtain the first partial derivative, and calculate the partial derivative of the axial objective function with respect to the minimum distance to obtain the second partial derivative;

[0034] Calculate the partial derivative of the radial objective function with respect to the casing curve parameters to obtain the third partial derivative, and calculate the partial derivative of the radial objective function with respect to the minimum distance to obtain the fourth partial derivative;

[0035] Based on the first partial derivative, the second partial derivative, the third partial derivative, the fourth partial derivative, the axial function value, and the radial function value, a system of linear equations is constructed and solved to obtain the casing parameter compensation value corresponding to the casing curve parameter and the distance compensation value corresponding to the minimum distance.

[0036] The casing curve parameters are added to the casing parameter compensation value to obtain the updated casing curve parameters, and the minimum distance is added to the distance compensation value to obtain the updated minimum distance. The updated casing curve parameters and the updated minimum distance are then determined as the iteration parameters.

[0037] In one possible design, determining the nearest feature point corresponding to each feature point from the pressure surface curve based on the iterative search algorithm includes:

[0038] The feature point is offset by a set angle value along the circumferential direction to obtain a virtual target point;

[0039] A target error function is constructed based on the virtual target point, the circumferential angle of the feature point, and the set angle value; the virtual target point is determined by iterative search based on the golden section algorithm.

[0040] The set angle value is iteratively searched and updated based on the linear interpolation algorithm to determine the target angle value when the target error function is the set value;

[0041] Based on the target angle value, the nearest feature point corresponding to the feature point is determined on the pressure surface curve.

[0042] In one possible design, determining the width range of the flow channel based on each feature point and its nearest corresponding feature point includes:

[0043] Determine the arc length distance between each feature point in the suction surface curve and its nearest corresponding feature point;

[0044] The minimum and maximum arc length distances are determined from all arc length distances, and the width range corresponding to the flow channel is determined based on the minimum and maximum arc length distances.

[0045] According to a second aspect of the present disclosure, an automatic blade selection system for an impeller flow channel is provided, comprising:

[0046] The curve acquisition module is used to construct a three-dimensional geometric model corresponding to the bladed disk, and based on the three-dimensional geometric model, determine the hub spline curve and casing spline curve corresponding to the flow channel;

[0047] The depth determination module is used to parameterize the hub spline curve and the casing spline curve to obtain initial parameters, and to perform iterative calculations on each hub feature point based on the initial parameters to obtain the depth range corresponding to the flow channel.

[0048] The width determination module is used to determine the suction surface curve and pressure surface curve corresponding to the flow channel based on the three-dimensional geometric model, traverse each feature point in the suction surface curve, determine the nearest feature point corresponding to each feature point from the pressure surface curve based on an iterative search algorithm, and determine the width range corresponding to the flow channel based on each feature point and its corresponding nearest feature point.

[0049] An automatic tool selection module is used to determine the target tool corresponding to the flow channel based on the depth range and the width range.

[0050] In one possible design, the curve acquisition module is specifically used to extract discrete data point sets of the hub surface and casing surface from the three-dimensional geometric model, extract the hub feature point set corresponding to the hub surface from the discrete data point set along the flow channel direction, and perform cubic spline interpolation processing on the hub feature point set to generate the hub spline curve; and extract the casing feature point set corresponding to the casing surface from the discrete data point set, and perform cubic spline interpolation processing on the casing feature point set to generate the casing spline curve.

[0051] In one possible design, the depth determination module is specifically used to traverse each hub feature point on the hub spline curve, and perform the following operations for each hub feature point: connect adjacent casing feature points in the casing spline curve to obtain multiple straight line segments; determine the vertical distance from the hub feature point to each straight line segment; determine the minimum vertical distance and the target straight line segment and perpendicular foot corresponding to the minimum vertical distance; determine the hub feature point coordinates, the perpendicular foot coordinates, and the endpoint coordinates corresponding to the target straight line segment; construct and solve a two-dimensional linear equation system based on the hub feature point coordinates, the perpendicular foot coordinates, and the endpoint coordinates to obtain the casing curve parameters and the minimum distance corresponding to the hub feature point; and determine the casing curve parameters and the minimum distance as the initial parameters corresponding to the hub feature point.

[0052] In one possible design, the depth determination module is specifically used to determine each hub feature point from the hub spline curve and each casing feature point from the casing spline curve, using the initial parameters as the starting point for iteration; the hub feature points and casing feature points correspond one-to-one, determining the effective distance between each hub feature point and its corresponding casing feature point, and determining the casing feature point position corresponding to the minimum effective distance by iteratively adjusting the parameter positions of the casing feature points; and determining the depth range corresponding to the flow channel based on the casing feature point positions corresponding to each hub feature point.

[0053] In one possible design, the depth determination module is further configured to construct an axial objective function and a radial objective function based on the current chassis feature point coordinates, unit normal vector, and current hub feature point coordinates; solve the axial objective function based on the current chassis feature point and unit normal vector to obtain an axial function value; and solve the radial objective function to obtain a radial function value. If the absolute value of the axial function value is less than the axial tolerance threshold, and the absolute value of the radial function value is less than the radial tolerance threshold, then the position of the chassis feature point corresponding to the minimum effective spacing is determined. If the absolute value of the axial function value is not less than the axial tolerance threshold, or the absolute value of the radial function value is not less than the radial tolerance threshold, then the initial parameters are updated to obtain iterative parameters, and the parameter positions of the chassis feature points are adjusted based on the iterative parameters until the position of the chassis feature point corresponding to the minimum effective spacing is determined.

[0054] In one possible design, the depth determination module is further configured to extract casing curve parameters and a minimum distance from the initial parameters, calculate the partial derivative of the axial objective function with respect to the casing curve parameters to obtain a first partial derivative, calculate the partial derivative of the axial objective function with respect to the minimum distance to obtain a second partial derivative, calculate the partial derivative of the radial objective function with respect to the casing curve parameters to obtain a third partial derivative, and calculate the partial derivative of the radial objective function with respect to the minimum distance to obtain a fourth partial derivative, construct and solve a system of linear equations based on the first, second, third, and fourth partial derivatives, the axial function value, and the radial function value to obtain casing parameter compensation values ​​corresponding to the casing curve parameters and distance compensation values ​​corresponding to the minimum distance, add the casing curve parameters and the casing parameter compensation values ​​to obtain updated casing curve parameters, add the minimum distance and the distance compensation values ​​to obtain updated minimum distance, and determine the updated casing curve parameters and the updated minimum distance as the iteration parameters.

[0055] In one possible design, the width determination module is specifically used to offset the feature point circumferentially by a set angle value to obtain a virtual target point; based on the virtual target point, the circumferential angle of the feature point, and the set angle value, a target error function is constructed; the virtual target point is determined by iterative search based on the golden section algorithm; the set angle value is iteratively searched and updated based on the linear interpolation algorithm to determine the target angle value when the target error function is the set value; and based on the target angle value, the nearest feature point corresponding to the feature point is determined on the pressure surface curve.

[0056] In one possible design, the width determination module is further configured to determine the arc length distance between each feature point in the suction surface curve and its nearest corresponding feature point, determine the minimum arc length distance and the maximum arc length distance from all arc length distances, and determine the width range corresponding to the flow channel based on the minimum arc length distance and the maximum arc length distance.

[0057] According to a third aspect of the present disclosure, a computer device is provided, comprising:

[0058] The memory and processor, wherein the memory stores a computer program that, when executed by the processor, implements the method of the first aspect described above.

[0059] According to a fourth aspect of the present disclosure, a computer-readable storage medium is provided, wherein a computer program is stored therein, and when the computer program is executed by a processor, the method of the first aspect described above is implemented.

[0060] The technical solutions provided by the embodiments of this disclosure may include the following beneficial effects:

[0061] In this embodiment, the width and depth ranges corresponding to the flow channel are determined, and the geometric constraints of the tool are determined based on these ranges. The entire process is algorithm-driven, and the resulting width and depth ranges are repeatable and consistent, ensuring the quality of the flow channel machining and selecting a target tool. This significantly reduces tool change time and idle travel, avoids residual allowances and tool marks at the junctions of areas where multiple tools are used, and improves the machining accuracy and efficiency of the flow channel.

[0062] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0063] The accompanying drawings, which are incorporated in and form part of this disclosure, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.

[0064] Figure 1This is a schematic flowchart illustrating an automatic blade selection method for an impeller flow channel according to an exemplary embodiment of the present disclosure.

[0065] Figure 2 This is a schematic flowchart illustrating the process of determining the depth range corresponding to a flow channel according to an exemplary embodiment of the present disclosure.

[0066] Figure 3 This is a schematic flowchart illustrating the determination of the width range corresponding to a flow channel according to an exemplary embodiment of the present disclosure.

[0067] Figure 4 This is a schematic diagram of the data processing flow of a preset positioning algorithm according to an exemplary embodiment of the present disclosure.

[0068] Figure 5 This is a schematic diagram of the data processing flow of a preset optimization algorithm according to an exemplary embodiment of the present disclosure.

[0069] Figure 6 This is a schematic diagram of the data processing flow of a preset distance algorithm according to an exemplary embodiment of the present disclosure.

[0070] Figure 7 This is a schematic diagram of the structure of an automatic blade selection system for an impeller flow channel according to an exemplary embodiment of the present disclosure.

[0071] Figure 8 This is a schematic diagram of the structure of a computer device according to an exemplary embodiment of the present disclosure. Detailed Implementation

[0072] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numerals in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this disclosure as detailed in the appended claims.

[0073] The terminology used in this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. The singular forms “a,” “the,” and “the” as used in this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0074] It should be understood that although the terms first, second, third, etc., may be used in this disclosure to describe various information, such information should not be limited to these terms. These terms are used only to distinguish information of the same type from one another. For example, without departing from the scope of this disclosure, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0075] In related technologies, the critical profile of the flow channel is extracted, and the maximum applicable tool radius is calculated iteratively using a bisection method. The flow channel is then divided into multiple regions, and different sized tools are selected for roughing in each region. This multi-tool partitioning machining method has significant drawbacks: because different sized tools are used in different regions, residual allowances exist at the region junctions, affecting the machining quality of the flow channel; at the same time, the bisection method can only reduce the search interval by half each time, and to determine the maximum tool radius, it needs to be iterated repeatedly, resulting in longer solution time and low efficiency of multi-tool partitioning machining; in addition, frequent tool changes increase machining time and machine tool load, affecting overall production efficiency. Therefore, how to improve the machining accuracy and efficiency of the flow channel has become the main problem to be solved.

[0076] The automatic blade selection method for the impeller channel in this example embodiment will now be described in detail.

[0077] The terms used in the embodiments of this application are explained as follows:

[0078] Cartesian coordinate system: The position of a point in space is determined by three mutually perpendicular coordinate axes X, Y, and Z;

[0079] Cylindrical coordinate system: describes a point in space based on (r, θ, z), where r is the radial distance from the point to the z-axis and θ is the circumferential angle around the z-axis.

[0080] Hub spline curve: represents the inner ring and bottom boundary of the flow channel;

[0081] Casing spline curve: represents the outer ring and top boundary of the flow channel;

[0082] Suction surface curve: the outline of the convex surface of the target blade;

[0083] Pressure surface curve: the concave profile of the adjacent blades of the target blade;

[0084] The aforementioned hub spline curve and casing spline curve define the depth of the flow channel. The depth limits the maximum range of motion of the tool in the "up and down" direction, thus constraining the radius of the selectable tool. The circumferential distance between the aforementioned suction surface curve and pressure surface curve defines the width of the flow channel. The width limits the maximum range of motion of the tool in the "left and right" direction, thus constraining the maximum diameter and tool tip width of the selectable tool.

[0085] like Figure 1 As shown, Figure 1 This disclosure is a flowchart illustrating an automatic blade selection method for an impeller flow channel according to an exemplary embodiment, comprising the following steps:

[0086] In step S110, a three-dimensional geometric model corresponding to the bladed disk is constructed, and based on the three-dimensional geometric model, the hub spline curve and casing spline curve corresponding to the flow channel are determined.

[0087] In order to improve the processing efficiency and accuracy of the flow channel, this application embodiment needs to obtain the three-dimensional geometric model corresponding to the impeller. The three-dimensional geometric model can be imported based on the computer-aided design (CAD) model, or the actual impeller can be scanned and reconstructed in three dimensions.

[0088] To determine the depth of the flow channel, it is necessary to extract discrete data point sets of the hub surface and casing surface from the three-dimensional geometric model.

[0089] Specifically, the flow channel axis or cutting line is determined from the three-dimensional geometric model. The flow channel axis is the central reference line of the flow channel in fluid machinery, and the cutting line is the trajectory line of the cutting edge of the tool contacting the workpiece and completing the cutting action during the cutting process. Along the flow channel axis or cutting line, the cross-section intersection algorithm is used to cut the hub surface and casing surface with a series of planes perpendicular to the flow channel axis or curved surfaces along the axis normal, resulting in a series of intersection lines. These intersection lines are segments of the hub profile and casing profile at discrete positions. The intersection points of all cross sections on the same curved surface are sorted according to the flow channel direction to form two ordered discrete data point sets.

[0090] To obtain continuous and smooth hub spline curves and casing spline curves, it is necessary to extract the hub feature point set corresponding to the hub surface from the discrete data point set, and perform cubic spline interpolation on the hub feature point set to generate the hub spline curve. Similarly, it is necessary to extract the casing feature point set corresponding to the casing surface from the discrete data point set, and perform cubic spline interpolation on the casing feature point set to generate the casing spline curve.

[0091] For example, the discrete data point set is ,in, For all For each interval There exists a cubic polynomial , as well as All of these are undetermined coefficients, which are determined based on the cubic spline curve formula. Since the cubic spline curve formula is a well-known technique to those skilled in the art, it will not be elaborated on here.

[0092] By using the above method, the continuous and smooth hub spline curve and casing spline curve can be determined, which can make the flow channel cross-section transition uniform, ensuring the accuracy and efficiency of subsequent CNC machining of the flow channel.

[0093] In step S120, the hub spline curve and the casing spline curve are parameterized to obtain initial parameters, and the depth range corresponding to the flow channel is obtained by iterative calculation of each hub feature point based on the initial parameters.

[0094] Since the impeller is a rotating body, and the hub and casing are rotationally symmetric structures with their shapes and dimensions uniformly distributed circumferentially along the central axis (which can be the Z-axis), in order to simplify the calculation of flow channel cross-sectional parameters and avoid redundant calculations in the X and Y axis dimensions under the Cartesian coordinate system, it is necessary to transform the hub spline curve and casing spline curve from the Cartesian coordinate system to the cylindrical coordinate system.

[0095] To improve the efficiency of determining the flow channel depth, it is necessary to traverse every hub feature point on the hub spline curve. Since the operation process is the same for each hub feature point, this embodiment of the application will use the operation performed on one hub feature point as an example for illustration. The specific process is as follows:

[0096] Connect adjacent casing feature points in the casing spline curve to obtain multiple straight line segments. Then, determine the perpendicular distance from the hub feature point to each straight line segment, and determine the minimum perpendicular distance, the target straight line segment corresponding to the minimum perpendicular distance, and the foot of the perpendicular. Next, determine the hub feature point coordinates, the foot of the perpendicular coordinates, and the endpoint coordinates corresponding to the target straight line segment. Then, construct and solve a two-dimensional linear equation system based on the hub feature point coordinates, the foot of the perpendicular coordinates, and the endpoint coordinates to obtain the casing curve parameters and the minimum distance corresponding to the hub feature point. Finally, determine the casing curve parameters and the minimum distance as the initial parameters corresponding to the hub feature point.

[0097] Furthermore, based on the endpoint coordinates of the target straight line segment, a line segment vector is generated. The two endpoints of the target straight line segment are ZR10 and ZR11, and the line segment vector is DZRI = ZR11 - ZR10. A point of the target straight line segment can be represented as ZR10 + t × DZRI, where t is a parameter between 0 and 1. The target straight line segment is perpendicular to the line connecting the hub feature point and the perpendicular foot. The direction perpendicular to the target straight line segment is the normal direction, denoted as NOR, where NOR = DZRI × ZAXIS, and ZAXIS is the unit vector perpendicular to the current plane, which can be (0, 0, 1). Therefore, the hub feature point ZR0 can be represented as a linear combination of ZR10 plus DZRI and NOR: ZR0 = ZR10 + u × DZRI + v × NOR, where u and v are parameters to be determined.

[0098] DZRI and NOR are two-dimensional vectors. ZR0 = ZR10 + u × DZRI + v × NOR can be written in matrix form, with the coordinates of ZR10 being (0, 0), as follows:

[0099] [DZRI_x, NOR_x]·[u]=[ZR0_x-ZR10_x];

[0100] [DZRI_y, NOR_y]·[v]=[ZR0_y-ZR10_y];

[0101] Where DZRI_x is the coordinate component of the line segment vector in the X-axis direction, DZRI_y is the coordinate component of the line segment vector in the Y-axis direction, NOR_x is the coordinate component of the unit normal vector NOR in the X-axis direction, NOR_y is the coordinate component of the unit normal vector NOR in the Y-axis direction, ZR0_x is the coordinate component of ZR0 in the X-axis direction, ZR0_y is the coordinate component of ZR0 in the Y-axis direction, ZR10_x and ZR10_y are the coordinate components of ZR10 in the Y-axis direction, and u and v are parameters to be determined.

[0102] Based on the matrix formula above, a two-dimensional linear equation system is constructed as follows:

[0103] ;

[0104] Solving the above two-dimensional linear equations yields the values ​​of u and v. u is the casing curve parameter corresponding to the hub feature point ZR0, which represents the position on the target straight line segment. u is between 0 and 1. v is the minimum distance of the casing feature point along the normal direction, i.e., the position of the hub feature point ZR0.

[0105] It should be noted that 0≤u≤1 means the foot of the perpendicular is inside the straight line segment; u<0 means the foot of the perpendicular is outside the starting point ZR10 of the straight line segment, closer to the starting point; u>1 means the foot of the perpendicular is outside the ending point ZR11 of the straight line segment, closer to the ending point; the absolute value of v represents the perpendicular distance from the hub feature point to the straight line segment, and the sign of v indicates which side of the straight line segment the hub feature point is on.

[0106] To obtain more accurate casing feature points, iterative calculations need to be performed on each hub feature point based on initial parameters to obtain the depth range corresponding to the flow channel. The specific process is as follows:

[0107] To avoid blind searching, the initial parameters are used as the starting point for iteration. Each hub feature point is determined from the hub spline curve, and each casing feature point is determined from the casing spline curve. There is a one-to-one correspondence between the hub feature points and the casing feature points. The following explanation is based on a single hub feature point.

[0108] To obtain the normal vector at the casing feature point, it is necessary to calculate the coordinates, first derivative, and second derivative of the casing feature point on the casing spline curve based on the casing curve parameters corresponding to the casing feature point. The first derivative is the tangent vector at the casing feature point, and the second derivative is the curvature vector at the casing feature point. In this embodiment, the coordinates of the casing feature point are denoted as ZRPOI, the first derivative is denoted as ZRDER, and the second derivative is denoted as ZRDDER.

[0109] To obtain a unit normal vector, a vertical direction needs to be defined based on VVEC, which is the cross product of the axial unit vector and the tangent vector. VVEC is perpendicular to both the axial unit vector and the tangent vector, i.e., it points to the direction of the normal vector of the casing spline curve. An example of VVEC is as follows:

[0110] VVEC= , = (0, 0, 1);

[0111] Where VVEC is the unnormalized normal vector and ZRDER is the first derivative at ZRPOI.

[0112] To subsequently calculate the derivative of the normal vector and the projection related to curvature, it is necessary to calculate the cross product of the axial unit vector and the curvature vector to obtain VVEC2. VVEC2 reflects the curvature variation trend of the VVEC random box-spline curve. An example of VVEC2 is as follows:

[0113] ;

[0114] in, The middle vector of the cross product. It is the second derivative at ZRPOI.

[0115] To obtain the unit normal vector NOR, the above VVEC needs to be normalized so that the length of VVEC is 1. The specific formula for determining the magnitude of VVEC is as follows:

[0116] ;

[0117] ;

[0118] The above The square of the modulus. For the length of the module, , , This represents the components of VVEC along the axial direction of the coordinate system, which can be the components of VVEC in the X, Y, and Z directions.

[0119] Since VVECs have varying lengths, using them directly can lead to scaling issues in distance calculations. Therefore, VVECs are normalized to obtain NOR, where the length of NOR is 1. An example of NOR is shown below:

[0120] , , ;

[0121] The above NOR(1), NOR(2), and NOR(3) are the components of NOR in the axial directions of the coordinate system. , , Let VVEC be the component of VVEC in the axial direction of the coordinate system.

[0122] The unit normal vector (NOR) provides a standard directional reference, giving subsequent projections, distance calculations, etc., a clear geometric meaning and avoiding numerical problems caused by differences in vector length.

[0123] This application employs a numerical optimization method to continuously adjust the position of the hub feature point in the casing spline curve corresponding to the casing feature point. Specifically, it determines the effective distance between each hub feature point and its corresponding casing feature point, and iteratively adjusts the parameter position of the casing feature point. The parameter position is defined by the value state of preset design parameters. Changes in the parameter value will cause changes in the spatial position of the casing feature point, thereby indirectly changing the spatial position of the casing feature point and determining the position of the casing feature point corresponding to the minimum effective distance.

[0124] Specifically, based on the current coordinates of the casing feature points, the unit normal vector, and the current hub feature points, an axial objective function and a radial objective function are constructed. An example of the axial objective function is as follows:

[0125] ;

[0126] The above FZ represents the axial function value of the axial objective function. This represents the z-coordinate of the casing spline curve at the current casing feature point, i.e., its axial position. The minimum distance among the initial parameters of the current wheel hub feature point. Let NOR be the component of the unit normal vector NOR along the z-axis. Let z be the current z-coordinate of the hub feature point. The axial function value represents the axial deviation. Axial deviation = z-coordinate of the casing feature point + distance moved along the normal z-axis direction - z-coordinate of the hub feature point.

[0127] An example of a radial objective function is as follows:

[0128] ;

[0129] The above FR represents the radial function value of the radial objective function. Let r be the r-coordinate of the casing spline curve at the current casing feature point, i.e., the radial position. The minimum distance among the initial parameters of the current wheel hub feature point. Let NOR be the component of the unit normal vector NOR along the r-axis. Let r be the current hub feature point. The radial function value represents the radial deviation. Radial deviation = chassis feature point r coordinate + distance moved along the normal r-axis direction - hub feature point r coordinate.

[0130] Therefore, after determining the axial objective function and the radial objective function, the coordinates of the casing feature point corresponding to the current casing feature point and the unit normal vector are substituted into the axial objective function and the radial objective function to solve for the axial objective function and obtain the axial function value, and the radial objective function is solved to obtain the radial function value.

[0131] If the absolute value of the axial function value is less than the axial tolerance threshold, and the absolute value of the radial function value is less than the radial tolerance threshold, it means that the distance between the current casing feature point and the hub feature point along the normal vector direction is within the tolerance range. In this case, the distance between the hub feature point and the casing feature point is determined as the minimum effective distance. The distance between the hub feature point and the casing feature point can be the minimum distance, thus determining the feature point position corresponding to the minimum effective distance as the current casing feature point position.

[0132] If the absolute value of the axial function value is not less than the axial tolerance threshold, or the absolute value of the radial function value is not less than the radial tolerance threshold, it means that the distance between the current casing feature point and the hub feature point along the normal vector direction is not within the tolerance range. In this case, the initial parameters need to be updated to obtain the iterative parameters, and the position of the casing feature point is adjusted based on the iterative parameters until the position of the casing feature point corresponding to the minimum effective spacing is determined.

[0133] Furthermore, to determine the iteration parameters, it is necessary to calculate the partial derivatives of the axial objective function with respect to the casing curve parameters to obtain the first partial derivative. The first partial derivative characterizes the rate of change of the deviation in the z-direction when the casing curve parameters change. Additionally, the partial derivatives of the axial objective function with respect to the minimum distance are calculated to obtain the second partial derivative, which characterizes the rate of change of the deviation in the r-direction when the casing curve parameters change. Furthermore, the partial derivatives of the radial objective function with respect to the casing curve parameters are calculated to obtain the third partial derivative, which characterizes the rate of change of the deviation in the z-direction when the minimum distance changes. Finally, the partial derivatives of the radial objective function with respect to the minimum distance are calculated to obtain the fourth partial derivative, which characterizes the rate of change of the deviation in the r-direction when the minimum distance changes.

[0134] It should be noted that, in order to accurately calculate the partial derivatives of the axial and radial objective functions and improve numerical stability, it is necessary to determine the unit vector. The specific process for determining the unit vector is as follows:

[0135] To convert the component of VVEC2 in the VVEC direction into a scaling factor that controls the direction, a coefficient C1 for adjusting the direction needs to be calculated. The specific formula for determining C1 is as follows:

[0136] ;

[0137] The above VVEC2(1), VVEC2(2), and VVEC2(3) are the components of VVEC2 in the axial direction of the coordinate system. , , Let VVEC be the component of VVEC in the axial direction of the coordinate system.

[0138] C1 is the negative value of the negative projection length of vector VVEC2 onto the direction of vector VVEC, divided by the square of the magnitude of VVEC. C1 is used to adjust the intermediate vector, denoted as DNORDU, ensuring that DNORDU is perpendicular to the normal vector and lies within the tangent plane. An example of DNORDU is shown below:

[0139] ;

[0140] ;

[0141] ;

[0142] The above DNORDU , , intermediate vector The components along the axes of the coordinate system.

[0143] The above DNORDU is used to describe the direction of change of the normal vector. C1 controls the contribution of VVEC in different directions, so that DNORDU is more consistent with the curvature of the casing spline surface.

[0144] To ensure that the length of the intermediate vector DNORDU is 1, the intermediate vector DNORDU needs to be normalized. The normalization process is as follows:

[0145] ;

[0146] ;

[0147] ;

[0148] ;

[0149] Multiplying the reciprocal of the modulus by the components of the intermediate vector along different coordinate axes is equivalent to compressing or stretching the length of the intermediate vector to 1 to become a unit vector, thus retaining only the direction information.

[0150] DNORDU becomes a unit vector in the tangent plane, which together with the unit normal vector NOR forms two axes of a local orthogonal coordinate system. The third axis can be obtained by the cross product of NOR and DNORDU, thus constructing a local orthogonal coordinate system (NOR, DNORDU, NOR×DNORDU) at the current casing feature point in the casing spline curve.

[0151] Since NOR is a unit normal vector, its derivative with respect to the U-direction parameter UPAR of the hub distance from the casing. It must lie in the tangent plane, that is, perpendicular to NOR. Therefore, it can be represented as a linear combination of two orthogonal directions in the tangent plane, such as DNORDU and another tangent vector perpendicular to DNORDU.

[0152] The aforementioned unit vector provides a geometric reference for component calculations. The process of determining the unit vector is not independent of the partial derivative calculations, but rather a prerequisite and geometric basis for the correct and stable implementation of partial derivative calculations.

[0153] An example of the first partial derivative is as follows:

[0154] ;

[0155] The above The first partial derivative, This is the first partial derivative of FZ with respect to UPAR. The first partial derivative is actually the derivative of the unit normal vector with respect to the U-direction parameter UPAR of the hub distance from the casing. The expansion form in a locally orthogonal coordinate system Let DIS be the minimum distance among the initial parameters of the current hub feature point, representing the components of the tangent vector. , Let NOR be the component of the unit normal vector along the axial direction in different coordinate systems. and These are the components of the curvature vector along the axial direction in different coordinate systems, where 1, 2, and 3 represent different directions.

[0156] An example of the second partial derivative is as follows:

[0157] ;

[0158] The above The second partial derivative, Let FZ be the first partial derivative of DIS. Let NOR be the component of the normal vector NOR along the axial direction of the coordinate system.

[0159] An example of the third partial derivative is as follows:

[0160] ;

[0161] The above The third partial derivative, Let FR be the first partial derivative with respect to UPAR. Let be the component of the tangent vector along the axial direction of the coordinate system. The minimum distance among the initial parameters of the current wheel hub feature point. Let NOR be the components of the normal vector NOR in different coordinate systems along the axial directions. , These are the components of the curvature vector in the axial directions of different coordinate systems.

[0162] An example of the fourth partial derivative is as follows:

[0163] ;

[0164] The above The fourth partial derivative, Let FR be the first-order partial derivative with respect to DIS. Let NOR be the component of the normal vector NOR in different coordinate systems along the axial direction.

[0165] Based on the above, a system of linear equations is constructed using the first partial derivative, the second partial derivative, the third partial derivative, the fourth partial derivative, the axial function value, and the radial function value. The system of linear equations is shown below:

[0166] ;

[0167] Solving the above system of linear equations yields the compensation values ​​for the casing parameters corresponding to the casing curve parameters. and the distance compensation value corresponding to the minimum distance. .

[0168] The casing curve parameters are added to the casing parameter compensation value to obtain the updated casing curve parameters, and the minimum distance is added to the distance compensation value to obtain the updated minimum distance. The updated casing curve parameters and the updated minimum distance are determined as iteration parameters, and the next iteration is continued based on the iteration parameters. The above process is repeated until the feature point position corresponding to the minimum effective distance is determined, or the maximum number of iterations is reached.

[0169] The aforementioned iterative method can be Newton's method, which significantly improves the accuracy of depth calculation compared to the traditional bisection method or empirical estimation. At the same time, due to the fast convergence of its numerical method, it ensures computational efficiency, directly solving the problems of uneven processing quality and low processing efficiency, and ensuring that the tool does not overcut or leave excess material.

[0170] Based on the above method, the minimum effective spacing corresponding to each hub feature point can be determined, all the minimum effective spacings can be sorted, the maximum spacing and the minimum spacing can be determined from them, and the maximum spacing and the minimum spacing can be determined as the depth range corresponding to the flow channel.

[0171] An exemplary flowchart for determining the depth range corresponding to the flow channel is shown below. Figure 2 As shown, in Figure 2 In the process, the hub spline curve and the casing spline curve are input into the system. The system will traverse each hub feature point in the hub spline curve and each casing feature point in the casing spline curve. For each hub feature point, the initial parameters corresponding to each hub feature point are determined on the casing spline curve, namely: casing curve parameters and minimum distance. Then, |FZ| and |FR| corresponding to each hub feature point are calculated, where |FZ| is the absolute value of the axial function value and |FR| is the absolute value of the radial function value. The minimum distance is iteratively approximated based on |FZ| and |FR|, and it is determined whether |FZ| is less than the axial tolerance threshold and whether |FR| is less than the radial tolerance threshold. If so, the depth range corresponding to the flow channel is determined; otherwise, the process is repeated at the current hub feature point.

[0172] By using the above method, the depth range corresponding to the flow channel is determined, which establishes geometric constraints for adaptive tool selection and accurately calculates the minimum radial spacing of the flow channel. This ensures that the tool will not interfere with or overcut the hub during the flow channel machining process, thus guaranteeing the safety and feasibility of the machining process.

[0173] In step S130, based on the three-dimensional geometric model, the suction surface curve and pressure surface curve corresponding to the flow channel are determined. Each feature point in the suction surface curve is traversed, and the nearest feature point corresponding to each feature point is determined from the pressure surface curve based on the iterative search algorithm. Based on each feature point and its corresponding nearest feature point, the width range corresponding to the flow channel is determined.

[0174] After determining the depth range of the flow channel, in order to determine the maximum permissible diameter or effective cutting range of the machining tool for the flow channel, it is necessary to determine the corresponding width range of the flow channel. The specific determination process is as follows:

[0175] Create a curved surface that is perpendicular to the flow channel direction or consistent with the hub section. It is usually a surface of revolution or a ruled surface. Its generatrix is ​​along the flow channel axis. Based on this curved surface, cut the suction surface and the pressure surface to obtain the suction surface profile and the pressure surface profile.

[0176] The suction surface profile and the pressure surface profile are composed of discrete points. In this embodiment, two smooth parametric curves can be fitted respectively based on cubic spline interpolation, namely: the suction surface curve and the pressure surface curve. The process of fitting the suction surface curve and the pressure surface curve based on cubic spline interpolation is the same as the process of obtaining the hub spline curve and the casing spline curve, and will not be repeated here.

[0177] After determining the suction surface curve and the pressure surface curve, it is necessary to transform the suction surface curve and the pressure surface curve from the Cartesian coordinate system to the cylindrical coordinate system. Since the feature point corresponding to each feature point in the pressure surface curve is uncertain, this embodiment of the application assumes that the feature point is offset by a set angle value along the circumference to obtain a virtual target point. The virtual target point is determined by iterative search based on the Golden Section Search Algorithm (GSSA). The golden ratio can be 0.618. Different set angle values ​​result in different positions of the determined virtual target point. Therefore, a target error function can be constructed based on the virtual target point, the circumferential angle of the feature point, and the set angle value.

[0178] The target error function described above can be D(X) = θ_prs - (θ_suc + X), where θ_prs is the angle value of the feature point on the suction surface curve, θ_suc is the angle value of the virtual target point, and X is the set angle value.

[0179] Next, the set angle value is iteratively searched and updated based on the Linear Interpolation Algorithm (LIA). When the target error function is equal to the set value, the set value can be 0, and the current set angle value is determined as the final target angle value. Finally, based on this target angle value, a feature point can be determined on the pressure surface curve, which is the nearest feature point.

[0180] Specifically, taking a characteristic point on the suction surface curve as an example, the specific process is as follows:

[0181] The feature point is offset by an initial angle value along the circumference to obtain a virtual target point. The virtual target point, the suction surface curve, and the pressure surface curve are input into a preset positioning algorithm. The algorithm outputs the initial suction surface positioning point that is closest to the suction surface curve and the initial pressure surface positioning point that is closest to the pressure surface curve. The algorithm also calculates the initial angle error between the initial suction surface positioning point and the initial pressure surface positioning point.

[0182] The initial angle value is updated based on the initial angle error to obtain the first angle value. The feature point is shifted circumferentially by the first angle value to obtain the first virtual target point. The first virtual target point, the suction surface curve, and the pressure surface curve are input into the preset positioning algorithm to output the first suction surface positioning point and the first pressure surface positioning point, and the first angle error between the first suction surface positioning point and the first pressure surface positioning point is determined.

[0183] At this point, there are two points: (XL0, DL0) and (XHI, DHI), where XL0 is the initial angle value, DL0 is the initial angle error, XHI is the first angle value, and DHI is the first angle error. Based on these two points, a local approximation of D(X) near the initial point can be constructed. By updating the initial angle error, the first angle value is obtained. Compared to a random small step size, the first angle value is closer to the true solution, thus significantly accelerating the convergence speed of subsequent iterations.

[0184] The initial angle value, initial angle error, first angle value, and first angle error are input into a preset optimization algorithm. The preset optimization algorithm performs linear interpolation based on the above two points to predict a better angle value, which can be XMID, making D(XMID) closer to zero.

[0185] The initial angle value is updated based on the better angle value to obtain the second angle value. The feature point is shifted circumferentially along the second angle value to obtain the second virtual target point. The second virtual target point, the suction surface curve and the pressure surface curve are input into the preset positioning algorithm to output the second suction surface positioning point and the second pressure surface positioning point. The second angle error between the second suction surface positioning point and the second pressure surface positioning point is determined. The second angle error can be denoted as DMID.

[0186] Based on this, if the second angle error is less than the preset precision error, the minimum distance among the currently traversed feature points is recorded. The minimum distance is the distance between the second virtual target point and the second suction surface positioning point, or the distance between the second virtual target point and the second pressure surface positioning point, and the next feature point in the suction surface curve is traversed.

[0187] If DMID×DL0>0, it means the offset direction is correct. Then, update DL0 with the new DMID and update XL0 with XMID, and call the preset optimization algorithm to continue iterating. If DMID×DL0≤0, it means the offset direction is incorrect. Then, update XHI with XMID and update DHI with DMID, and call the preset optimization algorithm to continue iterating.

[0188] Based on the above process, after traversing all feature points in the suction surface curve, the nearest feature point corresponding to each feature point in the pressure surface curve will be obtained. The arc length distance between each feature point and its corresponding nearest feature point will be calculated. The arc length distance is the arc distance along the circumferential direction. The minimum arc length distance and the maximum arc length distance will be determined from all the arc length distances. Finally, based on the minimum arc length distance and the maximum arc length distance, the width range of the flow channel will be generated.

[0189] Optionally, multiply the minimum arc length by 2 to get the minimum width, and multiply the maximum arc length by 2 to get the maximum width.

[0190] An example flow chart for determining the width range corresponding to the flow channel is shown below. Figure 3 As shown, in Figure 3 In the process, the feature points of the suction surface curve and the pressure surface curve are traversed to determine the initial angle value as 0. The preset positioning algorithm is called to locate the initial suction surface positioning point and the initial pressure surface positioning point, and the initial angle error between the initial suction surface positioning point and the initial pressure surface positioning point is calculated. Then, the initial angle value is updated based on the initial angle error to obtain the first angle value. The preset positioning algorithm is called again to locate the first suction surface positioning point and the first pressure surface positioning point, and the first angle error between the first suction surface positioning point and the first pressure surface positioning point is calculated. Then, the initial angle value, the initial angle error, the first angle value, and the first angle error are input into the preset optimization algorithm, which outputs the optimized angle value. The preset positioning algorithm is then called again to determine the second angle error based on the optimized angle value.

[0191] If the second angle error is less than the preset accuracy error, the width range corresponding to the output channel is output; otherwise, the optimized angle value is updated again, and the above process is repeated.

[0192] The data processing flow diagram of the above-mentioned preset positioning algorithm is shown below. Figure 4 As shown, in Figure 4In the process, the feature point index I and offset STEPJ of the blade are input, and the specified point P (XLINE, YLINE) is obtained. The coordinates of the first point with a distance of STEPJ or less are calculated, and the index range [ILO, IHI] of the blade curve is determined. Then, the intermediate variable XLO is calculated based on the specified point P. Its value is XLINE plus STEPJ. The specified point [XLO, YLINE] is substituted into the index range [ILO, IHI], and the preset distance algorithm is called to calculate the nearest distance DL0. Subsequently, XHI is calculated. Its value is XLINE plus twice STEPJ. The specified point [XHI, YLINE] is substituted into the same index range [ILO, IHI], and the preset distance algorithm is called again to calculate the nearest distance DHI. Finally, the obtained parameters XLO, DL0, XHI, and DHI are substituted into the preset optimization algorithm to calculate the nearest distance DMID. When DMID is less than the preset precision error, the coordinates of the feature point corresponding to the current offset are determined. Otherwise, XMID is recalculated iteratively, and the above process is repeated.

[0193] The data processing flow diagram of the above-mentioned preset optimization algorithm is shown below. Figure 5 As shown, in Figure 5 In this application, the specified X coordinates (XLO, DL0) and minimum distances (XHI, DHI) are input into a preset optimization algorithm. Traditional binary search requires dividing the search interval [XLO, XHI] into two halves each time, and then adjusting XLO and XHI by comparing the value of the midpoint (XLO+XHI) / 2. This embodiment performs a linear interpolation within the interval [XLO, XHI]. The coordinates XMID of the point that makes D(X)=0 are estimated using the known points (XLO, DL0) and (XHI, DHI), where DL0 and DHI are the distance values ​​calculated at XLO and XHI, respectively.

[0194] Specifically, assume a linear relationship exists between (XLO, DL0) and (XHI, DHI), and that there exists a function D(X) within the interval [XLO, XHI] such that D(X) = 0. Linear approximation is then performed at the points (XLO, DL0) and (XHI, DHI) using linear interpolation, i.e.: And solve for the point XMID where D(X)=0, that is: Solving this equation, we get: Then, substituting (XMID, YLINE) and the interval [ILO, IHI] into the preset distance formula, we can calculate DMID.

[0195] The data processing flow diagram of the above-mentioned preset distance algorithm is shown below. Figure 6 As shown, in Figure 6In it, the specified point P(XLO, YLINE) and the initial search interval are input. First, the blade feature points within the initial search interval are divided according to the ratio DEL, the shortest distance from the blade feature points to the specified point P is calculated, and the point corresponding to the shortest distance and its initial index Fmin are found. Taking Fmin as the center, the initial search interval [F0, F3] of the golden section method is extended by DEL, where F0 = Fmin - DEL and F3 = Fmin + DEL, and the positions of the golden section feature points F1 and F2 are calculated according to the golden ratio, F1 = (F0 + (F3 - F0) × (1 - 0.618)), F2 = (F3 - (F3 - F0) × (1 - 0.618)). Calculate the distances D0 from F0 to the specified point P, D1 from F1 to the specified point, D2 from F2 to the specified point, and D3 from F3 to the specified point. The interval is iteratively reduced by comparing the distances from F1 and F2 to the specified point P, that is: if D1 < D2, update the index FNEW = (0.618) × (F1 - F0) + F0, thereby reducing the initial search interval [F0, F3] to [F0, F2]; otherwise, update the index FNEW = 0.618 × (F2 - F3) + F3, thereby reducing the initial search interval [F0, F3] to [F1, F3]. Calculate the distance DNEW from FNEW to the specified point until DNEW is less than the preset precision error. At this time, output DNEW as the minimum distance DMID from the blade to the specified point P.

[0196] Through the above method, the width range of the flow channel is determined, the circumferential rigid constraint of the flow channel is established, and with the core strategy of iteratively approaching the center line with the offset, the problem of the shortest distance between complex hyperboloids is transformed into an efficient problem of single-variable root finding and one-dimensional search, ensuring the calculation accuracy and improving the calculation efficiency.

[0197] In step S140, based on the depth range and the width range, the target tool corresponding to the flow channel is determined.

[0198] To ensure the accuracy of the flow channel machining, the radius of the tool is constrained based on the minimum width in the flow channel width, the length of the tool is constrained based on the maximum depth in the flow channel depth, and based on the minimum width and the maximum depth, the tool parameters are determined, and based on the tool parameters, the target tool is determined to ensure that there is no axial collision at the narrowest part of the flow channel and to ensure that the tool can machine to the deepest part of the flow channel.

[0199] The above tool parameters at least include: the diameter, length, axial cutting depth, radial step distance, etc. of the tool, which will not be elaborated here.

[0200] For example, the tool diameter can be the product of the minimum width and a set coefficient, which can be a value between 0.7 and 0.8. The set coefficient can be adjusted based on the actual flow channel machining scenario to ensure that the tool can swing in the flow channel and effectively cut the sidewalls, while avoiding interference with the sidewalls.

[0201] The tool length is the product of the maximum depth and the preset parameter, which can be a value between 1.1 and 1.2. This ensures that the tool length fully covers the flow channel depth and adds an extra 10%-20% depth as a safety margin to accommodate the tool holder, clamp, and possible tool overhang adjustments.

[0202] Furthermore, the axial depth of cut of the tool = (0.05~0.1) × tool diameter, and the radial step distance of the tool: (0.4~0.6) × tool diameter. When machining the flow channel with the tool, the axial depth of cut determines the depth of cut of the tool along the axial direction of the impeller flow channel, while the radial step distance determines the movement interval of the tool along the radial direction of the flow channel. The axial depth of cut and the radial step distance together determine the complete running trajectory and machining range of the tool during machining.

[0203] Based on the above tool parameters, an end mill is selected and applied to simulation software. If the ratio of the maximum depth to the minimum width of the flow channel is greater than the ratio threshold, it indicates an interference or insufficient rigidity problem. The adjustment path is then determined, and the specific process is as follows:

[0204] If sidewall interference or excessive tool rigidity causes cutting vibration, the diameter is reduced and the length-to-diameter ratio is increased. The length-to-diameter ratio is the effective overhang length of the tool cutting edge divided by the diameter of the tool cutting edge. The priority of the end mill is greater than that of the long neck end mill. The tool diameter setting coefficient is reduced from (0.7, 0.8) to (0.4, 0.6). The clearance between the tool and the sidewall is increased by reducing the diameter. The cost is a decrease in tool rigidity, that is, an increase in the length-to-diameter ratio, which requires further reduction of cutting parameters.

[0205] Specifically, if long-neck end mills still pose a risk of vibration or bottom interference, the tool geometry should be changed to optimize rigidity. In this case, long-neck end mills have a higher priority than tapered end mills. The tip diameter of the tool is (0.3~0.5) × minimum width. The taper angle is selected based on the ratio of the maximum depth to the minimum width. The larger the ratio, the smaller the required taper, so as to provide rigidity with the largest possible shank diameter while ensuring bottom clearance.

[0206] In summary, the target tool is a tapered tool, which is an ideal choice for deep cavity roughing. Its small tip diameter can effectively avoid sidewall interference, and its large shank diameter provides bending rigidity far exceeding that of a long neck tool with a constant diameter.

[0207] The method described above determines the width and depth ranges of the flow channel. Based on these ranges, the geometric constraints of the tool are determined. The entire process is algorithm-driven, ensuring repeatability and consistency in the obtained width and depth ranges. This guarantees the quality of the flow channel machining and allows for the selection of a target tool. It significantly reduces tool change time and idle travel, avoids residual allowances and tool marks at the junctions of areas where multiple tools are used, and improves the machining accuracy and efficiency of the flow channel.

[0208] like Figure 7 The diagram shown is a schematic representation of an automatic blade selection system for an impeller flow channel according to an exemplary embodiment, comprising the following modules:

[0209] The curve acquisition module 701 is used to construct a three-dimensional geometric model corresponding to the bladed disk, and based on the three-dimensional geometric model, determine the hub spline curve and casing spline curve corresponding to the flow channel;

[0210] The depth determination module 702 is used to parameterize the hub spline curve and the casing spline curve to obtain initial parameters, and to perform iterative calculations on each hub feature point based on the initial parameters to obtain the depth range corresponding to the flow channel.

[0211] The width determination module 703 is used to determine the suction surface curve and pressure surface curve corresponding to the flow channel based on the three-dimensional geometric model, traverse each feature point in the suction surface curve, determine the nearest feature point corresponding to each feature point from the pressure surface curve based on an iterative search algorithm, and determine the width range corresponding to the flow channel based on each feature point and its corresponding nearest feature point.

[0212] The automatic tool selection module 704 is used to determine the target tool corresponding to the flow channel based on the depth range and the width range.

[0213] In one possible design, the curve acquisition module 701 is specifically used to extract discrete data point sets of the hub surface and casing surface from the three-dimensional geometric model, extract the hub feature point set corresponding to the hub surface from the discrete data point set along the flow channel direction, and perform cubic spline interpolation processing on the hub feature point set to generate the hub spline curve; and extract the casing feature point set corresponding to the casing surface from the discrete data point set, and perform cubic spline interpolation processing on the casing feature point set to generate the casing spline curve.

[0214] In one possible design, the depth determination module 702 is specifically used to traverse each hub feature point on the hub spline curve and perform the following operations for each hub feature point: connect adjacent casing feature points in the casing spline curve to obtain multiple straight line segments; determine the vertical distance from the hub feature point to each straight line segment; determine the minimum vertical distance and the target straight line segment and perpendicular foot corresponding to the minimum vertical distance; determine the hub feature point coordinates, the perpendicular foot coordinates, and the endpoint coordinates corresponding to the target straight line segment; construct and solve a two-dimensional linear equation system based on the hub feature point coordinates, the perpendicular foot coordinates, and the endpoint coordinates to obtain the casing curve parameters and the minimum distance corresponding to the hub feature point; and determine the casing curve parameters and the minimum distance as the initial parameters corresponding to the hub feature point.

[0215] In one possible design, the depth determination module 702 is specifically used to determine each hub feature point from the hub spline curve and each casing feature point from the casing spline curve, using the initial parameters as the starting point for iteration; the hub feature points and the casing feature points correspond one-to-one, the effective distance between each hub feature point and the corresponding casing feature point is determined, and the position of the casing feature point corresponding to the minimum effective distance is determined by iteratively adjusting the parameter positions of the casing feature points; based on the casing feature point positions corresponding to each hub feature point, the depth range corresponding to the flow channel is determined.

[0216] In one possible design, the depth determination module 702 is further configured to construct an axial objective function and a radial objective function based on the current chassis feature point coordinates, the unit normal vector, and the current hub feature point coordinates; solve the axial objective function based on the current chassis feature point and the unit normal vector to obtain the axial function value; and solve the radial objective function to obtain the radial function value. If the absolute value of the axial function value is less than the axial tolerance threshold, and the absolute value of the radial function value is less than the radial tolerance threshold, then the position of the chassis feature point corresponding to the minimum effective spacing is determined. If the absolute value of the axial function value is not less than the axial tolerance threshold, or the absolute value of the radial function value is not less than the radial tolerance threshold, then the initial parameters are updated to obtain iterative parameters, and the parameter positions of the chassis feature points are adjusted based on the iterative parameters until the position of the chassis feature point corresponding to the minimum effective spacing is determined.

[0217] In one possible design, the depth determination module 702 is further configured to extract the casing curve parameters and minimum distance from the initial parameters, calculate the partial derivative of the axial objective function with respect to the casing curve parameters to obtain a first partial derivative, calculate the partial derivative of the axial objective function with respect to the minimum distance to obtain a second partial derivative, calculate the partial derivative of the radial objective function with respect to the casing curve parameters to obtain a third partial derivative, and calculate the partial derivative of the radial objective function with respect to the minimum distance to obtain a fourth partial derivative, construct and solve a system of linear equations based on the first, second, third, and fourth partial derivatives, the axial function value, and the radial function value to obtain the casing parameter compensation value corresponding to the casing curve parameters and the distance compensation value corresponding to the minimum distance, add the casing curve parameters and the casing parameter compensation value to obtain the updated casing curve parameters, add the minimum distance and the distance compensation value to obtain the updated minimum distance, and determine the updated casing curve parameters and the updated minimum distance as the iteration parameters.

[0218] In one possible design, the width determination module 703 is specifically used to offset the feature point circumferentially by a set angle value to obtain a virtual target point; based on the virtual target point, the circumferential angle of the feature point, and the set angle value, a target error function is constructed; the virtual target point is determined by iterative search based on the golden section algorithm; the set angle value is iteratively searched and updated based on the linear interpolation algorithm to determine the target angle value when the target error function is the set value; and based on the target angle value, the nearest feature point corresponding to the feature point is determined on the pressure surface curve.

[0219] In one possible design, the width determination module 703 is further configured to determine the arc length distance between each feature point in the suction surface curve and the corresponding nearest feature point, determine the minimum arc length distance and the maximum arc length distance from all arc length distances, and determine the width range corresponding to the flow channel based on the minimum arc length distance and the maximum arc length distance.

[0220] This disclosure provides a computer device, including:

[0221] A memory and a processor, wherein the memory stores a computer program that, when executed by the processor, implements the method of any of the above embodiments.

[0222] Corresponding to the embodiments of the foregoing methods, this specification also provides embodiments of the computer devices to which they are applied. Please refer to [link / reference needed] for details. Figure 8 , Figure 8 This is a basic structural block diagram of the computer device in this embodiment.

[0223] The computer device 8 includes a memory 81, a processor 82, and a network interface 83 that are interconnected via a system bus. It should be noted that only the computer device 8 with components 81-83 is shown in the figure; however, it should be understood that it is not required to implement all the shown components, and more or fewer components can be implemented alternatively. Those skilled in the art will understand that the computer device described here is a device capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions, and its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0224] The computer device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The computer device can interact with the user via a keyboard, mouse, remote control, touchpad, or voice control.

[0225] The memory 81 includes at least one type of readable storage medium, including flash memory, hard disk, multimedia card, card-type memory (e.g., SD or DX memory), random access memory (RAM), static random access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic memory, magnetic disk, optical disk, etc. In some embodiments, the memory 81 may be an internal storage unit of the computer device 8, such as the hard disk or memory of the computer device 8. In other embodiments, the memory 81 may also be an external storage device of the computer device 8, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. Of course, the memory 81 may include both internal storage units and external storage devices of the computer device 8. In this embodiment, the memory 81 is typically used to store the operating system and various information management operating systems installed on the computer device 8, such as computer-readable instructions for automatic tool selection methods in impeller flow channels. In addition, the memory 81 can also be used to temporarily store various types of data that have been output or will be output.

[0226] In some embodiments, the processor 82 may be a central processing unit (CPU), controller, microcontroller, microprocessor, or other data processing chip. The processor 82 is typically used to control the overall operation of the computer device 8. In this embodiment, the processor 82 is used to execute computer-readable instructions stored in the memory 81 or to process data, such as computer-readable instructions for executing an automatic tool selection method for a bladed disk flow path.

[0227] The network interface 83 may include a wireless network interface or a wired network interface, which is typically used to establish communication connections between the computer device 8 and other electronic devices.

[0228] This application also provides another embodiment, namely, a computer program product storing computer-readable instructions that can be executed by at least one processor to cause the at least one processor to perform the steps of the automatic tool selection method for the impeller flow channel as described above.

[0229] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0230] Other embodiments of this specification will readily occur to those skilled in the art upon consideration of the specification and practice of the invention claimed herein. This specification is intended to cover any variations, uses, or adaptations that follow the general principles of this specification and include common knowledge or customary techniques in the art not claimed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this specification are indicated by the following claims.

[0231] It should be understood that this specification is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this specification is limited only by the appended claims.

[0232] The above description is merely a preferred embodiment of this specification and is not intended to limit this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

Claims

1. An automatic blade selection method for a bladed disk flow channel, characterized in that, include: Construct a three-dimensional geometric model corresponding to the bladed disk, and based on the three-dimensional geometric model, determine the hub spline curve and casing spline curve corresponding to the flow channel; The hub spline curve and the casing spline curve are parameterized to obtain initial parameters, and the depth range corresponding to the flow channel is obtained by iterative calculation of each hub feature point based on the initial parameters. Based on the three-dimensional geometric model, the suction surface curve and pressure surface curve corresponding to the flow channel are determined. Each feature point in the suction surface curve is traversed. The nearest feature point corresponding to each feature point is determined from the pressure surface curve based on an iterative search algorithm. Based on each feature point and its corresponding nearest feature point, the width range corresponding to the flow channel is determined. Based on the depth range and the width range, the target tool corresponding to the flow channel is determined; The parameterization process for the hub spline curve and the casing spline curve to obtain initial parameters includes: For each hub feature point on the hub spline curve, perform the following operations: Connecting adjacent casing feature points in the casing spline curve yields multiple straight line segments; Determine the vertical distance from the hub feature point to each straight line segment, and determine the minimum vertical distance, the target straight line segment corresponding to the minimum vertical distance, and the foot of the perpendicular; Determine the coordinates of the hub feature point, the coordinates of the perpendicular foot, and the coordinates of the endpoints corresponding to the target straight line segment; Based on the coordinates of the hub feature point, the coordinates of the perpendicular foot, and the coordinates of the endpoint, a two-dimensional linear equation system is constructed and solved to obtain the casing curve parameters and minimum distance corresponding to the hub feature point. The casing curve parameters and the minimum distance are determined as the initial parameters corresponding to the hub feature points.

2. The method according to claim 1, characterized in that, The step of determining the hub spline curve and casing spline curve corresponding to the flow channel based on the three-dimensional geometric model includes: Extract discrete data point sets of the hub surface and casing surface from the three-dimensional geometric model; Along the flow channel direction, extract the hub feature point set corresponding to the hub surface from the discrete data point set, and perform cubic spline interpolation on the hub feature point set to generate the hub spline curve; Extract the set of casing feature points corresponding to the casing surface from the discrete data point set, and perform cubic spline interpolation on the set of casing feature points to generate the casing spline curve.

3. The method according to claim 1, characterized in that, The iterative calculation of each hub feature point based on the initial parameters to obtain the depth range corresponding to the flow channel includes: Using the initial parameters as the starting point of the iteration, each hub feature point is determined from the hub spline curve, and each casing feature point is determined from the casing spline curve; the hub feature points and the casing feature points correspond one-to-one. The effective distance between each hub feature point and the corresponding casing feature point is determined, and the position of the casing feature point corresponding to the minimum effective distance is determined by iteratively adjusting the parameter position of the casing feature point; The depth range of the flow channel is determined based on the location of the casing feature point corresponding to each hub feature point.

4. The method according to claim 3, characterized in that, The process of determining the effective distance between each hub feature point and its corresponding casing feature point, and determining the casing feature point position corresponding to the minimum effective distance by iteratively adjusting the parameter positions of the casing feature points, includes: Based on the current casing feature point coordinates, unit normal vector, and current hub feature point coordinates, construct axial and radial objective functions; Based on the current casing feature points and unit normal vector, the axial objective function is solved to obtain the axial function value, and the radial objective function is solved to obtain the radial function value; If the absolute value of the axial function value is less than the axial tolerance threshold, and the absolute value of the radial function value is less than the radial tolerance threshold, then the location of the casing feature point corresponding to the minimum effective spacing is determined. If the absolute value of the axial function value is not less than the axial tolerance threshold, or the absolute value of the radial function value is not less than the radial tolerance threshold, then the initial parameters are updated to obtain iterative parameters, and the parameter positions of the casing feature points are adjusted based on the iterative parameters until the position of the casing feature point corresponding to the minimum effective spacing is determined.

5. The method according to claim 4, characterized in that, The step of updating the initial parameters to obtain the iteration parameters includes: Extract the casing curve parameters and minimum distance from the initial parameters; Calculate the partial derivative of the axial objective function with respect to the casing curve parameters to obtain the first partial derivative, and calculate the partial derivative of the axial objective function with respect to the minimum distance to obtain the second partial derivative; Calculate the partial derivative of the radial objective function with respect to the casing curve parameters to obtain the third partial derivative, and calculate the partial derivative of the radial objective function with respect to the minimum distance to obtain the fourth partial derivative; Based on the first partial derivative, the second partial derivative, the third partial derivative, the fourth partial derivative, the axial function value, and the radial function value, a system of linear equations is constructed and solved to obtain the casing parameter compensation value corresponding to the casing curve parameter and the distance compensation value corresponding to the minimum distance. The casing curve parameters are added to the casing parameter compensation value to obtain the updated casing curve parameters, and the minimum distance is added to the distance compensation value to obtain the updated minimum distance. The updated casing curve parameters and the updated minimum distance are then determined as the iteration parameters.

6. The method according to claim 1, characterized in that, The step of determining the nearest feature point corresponding to each feature point from the pressure surface curve based on the iterative search algorithm includes: The feature point is offset by a set angle value along the circumferential direction to obtain a virtual target point; A target error function is constructed based on the virtual target point, the circumferential angle of the feature point, and the set angle value; the virtual target point is determined by iterative search based on the golden section algorithm. The set angle value is iteratively searched and updated based on the linear interpolation algorithm to determine the target angle value when the target error function is the set value; Based on the target angle value, the nearest feature point corresponding to the feature point is determined on the pressure surface curve.

7. The method according to claim 1, characterized in that, The step of determining the width range of the flow channel based on each feature point and its nearest corresponding feature point includes: Determine the arc length distance between each feature point in the suction surface curve and its nearest corresponding feature point; The minimum and maximum arc length distances are determined from all arc length distances, and the width range corresponding to the flow channel is determined based on the minimum and maximum arc length distances.

8. An automatic blade selection system for a bladed disk flow channel, characterized in that, The system includes: The curve acquisition module is used to construct a three-dimensional geometric model corresponding to the bladed disk, and based on the three-dimensional geometric model, determine the hub spline curve and casing spline curve corresponding to the flow channel; The depth determination module is used to parameterize the hub spline curve and the casing spline curve to obtain initial parameters, and to perform iterative calculations on each hub feature point based on the initial parameters to obtain the depth range corresponding to the flow channel. The width determination module is used to determine the suction surface curve and pressure surface curve corresponding to the flow channel based on the three-dimensional geometric model, traverse each feature point in the suction surface curve, determine the nearest feature point corresponding to each feature point from the pressure surface curve based on an iterative search algorithm, and determine the width range corresponding to the flow channel based on each feature point and its corresponding nearest feature point. An automatic tool selection module is used to determine the target tool corresponding to the flow channel based on the depth range and the width range; The parameterization process for the hub spline curve and the casing spline curve to obtain initial parameters includes: For each hub feature point on the hub spline curve, perform the following operations: Connecting adjacent casing feature points in the casing spline curve yields multiple straight line segments; Determine the vertical distance from the hub feature point to each straight line segment, and determine the minimum vertical distance, the target straight line segment corresponding to the minimum vertical distance, and the foot of the perpendicular; Determine the coordinates of the hub feature point, the coordinates of the perpendicular foot, and the coordinates of the endpoints corresponding to the target straight line segment; Based on the coordinates of the hub feature point, the coordinates of the perpendicular foot, and the coordinates of the endpoint, a two-dimensional linear equation system is constructed and solved to obtain the casing curve parameters and minimum distance corresponding to the hub feature point. The casing curve parameters and the minimum distance are determined as the initial parameters corresponding to the hub feature points.

9. A computer device, characterized in that, include: A memory and a processor, wherein the memory stores a computer program that, when executed by the processor, implements the automatic blade selection method for the impeller flow channel as described in any one of claims 1-7.

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