A complex curved surface machining row width fast calculation method, device, equipment and medium

Abstract

The application discloses a complex curved surface machining line width fast calculation method, device, equipment and medium, relates to numerical control machining technical field, and is used for solving the technical problems, such as lower calculation efficiency of prior art.The method comprises the following steps: according to the effective machining curved surface equation of a tool and the machining curved surface equation to be processed, an error distribution curve equation is established; the error distribution curve equation is subjected to Taylor expansion processing, and a first mathematical model is established; wherein the first mathematical model is used to represent the relationship between the error distribution curve and the curvature; the first mathematical model is analyzed and processed, and a second mathematical model is established; wherein the second mathematical model is used to represent the relationship between the curvature ratio and the machining line width; the machining line width is calculated according to the second mathematical model and the preset radial basis function; wherein the preset radial basis function is used to carry out interpolation on a specified group of function values in the data point set corresponding to the second mathematical model, so that the application can carry out high-dimensional interpolation through the radial basis function, thereby improving the calculation efficiency of the machining line width.

Description

Technical Field

[0001] This application relates to the field of CNC machining technology, and provides a method, apparatus, equipment and medium for rapid calculation of line width in complex surface machining. Background Technology

[0002] As is well known, machining line width (the actual machining width of each toolpath line) is a key machining parameter for CNC machining of complex curved surfaces. Its calculation efficiency directly affects the toolpath generation efficiency. High-efficiency machining line width calculation can significantly reduce toolpath generation time and the time spent on repetitive calculations when adjusting the overall machining scheme. At the same time, because the generated toolpath is smoother, the product machining accuracy and quality are also improved, thereby reducing the overall cost of workpiece machining. Based on this, researching toolpath optimization methods has significant theoretical and practical value.

[0003] Currently, researchers have proposed several tool trajectory optimization methods. For example, the Sturz method is proposed based on the position of the driving point on the curved surface and the information of the normal and tangential vectors at that point; or, the Sturz method is improved by extending the study of the effective cutting area of ​​the tool and the cross section of the workpiece surface to the curvature matching algorithm proposed by using the second-order approximation of differential geometry to examine the contact condition between the tool and the workpiece in the local area; or, a free surface machining algorithm based on two contact points (i.e., the multi-point method); or, a wide-line machining tool positioning optimization algorithm based on feature points on the error distribution curve (hereinafter referred to as the error distribution curve) is proposed by adjusting the tool positioning point from the contact point to a feature point on the machining error distribution curve (i.e., the midpoint method).

[0004] However, these methods do not delve into differential geometry to analyze the mathematical properties and spatial physical meaning of machining line width. Furthermore, since the machining line width of each toolpath depends entirely on the narrowest machining line width of all tool positions on that line, the machining efficiency is low. In addition, these methods require discretizing surfaces or tools for large iterative calculations, and the cumbersome computations result in low computational efficiency, which significantly limits the widespread application of wide-line machining toolpath optimization algorithms. Summary of the Invention

[0005] This application provides a method, apparatus, equipment, and medium for rapid calculation of line width in complex surface machining, which solves the technical problem of low calculation efficiency in the prior art.

[0006] On the one hand, a method for rapid calculation of line width in complex surface machining is provided, the method comprising:

[0007] Based on the effective machining surface equation and the surface to be machined equation, establish the error distribution curve equation;

[0008] The Taylor expansion of the error distribution curve equation is performed to establish a first mathematical model; wherein, the first mathematical model is used to represent the relationship between the error distribution curve and the curvature.

[0009] The first mathematical model is analyzed and processed to establish a second mathematical model; wherein, the second mathematical model is used to represent the relationship between the curvature ratio and the processing line width;

[0010] The processing row width is calculated based on the second mathematical model and the preset radial basis function; wherein the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model.

[0011] Optionally, the step of establishing the error distribution curve equation based on the effective machining surface equation and the surface to be machined includes:

[0012] Based on the effective machining surface equation and the surface to be machined equation, establish the error distribution surface equation;

[0013] Based on the error distribution surface equation, the error distribution curve constraints, and the preset spatial mapping relationship, the error distribution curve equation is established; wherein, the preset mapping relationship is used to map points on the error distribution curve to the error distribution curve on the two-dimensional plane.

[0014] Optionally, the step of performing Taylor expansion on the error distribution curve equation to establish the first mathematical model includes:

[0015] Taylor's formula and the curvature formula in Cartesian coordinates are used to perform Taylor expansion on the error distribution curve equation to construct multiple third mathematical models; wherein, the third mathematical model is used to represent the relationship between each point on the error distribution curve and the curvature;

[0016] Based on the multiple third mathematical models, the first mathematical model is established.

[0017] Optionally, the step of analyzing and processing the first mathematical model to establish the second mathematical model includes:

[0018] Based on the first mathematical model, an optimization objective equation set is established; wherein, the optimization objective equation set is used to describe the machining line width, the curvature on the error distribution curve, the curvature of the effective machining surface of the tool, and the maximum allowable machining error of the error distribution curve;

[0019] Based on the curvature of the error distribution curve and the curvature of the corresponding projection points on the surface to be processed, the optimization objective equations are simplified to establish the second mathematical model; wherein, the projection points on the surface to be processed correspond to the extreme points on the error distribution curve.

[0020] Optionally, the step of calculating the processing row width based on the second mathematical model and the preset radial basis function includes:

[0021] Based on the preset radial basis functions, the second mathematical model in the low-dimensional space is mapped to the second mathematical model in the high-dimensional space;

[0022] The processing row width is obtained based on the second mathematical model of the high-dimensional space.

[0023] Optionally, the first mathematical model can be represented by the following formula:

[0024]

[0025] in, This is the error distribution curve. On the error distribution curve The function value at point n, where n is the total number of points mapped by the error distribution curve. Let i be the i-th point on the error distribution curve. for curvature at that point For the point The small change at which a Taylor expansion is performed. for The second derivative of the function at the given value.

[0026] Optionally, the second mathematical model can be represented by the following formula:

[0027]

[0028] in, is a real-valued correction coefficient, related to the relative shapes of the tool and the surface. , , , These are the ratio of the maximum principal curvature of the contact point, the ratio of the minimum principal curvature of the contact point, the ratio of the maximum principal curvature of the extreme points on one side of the error distribution curve, and the ratio of the minimum principal curvature of the extreme points on one side of the error distribution curve, respectively.

[0029] On the one hand, a device for rapidly calculating the line width of complex curved surface machining is provided, the device comprising:

[0030] The first establishment unit is used to establish the error distribution curve equation based on the effective machining surface equation and the surface to be machined.

[0031] The second establishment unit is used to perform Taylor expansion processing on the error distribution curve equation to establish the first mathematical model; wherein, the first mathematical model is used to represent the relationship between the error distribution curve and the curvature;

[0032] The third unit is used to analyze and process the first mathematical model and establish a second mathematical model; wherein, the second mathematical model is used to represent the relationship between the curvature ratio and the processing line width;

[0033] The processing line width calculation unit is used to calculate the processing line width based on the second mathematical model and a preset radial basis function; wherein the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model.

[0034] On one hand, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement any of the methods described above.

[0035] On the one hand, a storage medium is provided that stores computer program instructions thereon, which, when executed by a processor, implement any of the methods described above.

[0036] Compared with the prior art, the beneficial effects of this application are as follows:

[0037] In this application, when calculating the machining width of a complex curved surface, firstly, an error distribution curve equation can be established based on the effective machining surface equation and the surface to be machined equation; then, a Taylor expansion of the error distribution curve equation can be performed to establish a first mathematical model; wherein, the first mathematical model is used to represent the relationship between the error distribution curve and the curvature; next, the first mathematical model can be analyzed to establish a second mathematical model; wherein, the second mathematical model is used to represent the relationship between the curvature ratio and the machining width; finally, the machining width can be calculated based on the second mathematical model and a preset radial basis function; wherein, the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model.

[0038] Based on this, in this application, since radial basis functions are used to quickly generate the machining width of complex surfaces and interpolation is used instead of iterative calculation, compared with the prior art, this application can combine radial basis functions with key machining parameters on the basis of fully considering the local neighborhood variation law of feature points on the error distribution curve, so that the calculation process of the narrowest machining width is traceable, thereby effectively improving the calculation efficiency of machining width and expanding the applicability of the wide-line machining tool position optimization algorithm. Attached Figure Description

[0039] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0040] Figure 1 This is a schematic diagram of an application scenario provided by an embodiment of this application;

[0041] Figure 2 A schematic diagram of a method for rapidly calculating the line width of complex curved surface machining provided in an embodiment of this application;

[0042] Figure 3 A schematic diagram illustrating the effective machining surface of a cutting tool according to an embodiment of this application;

[0043] Figure 4 A schematic diagram of the error distribution surface and error distribution curve of a two-point contact provided in an embodiment of this application;

[0044] Figure 5 A schematic diagram illustrating spatial mapping of an error distribution curve provided in an embodiment of this application;

[0045] Figure 6 A two-dimensional geometric relationship diagram illustrating the ratio of the machining row width to the minimum principal curvature of the cutting contact point, provided in an embodiment of this application;

[0046] Figure 7 A schematic diagram of a two-dimensional geometric relationship between the ratio of the processing line width to the minimum principal curvature of one extreme point on the error distribution curve, provided in an embodiment of this application;

[0047] Figure 8 A two-dimensional geometric relationship diagram of the ratio of the machining row width to the maximum principal curvature of the cutting contact point provided in the embodiments of this application;

[0048] Figure 9 A two-dimensional geometric diagram illustrating the ratio of the processing line width to the maximum principal curvature of one extreme point on the error distribution curve, as provided in an embodiment of this application.

[0049] Figure 10 A two-dimensional geometric relationship diagram of the ratio of the processing line width to the maximum and minimum principal curvature of the cutting contact point provided in the embodiments of this application;

[0050] Figure 11 A schematic diagram of a two-dimensional geometric relationship between the ratio of the maximum and minimum principal curvature of the extreme points on one side of the error distribution curve, provided in an embodiment of this application;

[0051] Figure 12A schematic diagram of the blade basin surface of a certain type of aero-engine provided in an embodiment of this application;

[0052] Figure 13 A schematic diagram comparing the processing row width result with the reference value provided in an embodiment of this application;

[0053] Figure 14 A time comparison diagram of the interpolation algorithm of this application and the conventional line width processing algorithm provided in the embodiments of this application;

[0054] Figure 15 A schematic diagram of a complex curved surface of an aircraft landing gear provided in an embodiment of this application;

[0055] Figure 16 Another comparative diagram of the processing row width result and the reference value provided in the embodiments of this application;

[0056] Figure 17 A schematic diagram showing another time comparison between the interpolation algorithm of this application and the conventional line width processing algorithm, provided for an embodiment of this application;

[0057] Figure 18 This is a schematic diagram of a device for rapidly calculating the line width of complex curved surface processing provided in an embodiment of this application.

[0058] The diagram is labeled as follows: 10- Rapid calculation device for line width of complex surface machining, 101- Processor, 102- Memory, 103- I / O interface, 104- Database, 180- Rapid calculation device for line width of complex surface machining, 1801- First establishment unit, 1802- Second establishment unit, 1803- Third establishment unit, 1804- Machining line width calculation unit. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application. Unless otherwise specified, the embodiments and features in the embodiments of this application can be arbitrarily combined with each other. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than that shown here.

[0060] As is well known, machining line width (the actual machining width of each toolpath line) is a key machining parameter for CNC machining of complex curved surfaces. Its calculation efficiency directly affects the toolpath generation efficiency. High-efficiency machining line width calculation can significantly reduce toolpath generation time and the time spent on repetitive calculations during overall machining scheme adjustments. Furthermore, because the generated toolpaths are smoother, the product machining accuracy and quality are improved, thereby reducing the overall cost of workpiece machining. Therefore, researching toolpath optimization methods has significant theoretical and practical value.

[0061] Currently, researchers have proposed several tool trajectory optimization methods. For example, the Sturz method is proposed based on the position of the driving point on the curved surface and the information of the normal and tangential vectors at that point; or, the Sturz method is improved by extending the study of the effective cutting area of ​​the tool and the cross section of the workpiece surface to the curvature matching algorithm proposed by using the second-order approximation of differential geometry to examine the contact condition between the tool and the workpiece in the local area; or, a free surface machining algorithm based on two contact points (i.e., the multi-point method); or, a wide-line machining tool positioning optimization algorithm based on feature points on the error distribution curve (hereinafter referred to as the error distribution curve) is proposed by adjusting the tool positioning point from the contact point to a feature point on the error distribution curve (i.e., the midpoint method).

[0062] However, these methods do not delve into differential geometry to analyze the mathematical properties and spatial physical meaning of machining line width. Furthermore, since the machining line width of each toolpath depends entirely on the narrowest machining line width of all tool positions on that line, the machining efficiency is low. In addition, these methods require discretizing surfaces or tools for large iterative calculations, and the cumbersome computations result in low computational efficiency, which significantly limits the widespread application of wide-line machining toolpath optimization algorithms.

[0063] Based on this, embodiments of this application provide a method for rapidly calculating the machining width of complex curved surfaces. In this method, firstly, an error distribution curve equation can be established based on the effective machining surface equation and the surface to be machined equation. Then, a Taylor expansion of the error distribution curve equation can be performed to establish a first mathematical model, which represents the relationship between the error distribution curve and curvature. Next, the first mathematical model can be analyzed to establish a second mathematical model, which represents the relationship between the curvature ratio and the machining width. Finally, the machining width can be calculated based on the second mathematical model and a preset radial basis function, where the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model. Based on this, in this application, since radial basis functions are used to quickly generate the machining width of complex surfaces and interpolation is used instead of iterative calculation, compared with the prior art, this application can combine radial basis functions with key machining parameters on the basis of fully considering the local neighborhood variation law of feature points on the error distribution curve, so that the calculation process of the narrowest machining width is traceable, thereby effectively improving the calculation efficiency of machining width and expanding the applicability of the wide-line machining tool position optimization algorithm.

[0064] After introducing the design concept of the embodiments of this application, the following is a brief introduction to the application scenarios to which the technical solutions of the embodiments of this application can be applied. It should be noted that the application scenarios described below are only for illustrating the embodiments of this application and are not intended to limit the scope. In specific implementation, the technical solutions provided by the embodiments of this application can be flexibly applied according to actual needs.

[0065] like Figure 1 The diagram shown is an application scenario illustration provided by an embodiment of this application. This application scenario may include a device 10 for rapidly calculating the line width of complex curved surfaces.

[0066] The complex surface machining line width fast calculation device 10 can be used to quickly calculate the machining line width of complex surfaces. For example, it can be an in-vehicle computer, a personal computer (PC), a server, or a laptop. The complex surface machining line width fast calculation device 10 may include one or more processors 101, memory 102, I / O interfaces 103, and a database 104. Specifically, the processor 101 can be a central processing unit (CPU) or a digital processing unit, etc. The memory 102 can be volatile memory, such as random-access memory (RAM); the memory 102 can also be non-volatile memory, such as read-only memory, flash memory, hard disk drive (HDD), or solid-state drive (SSD); or the memory 102 can be any other medium capable of carrying or storing desired program code in the form of instructions or data structures that can be accessed by a computer, but is not limited thereto. The memory 102 can be a combination of the above-mentioned memories. The memory 102 can store some program instructions of the method for quickly calculating the line width of complex surface machining provided in the embodiments of this application. When these program instructions are executed by the processor 101, they can be used to implement the steps of the method for quickly calculating the line width of complex surface machining provided in the embodiments of this application, so as to solve the technical problem of low calculation efficiency in the prior art. The database 104 can be used to store data such as the first mathematical model, the second mathematical model, and the preset radial basis function involved in the solution provided in the embodiments of this application.

[0067] In this embodiment, the complex surface machining line width fast calculation device 10 can obtain machining line width calculation instructions through the I / O interface 103. Then, the processor 101 of the complex surface machining line width fast calculation device 10 will solve the technical problems such as low calculation efficiency of the prior art according to the program instructions of the complex surface machining line width fast calculation method provided in this embodiment of the application in the memory 102. In addition, the first mathematical model, the second mathematical model, and the preset radial basis function can be stored in the database 104.

[0068] Of course, the methods provided in the embodiments of this application are not limited to... Figure 1 The application scenarios shown can also be used in other possible scenarios, and this application embodiment does not impose any limitations. Figure 1The functions that the various devices in the application scenarios shown can achieve will be described in subsequent method embodiments, and will not be elaborated on here. Below, the methods of the embodiments of this application will be described in conjunction with the accompanying drawings.

[0069] like Figure 2 The diagram shown is a flowchart illustrating a method for rapidly calculating the line width of complex curved surface machining according to an embodiment of this application. This method can... Figure 1 The complex curved surface machining process is performed using a rapid calculation device 10. The specific process flow is as follows.

[0070] Step 201: Establish the error distribution curve equation based on the effective machining surface equation and the surface to be machined equation.

[0071] In this application, as Figure 3 The diagram shown is a schematic representation of an effective machined surface provided by a tool according to an embodiment of this application. Figure 3 This application can establish an error distribution curve equation based on the relationship between tool curvature, tool position and orientation and the surface to be machined under a certain instant.

[0072] Specifically, firstly, we can assume that the effective machined surface of the toroidal cutting tool is as follows: The surface to be processed is ,like Figure 3 As shown, the surface to be processed parameters Curved surfaces can be effectively machined by cutting tools. The parameters are obtained through a unique functional mapping relationship. Based on this, the error distribution surface equation can be established according to the effective machining surface equation and the surface to be machined; in this application, this error distribution surface equation... It can be expressed using the following formula (1):

[0073] (1)

[0074] in, These are the position parameters on the generatrix of the toroidal tool. The angle of rotation of the generatrix around the tool rotation axis is given by formula (1). Formula (1) can be used to represent the error distribution surface at a certain instant when the tool is in a certain position and posture. The error distribution surface is constructed based on the surface parameters corresponding to the points on the error distribution surface and the specific values ​​of the error distribution.

[0075] like Figure 4 The diagram shown is a schematic representation of the error distribution surface and error distribution curve of a two-point contact provided in an embodiment of this application. In this application, the error distribution curve on the error distribution surface needs to satisfy the error distribution curve constraint condition shown in the following formula (2):

[0076] (2)

[0077] The error distribution curve is a spatial curve on the error distribution surface. Calculating its curvature distribution is complex. To simplify the calculation, a spatial mapping relationship can be established, such as... Figure 5 The diagram shown is a schematic diagram of spatial mapping of the error distribution curve provided in an embodiment of this application. The preset spatial mapping relationship can be represented by the following formula (3):

[0078] (3)

[0079] Furthermore, based on the preset spatial mapping relationship shown in formula (3), the error distribution curve can be mapped onto a two-dimensional plane, and the points on the mapped error distribution curve can be represented as follows: Furthermore, based on the point set on the mapped error distribution curve, the differentiable continuous function expression of the error distribution curve can be obtained as shown in the following formula (3):

[0080] (4)

[0081] Where P is a point on the mapped error distribution curve.

[0082] That is, in this application, the error distribution curve equation can be established based on the error distribution surface equation, the error distribution curve constraint conditions, and the preset spatial mapping relationship; wherein, the preset mapping relationship is used to map the points on the error distribution curve to the error distribution curve on the two-dimensional plane.

[0083] Step 202: Perform Taylor expansion on the error distribution curve equation to establish the first mathematical model.

[0084] In this application, the first mathematical model can be used to represent the relationship between the error distribution curve and the curvature.

[0085] Among them, the error distribution curve The known information at a point can be represented by the following formula (5):

[0086] (5)

[0087] Furthermore, due to the error distribution curve in curvature at point Since the variable is unknown, in this application, in order to establish the relationship between the error distribution curve and the curvature, it is possible to... Performing a Taylor expansion at the point yields the following formula (6). :

[0088] (6)

[0089] in, For the point A higher-order small quantity that undergoes a Taylor expansion at a given point.

[0090] Furthermore, based on Taylor's formula and the curvature formula of a curve in Cartesian coordinates, and ignoring higher-order infinitesimals of order two and above, we can obtain the expression shown in formula (7):

[0091] (7)

[0092] Then, according to formulas (5)-(7), the parameters shown in formula (8) are obtained. The expression:

[0093] (8)

[0094] Therefore, based on formulas (7) and (8), we can obtain the following formula (9). The third mathematical model at the point (the mathematical expression between the error distribution curve and the curvature):

[0095] (9)

[0096] Then, for the remaining points on the error distribution curve, the above method can be used. The method of solving the third mathematical model at a point is used to obtain the third mathematical model for the remaining points on the error distribution curve.

[0097] That is, in this application, multiple third mathematical models as shown in formula (9) can be constructed based on the error distribution curve equation, Taylor formula and curvature formula under Cartesian coordinates; wherein, the third mathematical model is used to represent the relationship between each point on the error distribution curve and the curvature.

[0098] Then, based on multiple third mathematical models, the first mathematical model can be established. That is, based on these multiple third mathematical models, a second mathematical model can be established between the entire error distribution curve and the curvature, as shown in formula (10):

[0099] (10)

[0100] Among them, point function value at From the first point function value at and curvature values ​​at each point Obtained through calculation.

[0101] Step 203: Analyze and process the first mathematical model to establish the second mathematical model.

[0102] In this application, a second mathematical model is used to represent the relationship between the curvature ratio and the processing line width.

[0103] Specifically, based on formula (10), the unknown variable in formula (10) is the curvature of the error distribution curve. According to the definition of the error distribution curve, it can be determined based on the current tool posture. The curvature of the surface effectively machined by the cutting tool and the curvature of the surface to be processed To determine the curvature on the error distribution curve. Based on this, in this application, according to the first mathematical model, the following set of optimization objective equations can be established as shown in formula (11); wherein, the set of optimization objective equations is used to describe the machining width, the curvature on the error distribution curve, the curvature of the effective machining surface of the tool, and the maximum allowable machining error of the error distribution curve.

[0104] (11)

[0105] As shown in formula (11), when the objective function is to maximize the machining width, the optimal tool posture is affected. Given that the tool's geometry is known, the curvature of the surface effectively machined by the tool is... It is also known that, therefore, only the curvature of the surface to be processed needs to be obtained. Then the curvature on the error distribution curve can be completely determined. This allows us to completely determine the shape of the error distribution curve.

[0106] In this application, the principal curvature value corresponding to the radius of rotation of the tool about the axis of rotation is defined as... The principal curvature value corresponding to the radius of the torus parent circle is The error distribution curve is within the maximum permissible machining error range. The portion within the range is called the effective error distribution curve. Under these constraints, the two points furthest apart determine the width of the processing line. To eliminate the influence of tool size on the mathematical model, a curvature ratio is specified. Extending the conclusion to machined surfaces of arbitrary size and rotary cutting tools, we assume the ratio of the maximum principal curvature is [value missing]. The minimum principal curvature ratio is .

[0107] Furthermore, considering the characteristic points on the error distribution curve that are sensitive to the influence of the machining line width, namely, the relationship between the principal curvature ratio of the projection points on the surface to be machined corresponding to the contact point and the extreme points on one side of the error distribution curve, and the machining line width. In this application, based on statistical principles, formula (11) can be simplified by analyzing the characteristics of the error distribution curve and the distribution characteristics of the curvature ratio of the points on the surface to be machined corresponding to the extreme points on the error distribution curve, thereby establishing a second mathematical model (mathematical model of curvature-machining line width) as shown in formula (12):

[0108] (12)

[0109] in, is a real-valued correction coefficient, related to the relative shapes of the tool and the surface. , , , These are the ratio of the maximum principal curvature of the contact point, the ratio of the minimum principal curvature of the contact point, the ratio of the maximum principal curvature of the extreme points on one side of the error distribution curve, and the ratio of the minimum principal curvature of the extreme points on one side of the error distribution curve, respectively.

[0110] like Figure 6 The diagram shown is a two-dimensional geometric relationship diagram of the ratio of the machining line width to the minimum principal curvature of the cutting contact point provided in an embodiment of this application. Figure 6 The minimum principal curvature k1 on the x-axis is... ;like Figure 7 The diagram shown illustrates a two-dimensional geometric relationship between the processing line width and the minimum principal curvature ratio of one extreme point on the error distribution curve, as provided in an embodiment of this application. Figure 7 The minimum principal curvature k2 on the x-axis is... ;like Figure 8 The diagram shown is a two-dimensional geometric relationship diagram of the ratio of the machining row width to the maximum principal curvature of the cutting contact point provided in an embodiment of this application. Figure 8 The maximum principal curvature k1 on the x-axis is... ;like Figure 9 The diagram shown illustrates a two-dimensional geometric relationship between the processing line width and the ratio of the maximum principal curvature of one extreme point on the error distribution curve, as provided in an embodiment of this application. Figure 9 The maximum principal curvature k2 on the x-axis is... ;like Figure 10 The diagram shown illustrates a two-dimensional geometric relationship between the processing line width and the ratio of the maximum and minimum principal curvature of the contact point, as provided in an embodiment of this application. Figure 11 The diagram shown is a two-dimensional geometric relationship diagram of the ratio of the maximum and minimum principal curvature of the processing line width and the extreme point on one side of the error distribution curve provided in the embodiments of this application.

[0111] Step 204: Calculate the processing line width based on the second mathematical model and the preset radial basis function.

[0112] In this application, the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model.

[0113] From the perspective of applied mathematics, there are 4 parameter variables in formula (12) and none of the variables have obvious linear correlation. Therefore, it has the problem of data linear inseparability in the "low-dimensional space", which makes it difficult to calculate the processing line width.

[0114] Furthermore, in order to solve the problem of linearly inseparable data, in this application, the functional relationship of the processing line width changing with the principal curvature can be mapped to a parametric surface in a "high-dimensional space". The data of all feature sampling points are used as interpolation parameters for scattered data points, and the processing line width is used as a property of the function. Both the interpolation parameters and the function property can be described by the parametric surface equation in the high-dimensional space. Thus, the processing line width can be obtained by solving the parametric surface equation system by optimizing the numerical method (i.e., by interpolation).

[0115] The basic principle of mapping from low-dimensional space to high-dimensional space is as follows:

[0116] Assumption and To represent the two coordinate values ​​of a point on a two-dimensional plane in the Cartesian coordinate system, the parametric surface in low-dimensional space can be represented by the quadratic curve equation of the following formula (13):

[0117] (13)

[0118] Next, consider constructing a five-dimensional "high-dimensional space," where the five coordinate values ​​of a point in this high-dimensional space can be respectively... Then, the hyperplane equation of formula (14) can be used to represent the parametric surface in the five-dimensional coordinate system:

[0119] (14)

[0120] Based on this, in this application, it is possible to... and Mapped to This transforms the problem of linearly inseparable data in low-dimensional space into a problem of linearly separable data in high-dimensional space. Then, a linear optimization algorithm is used to process the problem of linearly separable data.

[0121] Specifically, firstly, the second mathematical model in low-dimensional space can be mapped to a second mathematical model in high-dimensional space based on the preset radial basis function. In this application, a Gaussian radial basis function with high stability and good computational efficiency (of course, radial basis functions such as quadratic functions, inverse quadratic functions, and thin-plate spline functions can also be used) can be used as the interpolation function, wherein the Gaussian radial basis function can be expressed by the following formula (15):

[0122] (15)

[0123] Furthermore, the inner product of the Gaussian radial basis functions can be expressed by the following formula (16):

[0124] (16)

[0125] Then, you can Substituting the Taylor expansion into formula (16), we can obtain the following formula (17), which shows a mapping relationship from a low-dimensional space to a high-dimensional space:

[0126] (17)

[0127] Furthermore, based on the mapping relationship of the Gaussian radial basis function shown in formula (17), a set of function values ​​specified for any data point set in the low-dimensional space can be interpolated to obtain accurate results (defining a smoothing function). In this application, for the abstract functional relationship between the processing line width and the principal curvature of the surface to be processed, the processing line width can be defined as a function attribute, and the principal curvature of the surface to be processed can be used as a multidimensional independent variable data point set.

[0128] Then, the processing line width can be obtained directly from the second mathematical model in the high-dimensional space.

[0129] That is, it can be given Each has processing line width Multidimensional principal curvature data points and Gaussian radial basis functions For multidimensional principal curvature data points Any multidimensional principal curvature data point within the range of values Its interpolation form can be expressed by the following formula (18):

[0130] (18)

[0131] Among them, the norm between non-coincident points (i.e., spatial distance calculation) is based on the Euclidean norm of the spatial vector. Dimensional vector weight factor Depend on The system of linear equations of order 1 is solved, and the solution is obtained using the Gaussian radial basis functions. middle, As a scaling factor, its value will significantly change the shape of the interpolation function. Generally, it is considered to select a value between the minimum and maximum distances between all non-overlapping points in the multidimensional data point set. Using the interpolation form of formula (18), the processing line width of the corresponding data point is calculated. Specific Implementation Example 1:

[0133] This embodiment uses Windows 10 as the operating environment, OpenGL as the graphics engine, and Visual C++ 2022 as the development tool. The blade basin surface of a certain type of aero-engine is selected as the surface to be processed. Figure 12 The image shown is a schematic diagram of the blade basin surface of a certain type of aero-engine provided in an embodiment of this application.

[0134] In response to this Figure 12 The leaf basin surface shown can be processed using the rapid calculation method for the machining width of complex curved surfaces proposed in this application. The specific steps are as follows:

[0135] Step 1: Assume the expression of the surface to be processed is as follows: Effectively processed curved surfaces are Then, the error distribution surface shown in formula (1) can be obtained. Based on this, the error distribution curve on the error distribution surface can be mapped onto a two-dimensional plane, and the points on the mapped error distribution curve can be represented as... Therefore, the error distribution curve can be expressed as: .

[0136] Step 2: Based on the error distribution curve equation obtained in Step 1, and combined with formulas (5)-(9), the first mathematical model representing the relationship between the entire error distribution curve and curvature can be obtained. .

[0137] Step 3: Using the optimization objective equation set (11) established by the first mathematical model, the characteristics of the error distribution curve and the curvature ratio distribution characteristics of the points on the surface to be processed corresponding to the extreme points on the error distribution curve are analyzed, thereby establishing the second mathematical model. The second mathematical model corresponds to multiple discrete point sets of curvature ratio-processing line width (for example, by establishing the second mathematical model with a step size of 0.1, a total of 231 discrete point sets can be obtained), as shown in Table 1, which is a relational table of some discrete point sets provided in the embodiments of this application.

[0138] Table 1

[0139]

[0140] Step 4: On the curved surface of the aero-engine blade, select a set of feature point curvature points with a step size of 0.05. Using the discrete point set in Table 1 as a reference, perform radial basis function interpolation calculations based on formula (18) and the feature point curvature to obtain the approximate machining width. Figure 13 The diagram shown is a comparison between the processing line width result and the reference value provided in an embodiment of this application. It can be seen that, in terms of interpolation accuracy, the maximum interpolation error of this application is approximately... The vast majority of interpolation results perfectly match the benchmark values; for example... Figure 14 The diagram shown is a time comparison diagram between the interpolation algorithm of this application and the conventional line width processing algorithm provided in the embodiment of this application. It can be seen that in terms of calculation speed, the processing line width calculation time of each interpolation point of this application is shortened by about 85%. Specific Implementation Example 2:

[0142] The complex curved surface to be processed is the complex curved surface of an aircraft landing gear. The processing line width is calculated using the same rapid calculation method for complex curved surface processing described in Specific Embodiment 1, as follows: Figure 15 The image shown is a schematic diagram of a complex curved surface of an aircraft landing gear provided in an embodiment of this application.

[0143] against Figure 13 The geometric features of a component shown can be used to calculate the machining width by interpolating the curvature of feature points based on a preset radial basis function. For example... Figure 16 As shown, this is another comparative diagram of the processing row width result and the reference value provided in the embodiment of this application, as follows: Figure 17 The diagram shown is a time comparison diagram between the interpolation algorithm of this application and the conventional line width machining algorithm provided in the embodiment of this application. It can be seen that the machining line width calculated by this application is not only smoother, but the error is also within the allowable range, and the calculation time is shortened by more than 90%, which can effectively improve the toolpath calculation efficiency and greatly improve the overall machining efficiency including toolpath modification and adjustment.

[0144] In summary, this application establishes a functional relationship between the error distribution curve and the curvature ratio by theoretically analyzing the initial definition of the processing line width and combining spatial differential geometry. Based on statistical principles, it summarizes the trend of the processing line width with the curvature ratio and applies a high-dimensional data interpolation method based on radial basis functions to quickly calculate the processing line width. Thus, by fully considering the local neighborhood variation law of feature points on the error distribution curve, the high-dimensional data interpolation method is combined with key processing parameters, making the calculation process of the narrowest processing line width traceable, thereby effectively improving the calculation efficiency of the key processing line width.

[0145] Furthermore, the rapid calculation method for machining path width in this application is applicable to machining complex curved surfaces with arbitrary rotary tools. It can save a lot of calculation time, especially for large component models with a large number of complex curved surfaces, and can be further extended to the rapid generation of wide-path machining toolpaths.

[0146] Based on the same inventive concept, embodiments of this application provide a device 180 for rapid calculation of line width in complex curved surface processing, such as... Figure 18 As shown, the complex surface machining line width rapid calculation device 180 includes:

[0147] The first establishing unit 1801 is used to establish the error distribution curve equation based on the effective machining surface equation of the tool and the machining surface equation;

[0148] The second establishing unit 1802 is used to perform Taylor expansion processing on the error distribution curve equation to establish the first mathematical model; wherein, the first mathematical model is used to represent the relationship between the error distribution curve and the curvature;

[0149] The third unit 1803 is used to analyze and process the first mathematical model and establish a second mathematical model; wherein, the second mathematical model is used to represent the relationship between the curvature ratio and the processing line width;

[0150] The processing line width calculation unit 1804 is used to calculate the processing line width based on the second mathematical model and the preset radial basis function; wherein, the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model.

[0151] Optionally, the first establishment unit 1801 is also used for:

[0152] Based on the effective machining surface equation and the surface to be machined equation, establish the error distribution surface equation;

[0153] Based on the error distribution surface equation, the error distribution curve constraints, and the preset spatial mapping relationship, the error distribution curve equation is established; whereby the preset mapping relationship is used to map points on the error distribution curve to the error distribution curve on the two-dimensional plane.

[0154] Optionally, the second establishment unit 1802 is also used for:

[0155] Taylor's formula and the curvature formula in Cartesian coordinates are used to perform Taylor expansion on the error distribution curve equation to construct multiple third mathematical models; among them, the third mathematical models are used to represent the relationship between each point on the error distribution curve and the curvature.

[0156] Based on multiple third mathematical models, a first mathematical model is established.

[0157] Optionally, the third establishment unit 1803 is also used for:

[0158] Based on the first mathematical model, an optimization objective equation set is established; wherein, the optimization objective equation set is used to describe the machining line width, the curvature on the error distribution curve, the curvature of the effective machining surface of the tool, and the maximum allowable machining error of the error distribution curve;

[0159] Based on the curvature of the error distribution curve and the curvature of the corresponding projection points on the surface to be processed, the optimization objective equations are simplified to establish a second mathematical model; where the projection points on the surface to be processed correspond to the extreme points on the error distribution curve.

[0160] Optionally, the processing line width calculation unit 1804 is also used for:

[0161] Based on the preset radial basis functions, the second mathematical model in the low-dimensional space is mapped to the second mathematical model in the high-dimensional space;

[0162] The processing line width is obtained based on the second mathematical model of high-dimensional space.

[0163] The complex surface machining line width fast calculation device 180 can be used to perform... Figure 2 The method executed by the complex surface machining line width rapid calculation device in the illustrated embodiment is described above. Therefore, the functions that each functional module of the complex surface machining line width rapid calculation device 180 can achieve can be referred to. Figure 2 The embodiments shown are described in detail below.

[0164] In some possible implementations, various aspects of the methods provided in this application can also be implemented as a program product comprising program code that, when run on a computer device, causes the computer device to perform the steps of the methods according to the various exemplary embodiments of this application described above. For example, the computer device may perform actions such as... Figure 2 The method performed by the rapid calculation device for the line width of complex curved surface machining in the illustrated embodiment.

[0165] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks. Alternatively, if the integrated units of this application are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this application, or the parts that contribute to the prior art, can be embodied in the form of software products. These computer software products are stored in a storage medium and include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0166] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0167] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for rapid calculation of line width in complex surface machining, characterized in that, The method includes: Based on the effective machining surface equation and the surface to be machined equation, establish the error distribution curve equation; The Taylor expansion of the error distribution curve equation is performed to establish a first mathematical model; wherein, the first mathematical model is used to represent the relationship between the error distribution curve and the curvature. The first mathematical model is analyzed and processed to establish a second mathematical model; wherein the second mathematical model is used to represent the relationship between the curvature ratio and the processing line width; the steps of analyzing and processing the first mathematical model to establish the second mathematical model include: Based on the first mathematical model, an optimization objective equation set is established; wherein, the optimization objective equation set is used to describe the machining width, the curvature on the error distribution curve, the curvature of the effective machining surface of the tool, and the maximum allowable machining error of the error distribution curve; Based on the curvature of the error distribution curve and the curvature of the corresponding projection points on the surface to be processed, the optimization objective equations are simplified to establish the second mathematical model; wherein, the projection points on the surface to be processed correspond to the extreme points on the error distribution curve; The processing line width is calculated based on the second mathematical model and a preset radial basis function; wherein, the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model; the step of calculating the processing line width based on the second mathematical model and the preset radial basis function includes: Based on the preset radial basis functions, the second mathematical model in the low-dimensional space is mapped to the second mathematical model in the high-dimensional space; The processing row width is obtained based on the second mathematical model of the high-dimensional space.

2. The method as described in claim 1, characterized in that, The step of establishing the error distribution curve equation based on the effective machining surface equation and the surface to be machined includes: Based on the effective machining surface equation and the surface to be machined equation, establish the error distribution surface equation; Based on the error distribution surface equation, the error distribution curve constraint conditions, and the preset spatial mapping relationship, the error distribution curve equation is established; wherein, the preset spatial mapping relationship is used to map points on the error distribution curve to the error distribution curve on the two-dimensional plane.

3. The method as described in claim 1, characterized in that, The steps of performing Taylor expansion on the error distribution curve equation to establish the first mathematical model include: Taylor's formula and the curvature formula in Cartesian coordinates are used to perform Taylor expansion on the error distribution curve equation to construct multiple third mathematical models; wherein, the third mathematical model is used to represent the relationship between each point on the error distribution curve and the curvature; Based on the multiple third mathematical models, the first mathematical model is established.

4. The method as described in claim 1, characterized in that, The first mathematical model is represented by the following formula: in, This is the error distribution curve. On the error distribution curve The function value at point n, where n is the total number of points mapped by the error distribution curve. Let i be the i-th point on the error distribution curve. for curvature at that point For the point The small change at which a Taylor expansion is performed. for The second derivative of the function at the given value.

5. The method as described in claim 1, characterized in that, The second mathematical model is represented by the following formula: in, These are real-valued correction coefficients, related to the relative shapes of the tool and the surface. , , , These are the ratio of the maximum principal curvature of the contact point, the ratio of the minimum principal curvature of the contact point, the ratio of the maximum principal curvature of the extreme points on one side of the error distribution curve, and the ratio of the minimum principal curvature of the extreme points on one side of the error distribution curve, respectively.

6. A device for rapidly calculating the width of machining complex curved surfaces, characterized in that, The device includes: The first establishment unit is used to establish the error distribution curve equation based on the effective machining surface equation and the surface to be machined. The second establishment unit is used to perform Taylor expansion processing on the error distribution curve equation to establish the first mathematical model; wherein, the first mathematical model is used to represent the relationship between the error distribution curve and the curvature; The third unit is used to analyze and process the first mathematical model to establish a second mathematical model; wherein the second mathematical model is used to represent the relationship between the curvature ratio and the machining width; the step of analyzing and processing the first mathematical model to establish the second mathematical model includes: establishing an optimization objective equation set based on the first mathematical model; wherein the optimization objective equation set is used to describe the machining width, the curvature on the error distribution curve, the curvature of the effective machining surface of the tool, and the maximum allowable machining error of the error distribution curve; simplifying the optimization objective equation set based on the curvature of the error distribution curve and the curvature of the corresponding projection points on the surface to be machined to establish the second mathematical model; wherein the projection points on the surface to be machined correspond to the extreme points on the error distribution curve; The processing line width calculation unit is used to calculate the processing line width based on the second mathematical model and a preset radial basis function; wherein, the preset radial basis function is used to interpolate a set of function values ​​specified in the data point set corresponding to the second mathematical model; the step of calculating the processing line width based on the second mathematical model and the preset radial basis function includes: mapping the second mathematical model in low-dimensional space to a second mathematical model in high-dimensional space based on the preset radial basis function; and obtaining the processing line width based on the second mathematical model in high-dimensional space.

7. An electronic device, characterized in that, The device includes: Memory, used to store program instructions; A processor is configured to invoke program instructions stored in the memory and execute the method described in any one of claims 1-5 according to the obtained program instructions.

8. A storage medium, characterized in that, The storage medium stores computer-executable instructions for causing a computer to perform the method described in any one of claims 1-5.

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