A numerical integration-based model quantity processing method for industrial parts

Abstract

The application discloses a kind of industrial parts model algorithm processing methods based on numerical integration.The method includes obtaining topological surface according to the CAD three-dimensional model of the industrial parts constructed, obtaining the bounding box of the industrial parts according to the topological surface, and obtaining the reference plane using the minimum method of surface normal angle according to the bounding box;Differential element area and differential element volume of the industrial parts are determined according to the bounding box and the reference plane, and then area function and volume function under double integral form are obtained;Area function and volume function under double integral form are respectively converted and processed in turn, and the integral interval conversion processing and integral difference recursive method processing combined with boundary correction offset are carried out, respectively, to obtain the area and volume of the industrial parts.The method has the beneficial effects of reducing the possibility of instability caused by singular region, avoiding high-order numerical processing, reducing unnecessary iteration times and reducing the instability of integral boundary.

Description

Technical Field

[0001] This invention belongs to the field of industrial docking production, specifically involving a method for calculating quantities of industrial parts models based on numerical integration. Background Technology

[0002] In modern engineering construction and manufacturing, the application of computer-aided design (CAD) systems is quite common. During the design phase of engineering projects, engineers need to accurately process geometric features such as the volume and area of ​​industrial parts. These data directly relate to structural safety, material usage, and overall process optimization. Traditional quantity take-off methods suffer from several problems: difficulty in balancing accuracy and efficiency; unstable results when processing complex geometries containing singularities; lack of effective adaptive strategies; and difficulty in automatically adjusting processing accuracy based on specific geometric features.

[0003] Traditional computational methods generally fall into two categories. The first involves uniformly meshing or regularly discretizing the model, transforming computation based on surfaces and curves into computation based on planes and lines. To ensure high accuracy, this generates a large number of processing units and a fine mesh, leading to a sharp increase in processing time and resource consumption, while also introducing the problem of small, fragmented surfaces from mesh discretization. The second method uses numerical integration, directly processing based on the model's geometric information. When the model contains singularities or locally degenerate regions, numerical methods are prone to problems such as the Jacobian determinant tending to zero and a surge in local condition numbers, resulting in unstable results and significantly increasing the processing errors for key quantities such as volume and surface area. To ensure the accuracy of the numerical results, high-order integration methods are typically used, but this increases processing time. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention provides a numerical integration-based method for processing the computational quantity of industrial parts models, which solves the technical problems of instability in singular regions and integration boundaries and increased processing time due to the use of higher-order values.

[0005] The technical solution adopted in this invention includes:

[0006] I. A Numerical Integration-Based Method for Quantity Calculation of Industrial Part Models

[0007] S1. Construct a CAD 3D model of the industrial part in the computer, obtain all the topological surfaces of the industrial part based on the CAD 3D model, obtain the bounding box of the industrial part based on all the topological surfaces, and then obtain the reference plane based on the bounding box using the method of minimizing the included angle of the surface normals.

[0008] S2. Determine the differential unit area and differential unit volume of the industrial part based on the bounding box of the industrial part, and obtain the area function and volume function in the form of double integral based on the differential unit area and differential unit volume of the industrial part.

[0009] S3. The area function and volume function in the double integral form are respectively transformed into the form of double integral, transformed into the integral interval by combining the boundary correction offset, and processed by the integral difference recursion method to obtain the area and volume of the industrial part.

[0010] The calculation includes area and volume; the obtained area and volume of the industrial parts are used to further assist in the adjustment of the industrial parts, thereby manufacturing more precise industrial parts in docking production.

[0011] Step S1 specifically involves:

[0012] S11. Construct a CAD 3D model of the industrial part in the computer, and determine that the topological expression method of the CAD 3D model is boundary expression, thereby obtaining all the topological surfaces of the industrial part.

[0013] S12. Traverse all topological surfaces of the industrial part to obtain the boundary surface corresponding to each topological surface.

[0014] S13. Obtain the bounding box corresponding to each boundary surface based on the boundary surface, and merge the bounding boxes corresponding to all boundary surfaces to obtain the bounding box of the entire industrial part.

[0015] S14. Obtain the reference plane by using the method of minimizing the included angle of the surface normals based on the entire enclosure of the industrial part.

[0016] The method for minimizing the included angle of the surface normal in step S14 is as follows:

[0017] D1. Establish a three-dimensional spatial coordinate system about the x, y and z axes with the geometric center of the entire enclosing box of the industrial part as the center, and obtain the xoy standard plane, xoz standard plane and yoz standard plane respectively according to the three-dimensional spatial coordinate system.

[0018] D2. Obtain the surface normal of each boundary surface based on the boundary surface, and then obtain the angle between the surface normal of each boundary surface and the x, y and z axes in the three-dimensional spatial coordinate system.

[0019] D3. For each boundary surface normal, classify the surface normal into one of the following categories based on the magnitude of the angle between the surface normal and the x, y, and z axes: the category with the smallest angle between the x-axis, the category with the smallest angle between the y-axis, and the category with the smallest angle between the z-axis.

[0020] D4. Count the number of face normals in each category, take the axis corresponding to the category with the fewest face normals as the key axis, and take the standard plane perpendicular to the key axis as the reference plane.

[0021] Step S2 specifically involves:

[0022] S21. The bounding box of the entire industrial part is divided into several mesh units.

[0023] S22. Determine the differential cells of the industrial part based on all the divided grid cells and the bounding box of the entire industrial part, and determine the differential cell area and differential cell volume respectively based on the differential cells.

[0024] S23. Based on the reference plane obtained in step S1 and the differential unit area and differential unit volume obtained in step S22, obtain the area function and volume function in the form of double integrals respectively.

[0025] The area function and volume function of the industrial part obtained in step S23 are processed according to the following formula:

[0026] A rea =∫∫dA

[0027] V olume =∫∫dB

[0028] dA=|S u ′×S v ′|dudv

[0029] dB=|S u ′×S v ′|·D dist dudv

[0030] Among them, A rea and V olume Let dA and dB represent the area and volume functions in the form of double integrals, respectively; let dA and dB represent the area and volume of the differential unit, respectively; S u ′ and S v ′ represent the tangent vectors of a point on the parametric surface along the parameter u and along the parameter v, respectively; |S u ′×S v ′| represents taking vector S u ′ and S v The modulus of the vector obtained after the cross product; du and dv represent the derivatives with respect to parameters u and v, respectively, D dist This represents the directed distance from a point to the reference plane.

[0031] Step S3 specifically involves:

[0032] S31. Convert the area function and volume function in the double integral form obtained in step S2 into the quadratic integral form to obtain the area function and volume function in the quadratic integral form respectively.

[0033] S32. Perform integral interval transformation on the area function and volume function in the form of quadratic integrals, combined with boundary correction offset, to obtain the transformed area function and volume function, respectively.

[0034] S33. The transformed area function and volume function are used as computational functions in turn. The computational functions are processed by the Gauss-Kronrod integral difference recursive method to obtain the integral results corresponding to the transformed area function and the integrated results corresponding to the transformed volume function.

[0035] S34. The integral result of the transformed area function is taken as the area of ​​the final industrial part, and the integral result of the transformed volume function is taken as the volume of the final industrial part.

[0036] The integral interval transformation process for combining boundary correction offset in step S32 is set according to the following formula:

[0037] ∫ a b g(x)dx=3 / 4(ba)∫ -1 1 g(τ / 4(ba)(3-τ 2 )+1 / 2(a+b)+O)(1-τ 2 )dτ

[0038] O=1 / 4(ba)D 2 (D+3), D<D th

[0039] O=0, D≥D th

[0040] Where a and b represent the lower and upper limits of the original integration interval, respectively; x represents the independent variable of the original integral, g(x) represents a function of the independent variable x, dx represents the derivative with respect to the independent variable x, τ represents the newly introduced independent variable during the integration interval transformation, and dτ represents the derivative with respect to the independent variable τ; O is the boundary correction offset; D represents the distance from the independent variable τ to the upper or lower limit of the transformed integration interval; D th This indicates the preset distance threshold.

[0041] The Gauss-Kronrod-based integral difference recursion in step S33 is specifically as follows:

[0042] H1. Using the Gauss-Kronrod method, select N Gauss points and substitute them into the computational function to obtain the Gauss integral result. Then, select 2N+1 Kronrod points and substitute them into the computational function to obtain the Kronrod integral result.

[0043] H2. Subtract the Gauss integral result from the Kronrod integral result to obtain the integral difference value.

[0044] H3. Handling the integral difference:

[0045] If the integral difference is not greater than the preset integral difference threshold, then the Kronrod integral result obtained in step H2 is used as the integral result of the computational function.

[0046] If the integral difference is greater than the preset integral difference threshold, the integral interval of the computational function is bisected to obtain two sub-intervals. Each sub-interval is then used as a new integral interval. The computational functions under the new integral intervals are processed in the same way as steps H1-H3 until the integral difference of the computational functions under each integral interval that does not contain a sub-interval is not greater than the preset integral difference threshold. Then, the sum of the Kronrod integral results obtained by the computational functions under all integral intervals that do not contain sub-intervals is taken as the integral result of the computational function.

[0047] The integration interval is divided into two sub-intervals, thus the integration interval contains two sub-intervals.

[0048] II. A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described method.

[0049] 3. A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above method.

[0050] The innovation of this invention lies in the use of the method of minimizing the included angle of the surface normal, the recursive method of integral difference based on Gauss-Kronrod, and the method of integral interval transformation processing combined with boundary correction offset. This reduces the instability of singular regions and integral boundaries, brings the advantage of avoiding the processing of higher-order values, and achieves the beneficial effect of reducing errors.

[0051] The beneficial effects of this invention are:

[0052] 1. The present invention uses the method of minimum angle between surface normals to select the reference plane, which reduces the possibility of instability caused by singular regions and thus reduces errors.

[0053] 2. This invention adopts a Gauss-Kronrod-based integral difference recursion method, which avoids the processing of higher-order values ​​and reduces unnecessary iterations by adaptively subdividing the integral interval.

[0054] 3. The present invention adopts an integral interval transformation method that combines boundary correction offset, thereby reducing the instability of integral boundaries. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method of the present invention.

[0056] Figure 2 This is a diagram of the differential unit over the parameter domain in the method of the present invention.

[0057] Figure 3 This is a diagram of the volumetric prism unit of the present invention.

[0058] Figure 4 This is a diagram of a bearing component in an embodiment of the present invention.

[0059] Figure 5 This is a diagram of a nut part in an embodiment of the present invention.

[0060] Figure 6 and Figure 7 These are two diagrams of the mother parts of the nut part in an embodiment of the present invention. Detailed Implementation

[0061] The present invention will now be described in more detail with reference to the accompanying drawings and embodiments. However, the present invention is not limited thereto. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

[0062] Example 1

[0063] like Figure 1 As shown, the industrial part model quantity calculation method of this embodiment includes the following steps:

[0064] S1. Construct a CAD 3D model of the industrial part in the computer, obtain all the topological surfaces of the industrial part based on the CAD 3D model, obtain the bounding box of the industrial part based on all the topological surfaces, and then obtain the reference plane based on the bounding box using the method of minimizing the included angle of the surface normals.

[0065] S11. Construct a CAD 3D model of the industrial part in the computer and determine the topological representation method of the CAD 3D model as boundary representation (B-Rep) to obtain all the topological surfaces of the industrial part.

[0066] S12. Traverse all topological surfaces of the industrial part to obtain the boundary surface corresponding to each topological surface. The boundary surface includes the geometric data of the boundary surface.

[0067] S13. Obtain the bounding box corresponding to each boundary surface based on the boundary surface, and merge the bounding boxes corresponding to all boundary surfaces to obtain the bounding box of the entire industrial part.

[0068] S14. Obtain the reference plane by using the method of minimizing the included angle of the surface normals based on the entire enclosure of the industrial part.

[0069] The method for minimizing the included angle between the surface normals is as follows:

[0070] D1. Establish a three-dimensional spatial coordinate system about the x, y, and z axes, with the geometric center of the entire enclosing box of the industrial part as the center.

[0071] D2. Obtain the xoy standard plane, xoz standard plane, and yoz standard plane respectively according to the three-dimensional spatial coordinate system.

[0072] D3. Obtain the surface normal of each boundary surface based on the boundary surfaces.

[0073] D4. Obtain the angles between the surface normal of each boundary surface and the x, y, and z axes in the three-dimensional coordinate system.

[0074] D5. For the surface normal of each boundary surface, compare the angles it makes with the x, y, and z axes respectively:

[0075] If the angle between the plane normal and the x-axis is the smallest, then the plane normal is classified as having the smallest angle between the x-axis and the y-axis; if the angle between the plane normal and the z-axis is the smallest, then the plane normal is classified as having the smallest angle between the z-axis and the y-axis.

[0076] D6. Count the number of face normals contained in the category with the smallest x-axis angle, the category with the smallest y-axis angle, and the category with the smallest z-axis angle.

[0077] D7. Take the x, y, or z axis corresponding to the category with the fewest surface normals as the key axis, and the standard plane perpendicular to the key axis as the reference plane.

[0078] In practice, if the category with the smallest x-axis angle contains the fewest face normals, then the key axis is the x-axis, and the yoz standard plane is selected as the reference plane; if the category with the smallest y-axis angle contains the fewest face normals, then the key axis is the y-axis, and the xoz standard plane is selected as the reference plane; if the category with the smallest z-axis angle contains the fewest face normals, then the key axis is the z-axis, and the xoy standard plane is selected as the reference plane.

[0079] S2. Determine the differential unit area and differential unit volume of the industrial part based on the bounding box of the industrial part, and obtain the area function and volume function in the form of double integral based on the differential unit area and differential unit volume of the industrial part.

[0080] S21. The bounding box of the entire industrial part is divided into several mesh units.

[0081] In practice, a structured hexahedral meshing method can be used to mesh the entire bounding box of the industrial part to obtain several mesh elements.

[0082] S22. Determine the differential cells of the industrial part based on all the divided grid cells and the bounding box of the entire industrial part, and determine the differential cell area and differential cell volume respectively based on the differential cells.

[0083] In practical implementation, when determining the differential unit of an industrial part, the differential unit of the point point(u,v) in the parameter domain is determined by S. u ′du and S v Composed of 'dv, such as Figure 2 As shown.

[0084] S23. Based on the reference plane obtained in step S1 and the differential unit area and differential unit volume obtained in step S22, obtain the area function and volume function in the form of double integrals respectively.

[0085] The area and volume functions of the industrial parts are obtained by processing them using the following formulas:

[0086] A rea =∫∫dA

[0087] V olume =∫∫dB

[0088] dA=|S u ′×S v ′|dudv

[0089] dB=|S u ′×S v ′|·D dist dudv

[0090] S u = (αx / αu, αy / αu, αz / αu)

[0091] S v = (αx / αv, αy / αv, αz / αv)

[0092] Among them, A rea and V olumeLet dA and dB represent the area and volume functions in the form of double integrals, respectively; dA represents the area of ​​the differential element; dB represents the volume of the differential element (the volume of the smallest prism element from the differential element to the reference plane), such as... Figure 3 As shown; u and v represent two parameters of a point on the parametric surface; S u ′ and S v ′ represent the tangent vectors of points on the parametric surface of the industrial part along the parameter u direction and along the parameter v direction, respectively; |S u ′×S v ′| represents taking vector S u ′ and S v The modulus of the vector obtained after the cross product; du and dv represent the derivatives with respect to parameters u and v, respectively, D dist αx / αu, αy / αu, and αz / αu represent the directed distance from point (u,v) to the reference plane; αx / αu, αy / αu, and αz / αu represent the partial derivatives of spatial coordinates x, y, and z with respect to parameter u, respectively; αx / αv, αy / αv, and αz / αv represent the partial derivatives of spatial coordinates x, y, and z with respect to parameter v, respectively.

[0093] S3. The area and volume functions in the double integral form are sequentially transformed into double integral forms, combined with boundary correction offset transformation of the integral interval, and processed by the integral difference recursion method to obtain the area and volume of the industrial part. The calculation includes area and volume; the obtained area and volume of the industrial part are used to further assist in the adjustment of the industrial part, thereby manufacturing more precise industrial parts in docking production.

[0094] S31. Convert the area function and volume function in the double integral form obtained in step S2 into the quadratic integral form to obtain the area function and volume function in the quadratic integral form respectively.

[0095] The area function and volume function in the form of a double integral are set according to the following formulas:

[0096] M=∑ i=1 k ∫ t0 t1 ∫ Uref u(t) |S u ′×S v ′|(s,v(t))ds·|v t ′(t)|dt

[0097] T=∑ i=1 k ∫ t0 t1 ∫ Uref u(t) |S u ′×Sv ′|(s,v(t))·D dist (s,v(t))ds·|v t ′(t)|dt

[0098] Where M and T represent the area function and volume function in the form of a quadratic integral, respectively; k represents the number of parametric curves on the boundary surface; i represents the index; t represents the parameter; t0 and t1 represent the lower and upper limits of integration for parameter t, respectively; Uref represents the u-coordinate of the center point of the parameter domain; u(t) represents the upper limit of the inner integral of parameter t; s represents the integration variable of the inner integral, representing the variable in the direction of parameter u; v(t) represents the parameterization of the parametric curves on the boundary surface, v t '(t) denotes the derivative of v(t) with respect to the parameter t; |v'(t) t ′(t)| represents taking v t The magnitude of vector S'(t); u ′ and S v ′ represent the tangent vectors of a point on the industrial part along the direction of parameter u and along the direction of parameter v, respectively; |S u ′×S v ′| represents taking vector S u ′ and S v The magnitude of the vector obtained after the cross product; D dist () represents the directed distance from the point to the reference plane; dt represents the derivative with respect to the parameter t; ds represents the derivative with respect to the integration variable s.

[0099] S32. Perform integral interval transformation on the area function and volume function in the form of quadratic integrals, combined with boundary correction offset, to obtain the transformed area function and volume function, respectively.

[0100] The integral interval transformation process, which incorporates boundary correction offsets, is set according to the following formula:

[0101] ∫ a b g(x)dx=3 / 4(ba)∫ -1 1 g(τ / 4(ba)(3-τ 2 )+1 / 2(a+b)+O)(1-τ 2 )dτ

[0102] O=1 / 4(ba)D 2 (D+3), D<D th

[0103] O=0, D≥D th

[0104] Where a and b represent the lower and upper limits of the original integration interval, respectively; x represents the independent variable of the original integral; g() represents the function; g(x) represents the function with respect to the independent variable x; dx represents the derivative with respect to the independent variable x; τ represents the newly introduced independent variable during the integration interval transformation; dτ represents the derivative with respect to the independent variable τ; O is the boundary correction offset; D represents the distance from the independent variable τ to the upper limit 1 or lower limit -1 of the transformed integration interval; D th This represents the preset distance threshold; 1 and -1 represent the upper and lower limits of the integration interval after the transformation, respectively. The transformation relationship between x and τ is x = τ / 4(ba) (3-τ) 2 )+1 / 2(a+b)+O. In specific implementation, after the integral interval transformation process combined with the boundary correction offset, the transformed integral interval is [-1,1].

[0105] S33. The transformed area function and volume function are used as computational functions in turn. The computational functions are processed by the Gauss-Kronrod integral difference recursive method to obtain the integral results of the computational functions corresponding to the transformed area function and the transformed volume function, respectively.

[0106] The Gauss-Kronrod integral difference recursion is as follows:

[0107] H1. Using the Gauss-Kronrod method, select N Gauss points and substitute them into the computational function to obtain the Gauss integral result. Then, select 2N+1 Kronrod points and substitute them into the computational function to obtain the Kronrod integral result.

[0108] In practice, substituting N Gauss points into the computational function yields N Gauss values. Each Gauss value is summed according to its corresponding weight coefficient to obtain the final Gauss integral result. Similarly, substituting 2N+1 Kronrod points into the computational function yields 2N+1 Kronrod values. Each Kronrod value is summed according to its corresponding weight coefficient to obtain the final Kronrod integral result. In practice, N is set to 7, and 2N+1 is set to 15.

[0109] H2. Subtract the Gauss integral result from the Kronrod integral result to obtain the integral difference value.

[0110] H3. Handling the integral difference:

[0111] If the integral difference is less than or equal to the preset integral difference threshold, the Kronrod integral result obtained in step H2 is used as the integral result of the computational function; if the integral difference is greater than the preset integral difference threshold, the computational function is subjected to interval bisection integration.

[0112] The interval bisection integration process is as follows: the integration interval of the computational function is bisected to obtain two new integration intervals. The computational function under each of the two new integration intervals is then processed using the same method as steps H1-H2 to obtain the integral difference of the computational function under each new integration interval. Finally, the integral difference of the computational function under each new integration interval is evaluated and processed.

[0113] If the integral difference of the computational function in at least one new integration interval is greater than the preset integral difference threshold, then the binary integration process continues for each new integration interval that is greater than the preset integral difference threshold until the integral difference of the computational function in each new integration interval is no greater than the preset integral difference threshold; if the integral difference of the computational function in each new integration interval is no greater than the preset integral difference threshold, then the sum of the Kronrod integral results obtained from the computational functions in all integration intervals is taken as the integral result of the computational function.

[0114] In practice, the sum of the Kronrod integral results obtained by the computational functions under all integration intervals is the sum of the Kronrod integral results obtained by the computational functions under all integration intervals (including all subdivided integration intervals) under the interval [-1,1].

[0115] S34. The integral result of the calculation function corresponding to the transformed area function is used as the area of ​​the final industrial part, and the integral result of the calculation function corresponding to the transformed volume function is used as the volume of the final industrial part.

[0116] Example 2:

[0117] Using the same method as in Example 1 Figure 4 The bearing parts are processed. For example... Figure 4 As shown, the bearing components consist of multiple annular surfaces, cylindrical surfaces, and spherical surfaces.

[0118] In the process of processing, in order to determine the reference plane, the surface normal of each boundary surface is first obtained. For each boundary surface surface normal, the angle between the surface normal and the x-axis, y-axis and z-axis is compared respectively, and the key axis is the z-axis. The standard surface xoy perpendicular to the z-axis is used as the reference plane.

[0119] In the processing, after obtaining the area function and volume function in the double integral form of the bearing part, the area function and volume function are first converted into the quadratic integral form to obtain the area function and volume function in the quadratic integral form respectively. Then, the area function and volume function in the quadratic integral form are respectively processed by the integration interval transformation combined with the boundary correction offset (the preset distance threshold is 0.05) to map the upper and lower limits of numerical integration [a, b] to [-1, 1]. Then, the Gauss-Kronrod method with 7 Gauss points and 15 Kronrod points is used to obtain the integral difference of the area function and the integral difference of the volume function respectively. Finally, the integral difference is processed by the recursive method of integral difference, and the area of ​​the bearing part is finally obtained as 16288.351583995100 mm. 2 The volume is 37320.146765885000 mm. 3 .

[0120] To demonstrate the beneficial effects of the present invention, the following experiments were also conducted to create a comparison and highlight the advantages of the method of the present invention:

[0121] Since there are corresponding area calculation formulas for toroidal surfaces, cylindrical surfaces, and spherical surfaces, the bearing component in this embodiment has a precise area result of S = 4902π + 90π. 2 mm 2 Furthermore, the bearing part in this embodiment is obtained through rotational modeling, and the solid of revolution obtained by rotating the arc and line segment along the axis of symmetry can be calculated using integral formulas. Therefore, the bearing part in this embodiment has a precise volume result of V = 11738π + 45π. 2 mm 3 .

[0122] Finally, the area result obtained by the method in this embodiment is subtracted from the accurate area result, and the error of the area result is -1.087306389821e. -10 mm 2 The volume result obtained by the method in this embodiment is subtracted from the accurate volume result, and the error of the volume result is -1.014170922060e. -9 mm 3 .

[0123] Example 3:

[0124] Using the same method as in Example 1 Figure 5 The nuts and bolts are processed. For example... Figure 5 As shown, Figure 5 Nut parts are made of Figure 6 and Figure 7 The two parent parts are obtained by performing Boolean operations.

[0125] In the process of processing, in order to determine the reference plane, the surface normal of each boundary surface is first obtained. For each boundary surface surface normal, the angle between the surface normal and the x-axis, y-axis and z-axis is compared respectively, and the key axis is the z-axis. The standard surface xoy perpendicular to the z-axis is used as the reference plane.

[0126] Finally obtained Figure 5 The area of ​​the nut part is 731.921930459234 mm². 2 The volume is 875.438132951213 mm. 3 .

[0127] To demonstrate the beneficial effects of the present invention, the following experiments were also conducted to create a comparison and highlight the advantages of the method of the present invention:

[0128] Figure 6 The parts can be considered as being obtained by rotating circular arcs and line segments around a rotation axis. Figure 7 The part can be considered as being obtained by stretching circular arcs and line segments along a specific direction. Therefore, the nut part in this embodiment has a precise area result of S=12π. 2 +180π+48mm 2 The precise volume result is V = 12π 2 +784 / 3π-64mm 3 .

[0129] Finally, the area result obtained by the method in this embodiment is subtracted from the accurate area result, and the error of the area result is -1.086349289701e. -12 mm 2 The volume result obtained by the method in this embodiment is subtracted from the accurate volume result, and the error in the obtained volume result is within 8.063589081971e. -12 mm 3 .

[0130] Comparative Example 1:

[0131] Using the same methods as in Example 2 Figure 4 Bearing parts, for Figure 4 The bearing component was modeled using CAD, and the resulting 3D CAD model was imported into SolidWorks software. The calculated area of ​​the bearing component was 16288.349602590000 mm². 2 The volume result is 37320.141677160000 mm. 3 .

[0132] The area and volume results obtained from SolidWorks software were subtracted from the precise area and volume results in Example 2, respectively. The error of the SolidWorks area result was -1.981405208731e. -3 mm 2 The error in the volume result from SolidWorks software is -5.088726014171e. -3 mm 3 .

[0133] As can be seen from the error, the method of the present invention is effective in calculation. Figure 4 The area and volume of bearing parts are significantly better than those of SolidWorks software.

[0134] Comparative Example 2:

[0135] Using the same methods as in Example 2 Figure 4 Bearing parts, for Figure 4 The bearing component was modeled using CAD, and the resulting 3D CAD model was imported into Rhino software. The calculated area of ​​the bearing component was 16288.351600000000 mm². 2 The volume result is 37320.146700000000 mm. 3 .

[0136] The area and volume results obtained from Rhino software were subtracted from the precise area and volume results in Example 2, respectively. The error of the Rhino software area result was found to be 1.600479126936e. -5 mm 2 The error in the volume result obtained using Rhino software is -6.588601417092e. -5 mm 3 .

[0137] As can be seen from the error, the method of the present invention is effective in calculation. Figure 4 The area and volume of bearing parts are significantly better than those of Rhino software.

[0138] Comparative Example 3:

[0139] Using the same methods as in Example 3 Figure 5 Nut parts, for Figure 5 The nut part was modeled in CAD, and the resulting 3D CAD model was imported into SolidWorks software for calculation. Figure 5 The area of ​​the nut part is 731.921894140000 mm². 2 The volume result is 875.437915910000 mm. 3 .

[0140] The area and volume results obtained from SolidWorks software were subtracted from the precise area and volume results in Example 2, respectively. The error of the SolidWorks area result was -3.631923508635e. -5 mm 2 The error in the volume result from SolidWorks software is -2.170412049364e. -4 mm 3 .

[0141] As can be seen from the error, the method of the present invention is effective in calculation. Figure 5 The area and volume of the nuts are significantly better than those of SolidWorks software.

[0142] Comparative Example 4:

[0143] Using the same methods as in Example 3 Figure 5 Nut parts, for Figure 5 The nut part was modeled in CAD, and the resulting 3D CAD model was imported into Rhino software for calculation. Figure 5 The area of ​​the nut part is 731.925335000000 mm². 2 The volume result is 875.443810000000 mm. 3 .

[0144] The area and volume results obtained from Rhino software were subtracted from the precise area and volume results in Example 2, respectively. The error of the Rhino software area result was found to be 3.404540764914e. -3 mm 2 The error in the volume result obtained using Rhino software is 5.677048795064e. -3 mm 3 .

[0145] As can be seen from the error, the method of the present invention is effective in calculation. Figure 5 The area and volume of the nuts are significantly better than those of Rhino software.

[0146] This invention is not limited to the embodiments described above. The above description of specific embodiments is intended to illustrate and explain the technical solutions of this invention. The specific embodiments described above are merely illustrative and not restrictive. Without departing from the spirit and scope of the claims, those skilled in the art can make many specific modifications based on the teachings of this invention, and these modifications all fall within the scope of protection of this invention.

Claims

1. A method for quantity calculation of industrial parts models based on numerical integration, characterized in that, Includes the following steps: S1. Construct a CAD 3D model of the industrial part in the computer, obtain all the topological surfaces of the industrial part based on the CAD 3D model, obtain the bounding box of the industrial part based on all the topological surfaces, and then obtain the reference plane based on the bounding box using the method of minimizing the included angle of the surface normals. S2. Determine the differential unit area and differential unit volume of the industrial part based on the bounding box of the industrial part, and obtain the area function and volume function in the form of double integral based on the differential unit area and differential unit volume of the industrial part. S3. The area function and volume function in the double integral form are transformed into double integral form, and then the integral interval is transformed by combining the boundary correction offset and the integral difference recursion method to obtain the area and volume of the industrial part respectively. Step S3 specifically involves: S31. Convert the area function and volume function in the double integral form into the quadratic integral form to obtain the area function and volume function in the quadratic integral form respectively. S32. Perform integral interval transformation on the area function and volume function in the form of quadratic integrals, combined with boundary correction offset, to obtain the transformed area function and volume function, respectively. The integral interval transformation process for combining boundary correction offset in step S32 is set according to the following formula: ∫ a b g(x)dx=3 / 4(ba)∫ -1 1 g(τ / 4(ba)(3-τ) 2 )+1 / 2(a+b)+O)(1-τ 2 )dτ O=1 / 4(b-a)D 2 (D+3),D<D th O=0, D≥D th Where a and b represent the lower and upper limits of the original integration interval, respectively; x represents the independent variable of the original integral, g(x) represents a function of the independent variable x, dx represents the derivative with respect to the independent variable x, τ represents the newly introduced independent variable during the integration interval transformation, and dτ represents the derivative with respect to the independent variable τ; O is the boundary correction offset; D represents the distance from the independent variable τ to the upper or lower limit of the transformed integration interval; D th This indicates a preset distance threshold; S33. The transformed area function and volume function are used as calculation functions in turn. The calculation functions are processed by the Gauss-Kronrod-based integral difference recursion method to obtain the integral results corresponding to the transformed area function and the integral results corresponding to the transformed volume function. S34. The integral result of the transformed area function is taken as the area of ​​the final industrial part, and the integral result of the transformed volume function is taken as the volume of the final industrial part.

2. The method for quantity calculation of industrial parts models based on numerical integration according to claim 1, characterized in that, Step S1 specifically involves: S11. Construct a CAD 3D model of the industrial part in the computer and determine that the topological expression method of the CAD 3D model is boundary expression, thereby obtaining all the topological surfaces of the industrial part. S12. Traverse all topological surfaces of the industrial part to obtain the boundary surface corresponding to each topological surface; S13. Obtain the bounding box corresponding to each boundary surface based on the boundary surface, and merge the bounding boxes corresponding to all boundary surfaces to obtain the bounding box of the entire industrial part. S14. Obtain the reference plane by using the method of minimizing the included angle of the surface normals based on the entire enclosure of the industrial part.

3. The method for quantity calculation of industrial parts models based on numerical integration according to claim 2, characterized in that, The method for minimizing the included angle of the surface normal in step S14 is as follows: D1. Establish a three-dimensional spatial coordinate system about the x, y and z axes with the geometric center of the entire enclosing box of the industrial part as the center, and obtain the xoy standard plane, xoz standard plane and yoz standard plane respectively according to the three-dimensional spatial coordinate system. D2. Obtain the surface normal of each boundary surface based on the boundary surface, and then obtain the angle between the surface normal of each boundary surface and the x, y and z axes in the three-dimensional spatial coordinate system; D3. For the surface normal of each boundary surface, classify the surface normal into one of the following categories based on the magnitude of the angle between the surface normal and the x, y, and z axes: the category with the smallest angle between the x-axis, the category with the smallest angle between the y-axis, and the category with the smallest angle between the z-axis. D4. Count the number of face normals in each category, take the axis corresponding to the category with the fewest face normals as the key axis, and take the standard plane perpendicular to the key axis as the reference plane.

4. The method for quantity calculation of industrial parts models based on numerical integration according to claim 1, characterized in that, Step S2 specifically involves: S21. The bounding box of the entire industrial part is divided into several mesh units. S22. Determine the differential units of the industrial part based on all the divided grid cells and the bounding box of the entire industrial part, and determine the differential unit area and differential unit volume respectively based on the differential units. S23. Obtain the area function and volume function in the form of double integrals based on the reference plane, the area of ​​the differential unit, and the volume of the differential unit, respectively.

5. The method for quantity calculation of industrial parts models based on numerical integration according to claim 4, characterized in that: The area function and volume function of the industrial part obtained in step S23 are processed according to the following formula: A rea =∫∫dA In olume =∫∫dB dA=|S u ′×S v ′|dudv dB=|S u ′×S v ′|·D dist dudv Among them, A rea and V olume Let dA and dB represent the area and volume functions in the form of double integrals, respectively; let dA and dB represent the area and volume of the differential unit, respectively; S u ′ and S v ′ represent the tangent vectors of a point on the parametric surface along the parameter u and along the parameter v, respectively; |S u ′×S v ′| represents taking vector S u ′ and S v The modulus of the vector obtained after the cross product; du and dv represent the derivatives with respect to parameters u and v, respectively, D dist This represents the directed distance from a point to the reference plane.

6. The method for quantity calculation of industrial parts models based on numerical integration according to claim 1, characterized in that, The Gauss-Kronrod-based integral difference recursion in step S33 is specifically as follows: H1. Using the Gauss-Kronrod method, select N Gauss points and substitute them into the computational function to obtain the Gauss integral result. Then select 2N+1 Kronrod points and substitute them into the computational function to obtain the Kronrod integral result. H2. Subtract the Gaussian integral result from the Kronrod integral result to obtain the integral difference value; H3. Handling the integral difference: If the integral difference is not greater than the preset integral difference threshold, then the Kronrod integral result obtained in step H2 is used as the integral result of the computational function. If the integral difference is greater than the preset integral difference threshold, the integral interval of the computational function is bisected to obtain two sub-intervals. Each sub-interval is then used as a new integral interval. The computational functions under the new integral intervals are processed in the same way as steps H1-H3 until the integral difference of the computational functions under each integral interval that does not contain a sub-interval is not greater than the preset integral difference threshold. Then, the sum of the Kronrod integral results obtained by the computational functions under all integral intervals that do not contain sub-intervals is taken as the integral result of the computational function.

7. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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