Industrial part model calculation quantity processing method based on numerical integration

Abstract

The invention discloses an industrial part model calculation quantity processing method based on numerical integration. The method comprises the following steps: acquiring a topological surface according to a constructed CAD three-dimensional model of an industrial part, acquiring a bounding box of the industrial part according to the topological surface, and acquiring a reference plane according to the bounding box by adopting a surface normal included angle minimum method; respectively determining a differential unit area and a differential unit volume of the industrial part according to the bounding box and the reference plane, and respectively obtaining an area function and a volume function in a double integral form; and the area function and the volume function in the double integral form are respectively and sequentially subjected to secondary integral form conversion processing, integral interval conversion processing combined with boundary correction offset and integral difference recursion method processing, and the area and the volume of the industrial part are respectively obtained. The method has the beneficial effects that the possibility of instability caused by a singular region is reduced, the processing of high-order numerical values is avoided, unnecessary iterations are reduced, and the instability of an integral boundary is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of industrial docking production, and particularly relates to a method for calculating the quantity of industrial part models based on numerical integration. Background Technique

[0002] In modern engineering construction and manufacturing, the application of computer-aided design (CAD) systems has been quite common. In the design stage of engineering projects, engineers need to accurately process geometric characteristic quantities such as the volume and area of industrial parts. These data are directly related to structural safety, material usage, and the optimization of the overall process. Traditional quantity calculation and processing methods have problems such as difficulty in balancing accuracy and efficiency, unstable processing results for complex geometric bodies with singular points, lack of effective adaptive strategies, and difficulty in automatically adjusting the processing accuracy according to specific geometric characteristics.

[0003] There are generally two ways in traditional quantity calculation and processing methods. The first way is to perform uniform mesh division or regular discrete sampling on the model, converting the quantity calculation and processing based on surfaces and curves into that based on planes and line segments. To ensure high processing accuracy, a large number of processing units and fine meshes will be generated, resulting in a sharp increase in processing time and resource consumption, and at the same time introducing the problem of small fragmented surfaces generated by mesh discretization. The second way is to use numerical integration for processing and directly process according to the geometric information of the model. When the model contains singular points or local degenerate regions, problems such as the Jacobian determinant tending to zero and the local condition number increasing sharply are likely to occur in numerical processing methods, leading to unstable processing results, and then significantly increasing the processing errors of key quantities such as volume and surface area. To ensure the accuracy of numerical results, high-order integration methods are usually used for solution, but this will increase the processing time. Summary of the Invention

[0004] To solve the problems existing in the background technique, the present invention provides a method for calculating the quantity of industrial part models based on numerical integration, solving the technical problems of instability in singular regions and integral boundaries and the increase in processing time caused by using high-order numerical values.

[0005] The technical solutions adopted by the present invention include: 1. A method for calculating the quantity of industrial part models based on numerical integration S1. Construct a CAD three-dimensional model of an industrial part in a computer, obtain all topological surfaces of the industrial part according to the CAD three-dimensional model, obtain the bounding box of the industrial part according to all topological surfaces, and then obtain a reference plane by using the method with the smallest surface normal angle based on the bounding box.

[0006] S2. Determine the differential unit area and differential unit volume of the industrial part according to the bounding box of the industrial part, and obtain the area function and volume function in the form of double integral according to the differential unit area and differential unit volume of the industrial part respectively.

[0007] S3. Perform quadratic integral form conversion processing, integral interval conversion processing with boundary correction offset, and integral difference recursive method processing on the area function and volume function in the form of double integral respectively, and obtain the area and volume of the industrial part respectively.

[0008] The calculated quantities include area and volume; the obtained area and volume of the industrial part are used to further assist in the adjustment of the industrial part, so as to manufacture more precise industrial parts in the docking production.

[0009] The specific content of step S1 is as follows: S11. Construct a CAD three-dimensional model of the industrial part in the computer, and determine that the topological expression mode of the CAD three-dimensional model is boundary representation, so as to obtain all topological surfaces of the industrial part.

[0010] S12. Traverse all topological surfaces of the industrial part to obtain the corresponding boundary surfaces of each topological surface.

[0011] S13. Obtain the bounding box corresponding to each boundary surface according to the boundary surface, and merge the bounding boxes corresponding to all boundary surfaces to obtain the bounding box of the whole industrial part.

[0012] S14. Obtain the reference plane by using the method of the smallest face normal angle according to the bounding box of the whole industrial part.

[0013] The specific method of the smallest face normal angle in step S14 is as follows: D1. Establish a three-dimensional space coordinate system about the x, y, and z axes with the geometric center of the bounding box of the whole industrial part as the center, and obtain the xoy standard plane, xoz standard plane, and yoz standard plane respectively according to the three-dimensional space coordinate system.

[0014] D2. Obtain the face normal of each boundary surface according to the boundary surface, and then obtain the angles between the face normal of each boundary surface and the x, y, and z axes in the three-dimensional space coordinate system respectively.

[0015] D3. For the face normal of each boundary surface, divide the face normal into one of the categories of the smallest x-axis angle category, the smallest y-axis angle category, and the smallest z-axis angle category according to the magnitudes of the face normal and the x, y, and z axes respectively.

[0016] D4. Count the number of face normals included in each category respectively, and take the axis corresponding to the category with the smallest number of included face normals as the key axis, and the standard plane perpendicular to the key axis as the reference plane.

[0017] The specific content of step S2 is as follows: S21. Perform grid division on the bounding box of the whole industrial part to obtain a number of grid cells.

[0018] S22. Determine the differential element of the industrial part based on all the divided grid cells and the bounding box of the entire industrial part, and determine the differential element area and differential element volume according to the differential element respectively.

[0019] S23. Obtain the area function and volume function in the form of double integral respectively according to the reference plane obtained in step S1 and the differential element area and differential element volume obtained in step S22.

[0020] The area function and volume function of the industrial part obtained in step S23 are processed according to the following formulas: A rea = ∫∫ dA V olume = ∫∫ dB dA = |S u ′ × S v ′| dudv dB = |S u ′ × S v ′| · D dist dudv where A rea and V olume represent the area function and volume function in the form of double integral respectively; dA and dB represent the differential element area and differential element volume respectively; S u ′ and S v ′ represent the tangent vectors of the points on the parametric surface along the parametric u direction and along the parametric v direction respectively; |S u ′ × S v ′| represents taking the modulus of the vector obtained by cross - multiplying the vector S u ′ and S v ′; du and dv represent the differentials of the parameters u and v respectively, and D dist represents the directed distance from the point to the reference plane.

[0021] Step S3 is specifically as follows: S31. Convert both the area function and volume function in the form of double integral obtained in step S2 into the form of double integral, and obtain the area function and volume function in the form of double integral respectively.

[0022] S32. Perform the integral interval conversion processing combined with the boundary correction offset on the area function and volume function in the form of double integral respectively, and obtain the converted area function and volume function respectively.

[0023] S33. Respectively take the converted area function and volume function as the quantity calculation functions in sequence, and use the integral difference recursive method based on Gauss-Kronrod to process the quantity calculation functions, and respectively obtain the integral result corresponding to the converted area function and the integral result corresponding to the converted volume function.

[0024] S34. Take the integral result corresponding to the obtained converted area function as the area of the final industrial part, and take the integral result corresponding to the obtained converted volume function as the volume of the final industrial part.

[0025] The integral interval conversion processing combined with the boundary correction offset in step S32 is set according to the following formula: ∫ a b g(x)dx = 3 / 4(b - a)(1 - τ 2 )∫ -1 1 g(τ / 4(b - a)(3 - τ 2 ) + 1 / 2(a + b) + O)dτ O = 1 / 4(b - a)D 2 (D + 3), D < D th O = 0, D ≥ D th Wherein, a and b respectively represent the lower limit and upper limit of the original integral interval; x represents the independent variable of the original integral, g(x) represents the function about the independent variable x, dx represents the differential of the independent variable x, τ represents the newly introduced independent variable in the integral interval transformation process, dτ represents the differential of the independent variable τ; O is the boundary correction offset; D represents the distance from the independent variable τ to the upper limit or lower limit of the converted integral interval; D th represents the preset distance threshold.

[0026] The integral difference recursion based on Gauss-Kronrod in step S33 is specifically as follows: H1. Use the Gauss-Kronrod method to select N Gauss points and substitute them into the quantity calculation function for processing to obtain the Gauss integral result, and then select 2N + 1 Kronrod points and substitute them into the quantity calculation function for processing to obtain the Kronrod integral result.

[0027] H2. Subtract the Gauss integral result from the Kronrod integral result to obtain the integral difference.

[0028] H3. Perform judgment processing on the integral difference: If the integral difference is not greater than the preset integral difference threshold, then take the Kronrod integral result obtained in step H2 as the integral result of the quantity calculation function.

[0029] If the integral difference is greater than a preset integral difference threshold, the integral interval of the calculation quantity function is bisected to obtain two sub-intervals respectively, and each sub-interval is used as a new integral interval in turn. The calculation quantity function under the new integral interval is processed in the same way as in steps H1 - H3 until the integral difference of the calculation quantity function under each integral interval that does not contain sub-intervals is not greater than the preset integral difference threshold. Then, the sum of the Kronrod integral results obtained from the calculation quantity functions under all integral intervals that do not contain sub-intervals is used as the integral result of the calculation quantity function.

[0030] When the integral interval is bisected to obtain two sub-intervals respectively, it can be known that the integral interval contains two sub-intervals.

[0031] II. A computer device, including a memory and a processor, where the memory stores a computer program, and when the processor executes the computer program, the steps of the above method are implemented.

[0032] III. A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above method are implemented.

[0033] The innovation of the present invention lies in adopting the method of minimizing the surface normal angle, the integral difference recursive method based on Gauss-Kronrod, and the integral interval conversion processing method combined with the boundary correction offset, which reduces the instability of the singular region and the integral boundary, brings the advantage of avoiding high-order numerical processing, and achieves the beneficial effect of reducing errors.

[0034] The beneficial effects of the present invention are: 1. The present invention adopts the method of minimizing the surface normal angle to select the reference plane, reducing the possibility of instability caused by the singular region, and thus reducing errors.

[0035] 2. The present invention adopts the integral difference recursive method based on Gauss-Kronrod, avoiding the processing of high-order numerical values, and reducing unnecessary iteration times through the adaptive integral interval subdivision method.

[0036] 3. The present invention adopts the integral interval conversion processing method combined with the boundary correction offset, reducing the instability existing in the integral boundary. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 is a flowchart of the method of the present invention.

[0038] Figure 2 is a differential unit diagram on the parameter domain in the method of the present invention.

[0039] Figure 3This is the volume prism unit diagram of the present invention.

[0040] Figure 4 This is the bearing part diagram in the embodiment of the present invention.

[0041] Figure 5 This is the nut part diagram in the embodiment of the present invention.

[0042] Figure 6 and Figure 7 These are the two mother part diagrams of the nut part in the embodiment of the present invention. Detailed implementation manners

[0043] The present invention will be described in more detail below in conjunction with the drawings and embodiments. However, the present invention is not limited thereto. For those of ordinary skill in the art in the technical field, without departing from the principle of the present invention, several improvements and retouches can be made, and these improvements and retouches are also regarded as within the protection scope of the present invention. The content not described in detail in this specification belongs to the prior art well-known to those skilled in the art.

[0044] Embodiment 1:

[0045] As Figure 1 shown, the industrial part model quantity calculation processing method of this embodiment includes the following steps: S1. Construct a CAD three-dimensional model of the industrial part in the computer, obtain all topological surfaces of the industrial part according to the CAD three-dimensional model, obtain the bounding box of the industrial part according to all topological surfaces, and then obtain the reference plane by using the method of the minimum surface normal angle based on the bounding box.

[0046] S11. Construct a CAD three-dimensional model of the industrial part in the computer, and determine that the topological expression of the CAD three-dimensional model is boundary representation (B-Rep), so as to obtain all topological surfaces of the industrial part.

[0047] S12. Traverse all topological surfaces of the industrial part to obtain the corresponding boundary surfaces for each topological surface. The boundary surfaces include the geometric data of the boundary surfaces.

[0048] S13. Obtain the bounding box corresponding to each boundary surface according to the boundary surfaces, and merge the bounding boxes corresponding to all boundary surfaces to obtain the bounding box of the entire industrial part.

[0049] S14. Obtain the reference plane by using the method of the minimum surface normal angle based on the bounding box of the entire industrial part.

[0050] The method of the minimum surface normal angle is specifically as follows: D1. Establish a three-dimensional space coordinate system about the x, y, and z axes with the geometric center of the bounding box of the entire industrial part as the center.

[0051] D2. Obtain the xoy standard plane, xoz standard plane, and yoz standard plane respectively according to the three-dimensional space coordinate system.

[0052] D3. Obtain the surface normal of each boundary surface according to the boundary surface.

[0053] D4. Obtain the angles between the surface normal of each boundary surface and the x, y, and z axes in the three-dimensional space coordinate system respectively.

[0054] D5. For the surface normal of each boundary surface, compare the magnitudes of the angles with the x, y, and z axes respectively: If the angle between the surface normal and the x-axis is the smallest, then classify the surface normal into the category with the smallest x-axis angle; if the angle between the surface normal and the y-axis is the smallest, then classify the surface normal into the category with the smallest y-axis angle; if the angle between the surface normal and the z-axis is the smallest, then classify the surface normal into the category with the smallest z-axis angle.

[0055] D6. Count the number of surface normals included in each of the categories with the smallest x-axis angle, the smallest y-axis angle, and the smallest z-axis angle respectively.

[0056] D7. Take the x, y, or z axis corresponding to the category with the smallest number of surface normals as the key axis, and take the standard plane perpendicular to the key axis as the reference plane.

[0057] In specific implementation, if the category with the smallest x-axis angle contains the smallest number of surface normals, then the key axis is the x-axis, and then the yoz standard plane is selected as the reference plane; if the category with the smallest y-axis angle contains the smallest number of surface normals, then the key axis is the y-axis, and then the xoz standard plane is selected as the reference plane; if the category with the smallest z-axis angle contains the smallest number of surface normals, then the key axis is the z-axis, and then the xoy standard plane is selected as the reference plane.

[0058] S2. Determine the differential unit area and differential unit volume of the industrial part respectively according to the bounding box of the industrial part, and obtain the area function and volume function in the form of double integral respectively according to the differential unit area and differential unit volume of the industrial part.

[0059] S21. Perform mesh division on the bounding box of the entire industrial part to obtain a number of mesh units.

[0060] In specific implementation, the structured hexahedron mesh division method can be selected to perform mesh division on the bounding box of the entire industrial part to obtain a number of mesh units.

[0061] S22. Determine the differential unit of the industrial part according to all the divided mesh units and the bounding box of the entire industrial part, and determine the differential unit area and differential unit volume respectively according to the differential unit.

[0062] In specific implementation, when determining the differential element of an industrial part, the differential element of the point point(u, v) on the parameter domain consists of S u ′du and S v ′dv, as Figure 2 shown.

[0063] S23. Obtain the area function and volume function in the form of double integral respectively according to the reference plane obtained in step S1 and the differential element area and differential element volume obtained in step S22; The obtained area function and volume function of the industrial part are obtained by processing according to the following formulas: A rea = ∫∫dA V olume = ∫∫dB dA = |S u ′ × S v ′|dudv dB = |S u ′ × S v ′|·D dist dudv S u ′ = (αx / αu, αy / αu, αz / αu) S v ′ = (αx / αv, αy / αv, αz / αv) Among them, A rea and V olume respectively represent the area function and volume function in the form of double integral; dA represents the differential element area; dB represents the differential element volume (the volume of the smallest prism element from the differential element to the reference plane), as Figure 3 shown; u and v represent the two parameters of the point on the parametric surface; S u ′ and S v ′ respectively represent the tangent vectors of the point on the parametric surface of the industrial part along the parameter u direction and along the parameter v direction; |S u ′ × S v ′| represents taking the modulus of the vector obtained after cross - multiplying the vector S u ′ and S v ′; du and dv respectively represent the differentials of the parameters u and v, D dist represents the directed distance from the point point(u, v) to the reference plane; αx / αu, αy / αu, and αz / αu respectively represent the partial derivatives of the spatial coordinates x, y, z with respect to the parameter u; αx / αv, αy / αv, and αz / αv respectively represent the partial derivatives of the spatial coordinates x, y, z with respect to the parameter v.

[0064] S3. Convert the area function and volume function in the form of double integral into the form of double integral respectively, and perform the integral interval conversion processing combined with the boundary correction offset and the integral difference recursive method processing to obtain the area and volume of the industrial part. The calculated quantities include area and volume; the obtained area and volume of the industrial part are used to further assist in the adjustment of the industrial part, so as to manufacture more precise industrial parts in the docking production.

[0065] S31. Convert the area function and volume function in the form of double integral obtained in step S2 into the form of double integral respectively, and obtain the area function and volume function in the form of double integral respectively.

[0066] The area function and volume function in the form of double integral are set according to the following formulas respectively: M = ∑ i=1 k ∫ t0 t1 ∫ Uref u(t) |S u ′ × S v ′|(s, v(t))ds · |v t ′(t)|dt T = ∑ i=1 k ∫ t0 t1 ∫ Uref u(t) |S u ′ × S v ′|(s, v(t)) · D dist (s, v(t))ds · |v t ′(t)|dt Among them, M and T represent the area function and volume function in the form of double 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 the integral of the 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 the parameter t; s represents the integral variable of the inner integral, representing the variable in the u direction of the parameter; v(t) represents the parameterization of the parametric curve on the boundary surface, v t ′(t) represents the derivative of v(t) with respect to the parameter t; |v t ′(t)| represents taking the t ′(t) vector modulus; S u ′ and S v ′ respectively represent the tangent vectors of the points on the industrial part along the parameter u direction and the parameter v direction; |S u ′ × S v ′| represents taking the vector S u ′ and Sv The modulus of the vector obtained after cross - multiplication; D dist () represents a function of the directed distance from a point to a reference plane; dt represents the differential with respect to the parameter t; ds represents the differential with respect to the integration variable s.

[0067] S32. Perform integral interval conversion processing with combined boundary correction offsets on the area function and volume function in the double - integral form respectively, and obtain the converted area function and volume function respectively.

[0068] The integral interval conversion processing with combined boundary correction offsets is set according to the following formula: ∫ a b g(x)dx = 3 / 4(b - a)(1 - τ 2 )∫ -1 1 g(τ / 4(b - a)(3 - τ 2 ) + 1 / 2(a + b)+O)dτ O = 1 / 4(b - a)D 2 (D + 3), D < D th O = 0, D≥D th Among them, a and b represent the lower limit and upper limit of the original integral interval respectively; x represents the independent variable of the original integral; g( ) represents a function; g(x) represents a function of the independent variable x; dx represents the differential with respect to the independent variable x; τ represents the newly introduced independent variable in the integral interval transformation process; dτ represents the differential 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 converted integral interval; D th represents a preset distance threshold; 1 and - 1 represent the upper limit and lower limit of the converted integral interval respectively. Among them, the transformation relationship between x and τ is x = τ / 4(b - a)(3 - τ 2 ) + 1 / 2(a + b)+O. In specific implementation, after the integral interval conversion processing with combined boundary correction offsets, the converted integral interval is [- 1,1].

[0069] S33. Respectively take the converted area function and volume function as the quantity functions in turn, and use the integral difference recursive method based on Gauss - Kronrod to process the quantity functions, and obtain the integral results of the quantity functions corresponding to the converted area function and the integral results of the quantity functions corresponding to the converted volume function respectively.

[0070] The integral difference recursion based on Gauss - Kronrod is specifically: H1. Select N Gauss points using the Gauss-Kronrod method, substitute them into the calculation quantity function for processing to obtain the Gauss integral result, and then select 2N + 1 Kronrod points, substitute them into the calculation quantity function for processing to obtain the Kronrod integral result.

[0071] In specific implementation, substituting N Gauss points into the calculation quantity function will obtain N Gauss values, and each Gauss value is added according to the corresponding weight coefficient to finally obtain the Gauss integral result; substituting 2N + 1 Kronrod points into the calculation quantity function will obtain 2N + 1 Kronrod values, and each Kronrod value is added according to the corresponding weight coefficient to finally obtain the Kronrod integral result. In specific implementation, N is taken as 7 and 2N + 1 is taken as 15.

[0072] H2. Subtract the Gauss integral result from the Kronrod integral result to obtain the integral difference.

[0073] H3. Perform judgment processing on the integral difference: If the integral difference is less than or equal to the preset integral difference threshold, then take the Kronrod integral result obtained in step H2 as the integral result of the calculation quantity function; if the integral difference is greater than the preset integral difference threshold, then perform interval bisection integral processing on the calculation quantity function.

[0074] The interval bisection integral processing is specifically as follows: bisect the integral interval of the calculation quantity function to obtain two new integral intervals, and process the calculation quantity function under each of the two new integral intervals according to the same method as steps H1 - H2 to obtain the integral difference of the calculation quantity function under each new integral interval, and perform judgment processing on the integral difference of the calculation quantity function under each new integral interval: If the integral difference of the calculation quantity function under at least one new integral interval is greater than the preset integral difference threshold, then continue to perform bisection integral processing on each new integral interval whose integral difference is greater than the preset integral difference threshold until the integral difference of the calculation quantity function under each new integral interval is not greater than the preset integral difference threshold; if the integral difference of the calculation quantity function under each new integral interval is not greater than the preset integral difference threshold, then take the sum of the Kronrod integral results obtained by the calculation quantity function under all integral intervals as the integral result of the calculation quantity function.

[0075] In specific implementation, the sum of the Kronrod integral results obtained by the calculation quantity function under all integral intervals is the sum of the Kronrod integral results obtained by the calculation quantity function under all integral intervals (including all subdivided integral intervals) in the [-1, 1] interval.

[0076] S34. The integral result of the obtained transformed area function corresponding to the quantity calculation function is used as the area of the final industrial part, and the integral result of the obtained transformed volume function corresponding to the quantity calculation function is used as the volume of the final industrial part.

[0077] Example 2: Use the same method as in Example 1 to Figure 4 process the bearing part. As Figure 4 shown, the bearing part is composed of multiple toroidal surfaces, cylindrical surfaces and spherical surfaces.

[0078] During the processing, to determine the reference plane, first obtain the surface normal of each boundary surface. After comparing the magnitudes of the angles between the surface normal of each boundary surface and the x-axis, y-axis and z-axis respectively, the key axis is obtained as the z-axis, and the standard plane xoy perpendicular to the z-axis is used as the reference plane.

[0079] During the processing, after obtaining the area function and volume function of the bearing part in the form of double integral, first convert the area function and volume function into the form of double integral to obtain the area function and volume function in the form of double integral respectively; then perform the integral interval conversion processing of combining the boundary correction offset (the preset distance threshold is 0.05) on the area function and volume function in the form of double integral to map the numerical integral upper and lower limits [a, b] to [-1, 1], and then use the Gauss-Kronrod method with 7 Gauss points and 15 Kronrod points to obtain the integral difference of the area function and the integral difference of the volume function respectively; then process the integral difference by the integral difference recursive method, and finally obtain the area of the bearing part as 16288.351583995100 mm 2 , and the volume is 37320.146765885000 mm 3 .

[0080] To present the beneficial effects of the present invention, the present invention also conducted the following experiments for comparison to highlight the advantages of the method of the present invention: Since there are corresponding area calculation formulas for the toroidal surface, cylindrical surface and spherical surface, the bearing part of this embodiment has an accurate area result of S = 4902π + 90π 2 mm 2 , and at the same time, the bearing part of this embodiment is obtained by rotational modeling operation, and the rotating body obtained by rotating the arc and line segment along the axis of symmetry can be calculated using the integral formula, so the bearing part of this embodiment has an accurate volume result of V = 11738π + 45π 2 mm 3 .

[0081] Finally, the area result obtained by the method of this embodiment is subtracted from the exact area result, and the error of the area result is -1.087306389821e -10 mm 2 ; the volume result obtained by the method of this embodiment is subtracted from the exact volume result, and the error of the volume result is -1.014170922060e -9 mm 3 .

[0082] Example 3: The same method as in Example 1 is used to process Figure 5 the nut part. As Figure 5 shown, Figure 5 the nut part is obtained by performing a Boolean operation on Figure 6 and Figure 7 two mother parts.

[0083] During the processing, to determine the reference plane, first obtain the surface normal of each boundary surface. After comparing the magnitudes of the angles between the surface normal of each boundary surface and the x-axis, y-axis, and z-axis respectively, the key axis is determined to be the z-axis, and the standard plane xoy perpendicular to the z-axis is used as the reference plane.

[0084] Finally, the area of the nut part Figure 5 obtained is 731.921930459234 mm 2 , and the volume is 875.438132951213 mm 3 .

[0085] To present the beneficial effects of the present invention, the following experiments are also conducted in the present invention for comparison to highlight the advantages of the method of the present invention: Figure 6 The part Figure 7 can be regarded as being obtained by rotating an arc and a line segment around a rotation axis, 2 and the part 2 can be regarded as being obtained by stretching an arc and a line segment along a specific direction. Therefore, the nut part in this embodiment has an exact area result of S = 12π 2 + 180π + 48 mm 3 .

[0086] Finally, the area result obtained by the method of this embodiment is subtracted from the exact area result, and the error of the area result is within -1.086349289701e -12 mm 2 ; the volume result obtained by the method of this embodiment is subtracted from the exact volume result, and the error of the volume result is within 8.063589081971e -12 mm3 。

[0087] Comparative Example 1: Using the same Figure 4 bearing parts as in Example 2, Figure 4 perform CAD modeling on the 2 bearing parts, and input the obtained CAD three-dimensional model into Solid Works software. The calculated area result of the bearing parts is 16288.349602590000 mm 3 and the volume result is 37320.141677160000 mm

[0088] The area result and volume result obtained by Solid Works software are respectively subtracted from the accurate area result and volume result in Example 2, and the error of the area result of Solid Works software is obtained as -1.981405208731e -3 mm 2 , and the error of the volume result of Solid Works software is -5.088726014171e -3 mm 3 。

[0089] It can be seen from the errors that the method of the present invention is significantly superior to SolidWorks software in calculating the Figure 4 area and volume of the bearing parts.

[0090] Comparative Example 2: Using the same Figure 4 bearing parts as in Example 2, Figure 4 perform CAD modeling on the 2 bearing parts, and input the obtained CAD three-dimensional model into Rhino software. The calculated area result of the bearing parts is 16288.351600000000 mm 3 and the volume result is 37320.146700000000 mm

[0091] The area result and volume result obtained by Rhino software are respectively subtracted from the accurate area result and volume result in Example 2, and the error of the area result of Rhino software is obtained as 1.600479126936e -5 mm 2 , and the error of the volume result of Rhino software is -6.588601417092e -5 mm 3 。

[0092] It can be seen from the errors that the method of the present invention is significantly superior to Rhino software in calculating the Figure 4 area and volume of the bearing parts.

[0093] Comparative Example 3: Use the same Figure 5 nut parts as in Example 3. Perform CAD modeling on the Figure 5 nut parts. Input the obtained CAD three-dimensional model into Solid Works software and calculate to obtain Figure 5 the area result of the nut parts as 731.921894140000 mm 2 and the volume result as 875.437915910000 mm 3 .

[0094] Take the differences between the area result and volume result obtained by Solid Works software and the accurate area result and volume result in Example 2 respectively. The error of the area result of Solid Works software is -3.631923508635e -5 mm 2 , and the error of the volume result of Solid Works software is -2.170412049364e -4 mm 3 .

[0095] It can be seen from the errors that the method of the present invention is significantly superior to SolidWorks software in calculating the Figure 5 area and volume of the nut parts.

[0096] Comparative Example 4: Use the same Figure 5 nut parts as in Example 3. Perform CAD modeling on the Figure 5 nut parts. Input the obtained CAD three-dimensional model into Rhino software and calculate to obtain Figure 5 the area result of the nut parts as 731.925335000000 mm 2 and the volume result as 875.443810000000 mm 3 .

[0097] Take the differences between the area result and volume result obtained by Rhino software and the accurate area result and volume result in Example 2 respectively. The error of the area result of Rhino software is 3.404540764914e -3 mm 2 , and the error of the volume result of Rhino software is 5.677048795064e -3 mm 3 .

[0098] It can be seen from the errors that the method of the present invention is in calculating Figure 5Both the area and volume of the nut parts are significantly better than those of Rhino software.

[0099] The present invention is not limited to the embodiments described above. The above description of the specific embodiments is intended to describe and illustrate the technical solutions of the present invention. The above specific embodiments are merely illustrative and not restrictive. Without departing from the spirit of the present invention and the scope protected by the claims, those of ordinary skill in the art can make many specific transformations in form under the inspiration of the present invention, and these all fall within the protection scope of the present invention.

Claims

1. An industrial part model quantity calculation processing method based on numerical integration, characterized in that, It includes the following steps: S1. Build a CAD three-dimensional model of the industrial part in the computer, obtain all the topological surfaces of the industrial part according to the CAD three-dimensional model, obtain the bounding box of the industrial part based on all the topological surfaces, and then obtain the reference plane by using the method of minimizing the surface normal angle according to the bounding box; S2. Determine the differential unit area and differential unit volume of the industrial part respectively according to the bounding box of the industrial part, and obtain the area function and volume function in the form of double integral respectively according to the differential unit area and differential unit volume of the industrial part; S3. Perform quadratic integral form conversion processing, integral interval conversion processing combined with boundary correction offset, and integral difference recursive method processing on the area function and volume function in the form of double integral in sequence respectively to obtain the area and volume of the industrial part respectively.

2. The industrial part model quantity calculation processing method based on numerical integration according to claim 1, wherein The specific content of step S1 is as follows: S11. Build a CAD three-dimensional model of the industrial part in the computer, and determine that the topological expression of the CAD three-dimensional model is boundary representation, so as to obtain all the topological surfaces of the industrial part; S12. Traverse all the topological surfaces of the industrial part to obtain the corresponding boundary surface of each topological surface; S13. Obtain the bounding box corresponding to each boundary surface according to the boundary surface, and merge the bounding boxes corresponding to all the boundary surfaces to obtain the bounding box of the whole industrial part; S14. Obtain the reference plane by using the method of minimizing the surface normal angle according to the bounding box of the whole industrial part.

3. The method for calculating the quantity of an industrial part model based on numerical integration according to claim 2, wherein The method of minimizing the surface normal angle in step S14 is specifically as follows: D1. Establish a three-dimensional space coordinate system about the x, y, and z axes with the geometric center of the bounding box of the whole industrial part as the center, and obtain the xoy standard plane, xoz standard plane, and yoz standard plane respectively according to the three-dimensional space coordinate system; D2. Obtain the surface normal of each boundary surface according to the boundary surface, and then obtain the angles between the surface normal of each boundary surface and the x, y, and z axes in the three-dimensional space coordinate system respectively; D3. For the surface normal of each boundary surface, divide the surface normal into one of the categories of the smallest x-axis angle category, the smallest y-axis angle category, and the smallest z-axis angle category respectively according to the magnitudes of the surface normal and the x, y, and z axes respectively; D4. Count the number of surface normals included in each category respectively, take the axis corresponding to the category with the smallest number of included surface normals as the key axis, and take the standard plane perpendicular to the key axis as the reference plane.

4. A method for calculating the quantity of industrial part models based on numerical integration according to claim 1, characterized in that, The specific content of step S2 is as follows: S21. Perform grid division on the bounding box of the whole industrial part to obtain a number of grid units; S22. Determine the differential unit of the industrial part according to all the divided grid units and the bounding box of the whole industrial part, and determine the differential unit area and differential unit volume respectively according to the differential unit; S23. Obtain the area function and volume function in the form of double integral respectively according to the reference plane, differential unit area, and differential unit volume.

5. The method for calculating the quantity of an industrial part model based on numerical integration according to claim 4, wherein: The area function and volume function of the industrial part obtained in step S23 are processed according to the following formula: A rea = ∫∫ dA V olume = ∫∫ dB dA = |S u ′ × S v ′|dudv dB = |S u ′ × S v ′| · D dist dudv Among them, A rea and V olume respectively represent the area function and the volume function in the form of double integral; dA and dB respectively represent the differential element area and the differential element volume; S u ′ and S v ′ respectively represent the tangent vectors of the points on the parametric surface along the parametric u direction and along the parametric v direction; |S u ′ × S v ′| represents taking the modulus of the vector obtained after cross - multiplying the vectors S u ′ and S v ′; du and dv respectively represent the differentials of the parameters u and v, and D dist represents the directed distance from the point to the reference plane.

6. The industrial part model quantity calculation processing method based on numerical integration according to claim 1, wherein, The specific content of step S3 is as follows: S31. Convert both the area function and the volume function in the form of double integral into the form of double integral, and obtain the area function and the volume function in the form of double integral respectively; S32. Perform the integral interval conversion process with combined boundary correction offset on the area function and the volume function in the form of double integral respectively, and obtain the converted area function and the volume function respectively; S33. Take the converted area function and the volume function as the quantity calculation functions in turn, and use the integral difference recursive method based on Gauss-Kronrod to process the quantity calculation functions, and obtain the integral result corresponding to the converted area function and the integral result corresponding to the converted volume function respectively; S34. Take the integral result corresponding to the converted area function as the area of the final industrial part, and take the integral result corresponding to the converted volume function as the volume of the final industrial part.

7. A method for calculating the quantity of an industrial part model based on numerical integration according to claim 6, characterized in that: The integral interval conversion process with combined boundary correction offset in step S32 is set according to the following formula: ∫ a b g(x)dx = 3 / 4(b - a)(1 - τ 2 )∫ -1 1 g(τ / 4(b - a)(3 - τ 2 ) + 1 / 2(a + b) + O)dτ O = 1 / 4(b - a)D 2 (D + 3), D < D th O = 0, D ≥ D th Among them, a and b respectively represent the lower and upper limits of the original integration interval; x represents the independent variable of the original integration, g(x) represents the function with respect to the independent variable x, dx represents the differential of the independent variable x, τ represents the newly introduced independent variable during the integration interval transformation process, dτ represents the differential of 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 represents a preset distance threshold.

8. A method for calculating the quantity of industrial part models based on numerical integration according to claim 6, characterized in that, The integral difference recursion based on Gauss-Kronrod in step S33 is specifically: H1. Select N Gauss points by using the Gauss-Kronrod method and substitute them into the quantity calculation function for processing to obtain the Gauss integral result, and then select 2N + 1 Kronrod points and substitute them into the quantity calculation function for processing to obtain the Kronrod integral result; H2. Subtract the Gauss integral result from the Kronrod integral result to obtain the integral difference; H3. Perform judgment processing on the integral difference: If the integral difference is not greater than the preset integral difference threshold, take the Kronrod integral result obtained in step H2 as the integral result of the quantity calculation function; If the integral difference is greater than the preset integral difference threshold, bisect the integral interval of the quantity calculation function to obtain two sub-intervals respectively, and take each sub-interval as a new integral interval in turn. Process the quantity calculation function under the new integral interval according to the same method as steps H1 - H3 until the integral difference of the quantity calculation function under each integral interval that does not contain sub-intervals is not greater than the preset integral difference threshold. Then take the sum of the Kronrod integral results of the quantity calculation functions under all integral intervals that do not contain sub-intervals as the integral result of the quantity calculation function.

9. A computer device, comprising a memory and a processor, the memory storing a computer program, characterized in that: The processor realizes the steps of the method according to any one of claims 1 to 8 when executing the computer program.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program realizes the steps of the method according to any one of claims 1 to 8 when executed by the processor.

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