A method for designing a slot-shaped machine casing treatment along a free-form boundary curve
Patent Information
- Application Number
- CN202611089868.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-22
- Publication Date
- 2026-10-27
AI Technical Summary
[0005]本发明为解决现有轴向缝式机匣处理设计中缝几何自由度低、缝轴向边界曲线独立调节能力欠缺的问题，进而提出一种沿边界曲线自由造型的缝式机匣处理设计方法
1、本发明采用缝几何全参数化驱动，只需修改基础参数即可快速生成缝的几何结构，各参数内在相互约束，从而大幅减轻缝的自由造型设计难度。
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Figure CN122987238A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of casing processing technology, specifically to a slotted casing processing device with free-form shape along the boundary curve. Calculation method. Background Technology
[0002] Axial slotted casing treatment is a typical passive stabilization technology that has been widely used in the stabilization design of compressors and fans. Current research on some basic parameters of slotted casing treatment (such as slot depth, slot width, and radial tilt angle) is relatively complete. However, research on design methods for slotted casing treatment that balance high stabilization capability with low efficiency loss is insufficient, and the related flow mechanisms also need further exploration.
[0003] Each slot in a conventional axial slotted casing contains 12 independent boundary curves. Traditional manual modeling methods are time-consuming and labor-intensive, and it is difficult to quickly change the shape of the slots for optimization. Therefore, designers need to be able to quickly perform geometric parametric modeling of the slots. This facilitates controlled variable design and allows for in-depth research into the mechanisms of stability expansion and efficiency loss. Furthermore, it allows for targeted adjustment of the slot boundary curves based on the actual flow conditions within the slot, achieving a better stability expansion design. Existing parametric methods mostly involve changing parameters of a fixed shape, lacking means to independently and freely deform the four axial boundary curves of the slot. Deforming the slot boundary curves using global coordinates can easily alter the connection state between the slot and the casing wall, causing geometric connection errors to exceed constraints.
[0004] Therefore, there is an urgent need to develop a parameterized modeling method for seam geometry that can both meet the error constraint requirements of the geometric connection between the seam and the casing surface and flexibly control the shape of the axial boundary curve. Summary of the Invention
[0005] To address the problems of low geometric freedom of the seam and lack of independent adjustment capability of the seam axial boundary curve in existing axial slotted casing processing designs, this invention proposes a design method for slotted casing processing that allows for free shaping along the boundary curve.
[0006] The technical solution adopted by the present invention to solve the above problems is as follows: This invention proposes a design method for a slotted casing with free-form shape along a boundary curve, comprising the following steps: Step 1: Obtain design parameters, including the inner wall radius R of the casing, the axial positions z1 and z2 before and after the seam, and the seam area ratio. s Number of blades N, number of single-channel slits n, slit radial depth h radial inclination angles of the front and rear walls α 1, α 2, and axial deflection angle β ; Step 2: Based on the number of blades N, the number of single-channel slits n, and the slit area ratio s Calculate the central angle corresponding to the seam width to determine the circumferential position of each seam; Step 3: For each seam, calculate 8 vertices based on the design parameters, including four points P1, P2, P3, P4 on the bottom surface of the seam and four points Q1, Q2, Q3, Q4 on the top surface of the seam. Points P1~P4 on the bottom surface of the seam are located on the cylindrical surface r=R, and points Q1~Q4 on the top surface of the seam are required to satisfy the coordinate vector magnitude || of the vertical cross-section S3. Q | = R+ h The radial boundary curve length L is calculated by solving a quadratic equation; P1P3 and P2P4 are calculated according to the axial deflection angle. β To achieve the same circumferential angular displacement and maintain parallelism; Step 4: Generate 12 boundary curves from the 8 vertices. Process the axial boundary curves of the top and bottom surfaces of the seam as constant velocity spirals directly connecting the endpoints on the cylindrical surface, and generate the remaining boundary curves by linear interpolation of the endpoints. Step 5: For the discrete points on the four axial boundary curves, establish a local coordinate system {T,B,C} that varies along the boundary curves, where T is the tangential vector along the boundary curve; B is the cylindrical radial direction pointing from a point on the casing axis to a point on the boundary curve; and C is the circumferential direction of the arc where the point is located. The three coordinates constitute the local coordinate system. Step 6: Receive user-defined mapping function f (t, edge_id), this function uses the normalized arc length parameter t ∈ [0,1] and the boundary curve number edge_id are taken as inputs, and the output is the displacement vector [d] in three directions of the local coordinate system. T ,d B , d C ]; Step 7: For each discrete point on each axial boundary curve, excluding the two endpoints, calculate the arc length parameter based on its normalized arc length parameter. t Calling the mapping function to obtain the displacement vector r =d T T+ d B B+ d C C, and superimpose the displacement onto the original global coordinates: r' = r +d T T+ d B B+ d C C; For the two endpoints, the forced displacement is zero to ensure that the positions of the 8 vertices remain unchanged after deformation; Step 8: Output all boundary curves as geometric model files for mesh generation software to read.
[0007] Furthermore, in step 3, the length L of the radial boundary curve is obtained by solving the following vector equation and quadratic equation:
[0008] Where P is the position vector of a point on the bottom surface of the seam, and Q is the position vector of a corresponding point on the top surface of the seam. e l The unit displacement vector is L; it is obtained by solving the positive root of the quadratic equation, thus ensuring that the distance from the top point Q to the axis is always equal to R+. h This ensures that the radial depth is unaffected by changes in the tilt angle;
[0009] When Rsin α < <R+ h When the square root is expanded, the first-order terms exactly recover R / cos α However, higher-order terms include the effects of cylindrical geometry. Directly using L = R / cos α This will cause the actual radius of the top surface point Q to deviate from R+. h It cannot be guaranteed that the depth will be constant. h .
[0010] Furthermore, in step 3, the obtained radial boundary curve length L is substituted back into equation (1) to directly obtain the coordinates of point Q.
[0011] Furthermore, in step 3, the starting angle of the left boundary curve P1P3 on the bottom surface of the seam is... i 1. The endpoint angle is i 1+ dth The starting angle of the right boundary curve P2P4 is i 2. The endpoint angle is i 2+ dth , dth Due to axial deflection angle β The same circumferential angular displacement is obtained on both sides. dth Therefore, the two boundary curves remain parallel on the cylindrical surface.
[0012] Furthermore, in step 4, the axial boundary curves P1P3 and P2P4 on the bottom surface of the seam are treated as constant-velocity helices on a cylindrical surface with radius R, while the axial boundary curves Q1Q3 and Q2Q4 on the top surface of the seam are treated by directly utilizing the vertex angle on a cylindrical surface with radius R+. hA constant-velocity helix is constructed on the cylindrical surface. The remaining radial and circumferential boundary curves are generated by linear interpolation between corresponding vertices. All boundary curves need to be generated by calculating discrete points and using the line type specified in the IGG file. The bottom axial boundary curves (P1P3, P2P4) are helices on a cylindrical surface with radius R, and the angles satisfy a linear change:
[0013] The coordinates of the discrete point are:
[0014] The top surface axial boundary curves (Q1Q3, Q2Q4) are of radius R+ h A helix on a cylindrical surface, the angle of which changes linearly:
[0015] The coordinates of the discrete point are:
[0016] The discrete points of the radial and circumferential boundary curves are solved directly by linear interpolation from 8 fixed endpoints, without participating in any deformation, to ensure that the cross-sectional shape of the seam is strictly controlled.
[0017] Furthermore, in step 4, when generating the axial boundary curve Q1Q3 of the top surface of the processing seam, the circumferential angles of vertices Q1 and Q3 are used. i Q1 , i Q3 Linear interpolation yields the angle at the midpoint, thus allowing the calculation of the angle within the radius R+. h A straight spiral is obtained on the cylindrical surface, avoiding lateral distortion caused by inclination angle interpolation.
[0018] Furthermore, the tangential direction T mentioned in step 5 is approximately calculated using the adjacent difference of discrete points, and the radial direction B is the radial unit vector [cosθ] in cylindrical coordinates. i , sin i [, 0], C is the circumferential unit vector in cylindrical coordinates [-sin i cos i [, 0], which makes the deformation direction strictly bound to the geometric trend of the boundary curve itself.
[0019] Furthermore, in step 6, the mapping function f (t, edge_id) allows for independent control of the four axial boundary curves, where the displacement vector [d T , d B , d C] These correspond to the deformation amounts along the boundary curve direction, radial direction, and circumferential direction of torsion, respectively; where d T Deformation along the boundary curve does not change the curve shape; it merely serves as a component of the displacement vector to complete its full form. The component that produces actual deformation is d. B With d C .
[0020] Furthermore, the geometric model file output in step 8 is in IGG format, containing curve definitions, project configurations, and boundary condition information, which can be directly used for NUMECA mesh generation.
[0021] The beneficial effects of this invention are: 1. This invention adopts fully parameterized seam geometry driving, which can quickly generate the geometric structure of the seam by only modifying the basic parameters. The parameters are mutually constrained, thereby greatly reducing the difficulty of free-form seam design.
[0022] 2. This invention features intuitive and controllable mapping deformation based on a local coordinate system, enabling complex 3D modeling through simple mathematical expressions. It performs nonlinear mapping on four axial boundary curves based on a local coordinate system (T-tangential, B-radial, C-circumferential). Its core innovation lies in the fact that the deformation process is established on a local coordinate system bound to the geometrical trend of each boundary curve, rather than using a global Cartesian coordinate system as a reference. Instead, the deformed coordinates are transformed back to the global Cartesian coordinate system. This gives the deformation along the boundary curves a clear and intuitive physical meaning, conforming to engineering thinking habits.
[0023] 3. This invention calculates all boundary curves and mapped deformations of the treatment seam based on a cylindrical coordinate system, while forcibly fixing the endpoints. This ensures that the geometric connection between the treatment seam and the casing wall meets the error constraint requirements, eliminating the need for subsequent repairs. This constraint is not automatically satisfied in many free deformation methods and requires additional processing.
[0024] 4. This invention outputs all boundary curves as geometric model files in IGG .geom format, which can be directly imported into NUMECA for mesh generation. This significantly reduces repetitive modeling work in engineering practice and improves the stability of seam geometry generation. Attached Figure Description
[0025] Figure 1 This is a schematic diagram of the geometric parameters of the seam. Figure 2 This is a schematic diagram showing the geometric relationship of the circumferential positions of the front and rear ends of the seam. Figure 3 This is a schematic diagram illustrating the construction of the radial boundary curve length of the seam. Figure 4 This is a schematic diagram of the processing seam geometry before and after implementing the free-form shape of the boundary curve; Figure 5 These are the compressor characteristic curves before and after implementing the boundary curve free modeling. Detailed Implementation
[0026] This embodiment provides a design method for a slotted casing with free-form shape along its axis. It generates all boundary curves parametrically and utilizes nonlinear mapping based on the local coordinate system of the axial boundary curves to allow users to arbitrarily deform the axial boundary curves radially and circumferentially, while fixing the endpoints to ensure a smooth connection between the slot and the casing wall. The method includes the following steps: Step 1: Obtain design parameters, including the inner wall radius R of the casing, the axial positions z1 and z2 before and after the seam, and the seam area ratio. s Number of blades N, number of single-channel slits n, slit radial depth h radial inclination angles of the front and rear walls α 1, α 2, and axial deflection angle β For details, please refer to Table 1 and... Figure 1 ;
[0027] Step 2: Based on the number of blades N, the number of single-channel slits n, and the slit area ratio s Calculate the central angle corresponding to the seam width i slot and the central angle corresponding to the seam spacing i gap , i slot =2 πs / Nn, i gap =2 π (1 - s ) / Nn, determine the circumferential position of each seam; Step 3: For each seam, calculate 8 vertices based on the design parameters, including four points P1, P2, P3, P4 on the bottom surface of the seam and four points Q1, Q2, Q3, Q4 on the top surface of the seam. Front end: P1 ( i 1, z1), P2( i 2, z1), where i 2= i 1+ i slot ; and axial deflection angle βThis ensures that the left boundary curve P1P3 and the right boundary curve P2P4 of the treatment joint bottom surface achieve equal circumferential angular displacement. dth = tan β (z2– z1) / R, such as Figure 2 This keeps the two boundary curves parallel; then P3( i 1+ d i , z2), P4( i 2+ dth This ensures that P1P3 and P2P4 have the same angular displacement, and the two boundary curves are parallel (before transformation); P is a point on the bottom surface of the treatment seam, and its Cartesian coordinates are P(Rcos... i Rsin i Let Q be a point on the top surface of the seam, and let P be a point along the unit displacement vector. e l The displacement L of the moving radial boundary curve is obtained, satisfying the coordinate vector magnitude of the vertical cross-section S3. Q | = R+ h The radial depth of the seam is strictly equal to the length L of the radial boundary curve by solving a quadratic equation. h ,like Figure 3 For each bottom point P, define a unit vector in the radial direction. e r = [cos i , sin i [0], radial tilt angle α Indicates radial boundary curve deviation e r The angle, therefore the unit displacement vector e l = [cos( i + α ), sin( i + α ), 0]. Then we can obtain the following equation.
[0028] The length L of the radial boundary curve is obtained by solving the positive root of the quadratic equation, thus ensuring that the distance from the top point Q to the axis is always equal to R+. h This ensures that the radial depth is unaffected by changes in the tilt angle.
[0029]
[0030] It can be seen that when Rsin α < <R+ h When the square root can be expanded, the first-order term exactly restores R / cos αHowever, higher-order terms include the effects of cylindrical geometry. Directly using L = R / cos α This will cause the actual radius of the top surface point Q to deviate from R+. h It cannot be guaranteed that the depth will be constant. h .
[0031] Finally, substitute L back into equation (1) to directly obtain the coordinates of point Q.
[0032] The starting angle of the left boundary curve P1P3 on the bottom surface of the treatment seam is... i 1. The endpoint angle is i 1+ dth The starting angle of the right boundary curve P2P4 is i 2. The endpoint angle is i 2+ dth Both sides have the same circumferential angular displacement dth Therefore, the two boundary curves remain parallel on the cylindrical surface.
[0033] Step 4: Generate 12 boundary curves from the 8 vertices. The axial boundary curves P1P3 and P2P4 on the bottom surface of the seam are constant-velocity spirals on a cylindrical surface with radius R. The axial boundary curves Q1Q3 and Q2Q4 on the top surface of the seam directly utilize the vertex angles on a cylindrical surface with radius R+. h A constant-velocity helix is constructed on the cylindrical surface. The remaining radial and circumferential boundary curves are generated by linear interpolation between corresponding vertices. The construction of all boundary curves requires calculating discrete points and using the linetype specified in the IGG file. The bottom axial boundary curves (P1P3, P2P4) are helices on a cylindrical surface with radius R, satisfying a linear change in angle.
[0034] The coordinates of the discrete point are:
[0035] The top surface axial boundary curves (Q1Q3, Q2Q4) are of radius R+ h The helix on the cylindrical surface satisfies a linear change in angle:
[0036] The coordinates of the discrete point are:
[0037] The radial and circumferential boundary curves (a total of 8) are generated directly from 8 fixed endpoints through linear interpolation to create discrete points. They do not participate in any deformation, thus ensuring that the cross-sectional shape of the seam is strictly controlled.
[0038] In step 4, when generating the axial boundary curve Q1Q3 of the top surface of the processing seam, the circumferential angles of vertices Q1 and Q3 are used. i Q1 , i Q3 Linear interpolation yields the angle at the midpoint, thus allowing the calculation of the angle within the radius R+. h A straight spiral is obtained on the cylindrical surface, avoiding lateral distortion caused by inclination angle interpolation.
[0039] Step 5: For discrete points on the four axial boundary curves, establish a local coordinate system {T,B,C} that varies along the boundary curves, where T is the tangential vector along the boundary curve (the central difference approximates the unit tangential vector); B is the radial direction of the cylindrical surface pointing from a point on the casing axis to a point on the boundary curve (i.e., the radial direction of the cylindrical coordinate system); and C is the circumferential direction of the arc where the point is located. The three coordinates constitute the local coordinate system. The tangential direction T is approximately calculated using the adjacent difference method of discrete points, and the radial direction B is the radial unit vector [cosθ] in cylindrical coordinates. i , sin i [, 0], where the circumferential C is the circumferential unit vector [-sin] in cylindrical coordinates. i cos i ,0].
[0040] Step 6: Receive user-defined mapping function f (t, edge_id), this function uses the normalized arc length parameter t ∈ [0,1] and the boundary curve number edge_id are taken as inputs, and the output is the displacement vector [d] in three directions of the local coordinate system. T ,d B , d C ]; The mapping function f (t, edge_id) allows for independent control of the four axial boundary curves, where the displacement vector [d T , d B , d C These correspond to the deformation amounts along the boundary curve direction, radial direction, and circumferential direction of torsion, respectively. Where d... T Deformation along the boundary curve does not change the curve shape; it merely serves as a component of the displacement vector to complete its full form. The component that produces actual deformation is d. B With d C ; Step 7: For each discrete point on each axial boundary curve, excluding the two endpoints, calculate the arc length parameter based on its normalized arc length parameter. t Calling the mapping function to obtain the displacement vector r =d T T+ d B B+ d C C, and superimpose the displacement onto the original global coordinates: r' = r +d T T+ d B B+ d C C; For the two endpoints, the forced displacement is zero, thus ensuring that the positions of the eight vertices remain unchanged after deformation; Step 8: Output all boundary curves as geometric model files for mesh generation software to read.
[0041] The geometric model file is in IGG format and contains curve definitions, project configurations, and boundary condition information, which can be directly used for NUMECA mesh generation.
[0042] Example: 1. Input design parameters. In this embodiment, the inner wall radius of the casing is R=275mm, the axial positions before and after the seam are z1=38.544mm and z2=59.378mm, and the seam area ratio is... s =0.25, number of blades N=20, number of single-channel slots n=3, slot radial depth h =7.5mm, radial inclination angle of front and rear walls α 1 = 40° α 2 = -45°, and axial deflection angle β =-66°; 2. Based on the number of blades N, the number of single-channel slits n, and the slit area ratio s Calculate the central angle corresponding to the seam width i slot and the central angle corresponding to the seam spacing i gap , i slot =2 πs / Nn, i gap =2 π (1 - s ) / Nn, determine the circumferential position of each seam; 3. Fix 8 vertices: Process the bottom surface points P1~P4 of the seam located on the cylindrical surface r=R, and process the top surface points Q1~Q4 of the seam to satisfy | Q | = R+ h The radial boundary curve length L is calculated by solving a quadratic equation; the axial deflection angle is also calculated. βTo ensure that P1P3 and P2P4 have the same circumferential angular displacement, thus maintaining parallelism; 4. Calculate discrete points and generate 12 boundary curves based on the line type. The axial boundary curves of the top and bottom surfaces of the seam are constant velocity spirals that are directly connected to the endpoints on the cylindrical surface. The discrete points of the remaining boundary curves are calculated by linear interpolation of the endpoints. 5. For the discrete points in the middle of the four axial boundary curves, construct a local coordinate system {T,B,C}, where T is the tangential direction along the boundary curve, B is the radial direction, and C is the circumferential direction of the arc where the point is located. The three constitute the local coordinate system. 6. User-provided mapping functions f (t, edge_id), returns the displacement vector [dT, dB, dC]. The system superimposes the corresponding displacement onto the non-endpoints of each axial boundary curve. The endpoints are forced to remain stationary. In this embodiment, the input is @(t, edge_id) [0, 0, 1.5*sin(2*pi*t)]; 7. Output geometry files for later use.
[0043] 8. Based on the above parameters, using this method, create single-channel deflection jet slits with different radial inclination angles at the front and rear ends before and after free modeling, such as... Figure 4 The results show that the axial torsional deformation slotted casing structure (AS) used in this invention can improve the stability margin from 9.2% to 18.0% with only a 0.57% loss in peak efficiency, which is significantly better than the non-freely torsional deflecting jet slot (DS), which only achieves a stability margin of 13% with a 0.78% loss in peak efficiency. Characteristic curves are shown below. Figure 5 As shown.
[0044] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent substitutions, and improvements made to the above embodiments without departing from the scope of the present invention, based on the technical essence of the present invention and within the spirit and principles of the present invention, shall still fall within the protection scope of the present invention.
Claims
1. A design method for a slotted casing with free-form shape along a boundary curve, characterized in that, The method includes the following steps: Step 1: Obtain design parameters, including the inner wall radius R of the casing, the axial positions z1 and z2 before and after the seam, and the seam area ratio. s Number of blades N, number of single-channel slits n, slit radial depth h radial inclination angles of the front and rear walls of the seam α 1, α 2, and the axial deflection angle of the seam. β ; Step 2: Calculate the central angle corresponding to the slit width based on the number of blades N, the number of single-channel slits n, and the slit area ratio s, and determine the circumferential position of each slit; Step 3: For each seam, calculate 8 vertices based on the design parameters, including four points P1, P2, P3, P4 on the bottom surface of the seam and four points Q1, Q2, Q3, Q4 on the top surface of the seam. Points P1 to P4 on the bottom surface of the seam are located on the cylindrical surface r=R, and points Q1 to Q4 on the top surface of the seam are required to satisfy the coordinate vector magnitude || of the vertical cross-section S3. Q | = R+ h The radial boundary curve length L is calculated by solving a quadratic equation; P1P3 and P2P4 are calculated according to the axial deflection angle. β To achieve the same circumferential angular displacement and maintain parallelism; Step 4: Generate 12 boundary curves from the 8 vertices. Process the axial boundary curves of the top and bottom surfaces of the seam as constant velocity spirals directly connecting the endpoints on the cylindrical surface, and generate the remaining boundary curves by linear interpolation of the endpoints. Step 5: For the discrete points on the four axial boundary curves, establish a local coordinate system {T,B,C} that varies along the boundary curves, where T is the tangential vector along the boundary curve; B is the cylindrical radial direction pointing from a point on the casing axis to a point on the boundary curve; and C is the circumferential direction of the arc where the point is located. The three coordinates constitute the local coordinate system. Step 6: Receive user-defined mapping function f (t, edge_id), this function uses the normalized arc length parameter t ∈ [0,1] and the boundary curve number edge_id are taken as inputs, and the output is the displacement vector [d] in three directions of the local coordinate system. T ,d B , d C ]; Step 7: For each discrete point on each axial boundary curve, excluding the two endpoints, calculate the arc length parameter based on its normalized arc length parameter. t Calling the mapping function to obtain the displacement vector r = d T T + d B B + d C C, and superimpose the displacement onto the original global coordinates: r' = r + d T T + d B B + d C C; For the two endpoints, the forced displacement is zero to ensure that the positions of the 8 vertices remain unchanged after deformation; Step 8: Output all boundary curves as geometric model files for mesh generation software to read.
2. The design method for a slotted casing with free-form shape along a boundary curve according to claim 1, characterized in that, In step 3, the length L of the radial boundary curve is obtained by solving the following vector equation and quadratic equation: Where P is the position vector of a point on the bottom surface of the seam, and Q is the position vector of a corresponding point on the top surface of the seam. e l The unit displacement vector is L; it is obtained by solving the positive root of the quadratic equation, thus ensuring that the distance from the top point Q to the axis is always equal to R+. h This ensures that the radial depth is unaffected by changes in the tilt angle; When Rsin α < <R+ h When the square root is expanded, the first-order terms exactly recover R / cos α However, higher-order terms include the effects of cylindrical geometry. Directly using L = R / cos α This will cause the actual radius of the top surface point Q to deviate from R+. h It cannot be guaranteed that the depth will be constant. h .
3. The design method for a slotted casing with free-form shape along a boundary curve according to claim 2, characterized in that, In step 3, the obtained radial boundary curve length L is substituted back into equation (1) to directly obtain the coordinates of point Q.
4. The design method for a slotted casing with free-form shape along a boundary curve according to claim 3, characterized in that, In step 3, the starting angle of the left boundary curve P1P3 on the bottom surface of the seam is... θ 1. The endpoint angle is θ 1 + δθ The starting angle of the right boundary curve P2P4 is θ 2. The endpoint angle is θ 2 + δθ , δθ Due to axial deflection angle β The same circumferential angular displacement is obtained on both sides. δθ Therefore, the two boundary curves remain parallel on the cylindrical surface.
5. The design method for a slotted casing with free-form shape along a boundary curve according to claim 4, characterized in that, In step 4, the axial boundary curves P1P3 and P2P4 on the bottom surface of the seam are treated as constant-velocity helices on a cylindrical surface with radius R. The axial boundary curves Q1Q3 and Q2Q4 on the top surface of the seam are treated by directly utilizing the vertex angle on a cylindrical surface with radius R+. h A constant-velocity helix is constructed on the cylindrical surface. The remaining radial and circumferential boundary curves are generated by linear interpolation between corresponding vertices. All boundary curves need to be generated by calculating discrete points and using the line type specified in the IGG file. The bottom axial boundary curves (P1P3, P2P4) are helices on a cylindrical surface with radius R, and the angles satisfy a linear change: The coordinates of the discrete point are: The top surface axial boundary curves (Q1Q3, Q2Q4) are of radius R+ h A helix on a cylindrical surface, the angle of which changes linearly: The coordinates of the discrete point are: The discrete points of the radial and circumferential boundary curves are solved directly by linear interpolation from 8 fixed endpoints, without participating in any deformation, to ensure that the cross-sectional shape of the seam is strictly controlled.
6. The design method for a slotted casing with free-form shape along a boundary curve according to claim 5, characterized in that, In step 4, when generating the axial boundary curve Q1Q3 of the top surface of the processing seam, the circumferential angles of vertices Q1 and Q3 are used. θ Q1 , θ Q3 Linear interpolation yields the angle at the midpoint, thus allowing the calculation of the angle within the radius R+. h A straight spiral is obtained on the cylindrical surface, avoiding lateral distortion caused by inclination angle interpolation.
7. The design method for a slotted casing with free-form shape along a boundary curve according to claim 6, characterized in that, The tangential direction T mentioned in step 5 is approximately calculated using the adjacent difference of discrete points, and the radial direction B is the radial unit vector [cos...] in cylindrical coordinates. θ , sin θ [, 0], C is the circumferential unit vector in cylindrical coordinates [-sin θ cos θ [, 0], which makes the deformation direction strictly bound to the geometric trend of the boundary curve itself.
8. The design method for a slotted casing with free-form shape along a boundary curve according to claim 7, characterized in that, In step 6, the mapping function f (t, edge_id) allows for independent control of the four axial boundary curves, where the displacement vector [d T , d B , d C ] These correspond to the deformation amounts along the boundary curve direction, radial direction, and circumferential direction of torsion, respectively; where d T Deformation along the boundary curve does not change the curve shape; it merely serves as a component of the displacement vector to complete its full form. The component that produces actual deformation is d. B With d C .
9. The design method for a slotted casing with free-form shape along a boundary curve according to claim 8, characterized in that, The geometric model file output in step 8 is in IGG format and contains curve definitions, project configurations, and boundary condition information, which can be directly used for NUMECA mesh generation.