A method for solving the optimal spatial position of ceramic core based on wall thickness tolerance constraints

Abstract

The present invention relates to a method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints, and belongs to the technical field of precision casting for hollow turbine blades for aircraft engines. The method comprises the following steps: obtaining data on the inner and outer contour points of the blade; determining the optimal spatial position profile of the blade wall thickness; introducing a wall thickness tolerance weight factor to construct a ceramic core optimal spatial position model; solving the ceramic core optimal spatial position model; and determining the actual optimal spatial position of the ceramic core within the wax mold. The present invention considers the variable wall thickness tolerance characteristics of the blade, defines a wall thickness tolerance weight factor, and introduces it into the calculation of the ceramic core's optimal spatial position, thereby reducing the impact of ceramic core profile deviations on the wall thickness accuracy of the blade wax mold, thereby achieving the purpose of precisely controlling the wall thickness accuracy of the hollow turbine blade.

Description

Technical Field

[0001] The invention belongs to the technical field of precision casting of hollow turbine blades of aircraft engines, and particularly relates to a method for solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints. Background Art

[0002] As the core hot-end component of aircraft engines, turbine blades currently utilize ultra-high-temperature heat-resistant alloys and internally cooled hollow structures to meet performance requirements under high temperatures and high pressures. During blade manufacturing, blade wall thickness accuracy is a crucial factor in ensuring blade strength and cooling efficiency, and has a decisive impact on blade life. Due to material and structural limitations, hollow turbine blades are primarily manufactured using zero-residue investment casting. Under the premise of stable material and process control, blade wall thickness accuracy is primarily derived from the wax pattern wall thickness accuracy and is ensured by the matching relationship between the ceramic core and the mold cavity surface. Currently, the position of the ceramic core within the wax pattern is primarily controlled by positioning elements, but determining the initial spatial position of the ceramic core during this control is crucial. Therefore, calculating the optimal spatial position of the ceramic core within the wax pattern, leveraging the variable wall thickness characteristics of the blade to control the wax pattern wall thickness accuracy, is a critical bottleneck that needs to be addressed.

[0003] The goal of the core position optimization problem is to find the optimal spatial position of a core with profile deviations within the blade, ensuring that the core profile and the blade profile meet the optimal spatial position matching relationship. Therefore, the core position optimization problem is transformed into a model matching problem for solution. Furthermore, considering that different regions of the blade have different wall thickness accuracy requirements, it is necessary to consider introducing the wall thickness tolerance as a constraint weight into the matching model. This allows the core profile deviation to fall within the blade's variable wall thickness tolerance range, thereby reducing the impact of the core profile error on the blade's wall thickness accuracy. Summary of the Invention

[0004] Technical issues to be solved:

[0005] In order to avoid the shortcomings of the existing technology, the present invention provides a method for solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints. The method takes the theoretical ceramic core as the target, uses the actual ceramic core profile detection results to perform model alignment to obtain the ceramic core profile error, and simultaneously determines the optimal position profile of the blade wall thickness, analyzes the difference in wall thickness changes at different positions of the blade, and then matches and calculates the inner contour measurement point with the optimal wall thickness position profile, thereby solving the optimal spatial position of the deformed ceramic core in the blade, and finally completing the solution to the optimal spatial position of the ceramic core.

[0006] The technical solution of the present invention is: a method for solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints, the specific steps are as follows:

[0007] Construct a theoretical model of a hollow turbine blade and obtain the inner and outer contour point data of the blade; discretize the theoretical model of the hollow turbine blade into multiple sections along the stacking axis, and discretize the inner and outer contours of each section into a discrete point cloud according to the chord tolerance constraint;

[0008] Determine the optimal spatial position profile of the blade wall thickness; offset the outer contour points of the blade theoretical model inward along the normal vector direction by the wall thickness value to obtain the optimal inner contour position point of the blade wall thickness; perform cross-section line fitting based on the B-spline curve to obtain the reconstructed theoretical blade wall thickness optimal position profile;

[0009] Constructing an optimal spatial position model of the ceramic core based on the wall thickness tolerance constraint; introducing a wall thickness tolerance weight factor into the optimal spatial position model of the ceramic core;

[0010] Solving the optimal spatial position model of the ceramic core; based on the optimal spatial position model of the ceramic core, performing a three-dimensional rigid registration transformation on the inner contour point cloud of the actually measured three-dimensional ceramic core model and the theoretical blade wall thickness optimal position surface, solving the optimal spatial position model of the ceramic core using the SVD singular value decomposition algorithm, and obtaining the angular parameters of rotation along the X, Y, and Z axes and the translation parameters of movement along the X, Y, and Z axes;

[0011] Determine the optimal spatial position of the actual ceramic core inside the wax mold; iteratively calculate the three-dimensional rigid registration transformation of the inner contour point cloud of the actually measured three-dimensional ceramic core model to solve the spatial coordinate transformation matrix. Based on the spatial coordinate transformation matrix, the spatial position of the ceramic core is reversely adjusted in the mold to obtain the optimal spatial position of the actual ceramic core inside the wax mold.

[0012] A further technical solution of the present invention is that the calculation expression of the optimal inner contour position point of the blade wall thickness is as follows:

[0013] s ij =g ij +t ij

[0014] Among them, s ij Optimal inner contour position point of blade wall thickness, g ij represents the jth point on the i-th section of the outer contour of the blade theoretical model, t ij Indicates point g ij In the blade theoretical model, the wall thickness direction vector of the corresponding points of the inner and outer contours is expressed as the theoretical wall thickness value of the point g that is simultaneously inscribed on the parameterized section line of the blade theoretical outer contour. i ' j Parametric cross-section line F with inner contour i ins The Euclidean distance between the tangent points of (u).

[0015] A further technical solution of the present invention is: the theoretical wall thickness value tij The calculation method is:

[0016] Set the parameterized cross-section line of the inner and outer contours of the blade theoretical model, the expression is F i ins (u), F i out (u);

[0017] Point g on the outer contour of the blade theoretical model ij Projection to the outer contour parameterized section line F i out (u), we get the projection point g i ' j ;

[0018] Based on the projection point g i ' j Determine the center of the inscribed circle The position of is expressed as follows:

[0019]

[0020] The inscribed circle is inscribed in the parameterized section line point g of the blade theoretical outer contour. i ' j Parametric cross-section line F with inner contour i ins (u), Δr represents the wall thickness search radius increment, and n represents the number of wall thickness search iterations; n g Indicates point g i ' j The unit normal vector pointing to the outside of the blade is calculated as:

[0021]

[0022] in, Represents the projection point g i ' j The partial differential value, u g Represents the projection point g i ' j The parametric cross-section line F in the inner contour of the blade i ins (u) parameter values.

[0023] The center of the inscribed circle Parameterized section line F projected onto the inner contour of the blade i ins (u), we get the projection point s i ' j ; Calculate the center of the circle at the same time With point g i ' j and the projection point si ' j The Euclidean distance difference between:

[0024]

[0025] If the distance difference satisfies the set convergence tolerance ε o ,Right now: Then click g ij The corresponding theoretical wall thickness value is expressed as:

[0026] t ij =|g i ' j -s i ' j |

[0027] Otherwise, let n=n+1 and update The above iterative calculation is repeated until the set convergence tolerance is met.

[0028] A further technical solution of the present invention is: the expression of the optimal position profile of the theoretical blade wall thickness is:

[0029]

[0030] in, The projection point s on the parameterized section line representing the inner contour of the blade i ' j The control vertices of the reconstructed surface with optimal wall thickness, e and f represent the number of spline curves and cross sections respectively; B e,k (u) and B f,k (v) represents the B-spline basis function in the tangent direction u and the normal direction v.

[0031] A further technical solution of the present invention is: the expression of the optimal spatial position model of the ceramic core is:

[0032]

[0033] Among them, p ij Represents the jth contour point on the i-th section of the actually measured ceramic core 3D model; For point p ij The projection point on the profile at the optimum position of blade wall thickness; w ij For point p ij The corresponding wall thickness tolerance weight factor; R represents the rotation matrix, and T represents the translation matrix.

[0034] A further technical solution of the present invention is: the wall thickness tolerance weight factor is expressed as:

[0035]

[0036] Among them, H L 、H S are the contour point sets of the front and rear edge regions and the basin back region of the theoretical ceramic core cross section respectively; T ij For point p ij Theoretical wall thickness of blade at T i min is the minimum theoretical wall thickness among all contour points on section i; δ h , δ l Wall thickness tolerance of the front and rear edge areas and the pelvic back area respectively; and Represents the quantity balance factor, which is used to eliminate the impact of quantity differences on registration accuracy.

[0037] A further technical solution of the present invention is: the inner contour point cloud p of the actually measured three-dimensional model of the ceramic core ij The position expression after three-dimensional rigid registration transformation with the optimal spatial position profile of the theoretical blade wall thickness is:

[0038] p i ' j =ΔR·p ij +ΔT

[0039] in: Represents the rotation vector; ΔT=[Δδ x Δδ y Δδ z ] T represents the translation vector; p ij represents the actual measured position coordinates of the initial spatial position of the ceramic core contour point i on the section j; p i ' j Represents the position coordinates of section j of the optimal spatial position contour point i of the ceramic core.

[0040] A further technical solution of the present invention is that the expression for the optimal spatial position of the actual ceramic core inside the wax mold is:

[0041]

[0042] in, are the control vertices of the actual ceramic core reconstruction surface before registration, e and f represent the spline curve and the number of sections; R′ represents the rotation matrix after iterative calculation, and T′ represents the translation vector after iterative calculation.

[0043] A further technical solution of the present invention is: the method for solving the space coordinate transformation matrix is:

[0044] Assumptions is the initial pose point cloud information matrix of the ceramic core, Denoted as the optimal spatial pose point cloud information matrix of the ceramic core, then the information matrix and The spatial transformation relationship is:

[0045]

[0046] in,

[0047]

[0048] Where, Η is the spatial transformation composite matrix; Represents four point cloud data at different cross-section heights in the initial ceramic core position point cloud; represents the point cloud data corresponding to the ceramic core under the optimal spatial position of the ceramic core; the above two sets of point cloud data are brought into the optimal spatial position model of the ceramic core, and the solution of the composite matrix H is obtained by inverse calculation:

[0049] R′=R -1

[0050] T′=-T.

[0051] An electronic device comprises at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute a method for solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints.

[0052] Beneficial effects

[0053] The beneficial effects of the present invention are as follows: To address the current problem of blade wall thickness accuracy deviation caused by actual ceramic core profile errors, the present invention provides a method for solving the optimal spatial position of the ceramic core based on wall thickness tolerance constraints. By constructing the optimal wall thickness profile of the blade by offsetting the wall thickness value inward along the normal vector direction of the blade outer contour, the optimal spatial position of the actual ceramic core in the blade is determined. Simultaneously, considering the variable wall thickness tolerance characteristics of the blade, a wall thickness tolerance weight factor is defined and introduced into the calculation of the optimal spatial position of the ceramic core, thereby reducing the impact of ceramic core profile deviation on the wall thickness accuracy of the blade wax mold, and achieving the goal of precise control of the wall thickness accuracy of the hollow turbine blade. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the detection section division of the hollow turbine blade in the present invention;

[0055] Figure 2 This is a schematic diagram of the optimal wall thickness profile structure of the hollow turbine blade of the present invention;

[0056] Figure 3 Schematic diagram of the wall thickness tolerance weight distribution and area division of the hollow turbine blade in the present invention;

[0057] Figure 4 This is a schematic diagram of the optimal spatial posture adjustment of the ceramic core of the hollow turbine blade in the present invention. DETAILED DESCRIPTION

[0058] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0059] Based on the problem that the actual ceramic core surface error affects the blade wall thickness accuracy, the present invention proposes a method for solving the optimal spatial position of the ceramic core based on wall thickness tolerance constraints, which includes constructing the optimal wall thickness surface model of the blade, defining the wall thickness tolerance weight factor, and solving the optimal spatial position of the ceramic core.

[0060] Reference Figure 1-4 As shown, the specific steps of the method for solving the optimal spatial posture of a ceramic core based on wall thickness tolerance constraints in a specific example of a hollow turbine blade are as follows:

[0061] Step 1: Construct a theoretical model of a hollow turbine blade, divide it into test sections along the stacking axis, and discretize the point cloud according to the chord tolerance. If the section height is 5.1 mm and the chord tolerance is set to 0.1 mm, the number of discrete points per section is 132.

[0062] Step 2: Determine the optimal spatial position profile of the blade wall thickness.

[0063] Assume g ij Indicates the jth point of the i-th section of the outer contour of the blade theoretical model, and the optimal inner contour position point s of the blade wall thickness ij The wall thickness can be obtained by offsetting the outer contour point of the blade inward along the normal direction:

[0064] s ij =g ij +t ij

[0065] Among them, t ij For point g ij The wall thickness direction vector of the corresponding point in the theoretical model, its magnitude (i.e. theoretical wall thickness value) can be expressed as the Euclidean distance between the corresponding point inscribed in the outer contour line of the blade theoretical section and the inscribed point of the ceramic core theoretical section line. ij Calculation method:

[0066] Set the parameterized cross-section line of the inner and outer contours of the blade theoretical model, the expression is F i ins (u), F i out (u);

[0067] Point g on the outer contour of the blade theoretical model ijProjection to the outer contour parameterized section line F i out (u), we get the projection point g i ' j ;

[0068] Based on the projection point g i ' j Determine the center of the inscribed circle The position of is expressed as follows:

[0069]

[0070] The inscribed circle is inscribed in the parameterized section line point g of the blade theoretical outer contour. i ' j Parametric cross-section line F with inner contour i ins (u), Δr represents the wall thickness search radius increment, n represents the number of wall thickness search iterations, n g Indicates point g i ' j The unit normal vector pointing to the outside of the blade; the point g i ' j The calculation formula for the unit normal vector pointing to the outside of the blade is:

[0071]

[0072] in, Represents the projection point g i ' j The partial differential value, u g Represents the projection point g i ' j The parametric cross-section line F in the inner contour of the blade i ins (u) parameter values.

[0073] The center of the inscribed circle Parameterized section line F projected onto the inner contour of the blade i ins (u), we get the projection point s i ' j ; Calculate the center of the circle at the same time With point g i ' j and the projection point s i ' j The Euclidean distance difference between:

[0074]

[0075] If the distance difference satisfies a certain convergence tolerance ε o ,Right now: Then click g ij The corresponding theoretical wall thickness value is expressed as:

[0076] t ij =|g i ' j -s i ' j |

[0077] Otherwise, let n=n+1 and update The above iterative calculation is repeated until the set convergence tolerance is met.

[0078] The projection point s i ' j Perform cross-section line fitting and uniform parameterization into B-spline curves to perform 3D reconstruction of the optimal wall thickness profile. Finally, the reconstructed blade wall thickness optimal position profile is obtained:

[0079]

[0080] in, Represents the blade outer contour point set s i ' j The control vertices of the optimal wall thickness surface are reconstructed, e and f represent the number of spline curves and cross sections respectively. e,k (u) and B f,k (v) represents the B-spline basis functions in the u direction (tangent direction) and the v direction (normal direction).

[0081] Step 3: Establish the optimal spatial position model of the ceramic core based on wall thickness tolerance constraints.

[0082] Generally speaking, the tolerance requirements for variable wall thickness in different areas of the blade are different. The wall thickness is thinner at the leading and trailing edges of the blade, and the wall thickness tolerance is smaller; the wall thickness is thicker at the base and back of the blade, and the wall thickness tolerance is larger. To improve the model matching accuracy of the deformed ceramic core, it is necessary to assign a higher matching weight to the areas with larger wall thickness tolerances, that is, to prioritize the registration accuracy at the leading and trailing edges. Therefore, the optimal spatial pose model of the ceramic core based on the wall thickness tolerance constraint can introduce a wall thickness tolerance weight factor on the traditional ICP registration model:

[0083]

[0084] Where p ij Represents the jth contour point on the i-th section of the actual ceramic core 3D model; For point p ij The projection point on the surface with the best wall thickness; w ij For point p ij The corresponding weight factor is defined based on the blade wall thickness tolerance characteristics and the difference in the number of point clouds in different areas.

[0085] Since the weight assigned to the location with thicker wall thickness is lower and the weight assigned to the location with thinner wall thickness is higher, the wall thickness tolerance weight factor for a certain section can be defined as:

[0086]

[0087] Where H L 、H S are the contour point sets of the front and rear edge areas of the ceramic core and the basin back area respectively; T ij For point p ij The theoretical wall thickness of the blade is at T. Since the wall thickness of the leading and trailing edges of the blade is relatively small, the introduction of this value can ensure that the contour points in the leading and trailing edges have a higher matching weight. i min is the minimum theoretical wall thickness among all contour points on section i. This value is introduced mainly to eliminate the influence of the magnitude of the wall thickness on the weight factor; δ h , δ l The wall thickness tolerance of the front and rear edge areas and the pelvic back area is respectively. Since the front and rear edge areas have smaller tolerances, the introduction of this value can ensure that the contour points in the front and rear edge areas have higher matching weights. In addition, considering that the number of contour points in the front and rear edge areas is significantly smaller than that in the pelvic back area, the number balance factor is introduced. and To eliminate the influence of quantity difference on registration accuracy, such as Figure 3 shown.

[0088] Taking a certain cross section as an example, the weights of the ceramic core cross section point cloud at the leading and trailing edges are 1.2-1.8; the weights at the blade basin and back are 0.7-0.9;

[0089] Step 4: Solve the optimal spatial position model of the ceramic core based on wall thickness tolerance constraints.

[0090] Based on the optimal spatial position model of the ceramic core, the point cloud p of the actual detected blade inner contour (i.e., the ceramic core outer contour) is ij The optimal position profile S of the theoretical blade wall thickness W (u, v) is transformed into a three-dimensional rigid registration, and the SVD singular value decomposition algorithm is used to solve the optimal spatial pose model of the ceramic core, that is, to solve the angle parameters of rotation along the X, Y, and Z axes. And the translation parameter Δδ along the X, Y, and Z axes x ,Δδ y ,Δδ z Then, the outer contour point p of the ceramic core ij The position after spatial transformation in the leaf is expressed as:

[0091] p′ ij =ΔR·pij +ΔT

[0092] Where: Represents the rotation vector; ΔT=[Δδ x Δδ y Δδ z ] T represents the translation vector; p ij represents the initial spatial position of the ceramic core, and the coordinates of the position of the contour point i on the section j; p′ ij Represents the position coordinates of section j of the optimal spatial position contour point i of the ceramic core.

[0093] Step 5: Optimal spatial position of the actual ceramic core inside the wax mold

[0094] After iterative calculation in step 4, the actual ceramic core posture space transformation solution is as follows: Assume is the initial pose point cloud information matrix of the ceramic core, Denoted as the optimal spatial pose point cloud information matrix of the ceramic core, then the information matrix and The spatial transformation relationship is:

[0095]

[0096] in

[0097]

[0098]

[0099] Where H is the spatial transformation composite matrix. Represents four point cloud data at different cross-section heights in the initial ceramic core pose point cloud; Indicates the point cloud data corresponding to the ceramic core under the optimal spatial position of the ceramic core. Substitute the above two sets of point cloud data into the optimal spatial position model of the ceramic core, and inversely obtain the solution of the composite matrix H:

[0100] R′=R -1

[0101] T′=-T

[0102] Assume that the surface equation under the theoretical ceramic core space position is S D (u, v), then the rotation matrix R′ and translation vector T′ obtained based on the above registration model, the surface equation of the ceramic core after reverse adjustment in the mold (i.e., the optimal spatial position of the ceramic core inside the wax mold) can be expressed as:

[0103]

[0104] Where, are the control vertices of the actual ceramic core reconstruction surface before registration, e and f represent the number of spline curves and sections, and the position of the actual ceramic core surface after reconstruction is the initial spatial position inside the wax mold, such as Figure 4 shown.

[0105] In this embodiment, an information matrix is ​​constructed to solve the rotation matrix and translation matrix of the actual ceramic core under the optimal spatial posture:

[0106]

[0107] By comparing with the traditional ICP, under the same number of iterations, the maximum deviation obtained by the model matching algorithm with wall thickness tolerance constraint is reduced. The adjustment amount along the xyz direction after conversion to Euler angles is shown in Table 1:

[0108] Table 1 Transformation parameters of weighted matching and non-weighted matching

[0109]

[0110]

[0111] Assume that the surface equation under the theoretical ceramic core space position is S D (u, v), then the rotation matrix R′ and translation vector T′ obtained based on the above registration model, the surface equation of the ceramic core in the initial spatial position after reverse adjustment in the mold (i.e., the optimal spatial position of the ceramic core inside the wax mold) can be expressed as:

[0112]

[0113] Finally, according to the spatial position of the ceramic core adjusted inside the wax mold obtained by the solution method of the optimal spatial posture of the ceramic core based on the wall thickness tolerance constraint, a precision casting wax mold is prepared, and subsequent shelling, sintering, casting, shelling, and core removal processes are completed to obtain the final casting hollow turbine blade. After wall thickness testing, it was found that the blade met the wall thickness tolerance requirements, and the maximum deviation of the leading and trailing edges was reduced from the original 0.22mm to 0.08mm; the maximum deviation of the wall thickness at the blade basin and back of the blade was reduced from the original 0.45mm to 0.19mm, thereby verifying the effectiveness of the solution method of the optimal spatial posture of the ceramic core based on the wall thickness tolerance constraint proposed in this invention.

[0114] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints, characterized by The specific steps are as follows: Construct a theoretical model of a hollow turbine blade and obtain the inner and outer contour point data of the blade; discretize the theoretical model of the hollow turbine blade into multiple sections along the stacking axis, and discretize the inner and outer contours of each section into a discrete point cloud according to the chord tolerance constraint; Determine the optimal spatial position profile of the blade wall thickness; offset the outer contour point of the blade theoretical model inward along the normal vector direction by the wall thickness value to obtain the optimal inner contour position point of the blade wall thickness; Perform cross-sectional line fitting based on the B-spline curve to obtain the optimal position profile of the theoretical blade wall thickness after reconstruction; Constructing an optimal spatial position model of the ceramic core based on the wall thickness tolerance constraint; introducing a wall thickness tolerance weight factor into the optimal spatial position model of the ceramic core; Solving the optimal spatial position model of the ceramic core; based on the optimal spatial position model of the ceramic core, performing a three-dimensional rigid registration transformation on the inner contour point cloud of the actually measured three-dimensional ceramic core model and the theoretical blade wall thickness optimal position surface, solving the optimal spatial position model of the ceramic core using the SVD singular value decomposition algorithm, and obtaining the angular parameters of rotation along the X, Y, and Z axes and the translation parameters of movement along the X, Y, and Z axes; Determine the optimal spatial position of the actual ceramic core inside the wax mold; iteratively calculate the three-dimensional rigid registration transformation of the inner contour point cloud of the actually measured three-dimensional ceramic core model to solve the spatial coordinate transformation matrix of the ceramic core from the initial position to the optimal position. At the same time, based on the inverse deformation principle, solve the actual spatial adjustment position of the ceramic core, and finally obtain the optimal spatial position of the actual ceramic core inside the wax mold.

2. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 1, characterized in that: The calculation expression of the optimal inner contour position point of the blade wall thickness is as follows: s ij =g ij +t ij Among them, s ij Optimal inner contour position point of blade wall thickness, g ij represents the jth point on the i-th section of the outer contour of the blade theoretical model, t ij Indicates point g ij In the blade theoretical model, the wall thickness direction vector of the corresponding points of the inner and outer contours is expressed as the theoretical wall thickness value of the point g that is simultaneously inscribed on the parameterized section line of the blade theoretical outer contour. i ' j Parametric cross-section line F with inner contour i ins The Euclidean distance between the tangent points of (u).

3. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 2, wherein: The theoretical wall thickness value t ij The calculation method is: Set the parameterized cross-section line of the inner and outer contours of the blade theoretical model, the expression is F i ins (u), F i out (u); Point g on the outer contour of the blade theoretical model ij Projection to the outer contour parameterized section line F i out (u), we get the projection point g i ' j ; Based on the projection point g i ' j Determine the center of the inscribed circle The position of is expressed as follows: The inscribed circle is inscribed in the parameterized section line point g of the blade theoretical outer contour. i ' j Parametric cross-section line F with inner contour i ins (u), Δr represents the wall thickness search radius increment, and n represents the number of wall thickness search iterations; n g Indicates point g i ' j The unit normal vector pointing to the outside of the blade is calculated as: in, Represents the projection point g i ' j The partial differential value, u g Represents the projection point g i ' j The parametric cross-section line F in the inner contour of the blade i ins (u) parameter values; The center of the inscribed circle Parameterized section line F projected onto the inner contour of the blade i ins (u), we get the projection point s i ' j ; Calculate the center of the circle at the same time With point g i ' j and the projection point s i ' j The Euclidean distance difference between: If the distance difference satisfies the set convergence tolerance ε o ,Right now: Then click g ij The corresponding theoretical wall thickness value is expressed as: t ij =|g i ' j -s i ' j | Otherwise, let n=n+1 and update The above iterative calculation is repeated until the set convergence tolerance is met.

4. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 3, wherein: The expression of the theoretical blade wall thickness optimal position profile is: in, The projection point s on the parameterized section line representing the inner contour of the blade i ' j The control vertices of the reconstructed surface with optimal wall thickness, e and f represent the number of spline curves and cross sections respectively; B e,k (u) and B f,k (v) represents the B-spline basis function in the tangent direction u and the normal direction v.

5. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 4, characterized in that: The expression of the optimal spatial position model of the ceramic core is: Among them, p ij Represents the jth contour point on the i-th section of the actually measured ceramic core 3D model; For point p ij The projection point on the profile at the optimum position of blade wall thickness; w ij For point p ij The corresponding wall thickness tolerance weight factor; R represents the rotation matrix, and T represents the translation matrix.

6. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 5, characterized in that: The wall thickness tolerance weight factor is expressed as: Among them, H L 、H S are the contour point sets of the front and rear edge regions and the basin back region of the theoretical ceramic core cross section respectively; T ij For point p ij Theoretical wall thickness of blade at T i min is the minimum theoretical wall thickness among all contour points on section i; δ h , δ l Wall thickness tolerance of the front and rear edge areas and the pelvic back area respectively; and Represents the quantity balance factor, which is used to eliminate the impact of quantity differences on registration accuracy.

7. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 6, characterized in that: The inner contour point cloud p of the actually measured ceramic core three-dimensional model ij The position expression after three-dimensional rigid registration transformation with the optimal spatial position profile of the theoretical blade wall thickness is: p i ′ j =ΔR·p ij +ΔT in: Represents the rotation vector; ΔT=[Δδ x Δδ y Δδ z ] T represents the translation vector; p ij represents the actual measured position coordinates of the initial spatial position of the ceramic core contour point i on the section j; p i ' j Represents the position coordinates of section j of the optimal spatial position contour point i of the ceramic core.

8. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 7, characterized in that: The expression for the optimal spatial position of the actual ceramic core inside the wax mold is: in, are the control vertices of the actual ceramic core reconstruction surface before registration, e and f represent the number of spline curves and sections; R′ represents the rotation matrix after iterative calculation, and T′ represents the translation vector after iterative calculation.

9. The method for determining the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 8, characterized in that: The solution method of the space coordinate transformation matrix is: Assumptions is the initial pose point cloud information matrix of the ceramic core, Denoted as the optimal spatial pose point cloud information matrix of the ceramic core, then the information matrix and The spatial transformation relationship is: in, is the spatial transformation composite matrix; Represents four point cloud data at different cross-section heights in the initial ceramic core position point cloud; represents the point cloud data corresponding to the ceramic core under the optimal spatial position of the ceramic core; the above two sets of point cloud data are brought into the optimal spatial position model of the ceramic core, and the solution of the composite matrix H is obtained by inverse calculation: R′=R -1 T′=-T.

10. An electronic device, characterized in that: The invention comprises at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor so that the at least one processor can execute the method for solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints as described in any one of claims 1 to 9.

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