Ceramic core optimal spatial position solving method based on wall thickness tolerance constraint

Abstract

The invention discloses a ceramic core optimal spatial position solving method based on wall thickness tolerance constraint, and belongs to the technical field of precision casting of hollow turbine blades of aero-engines. The method comprises the steps of obtaining blade inner and outer contour point data; determining a blade wall thickness optimal space position profile; introducing a wall thickness tolerance weight factor, and constructing an optimal spatial position model of the ceramic core; solving the optimal spatial position model of the ceramic core; and determining the actual optimal space position of the ceramic core in the wax pattern mold. According to the method, the variable wall thickness tolerance characteristic of the blade is considered, and the wall thickness tolerance weight factor is defined and introduced into the optimal space pose calculation of the ceramic core, so that the influence of the molded surface deviation of the ceramic core on the wax pattern wall thickness precision of the blade is reduced, and the aim of accurately controlling the wall thickness precision of the hollow turbine blade is fulfilled.

Description

Technical Field

[0001] The invention belongs to the technical field of precision casting of hollow turbine blades of aircraft engines, and in particular 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 aero-engines, turbine blades currently generally use ultra-high temperature heat-resistant alloys and internally cooled hollow structures to meet their performance requirements under high temperature and high pressure. In the blade manufacturing process, the wall thickness accuracy of the blade is an important indicator to ensure the strength and cooling efficiency of the blade, and has a decisive influence on the life of the blade. Limited by materials and structures, hollow turbine blades are mainly manufactured by non-residue investment casting. Under the premise of stable control of materials and processes, the wall thickness accuracy of the blade is mainly inherited from the wall thickness accuracy of the wax mold, and is guaranteed by the matching relationship between the ceramic core and the cavity surface. At present, the ceramic core in the wax mold mainly relies on positioning elements to achieve position control, but the initial spatial position acquisition of the ceramic core control is particularly important. Therefore, how to calculate the optimal spatial position state of the ceramic core inside the wax mold by the characteristics of the variable wall thickness of the blade to control the wall thickness accuracy of the wax mold is a key bottleneck problem that needs to be solved urgently.

[0003] The purpose of the ceramic core position optimization problem is to find the best spatial position of the ceramic core with profile deviation inside the blade, so that the ceramic core profile and the blade profile meet the best spatial position matching relationship. Therefore, the ceramic core position optimization problem is transformed into a model matching problem for solution. In addition, considering that different areas 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, which can make the ceramic core profile deviation enter the blade variable wall thickness tolerance range, thereby reducing the influence of the ceramic core profile error on the blade wall thickness accuracy. Summary of the invention

[0004] Technical issues to be solved:

[0005] In order to avoid the shortcomings of the prior art, 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 blade wall thickness optimal position profile, analyzes the wall thickness variation difference at different blade positions, and then matches and calculates the inner contour measurement point with the wall thickness optimal position profile, thereby solving for 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, and 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 profile, solving the optimal spatial position model of the ceramic core using the SVD singular value decomposition algorithm, and obtaining the angle 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, solve the spatial coordinate transformation matrix, and reversely adjust the spatial position of the ceramic core in the mold based on the spatial coordinate transformation matrix 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: 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 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 parametric 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 Parameterized section line F in the inner contour of the blade i ins (u) is the parameter value on the

[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 optimal wall thickness profile 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 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 Indicates the jth contour point on the i-th section of the ceramic core three-dimensional model actually measured; 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 The 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 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:

[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 initial spatial position of the ceramic core contour point i section j position coordinates; 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 alignment, 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.

[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] Wherein, H 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 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.

[0052] Beneficial Effects

[0053] The beneficial effects of the present invention are as follows: the present invention aims at the problem of blade wall thickness accuracy deviation caused by actual ceramic core profile error, and provides a method for solving the optimal spatial posture of ceramic core based on wall thickness tolerance constraint. The optimal wall thickness profile of the blade is constructed by offsetting the wall thickness value inward along the normal vector direction of the outer contour of the blade, thereby determining the optimal spatial position of the actual ceramic core in the blade. At the same time, considering the variable wall thickness tolerance characteristics of the blade, the wall thickness tolerance weight factor is defined and introduced into the calculation of the optimal spatial posture of the ceramic core, thereby reducing the influence of the ceramic core profile deviation on the wall thickness accuracy of the blade wax mold, and achieving the purpose of precise control of the wall thickness accuracy of the hollow turbine blade. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 It is a schematic diagram of the detection section division of the hollow turbine blade in the present invention;

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

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

[0057] Figure 4 It 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 be used 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 an optimal wall thickness surface model of the blade, defining a 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. The section height is 5.1 mm, the chord tolerance is set to 0.1 mm, and the number of discrete points in each section is 132.

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

[0063] Assume that 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 value 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., the 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 circle tangent point of the ceramic core theoretical section line. The theoretical wall thickness value t 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 parametric 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 at 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 Parameterized section line F in the inner contour of the blade i ins (u) is the parameter value on the

[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 The cross-section line is fitted and uniformly parameterized into a B-spline curve, so as to perform a three-dimensional 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 profile 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, the tolerance requirements for variable wall thickness of blades in different areas are different. The wall thickness is thinner in the leading and trailing edges of the blade, and the wall thickness tolerance is smaller; the wall thickness is thicker in the blade basin and back area, and the wall thickness tolerance is larger. In order to improve the model matching accuracy of the deformed ceramic core, it is necessary to assign a higher matching weight to the area with a larger wall thickness tolerance, that is, to give priority to ensuring 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 the wall thickness tolerance weight factor on the traditional ICP registration model:

[0083]

[0084] In the formula, 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 optimum wall thickness surface; w ij For point p ij The corresponding weight factor is defined according to the variable wall thickness tolerance characteristics of the blade and the difference in the number of point clouds in different areas.

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

[0086]

[0087] In the formula, 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 T. Since the wall thickness of the leading and trailing edges of the blade is 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 a smaller tolerance, the introduction of this value can ensure that the contour points in the front and rear edge areas have a higher matching weight; 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 differences 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 front and rear 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., ceramic core outer contour) is ij The optimum 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 posture 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 p′ represents the initial spatial position of the ceramic core, the position coordinates of the contour point i on the section j; 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 solution method for the spatial transformation of the ceramic core position 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] Wherein, 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 corresponding point cloud data of 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] In the formula, is the control vertex of the actual ceramic core reconstruction surface before registration, e and f represent the number of spline curves and sections, and the actual ceramic core surface position 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 into 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, the spatial position of the ceramic core adjusted inside the wax mold is obtained according to the solution method of the optimal spatial posture of the ceramic core based on the wall thickness tolerance constraint, and the precision casting wax mold is prepared, and the subsequent shell making, sintering, casting, shelling, core removal and other processes are completed to obtain the final casting hollow turbine blade. After wall thickness detection, it is found that the blade meets the wall thickness tolerance requirements, and the maximum deviation of the leading and trailing edges is reduced from the original 0.22mm to 0.08mm; the maximum deviation of the wall thickness at the blade basin and the back of the blade is 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 the present invention.

[0114] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary 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 intent 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 in that 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; Based on the B-spline curve, the cross-section line is fitted 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 profile, solving the optimal spatial position model of the ceramic core using the SVD singular value decomposition algorithm, and obtaining the angle 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 actual measured ceramic core three-dimensional 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 solving 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 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 solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 2, characterized in that: 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 parametric 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 Parameterized section line F in the inner contour of the blade i ins (u) parameter value on; 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 solving the optimal spatial position of a ceramic core based on wall thickness tolerance constraints according to claim 3, characterized in that: The expression of the optimal position profile of the theoretical blade wall thickness 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 optimal wall thickness profile 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 function in the tangent direction u and the normal direction v.

5. The method for solving 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 Indicates the jth contour point on the i-th section of the ceramic core three-dimensional model actually measured; 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 solving 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 The 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 solving 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 initial spatial position of the ceramic core contour point i section j position coordinates; 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 solving 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 alignment, 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 solving 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: It includes 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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