Customized conduit allowance processing calculation method

Abstract

The invention discloses a customized guide pipe allowance machining calculation method which is used for solving the problem that a customized guide pipe needs to be repeatedly compared and filed when a liquid rocket engine is assembled. According to the technical scheme, the method is divided into a measurement stage and a calculation stage, in the measurement stage, engine duct connector and constraint feature data are measured, meanwhile, to-be-assembled duct data are measured, in the calculation stage, the duct is rotated and translated to complete one-time assembly with the engine connector, the duct transformation relation is calculated, and the duct linear segment length and the rotation angle serve as variables. The perpendicularity of the two ends of the guide pipe serves as a target function, the distance between the guide pipe and an engine and other parts serves as constraint conditions, a mathematical optimization model is built, and then guide pipe cutting parameters are obtained. According to the method, the time and labor required by customized conduit production can be remarkably reduced, and the conduit production efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the field of customized catheter margin processing, and in particular to a customized catheter margin processing calculation method. Background Art

[0002] The piping system is an important component of liquid rocket engines. However, due to poor product size consistency and other reasons, a large number of conduits need to be customized. After the conduits are bent, the excess is processed according to the actual situation of the engine interface. It is necessary to manually hold the conduits and repeatedly test and file the engine pipe interface. This process requires multiple cutting of the excess, multiple test interfaces, and multiple filing of the pipe mouth. Manual testing and filing of conduits rely more on personnel experience, and the direction of the conduits is not easy to control, which may cause interference with other engine components. At the same time, the labor intensity is high, the efficiency is low, and the production time is long. Therefore, the assembly of the piping system has become a bottleneck link in improving the final assembly capacity of liquid rocket engines. Summary of the invention

[0003] In view of the defects and shortcomings in the above-mentioned prior art, the purpose of the present invention is to overcome the technical difficulties that customized ducts for liquid rocket engines require repeated manual testing and filing, and provide a duct allowance processing calculation method. This method adopts the concept of collaborative manufacturing, based on the actual data of the engine duct interface and constraint characteristics, considers the interference between the duct and the engine, eliminates the wall misalignment in duct processing, and calculates the duct processing allowance. This method can significantly reduce the time and manpower required for customized duct production and improve the production efficiency of ducts.

[0004] The technical solution adopted by the present invention to achieve the above-mentioned purpose is:

[0005] A customized catheter margin processing calculation method includes the following steps:

[0006] Measurement phase: Use measurement equipment to measure the engine's customized duct assembly interface, the position constraint features of the duct and pre-installed components on the engine, and extract the measured data of the duct's interfaces at both ends and their position constraint features; measure the duct model and extract the measured data of the duct model;

[0007] Calculation phase: According to the assembly catheter interface and its position constraint characteristics, as well as the measured data of the catheter model, the catheter and its assembly interface are initially assembled and aligned, the length of each straight segment of the catheter is adjusted and the rotation angle is adjusted, the optimal posture of the catheter is searched, and the cutting parameters at both ends of the catheter are calculated for accurate excess processing and to avoid interference between the catheter and prefabricated parts to achieve assembly.

[0008] The method of extracting measured data of the interfaces and position constraint features at both ends of the catheter comprises the following steps:

[0009] Fit the interface center point and unit direction vector data according to the interface cross-section circles at both ends of the catheter;

[0010] The prefabricated component is abstracted as a cylinder or a sphere, and the axis data of the cylinder and / or the center data of the sphere are extracted according to its position constraint characteristics;

[0011] The measured data of the extracted catheter model is the measured data of each key point of the extracted catheter model.

[0012] In the engine coordinate system:

[0013] The interfaces at the beginning and end of the assembly are defined as S end and E end respectively, and the center point of the S end interface is The unit direction vector is The E-terminal interface is The unit direction vector is

[0014] The constraints on the engine are of two types:

[0015] The i-th point (or sphere) feature is express;

[0016] The axis of the j-th cylindrical feature starts with Axis direction vector express;

[0017] The key points of the catheter model are P S , P T1 , P T2 …P T(2n-2) , P E ; where P S , P E The endpoints of the catheter; P Ti are the endpoints i of the remaining straight line segments, i∈{1,2,…,n-1}; n is the number of straight line segments of the catheter.

[0018] The calculation phase includes the following steps:

[0019] Step 1: Based on the interface data, take the interface center point at the S end of the catheter is the origin, is the X-axis, and The composed plane is X1O1Y1 plane, and the local right-handed coordinate system O1 is established;

[0020] Step 2: Find the transformation relationship between the local coordinate system O1 and the engine coordinate system, and find the data of the interfaces at both ends and each constraint feature under the local coordinate system O1;

[0021] Step 3: Make the catheter coordinate system coincide with the local coordinate system O1, then rotate and translate the catheter so that the straight segments at both ends of the catheter pass through the center points of the two interfaces respectively. And make And make the catheter P S , P T1 The point is in the X1O1Y1 plane, and the transformation relationship is calculated to find the coordinates of each key point of the catheter in the coordinate system O1, and the initial alignment of the catheter is obtained;

[0022] Step 4: The catheter is rotated by an angle θ around the X1 axis to obtain a first assembly of the catheter;

[0023] Step 5: Establish cutting planes at both ends of the catheter according to the interface normal plane;

[0024] Step 6: Keep the length l of the first straight line segment of the catheter A , the rotation angle θ is taken as a variable, and the verticality of the two ends of the catheter is taken as the objective function. A mathematical optimization model is established to solve the optimal

[0025] Find x=(l A ,θ)

[0026] Minimize f(x)=max(H1,H2)

[0027]

[0028] Where H1 and H2 represent the verticality of the two ends of the catheter, respectively. f(x) is the objective function constructed by the verticality of the catheter, which minimizes the verticality of the two ends of the catheter. The length of the first straight line segment at both ends of the catheter is l A , l B The value ranges are (L Amin , L Amax )、(L Bmin , L Bmax ) is used to ensure the weldability and assembly of both ends of the conduit; the spacing requirement between the conduit and the point features on the engine is d pi Less than the threshold d pimin , the spacing requirement between the duct and the cylindrical feature on the engine is d lj Less than the threshold d ljmin , used to prevent the duct from interfering with other parts on the engine;

[0029] Step 7: According to the optimal solution Calculate the cutting point P A , P B , cutting plane normal And cutting inclination angles γ1, γ2.

[0030] The conversion relationship between the local coordinate system O1 and the engine coordinate system is calculated as follows:

[0031] Step 2.1: From the S-side interface Starting from, take point P at unit length along the normal direction V , whose coordinates are: and The angle α is:

[0032]

[0033] Step 2.2: In the local coordinate system O1, the coordinates of the corresponding interface center points are: In the formula is the span of two interfaces;

[0034] Step 2.3: According to P V The coordinate values ​​of the three points in the engine coordinate system and the local coordinate system O1, solve the transformation relationship between the two coordinate systems:

[0035] P i F* =R1·P i F +T1 i∈{S,E,Pj,Lk},j∈{1,2,…},k∈{1,2,…}

[0036] Among them, P i F* is the point coordinate in the local coordinate system O1, P i F is the point coordinate in the engine coordinate system, R1 is the rotation matrix, and T1 is the translation matrix.

[0037] The coordinate transformation relationship for the initial assembly alignment of the catheter is calculated as follows:

[0038] Step 3.1: Rotate and translate the catheter so that the straight segments at both ends of the catheter pass through The corresponding point on the catheter is defined as P A , P B , while making the catheter point P S and P T1 In the X1O1Y1 plane, the length of the straight line segments at both ends is defined as l A , l B ;

[0039] Step 3.2: Specify l A The initial length of P is calculated in the catheter coordinate system according to the following formula A , P B coordinate:

[0040]

[0041] Step 3.3: Calculate P A , P B , P T1 Coordinates in local coordinate system O1: P′ A =(0,0,0), P′ B =(L SE ,0,0),P′ T1 =(-l A cosβ,-l A sinβ,0); and The angle β is:

[0042]

[0043] Step 3.4: According to the catheter coordinate system and the local coordinate system O1 P A , P B , P T1 The coordinates of the three points are obtained by the method described in step 2.3 to obtain the rotation matrix R2 and the translation matrix T2;

[0044] The catheter rotates around the X1 axis by an angle of θ, and the catheter rotation matrix R3 is as follows:

[0045]

[0046] Therefore, the catheter passes through the center point of the alignment interface After rotation by θ, the total transformation relationship is:

[0047] P i * =R3R2·P i +R3T2 i∈{S,T1,…,T(2n-2),E,A,B}

[0048] Where P i * Represents each point P on the catheter i The coordinates of the relevant points in the local coordinate system O1 after alignment and rotation.

[0049] The cutting planes at both ends of the catheter are the interface normal planes, and in the local coordinate system O1, the center points are The normal vector is

[0050] Furthermore, in the mathematical optimization model:

[0051] The calculation formulas for the cutting inclination angles γ1, γ2 and verticality H1, H2 at both ends of the catheter are:

[0052]

[0053]

[0054] H1=D·tanγ1, H2=D·tanγ2

[0055] In the formula are the unit normal vectors of the midline points of the two interfaces in the local coordinate system O1, is the unit direction vector of the straight line segments at both ends of the catheter in the local coordinate system O1, and D is the diameter of the catheter;

[0056] The distance constraint between the straight line segment of the duct and the point feature on the engine is:

[0057]

[0058] d pimin -d pi <0

[0059] Where d pimin represents the required minimum value of the catheter distance feature at the ith point, d pi is the calculated spacing value, is the point feature in the local coordinate system O1, is any point on the catheter segment, is the direction vector of the corresponding straight line segment of the catheter;

[0060] The distance d between the straight section of the conduit and the axis of the upper component of the engine lj Calculated as:

[0061]

[0062] d ljmin -d lj <0

[0063] Where d ljmin represents the required minimum value of the distance between the conduit and the jth cylindrical feature, d lj is the calculated spacing value, is any point on the axis of the component in the coordinate system O1, is any point on the straight segment of the catheter, is the direction vector of the line segment.

[0064] The optimal solution is Calculate the length of the straight segments at both ends of the catheter l A , l B , cutting point P A , P B And the cutting inclination angles γ1 and γ2, Inverse transformation to the catheter coordinate system to obtain the cutting plane normal vector

[0065] The present invention has the following beneficial effects and advantages:

[0066] 1. Realize the coordinated assembly of liquid rocket engines and the production of catheters, and improve the production efficiency of catheters. Traditional customized catheter production requires multiple trials and filings, which takes a lot of time. The present invention can quickly calculate the processing allowance of the catheter based on the engine interface data and catheter data, greatly improving the production efficiency of the catheter.

[0067] 2. Driven by measured data based on engine interface and constraint features, the spacing requirements between the duct and the engine are considered to avoid interference between the duct and other engine components. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A flowchart of a customized catheter margin processing calculation method;

[0069] Figure 2 It is a schematic diagram of the engine interface, constraint features and local coordinate system O1;

[0070] Figure 3 It is a schematic diagram of the catheter;

[0071] Figure 4 It is a schematic diagram of the calculation of the transformation relationship between the local coordinate system O1 and the engine coordinate system;

[0072] Figure 5 This is a schematic diagram of the initial alignment and rotation of the catheter;

[0073] Figure 6 Schematic diagram of the transformation relationship calculation for the initial alignment of the catheter;

[0074] Figure 7 Schematic diagram of the verticality of catheter cutting. DETAILED DESCRIPTION

[0075] The present invention is further described in detail below with reference to the accompanying drawings and implementation examples.

[0076] The customized duct margin processing calculation includes the measurement stage and the calculation stage. In the measurement stage, the interface characteristics and constraint characteristics of the liquid rocket engine duct are actually measured by measuring equipment, and the duct to be assembled is measured by measuring equipment as input data for the customized duct margin processing calculation. In the design stage, according to the measured engine interface, constraint feature data and measured duct data, the duct is rotated and translated to complete the first assembly with the engine interface, and a mathematical optimization model is constructed to find the optimal cutting position of the duct to complete the customized duct margin processing calculation.

[0077] A customized catheter margin processing calculation method includes the following steps:

[0078] Measurement phase: Measure the engine duct interface and constraint features to obtain the measured data of the duct interface and constraint features on the engine; measure the duct to obtain the duct model data.

[0079] Calculation phase: Initial assembly aligns the catheter and interface, adjusts the length of the straight segment and the rotation angle, and finds the optimal posture and cutting position of the catheter.

[0080] The measurement phase includes the following steps:

[0081] Step 1: If Figure 2 As shown, the duct interface, constraint features, etc. on the engine are measured, and the center data and normal data of the duct interface, the axis data and center data of the constraint features, etc. are extracted.

[0082] Step 2: If Figure 3 As shown, the catheter is measured to obtain data of each key point of the catheter.

[0083] like Figure 2 As shown, the two duct interfaces on the engine are defined as the S end and the E end respectively, and the center point of the S end interface is The unit direction vector is The E-terminal interface is The unit direction vector is

[0084] The constraint features mainly include two categories: one is the point (or sphere) feature on the engine, which is defined as represents the i-th point feature; the second is the cylindrical feature on the engine, and the starting point of the axis is The axis direction vector is Represents the axis of the jth cylindrical feature.

[0085] like Figure 3 As shown, each key point of the catheter is defined as P S , P T1 , P T2 …P T(2n-2) , P E ; where P S , P E The endpoints of the catheter; P Ti are the endpoints i of the remaining straight line segments, i∈{1,2,…,n-1}; n is the number of straight line segments of the catheter.

[0086] The calculation phase includes the following steps:

[0087] Step 1: If Figure 2 As shown, according to the interface data, As the origin, is the X-axis, and The composed plane is X1O1Y1 plane, and the local right-handed coordinate system O1 is established;

[0088] Step 2: Find the transformation relationship between the local coordinate system O1 and the engine coordinate system, and find the data of the two end interfaces and each constraint under the local coordinate system O1.

[0089] Step 2.1: From Start from the normal direction and take the point P at unit length V , whose coordinates are:

[0090]

[0091] and The angle α is:

[0092]

[0093] Step 2.2: If Figure 4 As shown, in the local coordinate system O1, the coordinates of the corresponding interface center points are:

[0094] In the formula It is the span of two interfaces.

[0095] Step 2.3: According to P V The coordinate values ​​of the three points in the engine coordinate system and the local coordinate system O1 are used to solve the transformation relationship between the two coordinate systems. The method in the paper "Besl, PJ, and HDMckay." A method for registration of 3-D shapes." IEEE Transactions on Pattern Analysis & Machine Intelligence 14.2 (1992): 239-256. " is used here, as follows:

[0096]

[0097] [U,S,V]=SVD(H)

[0098] R1=VU T

[0099] T1=-R1*centroid F +centroid O1

[0100] Where H is the covariance matrix, centroidF and centroid O1 yes P V The average center of the three points in the engine coordinate system and the local coordinate system O1, R1 is the rotation matrix, and T1 is the translation matrix.

[0101] Step 2.4: Based on the transformation relationship, the data of the interfaces at both ends and the constraints in the local coordinate system O1 can be obtained.

[0102] P i F* =R1·P i F +T1 i∈{S,E,Pj,Lk},j∈{1,2,…},k∈{1,2,…}

[0103] Step 3: Make the catheter coordinate system coincide with the local coordinate system O1, then rotate and translate the catheter so that the straight segments at both ends of the catheter pass through the center points of the two interfaces respectively. And make And make the catheter P S , P T1 The point is in the X1O1Y1 plane, the transformation relationship is calculated, the coordinates of each key point of the catheter in the coordinate system O1 are obtained, and the initial alignment of the catheter is obtained.

[0104] Step 3.1: If Figure 5 As shown, the catheter is rotated and translated so that the straight segments at both ends of the catheter pass through The corresponding point of the catheter is defined as P A , P B , while making the catheter point P S and P T1 In the X1O1Y1 plane, the length of the straight line segments at both ends is l A , l B .

[0105] Step 3.2: Specify l A The initial length of P is calculated in the catheter coordinate system. A , P B coordinate:

[0106]

[0107] According to the above formula, we can get the B A quadratic equation of one variable, taking l B >0, and then we get P B .

[0108] Step 3.3: If Figure 6 As shown, calculate P A , P B , P T1Coordinate P′ in local coordinate system O1 A , P′ B , P′ T1 .

[0109] P′ A =(0,0,0), P′ B =(L SE ,0,0)

[0110] and The angle β is:

[0111]

[0112] P′ T1 =(-l A cosβ,-l A sinβ,0)

[0113] Step 3.4: According to the catheter coordinate system and the local coordinate system O1 P A , P B , P T1 The coordinates of the three points are obtained by following the method described in step 2.3 to obtain the rotation matrix R2 and translation matrix T2.

[0114] Step 4: If Figure 5 As shown, the catheter is rotated around the X1 axis by an angle θ to obtain a catheter assembly. The rotation matrix R3 is as follows:

[0115]

[0116] The catheter passes through the center point of the alignment interface After rotation by θ, the total transformation relationship is:

[0117] P i * =R3R2·P i +R3T2 i∈{S,T1,…,T(2n-2),E,A,B}

[0118] Where P i * Represents each point P on the catheter i The coordinates of the relevant points in the local coordinate system O1 after alignment and rotation.

[0119] Step 5: If Figure 6 As shown in the figure, the cutting planes at both ends of the catheter are established according to the interface normal plane. The cutting planes at both ends of the catheter are the interface normal planes. In the local coordinate system O1, the center points are The normal vector is

[0120] Step 6: Keep the length l of the first straight line segment of the catheter A , the rotation angle θ is taken as a variable, and the verticality of the two ends of the catheter is taken as the objective function. A mathematical optimization model is established to solve the optimal

[0121] Find x=(l A ,θ)

[0122] Minimize f(x)=max(H1,H2)

[0123]

[0124] Where H1 and H2 represent the verticality of the two ends of the conduit, respectively. f(x) is the objective function constructed by the verticality of the conduit, which minimizes the verticality of the two ends of the conduit. To ensure the weldability and assembly of the two ends of the conduit, l A , l B The value ranges are (L Amin , L Amax )、(L Bmin , L Bmax ) To prevent the duct from interfering with other components on the engine, a constraint condition d is established. pimin -d pi <0 and d ljmin -d lj <0, which respectively indicates the spacing requirement between the duct and the point feature on the engine, and the spacing requirement between the duct and the cylindrical feature on the engine. The number of constraints depends on the actual situation of the engine.

[0125] Step 6.1: Define variables. The length l of the first straight line segment of the catheter is retained A , the rotation angle θ around the X1 axis is a variable.

[0126] Step 6.2: Define the objective function. The verticality and wall misalignment of the two ends of the catheter are required to be as small as possible. The arm misalignment of the catheter required by this method is zero, so the objective function is defined as the minimum verticality of the two ends of the catheter:

[0127] f(x)=max(H1,H2)

[0128] like Figure 7 As shown, the calculation formulas for the cutting inclination angles γ1, γ2 and verticality H1, H2 at both ends of the catheter are:

[0129]

[0130] H1=D·tanγ1, H2=D·tanγ2

[0131] In the formula are the unit normal vectors of the midline points of the two interfaces in the local coordinate system O1, is the unit direction vector of the straight line segments at both ends of the catheter in the local coordinate system O1, and D is the diameter of the catheter.

[0132] Step 6.3: Define constraints. To ensure the weldability and assembly of the two ends of the conduit, establish the length range constraints of the straight line segments at both ends of the conduit.

[0133] l Amin ≤l A ≤l Amax

[0134] l Bmin ≤l B ≤l Bmax

[0135] To prevent the duct from interfering with other engine components, the distance between the duct and the engine constraint features should be greater than the minimum required value. The distance constraint between the duct straight segment and the point feature on the engine is:

[0136]

[0137] d pimin -d pi <0

[0138] Where d pimin represents the required minimum value of the catheter distance feature at the ith point, d pi is the calculated spacing value, is the point feature in the local coordinate system O1, is any point on the catheter segment, is the direction vector of the corresponding straight line segment of the catheter.

[0139] The distance constraint between the straight section of the conduit and the axis of the upper engine component is:

[0140]

[0141] d ljmin -d lj <0

[0142] Where d ljmin represents the required minimum value of the distance between the conduit and the jth cylindrical feature, d lj is the calculated spacing value, is any point on the axis of the component in the coordinate system O1, is any point on the straight segment of the catheter, is the direction vector of the line segment.

[0143] Step 7: According to the optimal solution The length of the straight line segments at both ends of the catheter can be calculated A , l B , cutting point P A, P B And the cutting inclination angles γ1 and γ2, Inverse transformation to the catheter coordinate system to obtain the cutting plane normal vector

[0144] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A customized catheter margin processing calculation method, characterized in that: The following steps are involved: Measurement phase: Use measurement equipment to measure the engine's customized duct assembly interface, the position constraint features of the duct and pre-installed components on the engine, and extract the measured data of the duct's interfaces at both ends and their position constraint features; measure the duct model and extract the measured data of the duct model; Calculation phase: According to the assembly catheter interface and its position constraint characteristics, as well as the measured data of the catheter model, the catheter and its assembly interface are initially assembled and aligned, the length of each straight segment of the catheter is adjusted and the rotation angle is adjusted, the optimal posture of the catheter is searched, and the cutting parameters at both ends of the catheter are calculated for accurate excess processing and to avoid interference between the catheter and prefabricated parts to achieve assembly.

2. A customized catheter tube shape optimization design method according to claim 1, characterized in that: The method of extracting measured data of the interfaces and position constraint features at both ends of the catheter comprises the following steps: Fit the interface center point and unit direction vector data according to the interface cross-section circles at both ends of the catheter; The prefabricated component is abstracted as a cylinder or a sphere, and the axis data of the cylinder and / or the center data of the sphere are extracted according to its position constraint characteristics; The measured data of the extracted catheter model is the measured data of each key point of the extracted catheter model.

3. A customized catheter margin processing calculation method according to claim 2, characterized in that: In the engine coordinate system: The interfaces at the beginning and end of the assembly are defined as S end and E end respectively, and the center point of the S end interface is The unit direction vector is The E-terminal interface is The unit direction vector is The constraints on the engine are of two types: The i-th point (or sphere) feature is express; The axis of the j-th cylindrical feature is taken as the starting point Axis direction vector express; The key points of the catheter model are P S , P T1 , P T2 …P T(2n-2) , P E ; where P S , P E The endpoints of the catheter; P Ti are the endpoints i of the remaining straight line segments, i∈{1,2,…,n-1}; n is the number of straight line segments of the catheter.

4. A customized catheter margin processing calculation method according to claim 1, characterized in that: The calculation phase includes the following steps: Step 1: Based on the interface data, take the interface center point at the S end of the catheter is the origin, is the X-axis, and The composed plane is X1O1Y1 plane, and the local right-handed coordinate system O1 is established; Step 2: Find the transformation relationship between the local coordinate system O1 and the engine coordinate system, and find the data of the interfaces at both ends and each constraint feature under the local coordinate system O1; Step 3: Make the catheter coordinate system coincide with the local coordinate system O1, then rotate and translate the catheter so that the straight segments at both ends of the catheter pass through the center points of the two interfaces respectively. And make And make the catheter P S , P T1 The point is in the X1O1Y1 plane, and the transformation relationship is calculated to find the coordinates of each key point of the catheter in the coordinate system O1, and the initial alignment of the catheter is obtained; Step 4: The catheter is rotated by an angle θ around the X1 axis to obtain a first assembly of the catheter; Step 5: Establish cutting planes at both ends of the catheter according to the interface normal plane; Step 6: Keep the length l of the first straight line segment of the catheter A , the rotation angle θ is taken as a variable, and the verticality of the two ends of the catheter is taken as the objective function. A mathematical optimization model is established to solve the optimal Find x=(l A ,θ) Minimize f(x)=max(H1,H2) Where H1 and H2 represent the verticality of the two ends of the catheter, respectively. f(x) is the objective function constructed by the verticality of the catheter, which minimizes the verticality of the two ends of the catheter. The length of the first straight line segment at both ends of the catheter is l A , l B The value ranges are (L Amin , L Amax )、(L Bmin , L Bmax ) is used to ensure the weldability and assembly of both ends of the conduit; the spacing requirement between the conduit and the point features on the engine is d pi Less than the threshold d pimin , the spacing requirement between the duct and the cylindrical feature on the engine is d lj Less than the threshold d ljmin , used to prevent the duct from interfering with other parts on the engine; Step 7: According to the optimal solution Calculate the cutting point P A , P B , cutting plane normal And cutting inclination angles γ1, γ2.

5. A customized catheter margin processing calculation method according to claim 4, characterized in that: The conversion relationship between the local coordinate system O1 and the engine coordinate system is calculated as follows: Step 2.1: From the S-side interface Starting from, take point P at unit length along the normal direction V , whose coordinates are: and The angle α is: Step 2.2: In the local coordinate system O1, the coordinates of the corresponding interface center points are: In the formula is the span of two interfaces; Step 2.3: According to P V The coordinate values ​​of the three points in the engine coordinate system and the local coordinate system O1, solve the transformation relationship between the two coordinate systems: P i F* =R1·P i F +T1 i∈{S,E,Pj,Lk},j∈{1,2,…},k∈{1,2,…} Among them, P i F* is the point coordinate in the local coordinate system O1, P i F is the point coordinate in the engine coordinate system, R1 is the rotation matrix, and T1 is the translation matrix.

6. A customized catheter margin processing calculation method according to claim 4, characterized in that: The coordinate transformation relationship for the initial assembly alignment of the catheter is calculated as follows: Step 3.1: Rotate and translate the catheter so that the straight segments at both ends of the catheter pass through The corresponding point on the catheter is defined as P A , P B , while making the catheter point P S and P T1 In the X1O1Y1 plane, the length of the straight line segments at both ends is defined as l A , l B ; Step 3.2: Specify l A The initial length of P is calculated in the catheter coordinate system according to the following formula A , P B coordinate: Step 3.3: Calculate P A , P B , P T1 Coordinates in local coordinate system O1: P' A =(0,0,0), P' B =(L SE ,0,0),P' T1 =(-l A cosβ,-l A sinβ,0); and The angle β is: Step 3.4: According to P in the catheter coordinate system and the local coordinate system O1 A , P B , P T1 The coordinates of the three points are obtained by the method described in step 2.3 to obtain the rotation matrix R2 and the translation matrix T2; The catheter rotates around the X1 axis by an angle of θ, and the catheter rotation matrix R3 is as follows: Therefore, the catheter passes through the center point of the alignment interface After rotation by θ, the total transformation relationship is: P i * =R3R2·P i +R3T2 i∈{S,T1,…,T(2n-2),E,A,B} Where P i * Represents each point P on the catheter i The coordinates of the relevant points in the local coordinate system O1 after alignment and rotation.

7. A customized catheter margin processing calculation method according to claim 4, characterized in that: The cutting planes at both ends of the catheter are the interface normal planes, and in the local coordinate system O1, the center points are The normal vector is 8. A customized catheter margin processing calculation method according to claim 4, characterized in that: The optimal solution is Calculate the length of the straight line segments at both ends of the catheter A , l B , cutting point P A , P B And the cutting inclination angles γ1 and γ2, Inverse transformation to the catheter coordinate system to obtain the cutting plane normal vector

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