A customized catheter allowance machining calculation method

Abstract

The application discloses a customized pipe allowance processing calculation method, which is used for solving the problem that customized pipes need to be repeatedly compared and filed during assembly of a liquid rocket engine. The technical scheme is divided into a measurement stage and a calculation stage. In the measurement stage, engine pipe interface and constraint characteristic data are measured, and to-be-assembled pipe data are measured. In the calculation stage, the pipe is rotated and translated to complete one assembly with the engine interface, and pipe transformation relationship is calculated. The pipe linear segment length and the rotation angle are taken as variables, the pipe two-end perpendicularity is taken as an objective function, and the distance between the pipe and the engine and other components is taken as a constraint condition to construct a mathematical optimization model, and then pipe cutting parameters are obtained. The method can significantly reduce the time and manpower required for customized pipe production, and improve the production efficiency of the pipe.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of customized pipe allowance processing, in particular to a customized pipe allowance processing calculation method. BACKGROUND

[0002] The pipeline system is an important part of the liquid rocket engine, but due to poor product size consistency and other reasons, a large number of pipes need to be customized, and the allowance processing is carried out according to the actual situation of the engine interface after the pipe is bent. It needs to manually hold the pipe and repeatedly compare and test, file and repair the engine pipe interface. This process needs to cut the allowance several times, compare and test the interface several times, and file and repair the pipe several times. Manual comparison and repair of the pipe depend on the experience of personnel, and the direction of the pipe is not easy to control, which may cause interference with other components of the engine. At the same time, the labor intensity is large, the efficiency is low, and the production time is long. Therefore, the assembly of the pipeline system has become a bottleneck link for the improvement of the assembly capacity of the liquid rocket engine. SUMMARY

[0003] In view of the defects and deficiencies in the prior art, the present application aims to overcome the technical problems of manual repeated comparison and filing of customized pipes for liquid rocket engines, and provides a pipe allowance processing calculation method. The method uses the concept of collaborative manufacturing, is based on the actual data of the engine pipe interface and constraint features, considers the interference between the pipe and the engine, eliminates the pipe processing wall thickness, and calculates the processing allowance of the pipe. This method can significantly reduce the time and manpower required for customized pipe production and improve the production efficiency of the pipe.

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

[0005] A customized pipe allowance processing calculation method, comprising the following steps:

[0006] Measurement stage: using a measuring device to measure the customized pipe assembly interface of the engine, the position constraint features of the pipe and the pre-installed components on the engine, and extracting the measured data of the first and last end interfaces of the pipe and the position constraint features thereof; measuring the pipe model and extracting the measured data of the pipe model;

[0007] Calculation stage: according to the measured data of the assembled pipe interface and the position constraint features thereof and the pipe model, initially assemble and align the pipe and its assembly interface, adjust the length of each straight line segment of the pipe and the rotation angle, search for the best posture of the pipe, and calculate the cutting parameters at both ends of the pipe for accurate allowance processing and to avoid interference between the pipe and the pre-installed components to achieve assembly.

[0008] The step of extracting the measured data of the first and last end interfaces of the pipe and the position constraint features thereof includes the following steps:

[0009] According to the interface center point and unit direction vector data of the cross section circle fitting of the interface of the first end and the last end of the conduit;

[0010] The prefabricated part is abstracted as a cylinder or a ball, and the axis data of the cylinder and / or the center data of the ball are extracted according to the position constraint feature;

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

[0012] In the engine coordinate system:

[0013] The interfaces of the first end and the last end are defined as S end and E end respectively, the interface center point of the S end is The unit direction vector is The E end interface is The unit direction vector is

[0014] The constraint features on the engine include two types:

[0015] The i-th point (or ball) feature is represented by ;

[0016] The axis of the j-th cylinder feature is represented by the starting point The axis direction vector ;

[0017] The key points of the conduit model are P S , P T1 , P T2 …P T(2n-2) , P E ; wherein P S , P E are the end points of the two ends of the conduit; P Ti is the end point of each straight line segment i, i∈{1,2,…,n-1}; n is the number of straight line segments of the conduit.

[0018] The calculation stage includes the following steps:

[0019] Step 1: According to the interface data, the interface center point of the S end of the conduit is taken as the origin, is taken as the X axis, and the plane composed of and is taken as the X1O1Y1 plane, to establish a local right-handed coordinate system O1;

[0020] Step 2: Find the conversion relationship between the local coordinate system O1 and the engine coordinate system, and find the data of the two end interfaces and each constraint feature in 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 points are 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-stage assembly of the catheter;

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

[0024] Step 6: Keep the length l of the first straight segment of the catheter A , the rotation angle θ is a variable, and the verticality of the two ends of the catheter is used 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 components 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 and γ2.

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

[0031] Step 2.1: Interface from S Starting from the S interface, a point P is taken at a unit length in the normal direction V , whose coordinates are: The angle a between is:

[0032]

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

[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 are solved to obtain the conversion 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] Where 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 conversion relationship of the initial assembly alignment of the catheter is calculated as follows:

[0038] Step 3.1: Rotate and translate the catheter so that the straight line segments at both ends of the catheter pass through The corresponding points on the catheter are defined as P A , P B , and the catheter points P S and P T1 are in the X1O1Y1 plane, and the lengths of the straight line segments at both ends are defined as l A , l B ;

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

[0040]

[0041] Step 3.3: Calculate P A 、P B 、P T1 Coordinates in the local coordinate system O1: P′ A =(0,0,0), P′ B =(L SE ,0,0),P′ T1 =(-l A cosβ,-l A sinβ,0); where 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 and rotation 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 tan γ1, H2=D tan γ2

[0055] where are the unit normal vectors of the two interface midpoints in the local coordinate system O1, are the unit direction vectors of the two straight line segments of the duct in the local coordinate system O1, and D is the diameter of the duct;

[0056] The distance constraint of the straight line segments of the duct to the features on the engine is:

[0057]

[0058] d pimin -d pi <0

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

[0060] The distance d lj of the straight line segment of the duct to the axis of the component on the upper part of the engine is calculated as:

[0061]

[0062] d ljmin -d lj <0

[0063] where d ljmin represents the required minimum distance of the duct to the jth cylindrical feature, d lj is the calculated distance, is any point on the axis of the component in the coordinate system O1, is any point on the straight line segment of the duct, is the direction vector of the straight line segment.

[0064] The optimal solution is The lengths l A , l B , the cutting points P A , P B , and the cutting inclination angles γ1, γ2 of the two straight line segments of the duct at the two ends are calculated to obtain Inverse transform to the catheter coordinate system, get the cutting plane normal vector

[0065] The present application has the following advantages and points:

[0066] 1. The liquid rocket engine assembly and the catheter production are realized simultaneously, and the catheter production efficiency is improved. The traditional customized catheter production needs multiple trials and filing, which consumes a lot of time. The present application can quickly calculate the machining allowance of the catheter according to the engine interface data and the catheter data, thereby greatly improving the catheter production efficiency.

[0067] 2. Based on the measured data of the engine interface and the constraint features, the spacing requirements of the catheter and the engine are considered, and interference between the catheter and other components of the engine is avoided. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 A flowchart of a customized catheter allowance machining calculation method;

[0069] Figure 2 An engine interface and constraint feature and local coordinate system O1 schematic diagram;

[0070] Figure 3 A catheter schematic diagram;

[0071] Figure 4 A local coordinate system O1 and engine coordinate system transformation relationship calculation schematic diagram;

[0072] Figure 5 A catheter initial alignment and rotation schematic diagram;

[0073] Figure 6 A catheter initial alignment transformation relationship calculation schematic diagram;

[0074] Figure 7 A catheter cutting perpendicularity schematic diagram. DETAILED DESCRIPTION

[0075] The present application will be further described in detail below in combination with the drawings and implementation examples.

[0076] The customized catheter allowance machining calculation includes a measurement stage and a calculation stage. In the measurement stage, the liquid rocket engine catheter interface features and constraint features are actually measured by a measuring device, and the to-be-assembled catheter is measured by the measuring device as input data for the customized catheter allowance machining calculation. In the design stage, according to the actually measured engine interface, constraint feature data and actually measured catheter data, the catheter is rotated and translated to complete one assembly with the engine interface, a mathematical optimization model is constructed to find the best cutting pose of the catheter, and the customized catheter allowance machining calculation is completed.

[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 straight segment length and rotation angle, and finds the optimal catheter posture and cutting position.

[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 and the data of each key point of the catheter is obtained.

[0083] like Figure 2 As shown, the two conduit interfaces on the engine 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-end 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, the axis starting point is The axis direction vector is Represents the axis of the j-th 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 catheter straight line segments.

[0086] The calculation phase includes the following steps:

[0087] Step 1: If Figure 2 As shown, according to the interface data, As the origin, For X axis, the plane composed of Y1 and Z1 is X1O1Y1 plane, and a local right-handed coordinate system O1 is established. And The plane composed of Y1 and Z1 is X1O1Y1 plane, and a local right-handed coordinate system O1 is established.

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

[0089] Step 2.1: starting from , take the point P V with unit length along the normal direction, whose coordinates are:

[0090]

[0091] The angle α between is:

[0092]

[0093] Step 2.2: as shown in Figure 4 , the corresponding interface center point coordinates in local coordinate system O1 are respectively:

[0094] In the formula , the span of the two interfaces is

[0095] Step 2.3: according to P V , the coordinates of the three points in the engine coordinate system and the local coordinate system O1 are solved. This paper adopts the method in the paper "Besl, P. J., and H. D. McKay. "A method for registration of 3-D shapes." IEEE Transactions on Pattern Analysis & Machine Intelligence 14.2 (1992): 239-256.", which is as follows:

[0096]

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

[0098] R1 = VU T

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

[0100] In the formula, H is the covariance matrix, and centroidF and centroid O1 is 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: According to the conversion relationship, the data of the two end interfaces and each constraint 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 three: Make the catheter coordinate system coincide with the local coordinate system O1, and then rotate and translate the catheter so that the straight line segments at both ends of the catheter pass through the centers of the two interfaces and and make the catheter P S , P T1 points in the X1O1Y1 plane, calculate the conversion relationship, and obtain the coordinates of each key point of the catheter in the coordinate system O1 to obtain the initial alignment of the catheter.

[0104] Step 3.1: As shown in Figure 5 , rotate and translate the catheter so that the straight line segments at both ends of the catheter pass through The corresponding points of the catheter are defined as P A , P B , and at the same time, the catheter points P S and P T1 are in the X1O1Y1 plane, and the lengths of the straight line segments at both ends are l A , l B .

[0105] Step 3.2: Specify the initial length of l A , and calculate the coordinates of P A , P B in the catheter coordinate system:

[0106]

[0107] According to the above formula, a quadratic equation about l B can be obtained, and the solution of l B >0 is taken to obtain P B .

[0108] Step 3.3: As shown in Figure 6 , calculate P A , P B , P T1Coordinate P′ in the 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 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 and rotation 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 six: the length l A , the rotation angle θ as variables, and the perpendicularity of the two ends of the conduit 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 perpendicularity of the two ends of the conduit respectively, and f(x) is the objective function constructed by the perpendicularity of the conduit, minimizing the perpendicularity 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 range is (L Amin , L Amax ), (L Bmin , L Bmax ) respectively; to prevent interference between the conduit and other parts on the engine, the constraint conditions d pimin -d pi < 0 and d ljmin -d lj < 0 are established, which represent the distance requirements between the conduit and the point features on the engine and the distance requirements between the conduit and the cylindrical features on the engine respectively, and the number of constraints is determined according to the actual situation of the engine.

[0125] Step 6.1: define variables. The length l A of the first straight segment of the conduit and the rotation angle θ around the X1 axis are defined as variables.

[0126] Step 6.2: define the objective function. The perpendicularity and wall deviation of the two ends of the conduit are required to be as small as possible, and the wall deviation of the conduit obtained by this method is zero, so the objective function is defined as the minimum perpendicularity of the two ends of the conduit:

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

[0128] As shown in Figure 7 , the cutting inclination angles γ1 and γ2 and the perpendicularity H1 and H2 of the two ends of the conduit are calculated as follows:

[0129]

[0130] H1 = D tan γ1, H2 = D tan γ2

[0131] where are the unit normal vectors of the two interface midpoints in the local coordinate system O1, respectively, is the unit direction vector of the straight line segment at the two ends of the duct in the local coordinate system O1, and D is the diameter of the duct.

[0132] Step 6.3: Define the constraint condition. To ensure the weldability and assembly of the two ends of the duct, the length range constraint of the straight line segment at the two ends of the duct is established.

[0133] l Amin ≤l A ≤l Amax

[0134] l Bmin ≤l B ≤l Bmax

[0135] To prevent the duct from interfering with other components of the engine, the distance between the duct and each constraint feature of the engine should be greater than the minimum distance requirement. The distance constraint between the straight line segment of the duct 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 distance between the duct and the i-th point feature, d pi is the calculated distance, is the point feature in the local coordinate system O1, is any point on the duct line segment, is the direction vector of the corresponding straight line segment of the duct.

[0139] The distance constraint between the straight line segment of the duct and the axis of the component on the engine is:

[0140]

[0141] d ljmin -d lj <0

[0142] where d ljmin represents the required minimum value of the distance between the duct and the j-th cylindrical feature, d lj is the calculated distance, is any point on the axis of the component in the coordinate system O1, is any point on the straight line segment of the duct, is the direction vector of the straight line segment.

[0143] Step 7: According to the optimal solution obtained The lengths of the straight line segments at the two ends of the duct, l A , l B , and the cutting point P A, P B and cutting inclination angles γ1, γ2, which are determined by the cutting plane and the normal vector of the cutting plane, are calculated. Inverse transformation to the catheter coordinate system, get cutting plane normal vector

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

Claims

1. A customized pipe allowance machining calculation method, characterized by, The method comprises the following steps: The measurement stage: using a measuring device to measure the customized pipe fitting interface of the engine, the pipe and the position constraint features of the pre-installed components on the engine, and extract the measured data of the pipe first and last end interfaces and their position constraint features; measure the pipe model and extract the measured data of the pipe model; The calculation stage: according to the measured data of the fitting pipe interface and its position constraint features and the pipe model, initially assemble and align the pipe and its fitting interface, adjust the length of each linear segment of the pipe and the rotation angle, search for the optimal posture of the pipe, and calculate the cutting parameters at both ends of the pipe for precise allowance machining and to avoid interference between the pipe and the pre-installed components to realize assembly; the calculation stage comprises the following steps: Step 1: According to the interface data, the interface center point of the S end of the conduit is taken as the origin, the X axis is taken as the Y1 axis, and the plane composed of the Y1 axis and the Z axis is taken as the X1O1Y1 plane to establish a local right-hand coordinate system O1. Step 2: According to the interface data, the interface center point of the S end of the conduit is taken as the origin, the X axis is taken as the Y2 axis, and the plane composed of the Y2 axis and the Z axis is taken as the X2O2Y2 plane to establish a​​​ Step 2: find the conversion relationship between the local coordinate system O1 and the engine coordinate system, and find the data of the two end interfaces and each constraint feature in the local coordinate system O1; Step 3: make the coordinate system of the conduit coincide with the local coordinate system O1, and then rotate and translate the conduit so that the straight segments at both ends of the conduit pass through the center points of the two interfaces respectively and make and make the conduit P S , P T1 point in the XO1Y1 plane, calculate the transformation relationship, and obtain the coordinates of each key point of the conduit in the coordinate system O1 to obtain the initial alignment of the conduit; Step 4: rotate the pipe around the X1 axis by an angle θ to obtain the first assembly of the pipe; Step 5: establish the cutting planes at both ends of the pipe according to the interface method plane; Step 6: the length l of the first straight segment of the catheter is reserved A A mathematical optimization model is established with the rotation angle θ as a variable and the perpendicularity of the two ends of the catheter as an objective function, and 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 Greater than the threshold d pimin , the spacing requirement between the duct and the cylindrical feature on the engine is d lj Greater 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 obtained Calculate the cutting point P A , P B , the normal of the cutting plane and the cutting inclination angle γ1, γ2; the optimal solution is Calculate the length of the straight line segment l A , l B , the cutting point P A , P B and the cutting inclination angle γ1, γ2, and inverse transform to the catheter coordinate system to obtain the normal vector of the cutting plane 2. The method of claim 1, wherein, The measured data of the first and last end interfaces and the position constraint features of the pipe comprises the following steps: According to the cross-section circle of the first and last end interfaces of the pipe, fit the interface center point and unit direction vector data; Abstract the pre-installed components as cylinders or spheres, and extract the axis data of the cylinders and / or the center data of the spheres according to their position constraint features; The measured data of the pipe model is the measured data of each key point of the pipe model.

3. The method of claim 2, wherein, In the engine coordinate system: The assembly first and last end interfaces are defined as S end and E end respectively, the S end interface center point is The unit direction vector is The E end interface is The unit direction vector is The constraint features on the engine include two types: The ith point or sphere feature is represented by ; the axis of the jthcylindrical feature is represented by an origin point axis direction vector denotes; The key points of the conduit model are P S , P T1 , P T2 , …, P T(2n -2), P E ; wherein P S , P E are end points of two ends of the conduit; P Ti is an end point i of the remaining straight line segments, i∈{1,2,…,n-1}; and n is the number of straight line segments of the conduit.

4. The method of claim 1, wherein, The conversion relationship between the local coordinate system O1 and the engine coordinate system is calculated as follows: Step 2.1: From S interface Starting from point P at unit length along the normal direction V with coordinates: the angle a with is: Step 2.2: In the local coordinate system O1, the corresponding interface center point coordinates are respectively: wherein is the span of the 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 are solved to obtain the transformation relationship between the two coordinate systems: P i F* = R1·P i F + T1i∈{S, E, Pj, Lk}, j∈{1, 2,...}, k∈{1, 2,...} where 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.

5. The method of claim 1, wherein, The coordinate conversion relationship of the initial assembly and alignment of the pipe 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: Assigning / to the initial length of P A , P A , P B coordinates in the catheter coordinate system according to the following equations: Step 3.3: Calculate P A 、P B 、P T1 Coordinates in the local coordinate system O1: P′ A =(0,0,0), P′ B =(L SE ,0,0),P′ T1 =(-l A cosβ,-l A sinβ,0); where and The angle β is: Step 3.4: Obtain the rotation matrix R2 and the translation matrix T2 according to the coordinates of P A , P B , and P T1 in the local coordinate system O1 and the coordinate system of the catheter. The pipe rotation matrix R3 when the pipe rotates around the X1 axis by an angle θ is as follows: Thus, the conduit passes through the center point of the aligned interface and rotated by θ, the total transformation relationship is: P i * = R3R2·P i + R3T2i∈{S,T1,…,T(2n-2),E,A,B} where P i * denotes the coordinates of the points P i the coordinates of the relevant points in the local coordinate system O1 after alignment and rotation.

6. The method of claim 1, wherein, The cutting planes at both ends of the conduit are interface planes, and the center points in the local coordinate system O1 are The normal vector is

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