A method for removing excess from aerospace engine ducts

Abstract

The present invention relates to a method for removing excess material from an aerospace engine duct, comprising the following steps: Step 1: establishing an interface model and obtaining a set F of interface spatial postures; Step 2: establishing a duct model and obtaining a set D of duct spatial postures after cutting; Step 3: matching set F and set D to select n optimal combinations; Step 4: calculating all possible duct postures based on the determined n optimal interface postures, and finding the position with the smallest horseshoe value at both ends as the optimal cutting position output; Step 5: binding a robotic arm to the duct, determining the position of the cutting position of the cutting device in the robotic arm coordinate system, aligning the optimal duct cutting position determined in Step 4 with the cutting position of the cutting device, and calculating the posture coordinates of the final cutting position at the end of the robotic arm; Step 6: outputting the posture coordinates to implement robotic arm guidance control. The present invention can ensure that the horseshoe value and wall offset at both ends of the processed duct are minimized, and that the lengths of the straight segments at both ends are within a required range.

Description

Technical Field

[0001] The invention relates to the field of aerospace engine manufacturing, in particular to a method for removing excess from aerospace engine ducts. Background Art

[0002] For large spacecraft such as rockets, the assembly quality of their engines is crucial. As the delivery channel for oxidizers and fuel, the quality of the ducting directly affects the safety of the engine. A leak in the ducting can lead to the failure of the entire launch of the rocket or other aircraft. Because aerospace engines have many welded parts, which results in significant weld deformation, mass production of all ducting is currently not possible for aerospace engines. Some ducting requires a combination of on-site sampling and manual rubbing and repair. Therefore, duct filing plays a crucial role in the assembly of aerospace engines. Improper filing can affect duct welding quality, resulting in significant weld deformation and assembly stress. Under vibration conditions, the combined stress can lead to fatigue fracture or seal failure in the ducting, causing leakage.

[0003] As the final machining step before catheter assembly, catheter stock removal directly impacts post-assembly stress and determines the quality of the assembly. Currently, research on catheter assembly primarily focuses on the design phase. For example, genetic algorithms are used to generate catheter paths based on spatial layout, virtual assembly is performed using techniques such as visual assembly, and secondary development is performed using 3D design software to determine stock removal locations through virtual assembly. However, these methods suffer from issues such as the inability to avoid bending manufacturing errors, long program runtimes, and low efficiency. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for removing excess material from aerospace engine ducts. By studying the assembly problem of ducts with uncertain bend angles at both ends, an interface and duct mathematical model is established. The optimal cutting position is found through characteristic parameter matching and spatial posture transformation, and a robotic arm is guided for processing to ensure that the horseshoe value and wall offset at both ends of the processed duct are minimized, and the length of the straight segments at both ends is within the required range.

[0005] The object of the present invention is achieved through the following technical solutions:

[0006] A method for removing excess from an aerospace engine duct comprises the following steps:

[0007] Step 1: Establish an interface space posture model and obtain the interface space posture set F;

[0008] Step 2: Establish a catheter spatial posture model and obtain the catheter spatial posture collection D after cutting;

[0009] Step 3: Match the interface spatial posture set F and the cut catheter spatial posture set D, and select n optimal combinations;

[0010] Step 4: Calculate all possible catheter positions based on the determined n groups of optimal interface positions, and find the position with the smallest horseshoe value at both ends as the optimal cutting position output;

[0011] Step 5: Bind the robotic arm to the catheter, determine the cutting position of the cutting device in the robotic arm coordinate system, overlap the optimal cutting position of the catheter determined in step 4 with the cutting position of the cutting device, and calculate the pose coordinates of the final cutting position at the end of the robotic arm;

[0012] Step 6: Output the pose coordinates of the final cutting position of the robotic arm to achieve robotic arm guidance control.

[0013] In step 1, the interface is provided with an elbow that is fixedly connected to the catheter, and when the elbow rotates around its own central axis, the elbow drives the corresponding side connection end of the catheter to rotate to form a circle. Assuming that O1 is the center of the rotation circle of the catheter inlet connection end, O2 is the center of the rotation circle of the catheter outlet connection end, P1 is the end face center of the catheter inlet connection end, and P2 is the end face center of the catheter outlet connection end, a first coordinate system B is established with O1 as the center of the circle and the rotation axis n1 of the inlet end elbow as the Z axis. A second coordinate system C is established with O2 as the center of the circle and the rotation axis n2 of the outlet end elbow as the Z axis. Take the coordinate x A 、y A The main coordinate system A is established at the value point, and the first coordinate system B and the second coordinate system C are transformed to the main coordinate system A. In the main coordinate system A, the distance between the definition points P1 and P2 is L p12 , the angle between the straight line O1P1 and the straight line P1P2 is θ1, the angle between the straight line O2P2 and the straight line P2P1 is θ2, plane 1 is the plane determined by the point P1O2P2, plane 2 is the plane determined by the point P1O1P2, the angle between plane 1 and plane 2 is θ3, through L p12 , θ1, θ2, θ3 determine the spatial posture of the two interfaces, which can be expressed as:

[0014] F={L p12 , θ1, θ2, θ3}.

[0015] In step 2, the catheter cutting position is on the straight pipe segments at both ends. The center of the cutting surface on the straight pipe segment D1D2 at the catheter inlet is defined as P1′, and the center of the cutting surface on the straight pipe segment D3D4 at the catheter outlet is defined as P2′. Plane 3 is the plane determined by point D1D2P2′, and plane 4 is the plane determined by point D3D4P1′. The angle between the two planes is θ3′, the angle ∠D1P1′P2′ between the straight pipe segment D1D2 and the line segment P1′P2′ is θ1′, the angle ∠D3P2′P1′ between the straight pipe segment D3D4 and the line segment P1′P2′ is θ2′, and the distance between P1′ and P2′ is L p12 ', through L p12 ', θ1', θ2', θ3' determine the spatial posture of the catheter after cutting, which is expressed as:

[0016] D={L p12 ′, θ′1, θ′2, θ′3}.

[0017] In step 3, the difference C is obtained by subtracting the elements in the catheter set D from the elements in the interface set F. Since each item in C has a different impact on the horseshoe value and the amount of wall stagger, a different weight is set for each item, which is defined as:

[0018] C=FD={λ1(L p12 -L p12 ′), λ2(θ1-θ′1), λ3(θ2-θ′2), λ4(θ3-θ′3)};

[0019] Therefore, the degree of inconsistency between the interface and the catheter is described as:

[0020]

[0021] Find the n combinations of interfaces and conduits with the smallest |C|.

[0022] In step 4, the distance between the center point P1′ of the cutting surface at the inlet of the catheter and the catheter port D1 is defined as t. Since the optimal interface posture is determined in step 3, L p12 It is known that according to L p12 =L p12 ', find the center point P2' of the cutting surface at the outlet of the catheter, and D1D2 passes through point P1', D3D4 passes through point P1', and the catheter is limited to having only the degree of freedom of movement through points P1' and P2' at both ends and the degree of freedom of rotation around the axis P1'P2'. The degree of freedom of movement is represented by the distance t, and the degree of freedom of rotation is represented by the angle β of the catheter relative to the initial position. First determine the value of t, and then rotate the catheter 360° around the axis P1P2 to obtain all possible situations. Among them, find the position with the smallest horseshoe value at both ends as the optimal cutting surface output.

[0023] In step 4, the catheter is first translated from P1′P2′ to P1″P2″ with a translation amount of λ, and then rotated from P1″P2″ to P″1P″′2 with a rotation angle of ω and a rotation axis of N(n x , n y , n z ), the specific transformation is as follows:

[0024] D′ i =T(D i +λ) (7);

[0025] In the above formula, T is the rotation matrix around the axis N, Di is the original spatial posture of the catheter, and Di′ is the transformed spatial posture of the catheter;

[0026] The rotation matrix T around the axis N is derived as follows:

[0027]

[0028] λ=P″1-P′1

[0029] N=(P″2-P″1)×(P″′2-P″1)

[0030] ω=arccos((P″2-P″1)(P″′2-P″1) / |P″2-P″1||P″′2-P″1|).

[0031] In step 5, the three points J1 (x, y, z), J2 (x, y, z), and J3 (x, y, z) in space are determined to represent the initial position of the end gripper of the manipulator to form the measurement tool coordinate system B'. The three points J1', J2', and J3' in space are determined to represent the position of the end gripper of the manipulator at the cutting position to form the cutting tool coordinate system C'. The measurement tool coordinate system B' and the cutting tool coordinate system C' are obtained by rotation and translation of the manipulator coordinate system A', specifically:

[0032]

[0033] In the above formulas (9-1) and (9-2), E is the unit matrix, is the transformation matrix from coordinate system B′ to A′, is the transformation matrix from coordinate system C′ to A′;

[0034] According to the definition of ZYX Euler angle, first rotate the robot coordinate system A' around Z A The axis rotates by an angle α and then around the Y A The axis rotates by an angle of β and finally around Z A The axis rotates by an angle γ to obtain the rotation matrix for:

[0035]

[0036] The optimal cutting position of the catheter determined in step 4 is overlapped with the cutting position of the cutting device to determine the final cutting position of the catheter and obtain the transformation matrix T and translation vector G, and then obtain the conversion relationship between J and J′:

[0037] [J′1,J′2,J′3]=T·[J1,J2,J3]+G (12);

[0038] Substitute the initial end position of the robot arm into formula (11), then substitute the result of formula (11) into formula (9-1) to obtain J1, J2, and J3, then substitute J1, J2, and J3 into formula (12) to obtain J1′, J2′, and J3′, then substitute J1′, J2′, and J3′ into formula (9-2) to obtain the coordinates of the cutting tool coordinate system C′ in the robot arm coordinate system A′:

[0039]

[0040] Further analysis revealed:

[0041]

[0042] In the above formula (14), r ij Represents each element of the matrix;

[0043] Substitute formula (14) into the general formula of the robot (15):

[0044]

[0045] get:

[0046]

[0047] Then the final cutting position z{α, β, γ, x, y, z} of the end of the robotic arm is obtained, where [x, y, z] = J1′.

[0048] The advantages and positive effects of the present invention are:

[0049] 1. This paper studies the problem of assembling a catheter with uncertain bending angles at both ends, proposes a method for describing the spatial posture of the interface and the catheter, uses a length and three angles, a total of four values, to describe the spatial posture of the interface and the catheter, and establishes a mathematical model of the interface and the catheter.

[0050] 2. The present invention uses spatial description and transformation methods to find the best matching posture of the catheter and the interface, determine the cutting position information of the catheter, and further overlap the cutting surface with the cutting surface of the cutting device to determine the final cutting position.

[0051] 3. The present invention utilizes the spatial posture description method of the end of the robotic arm to calculate the position and posture coordinates of the robotic arm according to the catheter cutting position determined in the previous step, and finally completes the guided processing.

[0052] 4. The present invention shortens the program running time and ensures that the horseshoe value and wall offset at both ends of the processed catheter are minimized and the length of the straight sections at both ends are within the required range. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a schematic flow chart of the method of the present invention,

[0054] Figure 2 is a schematic diagram of the interface posture.

[0055] Figure 3 for Figure 2 Schematic diagram of interface pose coordinate system conversion in ,

[0056] Figure 4 is a schematic diagram of the interface space posture obtained after conversion,

[0057] Figure 5 is a schematic diagram of the catheter's spatial posture.

[0058] Figure 6 This is a schematic diagram of the catheter cutting plane.

[0059] Figure 7 To find the optimal assembly position diagram of the catheter,

[0060] Figure 8 This is a schematic diagram of the robotic arm guiding cutting.

[0061] Figure 9 The schematic diagram of the catheter structure used to verify the method of the present invention is as follows:

[0062] Figure 10 for Figure 9 Schematic diagram of the interface positions at both ends of the middle catheter.

[0063] Figure 11 for Figure 9 Schematic diagram of the catheter and the robotic arm,

[0064] Figure 12 This is a schematic diagram of the cutting position calibration during verification.

[0065] Figure 13 A schematic diagram of a catheter simulation for verifying the method of the present invention is shown below.

[0066] Figure 14 Schematic diagram of cutting simulation for verifying the method of the present invention Figure 1 ,

[0067] Figure 15To verify the cutting simulation of the method of the present invention Figure 2 . DETAILED DESCRIPTION

[0068] The present invention will be further described below in conjunction with the accompanying drawings.

[0069] The present invention first measures the position of the spatial interface by a measuring device to obtain the end face center and end face normal vector of the interface. Next, a robotic arm grabs the catheter and enters the bend measuring device for measurement to obtain the coordinates of the catheter's bending point, and reads the spatial posture coordinates of the robotic arm at this time. The position of the cutting surface and cutting center of the cutting device in the robotic arm coordinate system is obtained through calibration. The present invention then calculates the spatial posture of the interface by reading the interface data, calculates all the postures of the catheter by reading the bend data, compares the two, obtains a group of elements with the closest posture, determines the optimal spatial position of the interface and the approximate cutting position of the catheter, and then searches for the optimal cutting position near the cutting posture of the catheter based on the above horseshoe value minimum calculation result. Then, calculation is performed to ensure that the horseshoe value and the wall offset at both ends are minimized to obtain the optimal cutting position.

[0070] Based on the positions of the cutting surface and cutting center of the above-mentioned known cutting equipment in the robotic arm coordinate system, the final cutting position is obtained by coordinating the cutting position of the catheter with the cutting equipment, and the transformation matrix of the robotic arm and the translation amount from the initial position to the cutting position are calculated. Finally, the position coordinates of the robotic arm are obtained to realize the guidance of the robotic arm.

[0071] like Figures 1 to 8 As shown, the present invention includes the following steps:

[0072] Step 1: Establish an interface space posture model and obtain the interface space posture set F.

[0073] During the catheter assembly process, both ends of the catheter need to be connected to the corresponding interfaces, and the interfaces are provided with elbows, which are welded and fixed to the catheter. When the elbow rotates around its own central axis, the trajectory swept by the corresponding side connection end of the catheter by the elbow is a circle in space, such as Figure 2 As shown, O1 is the center of the circle formed by the rotation of the inlet connection end of the catheter, O2 is the center of the circle formed by the rotation of the outlet connection end of the catheter, R1 and R2 are the radii of the two circles respectively, and the coordinate of the center of O1 is D o1 =(x o1 ,y o1 , z o1 ), O2 center coordinate D o2 =(x o2 ,y o2 , z o2 ), the normal vector n1 of the plane where the circle O1 lies = (i n1 ,j n1, k n1 ), the normal vector n2 of the plane where the circle O2 lies=(i n2 ,j n2 , k n2 ), P1 is the end face center of the catheter inlet connection end (also the center of the bend end face of the inlet end interface), and P2 is the end face center of the catheter outlet connection end (also the center of the bend end face of the outlet end interface).

[0074] like Figure 3 As shown, with O1 as the center and the inlet bend rotation axis n1 as the Z axis, the first coordinate system B is established. Similarly, with O2 as the center and the outlet bend rotation axis n2 as the Z axis, the second coordinate system C is established. A 、y A The coordinate system A is established at the value point, and the first coordinate system B and the second coordinate system C are transformed to the coordinate system A. Specifically:

[0075] The transformation matrix of coordinate system B to coordinate system A is as follows:

[0076]

[0077] A Y B =n1× A X B

[0078] A Z B =n1

[0079]

[0080] in, A X B 、 A Y B 、 A Z B is the vector value of the three coordinate axes of coordinate system B in coordinate system A, from which the space circle swept by the center P1 of the end surface where the inlet bend is fixedly connected to the conduit is obtained:

[0081]

[0082] In the above formula (2), r is the rotation radius of the bend, and τ is a given angle from 0 to 360°, which means that any angle corresponds to an interface position. τ ranges from 0° to 360°, covering all possible interface positions.

[0083] Similarly, the space circle swept by the center P2 of the end face where the outlet bend is fixedly connected to the conduit is obtained.

[0084] In coordinate system A, the spatial posture of the interface can be calculated based on the end face centers P1 and P2 of the two ends of the bend and the normal vector n1 of the plane where the circle O1 is located and the normal vector n2 of the plane where the circle O2 is located.

[0085] Specifically: Figure 4 As shown, in order to describe the spatial posture of the two bends at any position, the distance between the definition points P1 and P2 is L p12 , the angle between the straight line O1P1 and the straight line P1P2 is θ1, the angle between the straight line O2P2 and the straight line P2P1 is θ2, plane 1 is the plane determined by point P1O2P2, plane 2 is the plane determined by point P1O1P2, the angle between plane 1 and plane 2 is θ3, since the elbow is part of the interface, so through L p12 , θ1, θ2, θ3 can completely determine the spatial posture of the two interfaces, which can be expressed as:

[0086] F={L p12 , θ1, θ2, θ3} (3).

[0087] Step 2: Establish a catheter spatial posture model and obtain the catheter spatial posture collection D after cutting.

[0088] like Figure 5 As shown, the catheter cutting position is on the straight pipe segments at both ends. Assume that the center of the cutting surface on the straight pipe segment D1D2 at the catheter inlet is P1′, and the center of the cutting surface on the straight pipe segment D3D4 at the catheter outlet is P2′. In order to describe the spatial posture of the catheter after cutting, plane 3 is defined as the plane determined by point D1D2P2′, and plane 4 is defined as the plane determined by point D3D4P1′. The angle between the two planes is θ3′, the angle ∠D1P1′P2′ between the straight pipe segment D1D2 and the line segment P1′P2′ is θ1′, the angle ∠D3P2′P1′ between the straight pipe segment D3D4 and the line segment P1′P2′ is θ2′, and the distance between P1′ and P2′ is L p12 ', through L p12 ', θ1', θ2', θ3' can completely determine the spatial posture of the catheter after cutting, which can be expressed as:

[0089] D={L p12 ′, θ′1, θ′2, θ′3} (4).

[0090] Step 3: Match the interface spatial posture set F and the cut catheter spatial posture set D, find the most similar elements and select n optimal combinations.

[0091] In order to find the two elements that are closest to the set of all interface positions and postures and the set of all catheter postures, the element in the catheter set D is subtracted from the element in the interface set F to obtain the difference C between the two. Since each item in C has a different impact on the horseshoe value and the amount of wall stagger, a different weight is set for each item, which is defined as:

[0092] C=FD={λ1(L p12 -L p12 ′), λ2(θ1-θ1′), λ3(θ2-θ2′), λ4(θ-3-θ3′)} (5);

[0093] Therefore, the degree of inconsistency between the interface and the catheter can be described as:

[0094]

[0095] The present invention matches the elements in the interface spatial posture set F and the catheter spatial posture set D with each other, and the matching quantification method is to calculate C according to the above formula, and sort the matching degree of each interface and catheter combination according to C, and find the n groups of interface and catheter combinations with the smallest |C| (that is, the n groups with the best matching degree). The purpose of taking out multiple groups is to ensure that there are other gap requirements in the future, and a better matching method can be selected from the existing matching results that meet the conditions. After determining the n groups of interface and catheter posture combinations, the optimal spatial position of the interface and the approximate cutting position of the catheter are determined.

[0096] Step 4: Calculate all possible catheter positions based on the determined n groups of optimal interface positions, and find the position with the smallest horseshoe value at both ends, which is the optimal cutting position output.

[0097] Welding is required during the assembly of the catheter. To ensure the welding quality, wall misalignment is undesirable and the horseshoe value of the two ports is desired to be minimized.

[0098] like Figure 6 As shown, the distance between the center point P1′ of the cutting surface at the inlet of the catheter and the catheter port D1 is defined as t, and the selected range is t∈[t-δ, t+δ]. Input the interface position data. In order to avoid the occurrence of the wall misalignment, it is necessary to ensure that P1 and P1′ coincide, and P2 and P2′ coincide, which is the L in step 1. p12 and L in step 2 p12 ' are equal, and line segment D1D2 passes through point P1', and line segment D3D4 passes through point P2'. Since the optimal n groups of interface and catheter combinations have been found in step 3, the obtained n groups of interface positions can be considered as the optimal posture set of the interface, that is, L p12 It is known that according to L p12 =L p12 ', the software can calculate the center point P2' of the cutting surface at the outlet of the catheter.

[0099] Next, we need to match the catheter and the interface to find the optimal assembly position of the catheter in the above n sets of optimal postures. Figure 6 As shown, line segment D1D2 is required to pass through point P1′, and line segment D3D4 is required to pass through point P1′. After adding these two restrictions, the catheter has only two degrees of freedom, namely the freedom of movement of the two ends of the catheter through points P1′ and P2′, and the freedom of rotation around the axis P1′P2′. The freedom of movement of the two ends of the catheter through points P1′ and P2′ can be represented by the distance t between point P1′ and port D1, and the freedom of rotation of the catheter around the axis P1′P2′ can be represented by the angle β relative to the initial position.

[0100] Through the above process, the catheter and the interface have been matched together. First, the value of t is determined according to the processing requirements. Then, by rotating the catheter 360° around the axis P1′P2′, all possible situations can be obtained. Then, through software analysis, the position with the smallest horseshoe value at both ends is found among these possible situations (this is a well-known technology in the field), which is the optimal position, thereby determining the optimal cutting surface and outputting it.

[0101] Specific as Figure 7 As shown, the catheter is first translated from P1′P2′ to P1″P2″, the translation amount is λ, and then rotated from P1″P2″ to P″1P″′2, the rotation angle is ω, and the rotation axis is N(n x , n y , n z ), the specific transformation is as follows:

[0102] D′ i =T(D i +λ) (7);

[0103] In the above formula, T is the rotation matrix around the axis N, Di is the original spatial posture of the catheter, and Di′ is the transformed spatial posture of the catheter.

[0104] The rotation matrix T around the axis N is derived as follows:

[0105]

[0106] like Figure 7 As shown:

[0107] λ=P″11-P′1

[0108] N=(P″2-P″1)×(P″′2-P″1)

[0109] ω=arccos((P″2-P″1)(P″′2-P″1) / |P″2-P″1||P″′2-P″1|).

[0110] Step 5: Bind the robotic arm to the catheter and determine the position of the cutting surface and cutting center of the cutting device in the robotic arm coordinate system. Then, overlap the catheter cutting position with the cutting position of the cutting device and calculate the pose coordinates of the final cutting position of the robotic arm end.

[0111] like Figure 8 As shown, after measurement, the coordinates of the catheter's bending point can be obtained. At this point, the software can read the position and posture of the end arm. The position and posture of the end arm are represented by a coordinate system with an origin at the center of the end flange, here called the tool coordinate system. The position and posture of the tool coordinate system are usually expressed using ZYX Euler angles and the coordinates of the flange center, that is, {α, β, γ, x, y, z}. Here, three points J1(x, y, z), J2(x, y, z), and J3(x, y, z) in space represent the initial position and posture of the end arm's gripper, and form the measurement tool coordinate system B'. Among them, J1 is the origin of the measurement tool coordinate system B', J2 is a point on the x-axis of the measurement tool coordinate system B'. In this embodiment, J1J2=1, and J3 is a point on the z-axis of the measurement tool coordinate system B'. In this embodiment, J1J3=1. Similarly, the position and posture of the end arm's gripper when the three points J1', J2', and J3' in space represent the cutting position, that is, the cutting tool coordinate system C'.

[0112] The measuring tool coordinate system B′ and the cutting tool coordinate system C′ can be obtained from the robot arm coordinate system A′ through rotation and translation, specifically:

[0113]

[0114] In the above formulas (9-1) and (9-2), E is the unit matrix, is the transformation matrix from coordinate system B′ to A′, is the transformation matrix from coordinate system C′ to A′.

[0115] According to the definition of ZYX Euler angle, first rotate the robot coordinate system A' around Z A The axis rotates by an angle α and then around the Y A The axis rotates by an angle of β and finally around Z A The axis rotates by an angle γ, and the rotation matrix is obtained. for:

[0116]

[0117] In the above formula (10), cα=cosα, sα=sinα, and the other symbols have similar meanings.

[0118] Arranged:

[0119]

[0120] The above formula (11) is a general expression of the robot end position, which can be found in the introduction to robotics.

[0121] The cutting surface of the cutting device and the position of the center point of the cutting surface in the robotic arm coordinate system can be obtained through software. The optimal cutting position of the catheter determined in step 4 is overlapped with the cutting position of the cutting device, that is, the cutting surface of the catheter is overlapped with the cutting surface of the cutting device. At the same time, the axis of the catheter is overlapped with the center point of the cutting surface of the cutting device. The orientation of the end of the robotic arm is determined according to the relative position of the robotic arm and the cutting device. When the reachability of the robotic arm is met, the final cutting position and posture of the catheter can be determined, and the transformation matrix T and translation vector G of the catheter from the initial posture to the cutting position and posture are obtained. This is a well-known technology in the art. Since the catheter is bound to the robotic arm, the conversion relationship between J and J' can be known:

[0122] [J1′,J2′,J3′]=T·[J1,J2,J3]+G (12);

[0123] The initial end position of the robot arm can be known and substituted into formula (11). Then, the result of formula (11) can be substituted into formula (9-1) to obtain J1, J2, and J3. Then, J1, J2, and J3 can be substituted into formula (12) to obtain the three virtual points J1′, J2′, and J3′ corresponding to the final cutting position. Then, J1′, J2′, and J3′ can be substituted into formula (9-2) to obtain the coordinates of the cutting tool coordinate system C′ in the robot arm coordinate system A′:

[0124]

[0125] Further analysis revealed:

[0126]

[0127] In the above formula (14), rij represents each element of the matrix. Here, since rij has been calculated (J1′, J2′, and J3′ are known), the matrix is known.

[0128] Substitute formula (14) into the general formula of the robot (15):

[0129]

[0130] Available:

[0131]

[0132] In the above formula (16), Atan2(y,x) is the inverse tangent function. -1 When (y / x), the quadrant is determined based on the signs of x and y. This gives the final cutting position z{α, β, γ, x, y, z} of the robot arm, where [x, y, z] = J1′.

[0133] Step 6: Output the final cutting position of the robot arm to achieve robot arm guidance control.

[0134] The present invention verifies that the above method is accurate and effective through experiments, specifically:

[0135] like Figure 9 As shown, the interface data of the catheter, the tube shape data of the catheter, the cutting position calibration data of the cutting equipment in the robot coordinate system, the posture coordinate data of the robot arm holding the catheter during the bending measurement, etc. are simulated in the CAD software.

[0136] Among them, interface data such as Figure 10 As shown in Table 1 below:

[0137] Table 1 Interface data

[0138] interface x y z i j k IN 602.140663 -278.32862 2302.553575 0.000732 0.003277 -0.999994 OUT 191.268554 -431.781439 2170.706549 0.952838 -0.236862 0.189727

[0139] Catheter data such as Figure 11 As shown in Table 2 below:

[0140] Table 2 Catheter data

[0141] dot number x y z D1 2770.974576 339.9878711 208.2042397 D2 2525.323543 -98.89748057 147.4682732 D3 2685.735433 259.7776643 170.677915 D4 2669.152943 245.08591 166.3085804 D5 2561.752069 155.2894117 155.2235245 D6 2527.762722 83.6908065 150.9442929

[0142] Robotic arm data such as Figure 11 As shown in Table 3 below:

[0143] Table 3 Robotic arm posture data

[0144] dot number x y z J1 2770.974576 339.9878711 208.2042397 J2 2525.323543 -98.89748057 147.4682732 J3 2685.735433 259.7776643 170.677915

[0145] Cutting position calibration data such as Figure 12 As shown in Table 4 below:

[0146] Table 4 Cutting position calibration data

[0147] dot number x y z o 1009.485336 1843.015107 569.193647 Q 1023.826458 2048.529892 569.054571 vector i j k N -0.000268375 -0.00118114 0.999999265

[0148] The above data are calculated according to the method of the present invention, and the calculation results are simulated and verified in a three-dimensional design. The catheter and the space interface are drawn according to the coordinates of the calculation results, and a base surface is generated at the interface end face, which is the catheter cutting surface. Figure 13 shown.

[0149] Place the catheter according to the three-point coordinates of the gripper. When the robotic arm cuts the inlet end of the catheter, the final position coordinates of the three-point gripper obtained by the simulation software are as follows: Figure 14 As shown in Table 5 below:

[0150] Table 5

[0151] dot number x y z J1 1205.72835 1444.82553 696.46108 J2 1130.67683 1409.00352 751.99533 J3 1162.34173 1534.92177 695.94241

[0152] When the robotic arm cuts the outlet of the catheter, the final position coordinates of the three points of the gripper obtained by the simulation software are as follows: Figure 15 As shown in Table 6 below:

[0153] Table 6

[0154] dot number x y z J1 771.59582 1987.10801 1269.78938 J2 725.94252 1899.35967 1255.09226 J3 839.98842 1963.06156 1200.91107

[0155] According to the method of the present invention, the coordinates of the three points of the gripper are substituted into equations (14) and (16) to obtain the position coordinates of the robotic arm. The calculation results are shown in Table 7 below:

[0156] Table 7

[0157]

[0158] In the model, the cutting plane of the catheter coincides with the cutting plane of the cutting device (that is, the inlet data of Table 7 coincides with the simulated Table 5 after conversion, and the outlet data of Table 7 coincides with the simulated Table 6 after conversion), which verifies the feasibility of the method of the present invention.

Claims

1. A method for removing excess from an aerospace engine duct, characterized by: The steps include: Step 1: Establish an interface space posture model and obtain the interface space posture set F; In step 1, the interface is provided with an elbow that is fixedly connected to the catheter, and when the elbow rotates around its own central axis, the elbow drives the corresponding side connection end of the catheter to rotate to form a circle. Assuming that O1 is the center of the rotation circle of the catheter inlet connection end, O2 is the center of the rotation circle of the catheter outlet connection end, P1 is the end face center of the catheter inlet connection end, and P2 is the end face center of the catheter outlet connection end, a first coordinate system B is established with O1 as the center of the circle and the rotation axis n1 of the inlet end elbow as the Z axis. A second coordinate system C is established with O2 as the center of the circle and the rotation axis n2 of the outlet end elbow as the Z axis. Take the coordinate x A 、y A The main coordinate system A is established at the value point, and the first coordinate system B and the second coordinate system C are transformed to the main coordinate system A. In the main coordinate system A, the distance between the definition points P1 and P2 is L p12 , the angle between the straight line O1P1 and the straight line P1P2 is θ1, the angle between the straight line O2P2 and the straight line P2P1 is θ2, plane 1 is the plane determined by the point P1O2P2, plane 2 is the plane determined by the point P1O1P2, the angle between plane 1 and plane 2 is θ3, through L p12 , θ1, θ2, θ3 determine the interface space posture set, which is expressed as: ； Step 2: Establish a catheter spatial posture model and obtain the catheter spatial posture collection D after cutting; In step 2, the catheter cutting position is on the straight pipe segments at both ends. The center of the cutting surface on the straight pipe segment D1D2 at the catheter inlet is defined as P1′, and the center of the cutting surface on the straight pipe segment D3D4 at the catheter outlet is defined as P2′. Plane 3 is the plane determined by point D1D2P2′, and plane 4 is the plane determined by point D3D4P1′. The angle between the two planes is θ3′, the angle ∠D1P1′P2′ between the straight pipe segment D1D2 and the line segment P1′P2′ is θ1′, the angle ∠D3P2′P1′ between the straight pipe segment D3D4 and the line segment P1′P2′ is θ2′, and the distance between P1′ and P2′ is L p12 ', through L p12 ', θ1', θ2', θ3' determine the set of spatial postures of the catheter after cutting, which can be expressed as: ； Step 3: Match the interface spatial posture set F and the cut catheter spatial posture set D, and select n optimal combinations; In step 3, the element in the interface space posture set F is subtracted from the element in the catheter space posture set D to obtain the difference C. Since each item in C has a different influence on the horseshoe value and the wall offset, different weights are set for each item. , defined as: ； Therefore, the degree of inconsistency between the interface and the catheter is described as: ； Find the n combinations of interfaces and conduits with the smallest |C|; Step 4: Calculate all possible catheter positions based on the determined n groups of optimal interface positions, and find the position with the smallest horseshoe value at both ends as the optimal cutting position output; In step 4, the distance between the center point P1′ of the cutting surface at the inlet of the catheter and the catheter port D1 is defined as t. Since the optimal interface posture is determined in step 3, L p12 It is known that according to L p12 =L p12 ', find the center point P2' of the cutting surface at the outlet of the catheter, and D1D2 passes through point P1', and D3D4 passes through point P2'. The catheter is limited to the only degree of freedom of movement through points P1' and P2' at both ends, and the degree of freedom of rotation around the axis P1'P2'. The degree of freedom of movement is represented by the distance t from point P1' to port D1, and the degree of freedom of rotation is represented by the angle β of the catheter relative to the initial position. First determine the value of t, then rotate the catheter 360° around the axis P1P2 to obtain all possible situations, and find the position with the smallest horseshoe value at both ends as the optimal cutting position output; Step 5: Bind the robotic arm to the catheter, determine the cutting position of the cutting device in the robotic arm coordinate system, overlap the optimal cutting position of the catheter determined in step 4 with the cutting position of the cutting device, and calculate the pose coordinates of the final cutting position at the end of the robotic arm; Step 6: Output the pose coordinates of the final cutting position of the robotic arm to achieve robotic arm guidance control.

2. The method for removing excess material from an aerospace engine duct according to claim 1, wherein: In step 4, the catheter is first translated from P1′P2′ to P1″P2″ with a translation amount of λ, and then rotated from P1″P2″ to , the rotation angle is ω, the rotation axis is N (n x , n y , n z ), the specific transformation is as follows: (7); The rotation matrix around axis N is derived T as follows: （8）； 。

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