Surface roughening machining track control method for large spherical crown type metal structural part

Abstract

The invention belongs to the technical field of roughening machining, and provides a surface roughening machining track control method for a large spherical crown type metal structural part. Firstly, robot machining step length calculation is carried out, trajectory interpolation points are generated from the top of the spherical crown type structural part, initial spiral trajectory points are generated in an equal-angle increment mode so as to guarantee the machining precision of the top, and meanwhile the Euclidean distance between each new trajectory point and the previous trajectory point is calculated; when the Euclidean distance between the two track points is greater than a set equal-step increment for the first time, deleting the current newly-generated track point coordinates, and converting into a generation mode using an equal processing step; and after setting of the machining step length is completed, according to the obtained machining step length, the posture of the robot at each track point is calculated. According to the method, it can be guaranteed that the overall step length of the spiral track points is naturally transited from the top to the bottom, the path is free of distortion, it can be guaranteed that the surface of the large spherical crown type metal structural part is evenly coarsened, and the practical value is very high.

Description

Technical Field

[0001] The invention belongs to the technical field of roughening processing, and in particular relates to a method for controlling a trajectory of roughening processing of a surface of a large spherical crown-like metal structural part. Background Art

[0002] In the fields of aerospace, energy, transportation, etc., there is a widespread type of large spherical crown components, which are the main load-bearing components of high-end equipment such as launch vehicles and strategic missiles. This type of component is made of "metal skin-insulating interlayer-metal skin" glued together, and has functions such as load-bearing and insulation, which puts forward extremely high requirements on the bonding performance indicators. In order to improve the bonding performance, these components often need to be roughened on the surface to increase the surface contact area and improve the mechanical interlocking ability. However, the bonding performance and the micromorphology of the bonding surface (surface roughness, texture direction and distribution state, etc.) show a complex nonlinear relationship. Too large or too small surface roughness will reduce the bonding performance. In order to ensure the best bonding strength, controllable roughening processing is often required to meet the specific surface roughness size and texture distribution state. Integrating the flexible grinding disc, motor and force control device at the end of the industrial robot can replace manual controllable roughening of large-sized components.

[0003] In the process of robot-controlled roughening, in order to effectively control the surface roughness and texture distribution of the component, it is necessary to accurately control the roughening processing step and the robot posture. Typical step control methods include equal step incremental processing (CN106054802A A method for adaptive processing trajectory planning of free-form surfaces; Li Wei Research on grinding and polishing trajectory planning of grinding and polishing robots based on line structured light vision guidance) and equal angle incremental processing (CN114460900A A processing method and device for the contour of special-shaped curved glass; CN202110562342.2 Circumferential regional variable spindle speed turning method for non-circular cross-section parts). Among them, equal step incremental processing sets the same processing step increment along the spiral direction. The curvature of the spiral at the top of large spherical crown components is larger, and the curvature of the spiral at the bottom is smaller. This step generation method will generate sparse trajectory points in the spiral trajectory at the top of the spherical crown components, and dense trajectory points in the spiral trajectory at the bottom. Equal angle incremental machining generates trajectory points by controlling the increment of the polar angle of the spiral line, that is, the difference between the polar angles of each two adjacent points is a constant value. This step generation method will generate a large number of dense trajectory points in the top spiral trajectory of spherical cap components, and sparse trajectory points in the bottom spiral trajectory. Therefore, simply using equal step incremental machining or equal angle incremental machining cannot guarantee the uniformity of the roughness and texture distribution of the machined surface.

[0004] To this end, the present invention proposes a trajectory control method for surface roughening processing of large spherical crown-like metal structural parts. A hybrid trajectory planning mode of equal angle increments and equal step size increments is used to generate robot processing trajectory points, and the robot posture is adjusted according to the trajectory points, which makes up for the shortcomings of the existing methods and can ensure uniform surface roughening of large spherical crown-like metal structural parts. Summary of the invention

[0005] The main technical problem solved by the present invention is to solve the problem of controllable roughening of the surface of large spherical crown metal structural parts, and a roughening processing trajectory control method with excellent technical effect is invented.

[0006] The technical solution of the present invention:

[0007] A method for controlling machining trajectory of surface roughening of large spherical crown-like metal structural parts is proposed. The robot machining step length is first calculated, and trajectory interpolation points are generated starting from the top of the spherical crown-like structural part. The initial spiral trajectory points are generated using an equal-angle increment method to ensure the machining accuracy of the top. At the same time, the Euclidean distance between each new trajectory point and the previous trajectory point is calculated. When the Euclidean distance between the two is greater than the set equal-step increment for the first time, the coordinates of the currently newly generated trajectory point are deleted, and the method of generating with equal machining step length is switched. After the machining step length is set, the robot posture of each trajectory point is solved according to the obtained machining step length.

[0008] The specific steps are as follows:

[0009] (1) With the center of the bottom surface of the large spherical crown component as the origin of the coordinate system, a Cartesian coordinate system O (x, y, z) is established. The coordinates of any point on the large spherical crown component are P m (x m ,y m ,z m ), where m = 0, 1, 2, ..., n is the index of the coordinate point, and n is the number of coordinate points; since the large spherical cap-like component is an ellipsoidal shape, it is a body of revolution with the z axis as the axis; therefore, any point P on the large spherical cap-like component m (x m ,y m ,z m ) can be expressed as P based on the cylindrical coordinate system m (r m ,α m ,z m ); In the two representations, the corresponding relationship between variables is:

[0010]

[0011] Among them, r m P m (r m ,α m,z m ) point, α m P m (r m ,α m ,z m ) point’s cylindrical coordinate angle;

[0012] (2) Starting from the top of a large spherical crown component, the trajectory points are generated using equal angle increments to ensure the machining accuracy of the top. The angle increment α s,m is a fixed value; the cylindrical coordinates of the first point are P1(r1,α1,z1); calculate the angle α2 of the second point:

[0013] α2=α1+α s,m (2)

[0014] Based on the Archimedean spiral, the interpolation method is used to establish the functional relationship between the cylindrical coordinate radius r and the angle α:

[0015]

[0016] In the formula, r i and α i It is obtained by discretizing the section s on the y=0 plane of the large spherical crown component, i=0,1,2,…,k is the index number of the discrete point, k is the number of discrete points; α i-1 ≤α≤α i , α i and α i-1 Corresponding to the nearest point Q on both sides of α i and Q i-1 The corresponding angle α value; using formula (3), the cylindrical coordinate angle α2 of the second point is substituted into the second point to obtain the cylindrical coordinate height z2 of the second point:

[0017]

[0018] Where a1 and b1 are the major axis and minor axis of the large spherical crown component, respectively. The cylindrical coordinates of point P1 (r1, α1, z1) and point P2 (r2, α2, z2) are converted to P1 (x1, y1, z1) and P2 (x2, y2, z2) in the Cartesian coordinate system using formula (1), and the Euclidean distance between points P1 (x1, y1, z1) and P2 (x2, y2, z2) is calculated:

[0019]

[0020] The calculated Euclidean distance d and the equal step increment l s Compare; if d≤l s, then continue to use the equal angle increment method to calculate the step length, and obtain the coordinates of the grinding trajectory points in sequence; when the Euclidean distance d is greater than the equal step increment l for the first time s , delete the newly generated trajectory point coordinates and convert them to generate grinding trajectory point coordinates using equal machining step increments;

[0021] (3) After converting to the equal step increment method, the previous trajectory point P m-1 (r m-1 ,α m-1 ,z m-1 ) is used as the basis to calculate the machining step length for each additional surface spacing l s The corresponding angle increment α s,m :

[0022]

[0023] At this time, click P m (r m ,α m ,z m ) is:

[0024] α m =α m-1 +α s,m (7)

[0025] Use formula (4) to calculate the height of the point column coordinates; use formula (1) to calculate the height of the point P m (r m ,α m ,z m ) Cylindrical coordinates are converted to Cartesian coordinates P m (x m ,y m ,z m ); and so on, obtain the polishing trajectory point coordinates P of all remaining points m (x m ,y m ,z m );

[0026] (4) Calculate each trajectory point P m (x m ,y m ,z m ) The z-axis posture of the robot flange at this point points to the inside of the surface; each trajectory point P m (x m ,y m ,z m ) is calculated by taking partial derivatives of the spherical cap surface equation with respect to x, y, and z in turn:

[0027]

[0028] Click P m (x m ,y m ,z m ) Surface tangent vector along the machining trajectory Initially record the x-axis posture of the robot flange, here use the current trajectory point P m Point to the next trajectory point P m+1 The direction is taken as the x-axis direction of the flange, and the calculation formula is:

[0029]

[0030] At this time, the robot is at point P m (x m ,y m ,z m ) of the flange in the y-axis From the vector product we get:

[0031]

[0032] Due to the above preliminary calculation of the x-axis posture of the robot flange, that is, the surface tangent vector It is not strictly related to the z-axis posture of the flange, i.e. the surface normal vector perpendicular to each other, for this purpose, the y-axis posture of the robot flange is used Determine the final x-axis orientation of the flange The calculation formula is:

[0033]

[0034] At this point, the posture of each processing trajectory point when the grinding disc has no inclination is solved;

[0035] Based on Rodriguez rotation formula, calculate the flange at each processing trajectory point P m (x m ,y m ,z m ) on the flange z-axis and the x-axis Around the y axis The vector coordinates after rotation at any angle; the z-axis vector after rotation is the final flange z-axis vector The calculation formula is:

[0036]

[0037] In the formula, R k By the rotation axis vector The calculation result is:

[0038]

[0039] Similarly, the x-axis vector of the rotated flange is The calculation formula is:

[0040]

[0041] In the formula, R k Calculated by formula (12);

[0042] Because the flange posture is around Rotate, so the y-axis posture remains unchanged after rotation;

[0043]

[0044] Robot flange posture at each processing trajectory point obtained after rotation and

[0045] Beneficial effects of the present invention: The equal step increment method of the present invention is mainly aimed at the bottom of the spherical crown component. The curvature of the spiral line here is small, and each increase in step length l s When the height value changes (|z m -z m-1 |) is relatively small. Therefore, the height value change can be ignored, and the three-dimensional step length calculation formula can be simplified to the arc length calculation formula in the two-dimensional plane. At this time, the step length l in the three-dimensional coordinate system s Approximately equal to r on the plane m-1 is the radius, α s,m is the arc length of the angle. This method can ensure uniform increments of equal angles and equal step sizes. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of robot polishing for large spherical crown components

[0047] Figure 2 Schematic diagram of the coordinate system for large spherical crown components

[0048] Figure 3 The interpolation point step size changes

[0049] Figure 4 Schematic diagram of the overall processing trajectory

[0050] Figure 5 is the posture of each trajectory point of the robot

[0051] In the figure: 1 industrial robot; 2 force control actuator; 3 grinding device; 4 ball crown type component. DETAILED DESCRIPTION

[0052] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0053] The long axis of the spherical crown component to be processed is a1 = 1500mm, b1 = 900mm. Angle increment α s,m =π / 20, surface spacing l s =100mm.

[0054] The specific implementation process of the technical solution adopted by the present invention includes:

[0055] Step 1: Install the large spherical crown component next to the industrial robot and perform a rough calibration to ensure that the industrial robot travel covers the component size, such as Figure 1 As shown. With the center of the bottom surface of the large spherical crown component as the origin of the coordinate system, establish the Cartesian coordinate system O (x, y, z), as shown Figure 2 shown.

[0056] (2) Generate trajectory points using equal angle increments starting from the top of the spherical crown component to ensure the machining accuracy of the top. The cylindrical coordinates of the first point are P1(r1,α1,z1). Based on the cylindrical coordinates of the first point, calculate the angle α2 of the second point:

[0057] α2=α1+α s,m (16)

[0058] Based on the Archimedean spiral, the interpolation method is used to establish the functional relationship between the cylindrical coordinate radius r and the angle α:

[0059]

[0060] In the formula, r i and α i It is obtained in advance by discretizing the section s on the y=0 plane of the large spherical crown component, i=0,1,2,…,k is the index number of the discrete point, and k is the number of discrete points. α i-1 ≤α≤α i , α i and α i-1 Corresponding to the nearest point Q on both sides of α i and Q i-1 The corresponding angle α value is as follows: Figure 2 As shown. Using formula (3), the cylindrical coordinate angle α2 of the second point is substituted into the equation to obtain the cylindrical coordinate height z2 of the second point:

[0061]

[0062] In the formula, a1 and b1 are the major axis and minor axis of the spherical cap component, respectively. The cylindrical coordinates of point P1 (r1, α1, z1) and point P2 (r2, α2, z2) are converted to P1 (x1, y1, z1) and P2 (x2, y2, z2) in the Cartesian coordinate system using formula (1), and the Euclidean distance between points P1 (x1, y1, z1) and P2 (x2, y2, z2) is calculated:

[0063]

[0064] The calculated Euclidean distance d and the equal step increment l s Compare. At points 1 to 153, d < l s , continue to use the equal angle increment method to calculate the step length, and obtain the coordinates of the grinding trajectory points in turn; d≥l appears for the first time at point 154 s , delete the newly generated trajectory point coordinates and convert them to generate grinding trajectory point coordinates using equal processing step increment method, such as Figure 3 shown.

[0065] (3) After converting to the equal step increment method, the previous trajectory point P m-1 (r m-1 ,α m-1 ,z m-1 ) is used as the basis to calculate the machining step length for each additional surface spacing l s The corresponding angle increment α s,m :

[0066]

[0067] At this time, point P m (r m ,α m ,z m ) is:

[0068] α m =α m-1 +α s,m (twenty one)

[0069] Use formula (4) to calculate the height of the point column coordinates. Use formula (1) to convert point P m (r m ,α m ,z m ) Cylindrical coordinates are converted to Cartesian coordinates P m (x m ,y m ,z m ). And so on, the coordinates of the grinding trajectory points of all the remaining points P are obtained. m (x m ,y m ,z m),like Figure 4 As shown in the figure, the total number of generated trajectory points is 2162. It can be seen from the observation that the step length of the spiral trajectory points is naturally transitioned from the top to the bottom, and the path is not distorted.

[0070] (4) Calculate each trajectory point P m (x m ,y m ,z m ) The robot flange z-axis posture at this point (direction pointing to the inside of the surface). Its normal vector can be calculated by taking partial derivatives of the spherical cap surface equation with respect to x, y, and z in sequence:

[0071]

[0072] Click P m (x m ,y m ,z m ) Surface tangent vector along the machining trajectory It can be initially recorded as the x-axis posture of the robot flange. Here, the current trajectory point P is used. m Point to the next trajectory point P m+1 The direction is taken as the x-axis direction of the flange, and the calculation formula is:

[0073]

[0074] At this time, the robot is at point P m (x m ,y m ,z m ) flange y-axis posture This can be obtained from the vector product:

[0075]

[0076] Due to the above preliminary calculation of the flange x-axis posture (surface tangent vector) Not strictly related to the z-axis orientation of the flange (surface normal vector) Perpendicular to each other, for this purpose, the flange y-axis attitude Determine the final flange x-axis posture The calculation formula is:

[0077]

[0078] At this point, the posture of each processing trajectory point when the grinding disc has no inclination is solved.

[0079] Based on Rodriguez rotation formula, calculate the flange at each processing trajectory point P m (x m ,y m ,zm ) on the flange z-axis and the x-axis Around the y axis The vector coordinates after rotation at any angle. The rotated z-axis vector is the final flange z-axis vector The calculation formula is:

[0080]

[0081] In the formula, R k The rotation axis vector The calculation result is:

[0082]

[0083] Similarly, the x-axis vector of the rotated flange The calculation formula is

[0084]

[0085] In the formula, R k Calculated by formula (12).

[0086] Because the flange posture is around Rotate so that the y-axis posture remains unchanged after rotation

[0087]

[0088] Robot flange posture at each processing trajectory point obtained after rotation and like Figure 5 shown.

[0089] The present invention uses a hybrid trajectory planning mode of equal angle increments and equal step increments to generate robot processing trajectory points. Overall, the step length of the spiral trajectory points transitions naturally from top to bottom, the path is not distorted, and the robot posture is adjusted according to the trajectory points, which makes up for the shortcomings of the existing methods and can ensure uniform roughening of the surface of large spherical crown metal structures, and has high practical value.

Claims

1. A trajectory control method for surface roughening of large spherical crown-like metal structural parts. It is characterized in that Here are the steps: (1) With the center of the bottom surface of the large spherical crown component as the origin of the coordinate system, a Cartesian coordinate system O (x, y, z) is established. The coordinates of any point on the large spherical crown component are P m (x m ,y m ,z m ), where m = 0, 1, 2, ..., n is the index of the coordinate point, and n is the number of coordinate points; since the large spherical cap-like component is an ellipsoidal shape, it is a body of revolution with the z axis as the axis; therefore, any point P on the large spherical cap-like component m (x m ,y m ,z m ) can be expressed as P based on the cylindrical coordinate system m (r m ,α m ,z m ); In the two representations, the corresponding relationship between the variables is: Among them, r m P m (r m ,α m ,z m ) point, α m P m (r m ,α m ,z m ) point’s cylindrical coordinate angle; (2) Starting from the top of a large spherical crown component, the trajectory points are generated using equal angle increments to ensure the machining accuracy of the top. The angle increment α s,m is a fixed value; the cylindrical coordinates of the first point are P 1 (r 1 ,α 1 ,z 1 ) ; Calculate the angle α of the second point 2 : α 2 ＝α 1 +α s,m (2) Based on the Archimedean spiral, the interpolation method is used to establish the functional relationship between the cylindrical coordinate radius r and the angle α: In the formula, r i and α i It is obtained by discretizing the section s on the y=0 plane of the large spherical crown component, i=0,1,2,…,k is the index number of the discrete point, k is the number of discrete points; α i-1 ≤α≤α i , α i and α i-1 Corresponding to the nearest point Q on both sides of α i and Q i-1 The corresponding angle α value; using formula (3), the cylindrical coordinate angle α of the second point is obtained 2 Substitute it and get the second point column coordinate height z 2 : In the formula, a 1 and b 1 are the major axis and minor axis of the large spherical crown component respectively; using formula (1) point P 1 (r 1 ,α 1 ,z 1 ) Cylindrical coordinates and point P 2 (r 2 ,α 2 ,z 2 ) Cylindrical coordinates are converted to Cartesian coordinates P 1 (x 1 ,y 1 ,z 1 ) and P 2 (x 2 ,y 2 ,z 2 ), and calculate P 1 (x 1 ,y 1 ,z 1 ) and P 2 (x 2 ,y 2 ,z 2 )The Euclidean distance between points: The calculated Euclidean distance d and the equal step increment l s Compare; if d≤l s , then continue to use the equal angle increment method to calculate the step length, and obtain the coordinates of the grinding trajectory points in sequence; when the Euclidean distance d is greater than the equal step increment l for the first time s , delete the newly generated trajectory point coordinates and convert them to generate grinding trajectory point coordinates using equal machining step increments; (3) After converting to the equal step increment method, the previous trajectory point P m-1 (r m-1 ,α m-1 ,z m-1 ) is used as the basis to calculate the machining step length for each additional surface spacing l s The corresponding angle increment α s,m : At this time, click P m (r m ,α m ,z m ) is: Use formula (4) to calculate the height of the point column coordinates; use formula (1) to calculate the height of the point P m (r m ,α m ,z m ) Cylindrical coordinates are converted to Cartesian coordinates P m (x m ,y m ,z m ); and so on, obtain the polishing trajectory point coordinates P of all remaining points m (x m ,y m ,z m ); (4) Calculate each trajectory point P m (x m ,y m ,z m ) The z-axis posture of the robot flange at this point points to the inside of the surface; each trajectory point P m (x m ,y m ,z m ) is calculated by taking partial derivatives of the spherical cap surface equation with respect to x, y, and z in turn: Surface tangent vector P of point Pm(xm,ym,zm) along the machining trajectory xt,temp =[x x,temp ,y x,temp ,z x,temp ] T Initially record the x-axis posture of the robot flange, here use the current trajectory point P m Point to the next trajectory point P m+1 The direction is taken as the x-axis direction of the flange, and the calculation formula is: At this time, the y-axis posture P of the robot flange at point Pm (xm, ym, zm) y,temp =[x y,temp ,y y,temp ,z y,temp ] T , from the vector product: Due to the above preliminary calculation of the x-axis posture of the robot flange, that is, the surface tangent vector It is not strictly related to the z-axis posture of the flange, i.e. the surface normal vector perpendicular to each other, for this purpose, the y-axis posture of the robot flange is used Determine the final x-axis orientation of the flange The calculation formula is: At this point, the posture of each processing trajectory point when the grinding disc has no inclination is solved; Based on the Rodrigues rotation formula, calculate the flange at each processing trajectory point P m (x m ,y m ,z m ) on the flange z-axis and the x-axis Around the y axis The vector coordinates after rotation at any angle; the z-axis vector after rotation is the final flange z-axis vector The calculation formula is: In the formula, R k By the rotation axis vector The calculation result is: Similarly, the x-axis vector of the rotated flange is The calculation formula is: In the formula, R k Calculated by formula (12); Because the flange posture is around Rotate, so the y-axis posture remains unchanged after rotation; Robot flange posture at each processing trajectory point obtained after rotation and

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