Discussion on Management Scheme of Simulation Machine Tool Interpolation

The structural model of the virtual axis machine tool model structure model, the coordinate system is established by the method. The posture of the moving platform in the working space is described by Euler angle. The three consecutive rotations of the workpiece coordinate system are: rotating around the machine coordinate system Z axis. The angle, the rotation angle of the X' axis after the transformation, and the rotation angle of the Z′′ axis after the transformation. The distance between the two hinges of the i-th branch is represented by Li. Li=si-rBi(i=1, 2,...,6) Where si and rBi represent the position vectors of the hinge points bi and Bi respectively in a fixed coordinate system. If li is the i-th branch length and qi is the i-th branch unit direction vector, then qi=Li/li( 2) The inverse solution is l2i=LiLi, and the velocity expression obtained by time is li=qiVbi where Vbi represents the velocity of the hinge point bi. The i, j, k represent the machine platform coordinate system along X, Y, respectively. For the unit vector of the Z axis, the first derivative matrix of the inverse solution of the platform (Jacobi matrix) is JqP=q1TJb1Pq2TJb2P...q6TJb6P, where JbiP= Let the position of the tool at the starting point P1 and the end point P2 of the linear path segment be (x1, y1, z1, 1, 1, 1) and (x2, y2, z2, 2, 2, 2), and s be the line between P1P2 The distance, sx, sy, sz is the direction cosine of the straight line P1P2, and si is the combined feed amount of the i-th interpolation period, and the spatial absolute coordinates and posture of each interpolation point can be obtained. This interpolation strategy can better control tool movement in most cases, but in some special cases, it may cause interference during processing. For example, when moving from pose P1=T to P2=<100,0,0,-90,-15,90>T, the root cause of the tortuous path is obtained: Euler angle is not a relatively fixed coordinate system. The posture description, at this time, the diagonal interpolation adopts the processing method of synchronous acceleration and deceleration with the position coordinate, that is, the following formula is established during the interpolation process to be (k)2-1=x(k)x2-x1=L (k) L, double-track interpolation In order to solve the problem in the system using Euler angle to describe the pose, we propose a double-track-based interpolation method according to the principle of the shortest motion path of the moving platform. Add a control line c1c2 to constrain the movement of the tool together with P1P2.

1c2 Set the space straight track segment P1P2 The starting point of the starting point is P1, P2, the line speed of the tool tip point is Vs, and the tool length is LT. (1) The control line c1c2 takes the origin of the coordinate system as the tool center, and the Z axis coincides with the tool rotation axis. The coordinates of the center of the moving platform in the moving coordinate system are Cr(0, 0, LT), and the starting point c1 is at the workpiece coordinate. The coordinates in the system are c1=(p1x, p1y, p1z)T+LTR1, the coordinates of the end point c2 in the workpiece coordinate system are c2=(p2x, p2y, p2z)T+LTR2, and the transformation matrix Ri is Ri=sinisini-cosisinicosi Further, the control line length Lc = c1c2 and the components Lcx, Lcy, Lcz of the control line on each axis of the workpiece coordinate system are obtained. (2) Interpolation First, the tool path is interpolated, and the coordinates (xi, yi, zi) of each interpolation point pi on the tool path can be obtained. The coordinates of each interpolation point ci on the control line can be obtained by the following formula: cTi=KpTi, and the constant matrix K is K= (3) Re-determination of the tool vector of each interpolation point On the basis of the above, the tool vector Ti of the i-th interpolation point can be re-determined as Ti=picipici, and the tool vector can be used to determine the posture of the moving platform, and the motion can be solved. Inverse solution; if you use Euler angle to solve the inverse solution, you need to restore this result to Euler angle. The interpolation strategy can ensure that the central motion path of the moving platform conforms to the shortest path principle on various motion trajectories.

(Finish)

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