Multi-calibration of three-dimensional error of CNC lathe based on several system principles

Formation of System Low Order Arrays For any multibody system, the defined topology can be digitally described using a low order array. In the low-order array, each body finally reaches the inertial reference coordinate system by the principle of serial number from large to small.

If the sequence number of the adjacent low-order body of K is J, then L1(K)=J, and L0(K)=K, L0(0)=0; the sequence number that does not appear in the L1(K) line corresponds to The end body, and the serial number that appears in the table corresponds to the branch. If you let nmax be the maximum order of the low-order operator required when the body reaches the inertial reference coordinate system, you can conclude that the nmax of each body is not the same, it depends on the topology of the multi-body system. Such a multi-body system can be traced back to the inertial reference coordinate system through the low-order body array to find its position and motion relationship with the inertial reference coordinate system. This description method is simple and easy to use, and has universal significance in practical engineering applications.

Analysis of Geometric Constraints Different mechanisms have different geometric constraints. For a three-axis CNC milling machine, there are five, X, Y, Z, and six geometric constraints between the body and the body. There is only a relative movement of a single degree of freedom to ensure the uniqueness of the movement of the CNC machine. There is also a six-degree-of-freedom error motion between the body and the body.

Transformation parameter determination between adjacent inter-body displacement vector and in-vivo position vector (coordinate parameter transformation) According to the geometric constraint, the transformation parameters X, Y, Z, and error E of the low-order volume array associated with the computed body in the system are calculated and Detected, formed Transform the matrix. Taking the transformation relationship of the body 1 and the body 2 as an example, the ideal motion between them is a linear motion, and the motion direction is the X-axis.

, The transformation matrix of the displacement vector and the error vector between the body 1 and the body 2, respectively. Xs2, Ys2, Zs2 and es2, es2, and es2 are the vector and azimuth angles of the position vector error of the second body, respectively. Xg2, Yg2, Zg2, and g2, g2, and g2 are the vector and azimuth angles of the displacement vector error between the No. 1 body and the No. 2 body, respectively. Xm is the moving distance in the X direction. Rotational motion is similar to linear motion and can also be represented by a matrix.

The geometric error model of the three-axis CNC milling machine is established by taking the XK0820 three-axis CNC milling machine as an example, and its kinematic chain coordinate system is as shown. Schematic diagram of XK0820 three-axis milling machine As mentioned above, we can gradually establish the transformation matrix between adjacent bodies.

With mathematica software, we can easily calculate the results of any matrix between adjacent bodies. After the transformation matrix between each adjacent body is established, we can represent the position of any machining point in the inertial reference frame and its error model.

For any given machining point P, the spatial positioning error is the P point in the worktable coordinate system n5, the slide coordinate system n4, the bed coordinate system n3, and the headstock coordinate system n2 are finally converted into the tool coordinate system n1. , the spatial error calculation equation of point P can be expressed as For the basic transformation of a typical body, a series of coordinate recursive relations of a low-order volume array can be used to obtain a geometric error model of a space point P.

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