Geometric error modeling and compensation for large-scale grinding machine tools with multi-axes

Abstract

Synthesis modeling of a geometric error-based traditional method for large-scale grinding machine tools with six axes is too complicated to perform in a real-time compensator with a built-in position control system, and it is difficult to obtain all of the error elements corresponding to the model. This paper proposed a novel strategy in which a machine may be considered as translation axes and rotary axes, and geometric errors of the translation axes and rotary axis are modeled and the geometric error models of the machine are very simple for real-time error compensation. The volumetric errors of the translation axes are measured using spatial circular curve ball bar test, and every element of the rotary axis is also obtained by a series of considerate ball bar tests. According to the characteristics of a position controller used in the machine, a synthesis error compensation system based on the NUM numerical control system was developed. Error compensation experiments were carried out, and the results show that the accuracy of the machine is improved significantly.

Appendix

E :

Spatial error vector

E _cx , E _cy , E _cz :

Projection of spatial errors of rotary axes along the x-, y-, and z-axes

E _tx , E _ty , E _tz :

Projection of spatial errors of translation axes along the x-, y-, and z-axes

E _x , E _y , E _z :

Projection of spatial deviation along the x-, y-, and z-axes

f _pt :

Error of single pitch deviation

f _p :

Total cumulative pitch deviation

f _Hα :

Profile slope deviation

f _fα :

Profile form deviation

f _α :

Total profile deviation

f _Hβ :

Helix slope deviation

f _fβ :

Helix form deviation

f _β :

Total helix deviation

Ln(j):

N order low-order body of typical j

T _ijP :

The static attitude transformation matrix of j body in the subcoordinate of i body

T _ijs :

The kinematic attitude transformation matrix of j body in the subcoordinate of i body

x, y, z, W :

Command position of the x-, y-, z-, and W-axes

α, β, $\gamma$ :

Rotational angles of the A-, B-, and C-axes

ΔT _ijP :

Error of static attitude transformation matrix

ΔT _ijS :

Error of kinematic attitude transformation matrix

ΔD :

The radius error measured by ball bar

Δφ _xz , Δφ _xy , Δφ _yz :

The squareness errors between the x- and z-axes, x- and y-axes, and y- and z-axes

Δα _zC :

Projection of parallelism between the z- and C-axes along the x-axis

Δβ _zC :

Projection of parallelism between the z- and C-axes along the y-axes

Δx, Δy, Δz :

The errors of the real point to ideal point in the locus along the x-, y-, and z-axes of multi-machine tools

Δx _x , Δy _x , Δz _x :

The linear position errors of the x-axis along the x-, y-, and z-axes

Δ$\alpha$ _x , Δ$\beta$ _x , Δ$\gamma$ _x :

The roll angle errors of the x-axis along the x-, y-, and z-axes