Abstract
A method for establishing machine tool’s spatial error model is put forward based on screw theory, which is different from the traditional error modeling method. By analyzing the position relationship between the ideal coordinate vector and the actual coordinate vector jointly affected by linear errors and angular errors, a single-axis screw conversion matrix error expression is brought up based on screw theory. Meanwhile, the comprehensive spatial error model of the CNC machine tool is derived by considering the influence of the workpiece motion chain and the tool motion chain on the model. Further, to compensating spatial errors of CNCs, such screw theory-based model is embedded in the error compensation system by means of integration of a few specific application examples. And in order to evaluate the compensation effects, an integrated evaluation method of quantitative spatial diagonal calculation and MATLAB simulation is proposed. Application results show that the screw theory-based spatial error model of tool has a very substantial compensation effect, which makes the position error of the machine tool decreased by about 80%.
Highlights
With the rapid development of modern industry, CNC processing is focusing on high even ultra high precision
The color separation diagram of the error field is obtained by means of the Matlab simulation tool (Fig. 11)
Our study shows that the accuracy indexes of 4 body diagonal accuracy of a CNC can be controlled within 20 μm at the same time and the accuracy of the tool is very high
Summary
With the rapid development of modern industry, CNC processing is focusing on high even ultra high precision. As a kind of primary precision processing tools, CNCs directly affect development of the entire manufacturing industry [1,2,3]. Geometric and thermal errors dominate CNCs [4, 5]. The former dominates the overall error of a tool. Study of modeling and compensation of spatial geometric errors has a history of ages. Modeling and compensation of spatial geometric errors of multi-axis CNCs are becoming more popular and challenging recently [6,7,8,9]. The tool error modeling theory is based on spatial errors. Ferreira et al applied the rigid body kinematics in 1986 to establish the parameterized relationship between the working
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