The Abbé error is a key factor for high-precision CNC machine tools. Unluckily, it is not taken into account in traditional machine tool volumetric error models. In this respect, based on the traditional machine tool volumetric error models, a new machine tool volumetric error model containing Abbé error is performed by analyzing the mechanism of Abbé error formation tool volumetric and based on 21-item geometric error measurement data, Abbé arm, and angle functional relationship. Moreover, integrated qualitative and quantitative simulation method for evaluation of machine tool space precision are correspondingly presented. Finally, an example was utilized to further verify the value of our model by means of analysis and comparison of the tooling precision prior to and after performance of compensation, and its validity and feasibility were proved. This study provides an important modeling method for high-precision machine tools and has very important theoretical significance and practical value.

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%.

In order to improve the precision of CNC machine tools effectively, a method for modeling and predicting their spatial errors based on spatial feature points was proposed. Taking three‐axis vertical CNC machine tools as the research object, we think that the whole space formed by machine tools’ working can be seen as the combination of a number of cubes, whose vertices are considered to be feature points, and others in the cubes are called nonfeature points. So, each nonfeature point’s errors can be predicted by the cube’s eight vertices’ errors. Based on the above ideas, an approach including the installing instrument for measuring any spatial feature point’s errors was put forward. In this way, all data of the feature points’ errors could be obtained. Moreover, according to these error data, the prediction model of nonfeature points’ errors was established by using the internal division ratio method. The method has the advantages of small interpolation operation, easy integration in the numerical control system, and high compensation precision. Finally, an example was used to prove its effectiveness and feasibility.

Abbe error is an important factor affecting high-precision machine tools, and the traditional modeling method does not consider Abbe error. Aiming at this problem, based on the traditional error model of machine tools and the formation mechanism of Abbe error, this paper establishes a machine tool spatial error model that considers Abbe error. Then combined with a specific machine tool, based on the measurement of 21 geometric errors of the machine tool to obtain relevant error data, through the combination of qualitative and quantitative accuracy evaluation methods, two models of traditional error model and error model considering Abbe error are analyzed. The accuracy of the machine tool is compared, and the comparison of the compensation effects of the two error models after compensation is also analyzed. The example verification shows that the machine tool spatial error model considering Abbe error is effective and feasible, and the compensation effect is better. It provides an important modeling method for improving the machining accuracy of precision machine tools.

Through analyzing the installation method of laser interferometer measurement aids and the planning of measurement path, a direct measurement method of the error data of the feature points in the whole space of the machine tool is proposed according to the principle of laser interferometry. On this basis, a spatial interpolation algorithm is used to calculating the precision of quasi-feature points based on the error data of 8 vertices (that is feature points) of the small cube in machine tool space.The error data of a small cube has been increased from 8 to 125，which provides a large amount of sample data for the full-space precision modeling of machine tool. Finally, after obtaining the full-space feature points and quasi-feature point accuracy data of the machine tool, a neural network prediction model of machine tool full-space precision is established.Example application verification shows that the prediction precision exceeds 94%.