Geometric Error Modeling And Analyzing For A5-axis Machine Tool Based On The Theory Of Multi-rigid-body System

With the development of science and technology, NC machine tools tend to high-speed, high efficiency, precision and automation; the processing performance requirement is increasingly high. Reasonable machining accuracy of the key components and reducing its original error are very important to guarantee the machining accuracy of NC machine tools. This paper takes a5-axis machine tool as an example to investigate the influence of the geometric errors of the key components on the work-piece machining error by virtue of the theory of multi-rigid-body kinematics. The effect of the original errors of the key components on the work-piece machining error was outlined. The some remarks of work is stressed as follows.Firstly, the paper analyzes the movement structure of the NC machine tool and establishes the model of movement errors for the NC machine tool based on the theory of multi-rigid-body kinematics, in which the relation of the moving components for the NC machine tool is treated as the low order body relation. Constraint equations of the error modeling for the NC machine tool are derived.Secondly, position matrix, position error matrix, displacement transformation matrix and displacement error transformation matrix are taken into the established mathematical model, which can describe the relation between the geometric error in any point and the thirty-seven basic errors. The sensitivities of X-geometric error, Y-geometric and Z-geometric to the thirty-seven basic errors are derived from the established mathematical model. The calculated results of the sensitivities demonstrate that the rotation errors make a large impact on the geometric error because of the linear relationship. However, the impact of linear original error on the geometric errors is small for the algebraic relationship. The geometric error in any point also bears linear relation to the verticality or parallelism errors, but it varies with different directions. Hence, their impact on the geometric error is much smaller than that of the rotational errors and is similar with that of linear errors.Finally, the simulation experiments for the model of movement errors are conducted by virtue of the Monte-Carlo method. The experimental data are fitted by the maximum likelihood estimation method. The fitting results of the geometric error in any point are demonstrated to be a normal distribution by K-S test. The mean and standard deviation of the geometric error for the machined straight lines and surfaces in the given linear orientation are obtained from the statistical analysis of the data obtained from the simulation experiments.