Optimal Design Method for Static Precision of Heavy-Duty Vertical Machining Center Based on Gravity Deformation Error Modelling

Abstract

Due to the large size and large span of heavy-duty machine tools, the structural deformation errors caused by gravity account for a large proportion of the static errors, and the influence of gravity deformation must thus be considered in the machine tool precision design. This paper proposes a precision design method for heavy-duty vertical machining centers based on gravity deformation error modelling. By abstracting the machine tool into a multibody system topology, the static error model of the machine tool is established based on the multibody system theory and a homogeneous coordinate transformation. Assuming that the static error of each motion axis is composed of two parts, i.e., the manufacturing-induced geometric error and the gravity deformation error, the machine tool stiffness model of the relationship between gravity and deformation error is developed using the spatial beam elements. In the modelling process, the stiffness coefficients and volume coefficients of the components are introduced to fully consider the influences of structural parameters on machine tool precision. Taking the machine tool static precision, the component stiffness coefficients and the volume coefficients as the design variables, based on the use of the worst condition method, error sensitivity analysis and global optimization algorithm, the optimal allocation of the static error budget of the machine tool and the structural design requirements of each component are determined, providing a valuable guide for the detailed structure design and manufacture processing of the machine tool components.

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“…In the design and optimisation of precision machines, to reduce the impact of dynamic errors within the machine on the stability of the device and the accuracy of the machining, the static and dynamic characteristics and the machine's thermal deformation must be analysed [9][10][11][12][13]. The use of a gantry symmetrical structure in the design of precision machine tools can effectively reduce the impact of thermal deformation on the device; in order to ensure its performance, the machine tool should be considered, first of all, with reference to the effect of gravity on its static deformation [14,15]In research to improve the machining accuracy of precision machine tools, Wang et al [16] promulgated a machine tool error model based on helix theory, identified the machine tool's weak points, and then optimised its design with harmonic response analysis to assess the device's layout form. The dynamic properties of machine tools greatly influence the precision of a device's machining [17].…”