Kinematic modeling of quasistatic errors of three-axis machining centers

Abstract Quasistatic error sources, which include thermal, mechanical loading and geometric error sources, are responsible for a very large proportion (typically, 70%) of the volumetric errors of a numerically controlled machine-tool. This paper, the first in a set of three, discusses the development of a very general model for the effects of geometric errors of the components of the kinematic chain (structural members and axes) of a machine on the volumetric errors in the work space. The effects of the other two sources are modeled as changes in the geometric error. The generality of the model arises from the fact that the errors along an axis of the machine can be characterized by any polynomial functions and the model is recursive in the order of these polynomials. This model can be used as the basis of a compensation scheme as well as in budgeting of errors on a machine-tool.

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