MATRIX MODELS OF MACHINING ACCURACY IN SINGLE-TOOL MULTI-PASS TURNING

Abstract

The design of multi-pass turning operations plays a critical role in modern high-precision manufacturing. This paper proposes a mathematical framework based on matrix models to predict and control machining accuracy throughout sequential turning passes. By decomposing the technological system into distinct subsystems—namely the spindle-chuck-workpiece and the carriage-toolholder-tool—a vector-based description of elastic displacements is established. The model incorporates the cumulative effects of system stiffness, tool geometry, and cutting conditions. A key focus is placed on "technological inheritance," where the dimensional scatter and workpiece stiffness from preceding passes serve as initial parameters for subsequent stages. The research demonstrates that accounting for the dynamic change in workpiece stiffness due to material removal is essential for accurate forecasting. Finally, the accuracy models are transformed into control models, identifying the carriage feed rate as the primary parameter for optimizing productivity while maintaining specified tolerances.

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