In the tool orientation planning for five-axis sculptured surface machining, the geometrical constraints are usually considered. Actually, the effect of nongeometrical constraints on tool orientation planning is also important. This paper studied one nongeometrical constraint which was cutting force induced static deflection under different tool orientations, and proposed a cutter deflection model based on that. In the study of the cutting force, the undeformed chip thickness in filleted end milling was modeled by geometrical analysis and coordinate transformation of points at the cutting edge. In study of static flexibility of multi-axis machine, static flexibility of the entire machining system was taken into consideration. The multi-axis machining system was divided into the transmission axes-handle (AH) end and the cutting tool end. The equivalent shank method was developed to calculate the static flexibility of the AH end. In this method, static flexibility anisotropy of the AH end was considered, and the equivalent lengths of the AH end were obtained from calibration experiments. In cutter deflection modeling, force manipulability ellipsoid (FME) was applied to analyze the static flexibility of the AH end in arbitrary directions. Based on the synthetic static flexibility and average cutting force, cutter deflections were derived and estimated through developing program realization. The predicted results were compared with the experimental data obtained by machining 300 M steel curved surface workpiece, and a good agreement was shown, which indicated the effectiveness of the cutter deflection model. Additional experiments of machining flat workpiece were performed, and the relationship of cutter deflections and tool orientations were revealed directly. This work could be further employed to optimize tool orientations for suppressing the surface errors due to cutter deflections and achieving higher machining accuracy.

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