Hyperbolic error analysis and parametric optimization of a round body form tool

This paper analyzes the prime reason which causes hyperbolic error when a round body form tool processes a cone, and points out the drawbacks when error is discussed in current educational books and documents. A mathematical model of the hyperbolic error on the axial plane of the workpiece is set up, as a round body form tool processes a cone. Through optimization theory analysis and calculation, the results indicate that if the cone length and the coning of the workpiece are fixed, the main elements which affect the hyperbolic error in the axial plane of the workpiece are the outside diameter of the tool, the rake angle, and the rear angle at the base point. If these three parameters are interfixed rationally, the mismachining tolerance of the round body form tool can be minimized, and the machining precision of the workpiece can be improved under the conditions that neither the work capacity of the tool design nor the cost of manufacturing the tool increases.