In CNC machining, machining errors are usually caused by some of the sources such as cutting tool deflection, cutting tool wear, machine tool vibration, improper coolant/lubrication, and negative thermal effect. To increase product accuracy, much research has been carried out on the prediction of machining errors. However, in milling of sculptured surface parts, due to their curved shapes, the geometries of cutting tools do not match the parts’ surfaces well if the tools cut along the tool paths on the surfaces in a point-to-point way. As a consequence, machining error is inevitable, even if there is no other source of error in ideal machining conditions. To predict machining errors caused by this tool-surface mismatch, several methods have been proposed. Some of them are simple, and some represent the geometry of machined surfaces using cutter-swept surfaces. But none of these methods is accurate and practical. In this research work, a generic, geometric approach to predicting machining errors caused by the tool-surface mismatch is proposed for 3-axis sculptured surface milling. First, a new geometric model of the furrow formed by an APT tool moving between two neighboring cutter contact (CC) points is built. Second, the mathematical formula of cutting circle envelopes is derived. Then an algorithm for calculating machining errors in each tool motion is provided. Finally, this new approach is applied to two practical parts for the accurate machining-error predictions, and these predictions are then compared to the inaccurate predictions made by two established methods to demonstrate the advantages of this approach. This approach can be used in tool path planning for high precision machining of sculptured surface parts.

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