Smoothing method of generating flank milling tool paths for five-axis flat-end machining considering constraints
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ORIGINAL ARTICLE
Smoothing method of generating flank milling tool paths for five-axis flat-end machining considering constraints Yao-An Lu 1 & Cheng-Yong Wang 1 Received: 4 October 2019 / Accepted: 5 August 2020 / Published online: 21 September 2020 # Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Gouging and collision avoidances, tool path smoothness, and geometric deviation should be considered concurrently when generating a five-axis flank milling tool path. The tool orientations of the generated tool path, which can achieve smooth rotary axis motions of the machine tool, can improve the machining quality. Tool orientation planning for five-axis ball-end machining does not affect the position of the ball center point. However, different from ball-end cutters, tool orientation adjustments for flatend machining will affect the cutter reference point position, which may cause local gouging between the bottom circular edge of the flat-end cutter and the constraint surfaces of the workpiece or excess uncut material left. Hence, generating a smooth flank milling tool path for five-axis flat-end machining which meets all the requirements is a challenge. To deal with this problem, a method of smoothness flank milling tool path generation for flat-end cutters considering constraints is developed in this research, which can minimize the angular accelerations of the rotary axes. B-spline curves are used to represent the displacements of the rotary axes so that the rotary axes’ motions along the tool path can be directly smoothed. The sum of the squares of the first, second, and third derivatives of the cutter reference point trajectory and the two rotary axes’ displacement curves are then utilized as the smoothness indicators for the five-axis tool paths. The method of tool orientation and positioning adjustments for flat-end cutters based on the differential rigid body motion is also presented, ensuring the bottom circular edge of a flat-end cutter is tangent to the constraint surfaces of the workpiece along the tool path. Besides, the discrete vector model is utilized to represent the workpiece geometry, and intersection points between the discrete vectors and the tool swept envelope are calculated to determine the geometric deviation for a flank milling tool path. Finally, a multi-objective optimization problem with constraints is established to generate flank milling paths with flat-end cutters. Numerical examples and machining tests are carried out to confirm the validity and effectiveness of the proposed approach. Keywords Flank milling, Flat-end cutter, Smooth tool path, Constraints
1 Introduction Five-axis milling is widely applied to manufacture sculptured surface parts in industries like automotive, aerospace, and die/ mold. Flat-end cutters can improve machining efficiency and profile accuracy compared with ball-end cutters in five-axis sculptured surface milling [1,2]. Therefore, flat-end cutters are widely employed in five-axis numerical control (NC) milling. Five-axis milling can be clas
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