CAD/CAM of Sculptured Surfaces on a Multi-Axis NC Machine: by Stephen Radzevich

By Stephen Radzevich

Many items are designed with aesthetic sculptured surfaces to augment their visual appeal, a tremendous consider purchaser pride, particularly for automobile and client electronics items. In different instances, items have sculptured surfaces to satisfy useful requisites. useful surfaces have interaction with the surroundings or with different surfaces. due to this, practical surfaces is additionally known as dynamic surfaces. sensible surfaces don't own the valuables to slip over itself, which explanations major complexity in machining of sculptured surfaces. the applying of multiaxis numerically managed (NC) machines is the one manner for a good machining of sculptured surfaces. relief of machining time is a serious factor whilst machining sculptured surfaces on multiaxis NC machines. to minimize the machining rate of a sculptured floor, the machining time needs to be as brief as attainable. desk of Contents: advent / Analytical illustration of Scupltured Surfaces / Kinematics of Sculptured-Surface Machining / Analytical Description of the Geometry of touch of the Sculptured floor and of the producing floor of the Form-Cutting device / Form-Cutting instruments of optimum layout / stipulations of right Sculptured-Surface iteration / envisioned Accuracy of the Machined Sculptured floor / optimum Sculptured-Surface Machining

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Extra info for CAD/CAM of Sculptured Surfaces on a Multi-Axis NC Machine: The DG/K-based Approach (Synthesis Lectures on Engineering)

Example text

Orientation motions of the first kind are represented by the only singular orientation motion {wn}. Orientation motions of the second kind are represented by six relative motions, of which the most general one is {wu, Vv, wn, wv, Vu}. Other orientation motions can be considered as particular orientation motions of the combined orientation motion {wu, Vv, wn, wv, Vu}. Elementary motions that comprise a combined orientation motion of the cutting tool are timed (synchronized) with one another. The rotational elementary motion wu about the xP axis is timed with the translational motion Vv along the yP axis.

The solution to the problem of synthesizing the optimal kinematics of generation of a sculptured surface on multiaxis NC machine can be drawn up from the analysis of the kinematics of multiparametric motion of the cutting tool relative to the work. 3 Coordinate System Transformations: Their Impact on Fundamental Forms of the Surfaces While moving, the surfaces P and T occupy various positions that are different from those in which the surfaces initially were described analytically. For the purpose of the analytical representation of the moving sculptured surface and of the moving generating surface of the cutting tool, appropriate operators of the coordinate system transformations are used.

35) and (36) in the form [ dU P* dV P* 0 0 ] T = Rs (1 → 2) · [ dU P dV P 0 0 ] T .  (42) and (43) represent the quadratic forms with respect to dUP and dVP. P fundamental forms initially represented in the coordinate system X1Y1Z1. P , should be premultiplied by Rs(1®2), and after that, postmultiplied by RsT(1®2).  (44) and (45) significantly simplifies formulae transformations.  (44) and (45) are valid for the generating surface T of the cutting tool. • • • • 29 chapter 4 Analytical Description of the Geometry of Contact of the Sculptured Surface and of the Generating Surface of the Form-Cutting Tool Priority of the sculptured surface to be machined over the rest of the elements of the machining process is the cornerstone of the DG/K-based method of surface generation.

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