C2 Continuous Blending of Time-Dependent Parametric Surfaces

Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

CNC Machining of Propeller to Better than Class Tolerances

Producing class S propellers and water jet impellers presents serious challenges for propeller manufacturers. To overcome these challenges and consistently manufacture propellers with superior quality, an integrated approach was adopted when developing and implementing a process for Computer Numerically Controlled (CNC) machining of propeller surfaces. Highlights of this process are: (1) CNC machining of all blade surfaces; extreme surface blending, (2) CNC machining to final form & finish without hand grinding and (3) high precision, better than class S. This paper will describe various challenges encountered in the production of CP propeller blades and how these challenges were overcome in order to produce accurate CP propeller blades which exceed class S tolerances.

Reconstruction of Composite Surface Based on CMM Point Data

In this paper, a novel surface reconstruction method is presented to creat a composite surface with point data on surface obtained by CMM. In this method, the 3th non-uniform B-spline algorithm is proposed to reconstruct every single free-form surface on the whole composite surface, and the algorithm for surface blending is proposed to merge every single surface together to achieve the level of G1 continuity. Furthermore, in order to check and visualize the reconstruction model, a special closed-loop RE system is developd by VC++ to constantly guide to measure and reconstruct untill the model fits in with requirements. Examples are included to illustrate the approach.