Improvement of FFD parametric approach in the application of a lifting body

Abstract

FFD (free-form deformation method) is one of the most commonly used parameterisation methods at present. It places the parameterised objects inside the control volume through coordinate system transformation, and controls the control volume through control points, thus realising the deformation control of its internal objects. Firstly, this paper systematically analyses and compares the characteristics and technical requirements of Bernstein, B-spline and NURBS (non-uniform rational b-splines) basic functions that can be adopted by FFD, and uses the minimum number of control points required to achieve the specified control effect threshold to express the control capability. Aiming at the problem of discontinuity at the right end in the actual calculation of B-spline basis function, a method of adding a small epsilon is proposed to solve it. Then, three basic functions are applied to the FFD parameterisation method, respectively, and the differences are compared from two aspects of the accurate expression of the model and the ability of deformation control. It is found that the BFFD (b-spline free-form deformation) approach owns better comprehensive performance when the control points are distributed correctly. In this paper, the BFFD method is improved, and a p-BFFD (reverse solution points based BFFD) method based on inverse solution is proposed to realise the free distribution of control points under the specified topology. Further, for the lifting body configuration, the control points of the p-BFFD method are brought closer to the airframe forming the EDGE-p-BFFD (edge constraints based p-BFFD) method. For the case in this paper, the proposed EDGE-p-BFFD method not only has fairly high parameterisation accuracy, but also reduces the expression error from 1.01E-3 to 1.25E-4, which is nearly ten times. It can also achieve effective lifting body guideline constraints, and has the ability of local deformation adapting to the configuration characteristics. In terms of the proportion of effective control points, the EDGE-p-BFFD method increases the proportion of effective control points from 36.7% to 50%, and the more control points, the more obvious the proportion increase effect. The new method also has better effect on the continuity of geometric deformation. At the same time, this paper introduces the independent deformation method of the upper and lower surfaces based on the double control body frames, which effectively avoids the deformation coupling problem of the simultaneous change of the upper and lower surfaces caused by the movement of control points in the traditional single control framework.