Primitive Curve Modeling Method of Compressor Blade Suction Surface Based on Second-order Ordinary Differential Equation

Abstract

The invention provides a compressor blade suction surface primitive curve modeling method based on a second order ordinary differential equation, and the method comprises the steps of pre-treating compressor blade primitive curve data; and selecting a second order ordinary coefficient linear non-homogeneous ordinary differential system for fitting to obtain an expression of a primitive curve. According to the boundary condition requirement, a second-order curve problem coinciding with the first and last points of the given data is transformed into a two-point boundary value problem; an Implicit Euler method is selected for solving an intermediate point of a primitive curve. In this way, the primitive curve is reconstructed. According to the invention, the problem that a first order system can't guarantee interpolation conditions at the first and last points at the same time is solved; a larger optimization operation space is obtained; and sensitive degree to a parameter matrix is reduced. Interpolation in the first and last points of data scatter is accurate, which has a great advantage in connecting data scatter that is fitted in sheets or segments; and the shape of a compressor blade can be restored in high precision.

Description

technical field [0001] The invention belongs to the field of computer-aided geometric design, relates to ordinary differential equations, numerical calculation, curve and surface modeling, etc., and is a modeling method using a new expression form in modeling design. Background technique [0002] Manufacturing is the foundation of the national economy and plays a vital role in the country's economic development. High-efficiency and high-precision CNC machining of complex curved surface workpieces has become an urgent demand for national strategic equipment and high-tech industries and a commanding height of manufacturing technology. [0003] At present, the main means of generating parametric curves and surfaces by computational geometry methods are: Bezier method, NURBS method, etc. The Bezier method requires harsh conditions for interpolation and smooth splicing, while the NURBS method is computationally complex. If the weight factor is not selected properly, it will lead...

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Problems solved by technology

[0006] The method of using the first-order ordinary differential equation can better obtain the expression form of the blade primitive curve that meets the above requirements, but because the ordinary differential equation can only satisfy one initial condition and is rigid, even if the expression with a good shape is very close to the original surface, It is also extremely sensitive to errors and parameters, and the end points of the primitive curves expressed by the first-order system on the suction surface and pressure surface of the blade cannot coincide, and can only be approached within a certain error range. If it is used for optimization, once a little Adjust the parameters of the coefficient matrix, the curve may change greatly and cannot be controlled, thus losing the meaning of optimization and can only be used for modeling

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