A New Method of Generating Complex Machined Surfaces.

The manufacture of complex contoured components, such as turbine blades, presents great difficulties for the production engineer, especially when these parts are required as single items or in small quantities. In this work the requirements for prototype turbine blades are examined and available methods of manufacture discussed. It is shown that most existing manufacturing techniques require a pattern or die that completely defines the shape of the required contour and that this prerequisite is not economically acceptable for small quantity batches. Two machining systems namely, numerically controlled machines and those using interpolating tracer control, which meet the small quantity specification, are discussed in detail and shown to have disadvantages with regard to cost and flexibility in operation. This work proposes a new method to provide a means of producing accurately machined parts having complex surfaces, with emphasis on low cost together with simple setting procedures. The complex contour is considered as the sum of a number of simple contours which may be defined by a single parameter. During the cutting operation these parameter values will either be constant or appear as a rate of change. Analogue signals describing these values are generated and the work and cutter movements guided by the sum of these signals. The generation of signals to provide for parameters such as taper or angular motion is relatively simple. However, the derivation of input data for the generation of section form requires far more sophisticated techniques and it is in this section of the work that completely new ideas are developed. The input methods investigated relate to devices utilising conformal mapping techniques, a powerful mathematical tool when working in two dimensions, which to the author's knowledge has not been considered in the field of machine tool control. The transformation from one plane represented by a regular figure, the input device, to a second plane which transforms to a predicted complex shape, the work/tool relationship, presents an ideal machine tool control situation. A particular transformation known as Zhukovsky's transformation is discussed in detail and used in the design of an input device. This transformation produces a family of aerofoil shaped curves, by applying a certain mapping technique to the flow about a circular cylinder