Research On Tool-Path Planning With Surrogate Model Method For Flank Milling Of The Ruled Surface

The processing method of ruled surface flank milling has more advantages when compared with the point milling processing method,consequently,it has become the main processing method of the ruled surface in recent years.Under the condition that the precision of five-axis numerical control machining of ruled surface has been a tough problem for many years,and built on the analysis of the present situation of the cutter location optimization of flank milling at home and abroad,the method based on the surrogate model is proposed.In addition,the research of the cutter location planning for the flank milling of ruled surface is discussed as well.This paper takes the rotary cutter as the main research object to explore a universal cutter location planning method,and finally the method is verified through the living examples.Aiming at the problem of complex tool axis trajectory planning for flank milling non-developable ruled surface with rotary cutters,an intuitive and simplified tool axis trajectory generation method was proposed.Starting from the overall objectives of using tool envelope surface to approximate to design surface,based on the envelope principle and geometric properties of rotary surface,the measure indices of length deviation and angular deviation were defined,so that the optimal approximation of tool envelope surface to design surface was converted into the multi-objective programming problem that the minimum sums of squares of both length deviation and angular deviation are satisfied synchronously at every tool position.Three rotational parameters and three translational parameters were used to identify the tool position and orientation,and the experiment design method based on Latin hypercube matrix was introduced.According to the updating strategy for the gradual subdivision of independent variable domain,the interpolated samples were generated,and adopting the surrogate model method of radial basis function,the specific functional relationship between objective function and parameters of position and orientation was established in the determination conditions of optimal single tool position.Besides,the optimal position and orientation parameters of single tool position were obtained by extremum method of multivariate function.Based on this,the optimized tool axis trajectory surface was further obtained.The actual example calculation showed that with this method the envelope error was reduced significantly,thus provided the theoretical basis for flank milling of non-developable ruled surface.Based on the response surface method,another cutter location optimization method of ruled surface flank milling is proposed.By using the normal benchmark radial emitted from the design surface of the ruled surface,the cutter envelope surface is described as the associated surface of the design surface,and the envelope error is represented by the minimum benchmark value intercepted by continuous cutter location.Moreover,the equivalence of the minimal benchmark value condition and the envelope condition are proved,for an instantaneous cutter location,the normal benchmark which is through the cutter shaft on the design surface is defined as the characteristic benchmark,and on this basis,the criteria for optimal pose of single cutter location is proposed:the quadratic sum of each characteristic benchmark length is the minimum.Apart from this,the experimental design method and stepwise compression tactic of cutter shaft pose space based on the face centered combination is put forward,furthermore using the response surface method to establish the explicit function relation between optimized objective function and pose parameters and then obtain the optimal pose parameter.The calculation results of examples have shown that,for the cutter location planning problem,the fitting precision of the established response surface model is high and the predicted results are accurate,besides the model can significantly reduce the cutter envelope error.It has also proved the rationality and validity of cutter location optimality criteria and the method of modelling and optimization based on the response surface.