Research On The Offset Theory Of Curve/Surface And Its Application In The Intelligent Design Of Die And Mould

The design and manufacture of mold is a very important part in the intelligent manufacturing.In the intellectualization process of mould design and manufacture,there are many technical problems to be further studied,such as parting surface design of injection mould,the design and automatic connection of cooling system,the design of trimming die insert of automobile panels,the intelligent design and processing of electrode,the automatic compensation of electrode translation and so on.Among them,there are a lot of complex geometric processing problems that need to be integrated with domain knowledge.The common geometric problems include: the equidistant/non-equidistant offset of curves and surfaces;automatic handling of the exceptions in offset results;the generation of fairing curve(including the fairing of offset results and the generation of fairing curves with constraints).At present,there is no effective and unified solution for these problems,and most of them rely on the repeated adjustment and modification by engineers,which is not only time-consuming,but also makes it difficult to guarantee the accuracy and smoothness of the design results.In this paper,the offset of complex curves and surfaces are studied,including the direct offset of curves and surfaces,exception handling and fairing of offset results.(1)A curve/surface offset algorithm based on the theory of Progressive Iteration Approximation is proposed.By automatically adjusting the position and number of control points,the accuracy of the offset curve and surface is gradually improved.The offset algorithm calculates fast,and the number of control points for the offset curve and surface generated with the same precision is small relatively.Moreover,the algorithm has a unified processing process for all kinds of offset directions and equidistant/non-equidistant curves and surfaces.(2)An algorithm based on the generation of spherical curve is proposed to solve the cracking of offset curves.The algorithm firstly calculates the Bezier curve with the minimal spherical distance,and then obtains the spherical curve by non-equidistant offset to connect the offset curves smoothly.A curve reconstruction algorithm based on the minimal energy theory and multi-objective optimization is proposed to solve the self-intersection and overlapping of offset curves.(3)The fairing problems in the intelligent design of mould are divided into oneway and two-way fairing problems.For the one-way fairing problem,the unsmooth part is detected and eliminated by the offsetting the offset curve again,and then a smooth segment is used to reconnect the offset curves.In order to solve the two-way fairing problem,a smoothing model based on the minimum energy theory and the point modification method is established,and a solving algorithm based on the analysis of the parameter sensitivity is proposed to fair offset curves automaticlly.(4)A constrained-fairing curve generation method is proposed.This method is used to generate the fairing curve with constraints in the engineering,and it can simultaneously satisfy specified endpoints,specified tangent vectors,specified length,specified minimal bending radius,and specified points to pass through.The method is computationally fast,and the generated curve is smooth and natural.By applying the offset and fairing technology of curve/surface into the intelligent design and manufacture of mould,and integrating the knowledge of corresponding fields,the solutions to the difficult geometric problems such as the design of trimming die for automobile panel,the design of injection mould parting surface,the design of cooling channels and electrode,are put forward.The proposed solutions are: the automatic trimming die inserts design for automobile panel based on 3D curve offset,the automatic design of injection mould parting surface based on 3D curve offset,the automatic design of cooling channels based on curve/surface offset and fairing technology,the intelligent design of electrode based on plane curve offset and automatic design of electrode translational compensation surface based on the non-equidistance offset of surface.These solutions have been applied into engineering,and they verify the feasibility and practicability of the curve/surface offset technology proposed in this paper.