The maths of curve of the list in numerical control process designing is handled

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Headline: ? Hill season fade and heart of Xiang of Bei of Xing of murder of  of inclined La of extensive bell be ignorant of casts  herd wearies fear of an ancient earthen utensil for steaming rise of  of inclined Chen of faithful another name for Guangdong Province of  U hut mothers model  casts  witch blows herd to weary ┝ of Gui of  of Qiu of ɑ of Lu of  of inclined La of  Pu  wearies   , below introduce these a few measure simply. (1) interpolation falls in a lot of circumstances, the outline appearance of product or workpiece often finds a specific mathematical expression very hard to come out their description, can get through experiment or mathematical computation the disperse with a series of not identical each other nods Xi only normally (X=0, 1, 2... ) the function that attend is worth F(xi) = Yi(i=0, 1, 2, ... N) , get a piece of Xi and the data with corresponding Yi are expressed namely. The function Y=f(x) that gives out this kind with data table form normally calls list function. Because accept the restriction of certain condition, the disperse that experimental observation gets nods the need that often cannot satisfy effective treatment, must insert the intermediate value of a few need again in what giving function table at this moment, what this says normally namely " interpolation " . The main train of thought of interpolation is to try to construct to list function F(x) first Y=p(x) of a simple function serves as approximate expression, calculate again next the approximation that the value of P(x) will come to get F(x) . A few kinds of common interpolation methods have Lagrange interpolation, Newton interpolation and batten interpolation to wait. (2) plan to close plan to close to also say to approach, in actual project, because experimental data often contains test error, afore-mentioned interpolation methods all ask earning curve is passed all model value drop, can make the curve is withholding everything to check an error instead, become especially when individual error is bigger, can make interpolation effect appears very not ideal. Accordingly, when solving real problem, can consider to abandon planning to add up to a curve to adopt this one requirement that handsome value orders, and use other method tectonic and approximate curve, ask it mirrors those who give place to give data to go as far as possible only situation can. As usual is used draft the least square method with one of methods, seek the sum of squares that will plan to add up to an error to reach the least value namely (best and approximate solution) will undertake planning to close approximately to the curve. The interpolation that mentions above, plan to add up to a process to wait, in the process designing job of CNC Machining, all be called commonly approach for the first time (or call first time maths the description) , because suffer numerical control machine tool to control functional limitation, approach obtains result to cannot be used at process designing directly commonly for the first time, and must obtain approach list curve linear or circular arc data, this plans to add up to a process to be called the 2nd times in process designing approach (or call maths the 2nd times to describe) . Plan commonly usedly to with the method circular arc batten plans to add up to list curve and batten of double circular arc to plan to add up to list curve at present two kinds of methods. (3) light is suitable it is to reduce in the fluid mobile (wait like plane, shipping, car) athletic obstruction, its outline appearance not only the requirement is done more streamline a few, and the requirement is beautiful, look comfortable pleasing to the eye, because this made the concept with suitable light. Visible, "Light is suitable " it is a concept on the project actually, because light is suitable the requirement is smooth, but do not wait for Yu Guangshun glossily, cannot go up with maths so " smooth " the concept is equal. The condition that arranges solely includes the requirement of two respects: It is smooth firstly, at least first-order derivative is successive; It is the curve goes secondly situation, its are concave and convex should accord with design purpose. But a large number of practice make clear, satisfy two afore-mentioned requirement only, still cannot achieve satisfactory result, reason still should raise the sufficient requirement that arranges solely, namely: Curvature size variation of the curve wants even. Glossy suitable issue is CAD and make (CAD/CAM) the special task that offer, also be very complex, the question with bigger difficulty. The smooth suitable method to curve and curved surface is very at present much, commonly used in CNC Machining practice is " law of local spring back " . CNC Milling