# Interpolation of digital integration method

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A shown function integral expresses, from the point of differential geometry concept, from hour when the 0 areas that beg place of function Y=f(t) curve to surround to hour T, usable integral is formulary: (1) the finite interval that if differentiate the time of 0~t,is Δ T into time-interval, when Δ T enough hour, can get similar formula: (2) the value of the F(t) when the Yi-1 in type is T=ti-1, this formula explains: What integral can use number is cumulative will be replaced approximately, its geometry meaning uses the sum of a series of small rectangular area to represent the area below function F(t) approximately namely, if be when digital operation, it is main unit with T extraction Δ " 1 " , criterion (2) type can simplify for: (3) if T of main unit Δ is installed enoughly small, can satisfy the precision that we need so. Popularly, every coordinate direction needs register of a function that be accumulated and an accumulator, its working process can use a figure 4.

2 express: In order to of register of the function that be accumulated deposits coordinate to be worth F(t) , accumulator also says remainder register is used at depositing the cumulative cost of coordinate. Every time Δ T appears, the F(t) in register of the function that be accumulated is worth with the numeric addition in accumulator, deposit cumulative result in accumulator, if the capacity of accumulator is an unit area, the size of the capacity of register of the function that be accumulated and accumulator is same, have in accumulator of area of every unit in cumulative process so spill over, when cumulative number reachs the capacity of accumulator, what produce spill over the gross area that gross asks namely, namely integral value. We know, digital integrator spills over the frequency of pulse and register of the function that be accumulated put number mediumly to spill over namely base the value becomes direct ratio, also want to complete the cumulative operation of same number with respect to every block, machining the time that every block place uses journey length no matter so is changeless. Accordingly, the feed speed of each block is abhorrent, affected the exterior quality of treatment so, especially the block productivity with short distance is low, to overcome this one weakness, make spill over pulse is even, spill over rate rises, use normally left move normalization processing. Alleged " left move normalization " it is to become when numerical value of the case that be accumulated is lesser, have I like register of the function that be accumulated before zero hour, be like direct iteration, need 2i second iteration at least so, ability output spills over pulse, cause output pulse rate to drop, because this is in actual digital integrator, in needing a register of the function that be accumulated before 0 move go be opposite namely be accumulated function comes true " left move normalization " processing. The course is different move after normalization is handled, integrator every are cumulative spill over twice once surely, because this rose not only,spill over speed still makes spill over pulse becomes evener. System of current CNC numerical control uses software to realize digital integral interpolation commonly [27] , what can cast hardware number integral completely so is left move the concept of normalization and the idea that generate feed pulse as a result of carry. Because be in software number integral, we are OK very install conveniently base value, after the addition operation that completes numerical value of the case that be accumulated and cumulative cost, cumulative result and base the value undertakes comparative, through dictating judgement is on direction of which reference axis quite pulse is outputted. CNC Milling