# The maths of round curve of Central Africa of numerical control process designing is handled

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The curve that be not a circle includes to divide a circle beyond all sorts of what can describe with equation is conic 2 curves (be like: Parabola, elliptical, hyperbola) , the flat curve of corkscrewed yarn of Archimedes spiral, logarithm and description of place of all sorts of parameter equation, polar coordinates equation and list curve are waited a moment. CNC Milling is being machined afore-mentioned when all sorts of curvilinear plane outline, cannot undertake process designing directly commonly, and after must be being handled through maths, with linear the method that one circular arc approachs will come true. But this one job is compared commonly complex, rely on manual processing sometimes already unlikely, must computer of have the aid of makes auxiliary processing, had better be to use the computer advanced language comes automatic process designing work out machine program. The plane that processing describes with mathematical equation is not graph of round curve outline, often use mutual connective spring line is approached and circular arc approachs a method, will undertake introductory respectively below. (1) spring line approachs a way generally speaking, because the interpolation node of spring line law all is on curvilinear outline, easy computation, cheng is made up a few handier also, so law of line of commonly used spring approachs the curve that be not a circle, its defect is interpolation error bigger, but should handle proper OK still and contented treatment to need only, the key depends on interpolation end length spending reach interpolation error to control. Because the curvature of each bits on all sorts of curves is different, if want to make each interpolation end length spends homogeneous phase to wait, criterion the error measurement of each paragraphs of interpolation is different. Conversely, if want to make error of each paragraphs of interpolation identical, criterion each interpolation end length is spent differ. Two kinds of commonly used processing techniques are below. 1) wait for interpolation paragraph the interpolation such as the law paragraph the law is to make every interpolation end length is spent equal, consequently interpolation error fills etc. The error of the biggest interpolation that must make arise when process designing is less than the 1/2 ～ 1/3 with poor allow, in order to satisfy treatment precision requirement. Assume the biggest error produces the curvature radius in the curve commonly the smallest part, calculate along normal direction of the curve, see plan institute is shown. Although this one hypothesis is not quite strict, but CNC Machining practice makes clear, it is applicable to most circumstance. The interpolation error law such as the interpolation error law such as 2) is the error that makes each interpolation is broken equal, be less than or be equal to permission interpolation error, the method that end length of this kind of affirmatory interpolation spends is called " wait for interpolation error law " . Apparent, by this law affirmatory each interpolation end length is spent differ, because this cries again " change the pace grows a way " . The advantage of this kind of method is interpolation paragraph amount comparing is afore-mentioned " wait for interpolation paragraph law " little. This to a few large with appearance part of complex the curve that be not a circle has greater sense. Bigger to curvature change curve, the division check the number that gets with this law is least, but computation is a bit numerous. (The circular arc that 2) circular arc approachs law curve is approached have the method such as curvature round law, round at 3 o'clock law and tangent circle law. Round at 3 o'clock law is to pass 3 foregone node to beg a circle, serve as a round block. Tangent circle law is to pass 4 foregone node to make two tangent circles respectively, pose a block of two circular arc. These two kinds of methods must be used first approach a method to beg each node point-blank, beg each circle again, computation is trivaller. A few kinds when tell about above in approaching computation, just calculated of curvilinear outline approach line segment or approach circular arc paragraph, the each node coordinate of the center of cutting tool of mathematical method computation that still needs to apply equidistant line or equidistant circle, regard process designing as data. CNC Milling

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