Numerical control nap becomes the interpolation of approximate double circular arc of molding sand annulus

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Summary: Use a kind of new curve processing technique -- interpolation of approximate double circular arc is right of groove of grinding circumgyrate curved surface shape sectional march Xian Guangshun handles emery wheel, simplified computational process, solved nap of emery wheel of numerical control of 3 axes linkage implement the design problem of program of aftertreatment numerical control. 1 foreword is in the course of study that make jar, the tool that seal coal tub -- the service life that the production quality of heal annulus decides its oneself not only, and the sealing of brim of mouth of the canister after affecting heal, affect food to last then ability. Accordingly, heal annulus coils the design that seals groove and treatment are very serious. To groove of face of circumgyrate of this kind of curve, ask figure is exact already, be out of shape in order to reduce obstruction, requirement surface is slick at the same time, in order to reduce attrition resistance. Use shape grinding treatment shapes this kind groove is a kind of effective technique, but the nap issue that needs to solve molding sand annulus. Collect appliance to have function of 3 axes linkage (two mobile axes and an axis of rotation) nap of numerical control emery wheel implement nap becomes molding sand annulus, the law that can make nap tool aims curve of emery wheel outline from beginning to end to, assure the appearance precision of molding sand annulus. But, software of automatic process designing does not have existing numerical control commonly the function of the order of numerical control of 3 axes linkage that handles two mobile axes to add one axis of rotation, because this needs to study method of curvilinear data processing, design program of appropriative aftertreatment numerical control. When undertaking numerical control process designing, the light that needs to solve curve of outline of molding sand annulus above all arranges processing issue. The appearance of groove of curvilinear circumgyrate face often is stated with list curve, the smooth processing technique of list curve often uses circular arc law and law of double circular arc to wait. This kind of method uses a group of tangent circular arc to describe a curve, make the curve is achieved overall and first-order smooth. When using circular arc law and law of double circular arc to undertake smooth processing, differentiate and beg take tangent circular arc to need to apply the maths with a series of complex calculation to plan to add up to equation, the requirement with curvilinear changeful appearance is satisfied hard when applying actually. For this, the article offers a kind of calculation the interpolation of approximate double circular arc that can tall, contented effective treatment needs concise, dependability. Use this method the design that achievable computer assists process designing program, after inputting list curve to count foothold coordinate each, can output grinding automatically to machine program of used numerical control code. Fundamental of interpolation of 2 approximate double circular arc is shown 1 times like the graph, before 4 data that take out list curve are nodded (1, 2, 3, 4) , take among them photograph adjacent at 3 o'clock (1, 2, 3 and 2, 3, 4) makes circular arc respectively (the centre of a circle is O1) and circular arc (the centre of a circle is O2) , beg give bit of 2 point law of two circular arc to (pass the corner A between O1 and O2) respectively, whether the value is more than according to A allow to be worth a decision whether interpolation, if corner A is too big, undertake interpolation, increase several fortified point. Operation move is as follows: If afore-mentioned making,circular arc is mixed, beg a corner A. If A ≤ Dq allows, criterion 1, two 2 curve (the circular arc that the centre of a circle is O1) contented already and smooth requirement, can output by this curve 1, two 2 CNC Machining code; Next in order to nod 2 for the a bitth take 4 several fortified point afresh (namely 2, 3, 4, 5) , begin move afresh (1) . If A >Dq allows, enter measure (3) . Beg go out and cut of two circular arc 2, the line segment midpoint of earning of 3 perpendicular at 2 o'clock bisector 3, as gain numeric point newly. Graph 1 make and two paragraphs of circular arc, beg give bit of 2 point law of two circular arc to (the corner A between the O4) of the centre of a circle of the O3 of the centre of a circle that passes circular arc respectively and circular arc, surely A<A(sees graph 1) . If A ≤ Dq allows, criterion 1, two 2 curve (the circular arc that the centre of a circle is O3) contented already and smooth requirement, can output by this curve 1, two 2 CNC Machining code; Take next 2, 3, 3, 4 4 several foothold begin move afresh (1) . If A>Dq allows, criterion with 1, 2, 3, 3 began move afresh at 4 o'clock (3) . Dq allows to be the deflexion point of view that nap tool allows in be machined actually, dq allows to take a cost smaller, the appearance precision that becomes molding sand annulus is taller. Classified discussion is in actual processing process, be opposite respectively dot 1, 2, 3 with the dot 2, 3, 4 beg circular arc equation or linear equation (be more than some set when circular arc radius when the value, can regard its linear) , the curve that makes 3 kinds of kinds possibly on the space concerns. When undertaking to different type curve light arranges processing, its interpolation and corner processing technique are endless also and same, show cent to narrate as follows: Type 1: The 1st, 2, mixed at 3 o'clock the 2nd, 3, formed respectively at 4 o'clock linear. Right now at 4 o'clock in all line, namely A=0, satisfy the smooth requirement that A ≤ Dq allows, do not need to have interpolation operation, can output corresponding 1, the CNC Machining code between 2 o'clock, undertake next next suddenly operation. Type 2: Intersect with one circular arc point-blank, if pursue,2 are shown. Right now, it is with the coordinate of node of circular arc photograph point-blank (X2, y2) and (X3, y3) , coordinate of the centre of a circle is (X0, y0) , radius is R, cross the centre of a circle to make circular arc bisector hand in circular arc at the dot (X2, y2) is perpendicular deuce bowstring at the dot (X23, y23) , each bits of coordinate all can be begged, because this has | CosA | = | CosA | =[(x0-x23)2+(y0-y23)2]½ 　 R(1) pursues 2 if | CosA | ≥ CosDq allows, namely | A | ≤ Dq allows, already satisfied smooth requirement, do not need the operation that undertakes interpolation is nodded, can be in output 1, undertake after the CNC Machining code between 2 o'clock next suddenly operation. If | CosA | <cosDq allows, namely | A | > Dq allows, do not satisfy smooth requirement, must have interpolation operation, insert bit of coordinate to be [(X23 + X2)/2, (Y23 + Y2)/2] . Type 3: Two circular arc intersect, if pursue,3 are shown. Be the same as in two circular arc to intersect (3a) seeing a picture and two circular arc are converse intersect (two kinds of circumstances issue 3b) seeing a picture, the coordinate of node of circular arc photograph all is (X2, y2) and (X3, y3) , coordinate of the centre of a circle all is respectively (X01, y01) and (X02, y02) , corresponding radius all is R1 and R2 respectively, cross the centre of a circle to make circular arc bisector hand in circular arc at the dot (X2, y2) and (X3, y3) is perpendicular deuce bowstring at the dot (X23, y23) , each bits of coordinate all can be begged, according to Yu Xian theorem all can be gotten | CosA | = | (X2-x01)(x2-x02)+(y2-y01)(y2-y02) | R1 R2(2) 　 (A)(b) pursues 3 if | CosA | ≥ CosDq allows, namely | A | ≤ Dq allows, satisfy smooth requirement, do not need to have interpolation operation, can be in output is corresponding 1, undertake after the CNC Machining code between 2 o'clock next suddenly operation. If | CosA | <CosDq allows, namely | A | > Dq allows, do not satisfy smooth requirement, must have interpolation operation, insert bit of coordinate to be [(X2 + X3)/2, (Y2 + Y3)/2] . Graph the program block diagram of interpolation of 4 approximate double circular arc is shown 4 times like the graph. 3 epilogues undertake a Xian Guangshun handle as a result of interpolation of approximate double circular arc according to circular arc corner, imitate nap of the emery wheel in process of nap of actual emery wheel implement when roll smooth and smooth transfer process, undertake smoothly because of what this can assure process of emery wheel nap, can obtain good emery wheel to grind bead cutting blade, but demand of better contented and actual production. CNC Milling