XII International PhD Workshop OWD 2010, October Determination Of Cylindrical Shape Parts With Solid Processing In Automatic Mode

Transcription

1 XII International PhD Workshop OWD October 00 Determination Of Clindrical Shape Parts With Solid Processing In Automatic Mode Tmchik G.S. Diorditsa I.M. Sktsuk V.I. Vsloukh S.P. Diorditsa A.M. National Technical Universit of Ukraine Kiev Poltechnic Institute Abstract The article is devoted to problems associated with geometric precision production clindrical parts on lathes with sstems of CNC. The possibilit of a high view of clindrical shapes using a comple adaptive sstem working process.. Basics In modern metal processing there are man problems associated with the manufacture of parts for which it is important not so much to get high accurac as the sie of perfect geometries. This problem sometimes does not allow to get the details of precision geometr seemingl technical in those processes where it should be achieved without much effort. This problem is an older bug of disconnected sstem MATD (machine - accessories - tools - detail) that causes a lot of complications. The nature of these complications is more mathematical problems than technical associated with direct binding into one sstem MATD order to get a closed technological circle. Most of these problems are solved directl it is the application of interim results measurement control devices that automaticall shifted to the processing tool. rom here is actualit of problem and proper raising of task and decision. The offered problem requires the net raising of task and was of its decision: - determination of mathematical apparatus is in relation to a task from the receipt of veritable form of treatment of the object; - consideration of situations which arise up in the process of measuring as on idealiing situations so with the gradual passing to the real; - determination of kinematics of optimum motion from point of balance between measuring time and minimum necessar information enough for the decision of problems correction of detail form; - a mathematical apparatus of correction form of detail is in order to receive geometricall regular shapes; - apparatus providing of construction technological process measuring of form and its correction. The article is third on offered issue in relation to lathe treatment and that is wh in it the problem phenomena will be eamined related to determination of the generalied form of detail. In a general plan theoretical subsoil was stopped up in process []. Partiall the problems were eamined in relation to milling treatment in process [] where the form of detail was eamined b a milling cutter. This problem was also partl considered in the previous articles. So in the article [3] was researched the possibilit of determination of the form of clindrical bod in the planes X and Y. In the article [4] was researched the possible methods of determination of longitudinal geometr of clinder details with foot-pace motion of instrument. or valuable consideration of the task it is necessar to consider the followings factors of influence on end-point result of measuring: to properties of surface as object of research with the purpose of determination of parameters with the most informing; motion of instrument with measuring in a spiral method; the information which possibilit to get at such method of instrument motion.. Research properties of detail surface We are considered the properties of surface in combination with the properties of curves that located on this surface to find out problems which arise up at research of it. According to metrical properties of surface (рic.) the first quadratic form turns out as follows. If a surface is set in a vectorial form in this case it will be: rr(u v) and accordingl u u(t) v v(t) r r(t) r(u(t)v(t)) shows b itself a curve on the surface. Then fair dependence: 6

2 dr du dv r u + r v. () dt dt dt The differential of length of arc concordantl: t s ds де t 0 ds ( & ( t)) + ( & ( t)) + ( & ( t)) dt will look like: ds (dr) Edu +dudv+gdv () where r E r G + + r r + +. In case if a surface is set as (у) then: E + G +. + Z + б (3) between points which answer the value of parameter of t 0 and t will be: t t s ds t t du E dt + du dt dv dt +. (4) dv G dt dt We can define the corner between two curves on the surface if r r(u (t)v (t)) and r r(u (t)v (t)) are two curves on the surface r r(uv) which intersect in the point of A. rom here the corner of crossing α (corner between positive directions of tangent in a point A) calculated on a formula: cosα E u& u& + ( u& ) + G Eu& + u& + G Eu& + u& + G (5) where u& and u& - accordingl the first derivative from u (t) and u (t) at the value of parameter which answers to the point A and others like that. If to take advantage of the second quadratic form of surface: -dndr Ldu + Mdudv + Ndv (6) that gives possibilit to define properties of curvature of the surface then for the second quadratic form of surface will be correct the following equaliations: L where l N n M m (7) а α A C B ρ в Y X Pic.. Curves are located on the surface: a - is a curve of longitudinal cut in the plane ZOX; б - is a curve of transversal cut in the plane ZOY; в is a curve ВАС for the trajectories of instrument motion; α - corner between planes of the cut. The first quadratic form determines all of the metrical properties of surface. Length of arc ВАС curve if it is set as r r(u(t)v(t)) on the surface 7

3 l n m du du (8). or main curvature in the fied point of surface A it is alwas possible to choose the same carthesian sstem of coordinates Х Y Z for which beginning of coordinates belongs A and the plane ХОY coincides with a tangent plane which passes through А. In this sstem of coordinates a surface (within the limits of point А) can be presented as х х(у) where dependence is eecuted: х(00) х(00) ( 00) 0 х. (9) The proper trihedron which accompanies surface in a point A will be consists of three unit vectors e e N e e which are directed near coordinate aes. Equation b the formula of Telor within the limits of point A will look like: (00) (00) õ + + (0) (00) If to take advantage of turn of the carthesian sstem of coordinates around to the ais Х it is possible to have: ( k + k ) +... () where sies k k is main curvatures of surface and 8 R R () k k it is the main radiuses of curvature. Sie K k k (3) it is Gaus curvature where H ( k + k ) (4) it is middle curvature in a point A.. In the appointed sstem of coordinates where a surface can be imaginable in a kind (8) the quadratic forms in a point A have the simplified kind: (dr) d +d - dndrk d +k d (5). or the arbitrar sstem of coordinates on surfaces we have equalities: LN M LG M EN K H (6) ( ) where main curvatures k k is a root of quadratic equation k -Hk+K0. Substantial advantage of this use in differential form consists in that we know these sies in the sstem of coordinates and know their conduct at transformation. And so it is possible to get epression of these sies in the arbitrar sstem of coordinates. or main curvature at the change of orientation we can change onl a sign so К in transition to the arbitrar sstem does not change. To find epression for К in the arbitrar sstem it is necessar onl to build skalar that in the certain sstem of coordinates coincides with k and k. So like that we got the skalar. Classification of points of surface (formula ()) allows to define the tpe of surface within the limits of point A (in the certain sstem of coordinates). If to cross a surface with a plane which passes through normal to the surface in a the point A we will get a normal crossing in the point A. In this case it is alwas will eist two mutuall perpendicular directions in which curvature of the proper normal cuts in the point A will equal main curvatures k та k. These directions are equivalent to directions of aes in the certain sstem of coordinates and will be equivalent to directions of main curvature and the proper crossings - to the main normal crossings of surface. If a secant plane will form a corner α with the ais e then for curvature of normal crossing k N in the point A will be correct this dependence (formula of Euler): k N k cos α + k sin α. (7) Accordingl in directions of main curvatures the curvature of the normal crossing k N takes

4 etreme (maimal and minimum) values. The are equivalent to main curvatures k k.. The connection between coordinates of touch of instrument with a detail and its form (method) As evidentl from the higher resulted mathematical consideration of the surface properties it is possible to make a few methods in relation to determination of epression of description of detail surface but in basis of all of these methods it must be the matri field of coordinates of surface. In an order to present which one coordinates of surface we have possibilit get we will consider what takes a place on the concretel select area of surface during registration of coordinate. Such situation arises up as a result of two meetings motions of instrument and is eplanation that takes a place at definition of coordinates of surface for picture. B such method of the motion foremost we determined the coordinate of point A which is maimall remote from the ais Х after a static coordinate. Besides during the proper snchroniation direct and to reverse motion (leftside and right-side рiс.3.) is confirmed coordinate of the point A with minimum divergence which is determined the sensitiveness of the touch sstem. This is take place over the trajectories of b>0 and b<0 concordantl acost in asint bt a>0 where b>0 is a right spiral line or b<0 is the left ( a a a іб б б ). spiral line 3 3 At a net step to the center of receipt of detail the radius of motion diminishes on L k and the sstem СNС registers the coordinates of surface С and В for left-side motion and and E for right-side. The got coordinates of five points surface ХОY are ponderable enough for the informative point of view. А n А i А 3 А А Pic.. There is a location of the special informative points on the surface of the detail. б á б 3 ( u v) 0 п 3 A A A 3 ( u v) 0 ( U V ) 0 Л Л С С 3 a a a 3 S Z B E X B 3 Y L k L k L k L k N Pic.. The trajectories of instrument motion are for the receipt of coordinates of surface of detail: а а а 3 of left-side trajector of motion and б б б 3 are right-side trajectories of motion. The source of this problem is that such amount of points of co-ordinates does not determine the tpe of surface. There is possibilit to conduct a few surfaces of different tpe in space through five points. It is visible from mathematical dependences ( ). It is therefore necessar in the certain coordinate to do et one touch with the purpose of determination of 9 coordinates of surface. Working another motion (L k) the sstem CNC gets the dut coordinates С з та В з in left-side motion and з та Е з at right-side motion. In such case general amount of coordinates is nine that gives possibilit with high authenticit to define the form of surface after the higher mentioned dependences. At the same time eamining the got coordinates in vectorial or self-

5 reactance kind (5) (6) there is possibilit to get matrices () and (7 8) for the first and second quadratic forms of surface which give possibilit to determinate it tpe. At such method of motion there are two important situations that closel associated with method of getting coordinates and which need to be perceived as clever limitation. At first it concern the feed of instrument on the coordinate Х and speeds of rotation ω. If ω infinitel grows at the stable serve of instrument S i coordinates of points В В 3 С С 3 from one side unlimited approach the coordinates of points Е Е 3 3 and in endlessness meet in one unit in the plane to the cut of detail with the coordinates of point A. So here will be a case of determination of form considered in a cut [3]. Accordingl in opposite case when ω 0 and S we will have a Д case considered in [4]. Thus coordinates of points В 3 С С 3 та Е Е 3 3 will be unlimited to approach one to one and to the planes ZOX. Secondl with the purpose of getting maimal speed at determination of form is desirable upon termination of measuring of ever pair of coordinates (В -С В 3-С 3 Е -Е 3 and others like that) to work off a step in a side the ais of rotation. This problem is especiall technical and touches the inertance of the motive sstem of machine-tool which is ponderable limit on speed of measuring process. If to select the actual speed of measuring of the form it is necessar to pa a regard to the second point of limitations because first is far less in it's inertance than inertance of mechanical motions. rom consideration of mathematical properties of surface it is possible to draw a conclusion about possibilit of use the few methods in relation to determination of it general view. The offered method of instrument motion on a spiral i Д Д trajector is researched from point of informative possibilities. We defined certainl basic limitations and optimum of measuring criteria. Bibliograph []. Скицюк В.І. Махмудов К.Г. Клочко Т.Р. Технологія ТОНТОР. - К.: Техніка с. []. Скицюк В.І. Сілін Р.С.. Методика торкання поверхні деталі боковою різальною стрічкою фрезерного інструменту з метою визначення координати її поверхні. - Вимірювальна та обчислювальна техніка в технологічних процесах Хмельницький 00 стр [3]. Скицюк В.І. Діордіца І.М. Науменко В.І. Засади визначення відхилень форми перерізу деталей циліндричного типу. Ж. //Вісник НТУУ "КПІ". Серія машинобудування. 005р.- Вип. 45.-С.6-3. [4]. Скицюк В.І. Діордіца І.М. Науменко В.І. Вимірювання форми деталі за статичного розташування та лінійного детермінованого руху різального інструмента. Ж. //Вісник НТУУ "КПІ". Серія приладобудування. 005р.-Вип.9.- С [5]. Гаврилов А.Н. Точность производства в приборостроении и машиностроении. - М.: Машиностроение с. Authors Tmchik G.S. Diorditsa I.M. Sktsuk V.I. Vsloukh S.P. Diorditsa A.M. National Technical Universit of Ukraine Kiev Poltechnic Institute Address: 37 Prospect Peremog Kiev Ukraine Telephone:+(38)(044) indior@ande.ru 0