Analyzing And Compensating The Error Of Machine Tools For Polishing Free-form Surfaces Parallel Kinematics Parts

1 IntroductionWith the development of automobile industry,electric industry and some newhigh-tech industries ,the larger is the proportion of NC machining parts withfree-form surface in all, the higher and higher requirements are made for qualityand efficiency of machining on free-form surfaces. After the roughing method isused, precision machining, such as polishing and polishing, is necessary to obtainrequired workpiece surfaces. Near for over ten years, With the development at ahigh speed in relevant science and technology, such as the technology of thecomputer and modern control theory, etc., flexibility machining become moreperfect. The automatic machining of free-form surfaces come to true basically.However, these subsequent processes of precision machining still depend mainlyon the handwork of skilled mechanists. Productivity effect of handwork is very lowand its quality is unstable. As to the machining of free-form surfaces, low cost andshort period and high quality were its main aim. As a result of that, the research ofa kind of increasingly automated polishing equipment is imperative. Series-parallelvirtual axis machine tools for polishing free-form surfaces meets therequirement .However ,how to improve the accuracy of this kind of machinetools is a difficult problem which troubles the experts of this field. This paperfocuses on analysing and compensating the motion error of this kind of structure.2 The structure theory and the kinematics analysis of this machine tool's parallel partOur machine tool adopts the structure of Figure 1 . And during the study ,we often use thepredigested model given by Figure 2. If there is no error ,the movable platform of this kind ofstructure will be with three translation degrees of freedom .And its center will have thekinematics equations given by Formula (1) and Formula (2).Figure 1. the structure of the parallel kinematics machine tool Figure 2. the predigested model of the machine tool3 The hardware of CNC & the building of control softwareThis machine tool adopts a kind of open numerical control system composed with PC andPMAC motion controller.And Figure 3 shows us its structure .It is very important for ensuringthe whole system working stably to set the values of PMAC controller and the servo system.Additionally ,in order to strengthen this machine tool, we build the control software whichfocuses on shakedown test﹑beginning point setting ﹑homing control ﹑CNC code supportand parameter setting4 Error analysis and compensation of the parallel kinematics structureThere are four main elements effecting the accuracy of out machine.They are:①the accuracy of geometry structure;②zero position error;③the accuracy of CNC system;④the control model of our system.Because the accuracy of CNC system is good enough, the error of the machine toolshould involve in other three elements. And we also can separate the first element to two partsby whether the element can lead to rotating the movable platform. The first part is so-called"the errors of geometry parameters "which can only lead to translation error ;and the secondpart is the factors which can involve the platform. Based on the control model of this machine ,this paper deduced the relationships between these elements and the error of our platform'smotion ,these elements didn't include those factors which could revolve the platform. And therelationship is given by Formula (3).With Matlab, we get a series of simulation figures .Andthese figures will be referenced when we experiment.a31 = 4Q1 + 24m2Q1 ? 2Q1Q2 ? 2Q1Q3 3 2 2a32 = 4Q2 + 24m2Q2 ? 2Q2Q1 ? 2Q2Q3 3 2 2a33 = 4Q3 + 24m2Q3 ? 2Q3Q1 ? 2Q3Q2 3 2 2a34 = 576m3 + 24(Q1 +Q2 +Q3 ) ?72ml2 2 2 2 2a35 = ?72m2l2 ?? 1 (B + B2 ? 4AC + C ?? ? 2A2 A B2 ? 4AC? ? ? K3 = ??? T 1 ? B ? 2A 2A B2 ? 4AC ? ? ? ??? 1 B2 ? 4AC ??? ?b11 b12 b13 b14K5 = b21 b22 ? b25? b15 ?? ? b23 b24 ??b31 b32 b33 b34 b35??b11 = 0b12 = ? 3 6m (Q2 ? z)b13 = 3 6m (Q3 ? z)b14 = ?12m2 ??(Q3 ? z)2 ?(Q2 ? z)2?? 3b15 = 3 6m (Q2 ?Q3)b31 = b21 = 1 3m (Q1 ? z)b22 = ? 1 6m (Q2 ? z)b23 = ? 1 (Q3 ? z) 6mb24 = ?12m2 ??2(Q1 ? z)2 ?(Q3 ? z)2 ? (Q2 ? z)2?? 1b25 = 1 (Q2 + Q3 ? 2Q1)0 6mb32 = 0b33 = 0b34 = 0b35 =1 ? 2 2 2 ? ? l2 ??x0 ?(2m ??y0)2 ? l2 ? 4m2 ? ? 2 2 ? ??Q2? ???Q1 ?? ? l2 ?(?x0 + 3m)2 ?(m +?y0)2 ? l2 ? 4m2 ?K1 = ?Q3 = l2 ?(?x0 ? 3m)2 ? (m +?y0)2 ? l2 ? 4m2 ? ? ? 2 2 ? ? ? ??m ? ? ? ??m ? ???l2 ?? ??l2 ? ? ? ?? ?? Then we get the forms of rotation unexpectably, through experiments and analysis.Theplatform revolves round Ym axle with the form given by Formula (4). Even through therotation round Xm axle has a more complex form.,it also can be described by Formula (5).After eliminating the influence of these kinds of rotations from the datum of measure ,we willget purer translation error surface .At last we compensate the translation error when theplatform's center moves in the plane given by Figure 4 ,and we get the Figure 5. β≈3.5×10-5·x (4) α= f (x, y) (5) Z Y (-50,50,0) (50,50,0) (0,0,0) x (-50,-50,0) (50,-50,0) Figure 4. the idealism plane which the platform's motion should shape...