# Planar orthogonality grating measures medium application in error of numerical control machine tool

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1µm, measure precision to be ± 0.

5µm. But DBB law presence is following and scant: ① because steel ball and magnetism are sunken an attrition between cause the machine tool is measured when 10m/min of feed speed prep above athletic precision is flabby calm; ② can undertake metrical along direction of circular interpolation radius only; ③ as a result of adjustable lever self-prossessed generation is out of shape wait for a reason, its measure precision integratedly to reach micron level hard. Normally interferometer and ball lever all cannot realize system of ④ most DBB to move to the machine tool when the measurement of precision, the measurement technique of planar orthogonality grating that uses article introduction is a very good choice. Grating of 2 planar orthogonality measures a way (KGM law) (1) surveys a system form planar orthogonality grating (Bross Grid Encode) measures a way (say KGM) is creation of German Heidenhain company again, its measurement the system uses the computer to control fashion, the input that undertakes metrical parameter with PC of Ⅲ of a Pentium, output, show and the reception that measures data and processing. Measurement unit is comprised by the planar grating that quarter have grain of high density bar and reading head. Should survey a system. (2) measures law of grating of principle plane orthogonality aptly at high speed and high accuracy. Use smooth diffractive principle, pass reading head and follow-up circuit, can numerate directly the accurate signal of athletic contrail position, its reading resolution can amount to 5nm. Planar grating diameter is 140 ～ 230mm, will planar grating places the workbench in NC machine tool to go up when the job, reading head installation is on the main shaft of the machine tool and fixed not rotational, make both clearance is 4mm, planar grating is in of workbench drive next as opposite as reading head translation, pass follow-up circuit and computer program processing, can get NC machine tool measures the error outline of orbit clearly. The characteristic of this method is: Measure precision tall, use blame contact to measure make measure agile, lesser to measuring the opposite motion speed when to restrain. (The devises KGM method measurement that 3) measures orbit orbit is very agile, the characteristic that law of its collect DBB and direct grating law measure at an organic whole, can make the circular motion with machine tool regular to main shaft photograph, linear motion already, still can make irregular complex and planar motion; Its measure error outline to be able to reflect the athletic error that causes as a result of mechanical construction not only, and the athletic error that because CNC servo controls systematic place to cause,still can reflect. Accordingly, the measurement that can devise KGM method at will according to metrical demand orbit. Programmable measures orbit to include: ① circle and circular arc; ② is linear (a reference axis tilts 0 ° , 45 ° or 90 ° ) ; ③ aiguille, right angle and join two linear obtuse angle; ④ a circular arc and a linear join; ⑤ the join of two circular arc. 3 errors are measured and parameter differentiates when the athletic error that uses logarithm of planar orthogonality grating to charge a machine tool undertakes metrical, the circle that should design according to place only (or irregular appearance) measure orbit to weave numerical control dictates drive machine tool is made relative to the motion at main shaft, the athletic error of the machine tool can be mirrorred in the data that computer place collects. Through building model of correct error parameter identification, can depart easily the each motion error that gives a machine tool. Because every reference axis of the machine tool can have 6 freedom to spend,will determine its space position, fixed position, linearity and corner can be shown when moving along either reference axis when the mobile component of the machine tool in all 6 errors, because 18 errors are shared machining center of this pair of 3 coordinate; In addition verticality error still exists between 3 reference axis, so coexistence of numerical control machine tool is in 21 primitive to why error. In the analytic process that moving to the orgnaization between numerical control machine tool, can regarding the spatial motion of either rigid body is to circle the synthesis that sits to origin moves and turn, consider displacement of the lines and angular displacement at the same time already, use neat second commutation matrix will express, the random in getting spatial mechanism fastened medium relation expression in different coordinate. In machining a process, because position of point of a knife is mixed,be by cutting position on workpiece same point, so the coupling between point of a knife and workpiece was formed close vector catenary. Undertake an analysis to this vector catenary, attainable the 21 geometry error that shows numerical control machine tool as follows: Because the individual geometry error of machining center is the positional function of corresponding axis coordinate, because this is OK,plan to close to get each individual geometry error with 3 multinomial of each axis coordinate. At the same time the convenience to analyse a problem, set TX=TY=TZ=Z=0, the type on the basis, the orbit error inside attainable XY plane is formulary (the formula after 1) plans to close (the parameter that Xy of the φ in 2)(3) type is reflective X axis and Y axis verticality, its size does not change along with what coordinate is worth and change. Because circular motion contrail reflected more information in process of machine tool campaign, because this choice error measures orbit,be circular motion contrail. The computational formula that machine tool error mirrors to the change of round radius is Δ R=(xCx+yCy)/R type in: Cx, cy -- the error that measures a dot to go up in X axis and Y axis type (2) and type (3) generation enters this type attainable the equation that contains 14 unknown number. We use broad sense inverse matrix, use a least square method to process data, beg the size that gives each error weight accurately comparably. For convenient computation, make earning equation and the parameter vector of the earning after planning to close following simplifying Yi=Xi β + =(XTX)-XTY+[1-(XTX)-XTX]U of E criterion β is as similar as its, can be in what parameter undertakes on YZ plane and ZX plane to plan to add up to the depart with error parameter. Use the parameter that plans to close, its era enters type (2) , type (in 3) , attainable the heft of a group of errors that concerns with coordinate change, the athletic precision of the machine tool when it reflected axis of X of edge of component of machine tool motion and Y axis shift. Take the place of metrical several foothold and the error parameter that answer relatively to it into formulary Δ R=(xCx+yCy)/R, with respect to R of attainable vector Δ , can compare accurately mapping to give the orbit curve of character of error of reflective XY plane. 3 measure an experiment to explain through the following experiment application is planar the program that orthogonal grating has athletic precision is measured to the machine tool, data processing and orbit mapping method. (The test that 1) experiment uses planar orthogonality grating to measure error of motion of numerical control machine tool is in CINCINNATI 750 undertakes on machining center of 3 coordinate vertical, the measurement of the design the circular contrail that orbit is R=50mm, measure data to get those who contain error of machine tool motion accurately, use means of manual control sampling, before beginning to measure namely, predefine measures coordinate value of on orbit 360 bits, weave according to this coordinate value machine tool of drive of program of NC numerical control moves next. Machine tool every interpolation is over to order halt 1 second, continue next interpolation is bit nexter. Set N=20000 of sampling check the number, v=1500mm/min of speed of machine tool motion, such, around the dot of each predefine, can collect 55 example to nod (sampling data) . (2) the athletic precision that data processing mirrors a machine tool for relatively can accurate ground, we undertook artificial processing to measuring gotten data. Book the 55 sampling data near the dot to do average processing to every above all, in getting these are nodded is in optional 14 groups of data, use the broad sense in front to go against formula to be able to get a group to plan to add up to parameter. Mix this groups of parameter (Xi, yi) generation enters type (1) , type (in 2) , be like,can get type (1) place shows the parameter of a group of errors about X axis and Y axis. (The data generation that 3) contrail mapping receives above consideration enters formulary Δ R=(xCx+yCy)/R in, attainable vector of R of a Δ , multiply next with enlarge coefficient, but the error contrail when accurately mapping gives this machine tool to make round interpolation move (each small division is 5µm) 4 epilogue the mapping method of the basic method that the article introduced to use planar orthogonality grating to undertake error of motion of numerical control machine tool is measured and error contrail design. Because error contrail design contained all error information on plane of machine tool XY, because this needs to undertake handling to this error contrail only, can judge a cause that causes an error to undertake compensating to the error, the writer still will develop the research work that judges to error compensation and error source further. CNC Milling