Be based on 3 coordinate to measure the application of the curved surface of curve of 4 EB batten of machine

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Summary article discussed the construction of EB batten, algorithm and property 4 times, discussed 3 coordinate to measure machine detect of the curved surface of curve of 4 EB batten of data plan to close, use the error assess model that fast iteration algorithm built area of outline of the spare parts that be measured. Gave out to use example. 3 coordinate measure the keyword Application Of Quartic BE-spline Based On CMMChen Hua of assess of error of machine EB batten, et Al 　 is in complex and mechanical spare parts (like cam of dambered surface graduation) , the mould contain spare parts of curved surface of complex three dimensional space to make, in measuring the modelling that reachs CAD, often need to have description and control to curved surface of three dimensional space, the need that creates graph or contented NC treatment on computer screen thereby, or draft metrical data to synthesize batten curved surface (curve) in order to satisfy the need of error assess. The curved surface of curve of 4 EB batten of article discussion is passed introduce geometrical meaning very apparent adjustable parameter, raised curvilinear curved surface greatly plan to close level. Batten of 4 1 EB 1.

Curve of batten of 4 1 EB allocate curvilinear Fi(t) by classics of basic curve Gi(t) and 4 times Pi(t) of EB batten curve is become. Namely Pi (T) =Gi (T) + KFi (T) (1;i=1 of ≤ of 0 ≤ T, 2... , it is OK that N-3) (1) 　 introduces K to be worth undertake adjustment to curvilinear appearance through changing it, the difference that makes its and feature polygonal but can small. When K=0, pi (T) =Gi (T) , 4 EB batten curve is basic curve, become the interpolation curve of diagnostic acme. The initial drop of basic music line segment and stop a dot to pass Ri+1 of corresponding diagnostic polygon acme, if Ri+2; widens by some kind of means two control apical R0 and Rn+1, can make curvilinear ｛ Gi (T) ｝ passes all giving apical R1, r2, ... , rn. If this N giving a point is drop of some music on-line value, criterion the curve is this N model the interpolation curve that is worth a dot [1] . 4 times the arrow of EB batten curve is worth equation for 1.

Curved surface of 4 EB batten can regard curved surface of batten of 4 2 EB is U, V of curve of batten of two direction EB accumulate continuously. Give M × N Ri of dimensional position vector, j(i=1, 2, ... , n;j=1, 2, ... , m) tectonic curved surface, equation of its arrow value is 1.

The character of batten of 4 3 EB [2] 　 　 (1) because meaning of a geometry introduced in EB batten equation,compare apparent parameter K, make the architect is opposite can intuitionisticly batten curve (curved surface) appearance undertakes adjustment, the difference that makes a feature polygonal thereby but can small. (2) applicable of 4 EB batten is a few givener special diagnostic acme will generate contain the curve that nods with the needle point-blank. (3) end points of line segment of music of 4 EB batten is in cut arrow to be concerned with basic music line segment only, and with allocate music line segment to have nothing to do. (4) use EB batten curve 4 times (curved surface) make interpolation curve (curved surface) when, its devise method and computational method all changeless, need to take parameter K only for 0, this is very useful to the work out of computational program. (5) is become when K=1/6, curve of 4 EB batten (curved surface) became B batten curve again (curved surface) . This shows, curve of 4 EB batten (curved surface) it is B batten curve (curved surface) develop is wide. The 2 error assess that measure data to plan to combine curved surface in assess 3 coordinate are measured of machine when planning to add up to the error between curved surface and actual measurement data, need computational space actual measurement to nod the distance that plans to combine curved surface. The article used algorithm of astringent of a kind of fast iteration [3, 4] beg dimensional either to nod the distance that plans to combine curved surface. Set P (X, y, z) the space outside be curved surface a bit, beg P to nod S of ∑ of parameter curved surface (U, w) distance. Among them Qi (Ui, wi) go up for curved surface a bit more aleatoric, select the map site on curved surface as P, it is iteration initiative dot. Qi+1 (Ui+1, wi+1) nod what go up in curved surface to hang down for P sufficient. ∑ S(u, w) cuts plane for what Qi nods, s is cutting the node on plane for PQi+1. When Qi and Qi+1 coincide, PQi+1 seeks the space that nods curved surface for place. Qui, qwi is in for Qi U, w just cuts vector to two when go up. Because if PQi+1 is the distance that nods curved surface,this has, inevitable S and Qi+1 coincide, s also nods what go up in curved surface to hang down for this sufficient. The distance that orders plane according to differential geometry gets 　 to search a method for the condition of the least space is, beg piece (11) the Δ U in type, Δ W. When (W of Δ U, Δ ) when ＞ ε (ε is to give small positive number arbitrarily) , replace Qi to undertake issueing computation one round with Qi+1. When (W of Δ U, Δ ) the iteration when ＜ ε stops, right now PQi+1=P-Qi+1=P-Qi=P-S=d points to entity as a result of arrow of law of formulary curved surface besides, so P is besides entity when D ＞ 0, p is in entity when D ＜ 0. Cam mechanism of graduation of dambered surface of 3 application example (see a picture 2) because the structure is compact, deliver torque big, special apply to graduation of high speed, high accuracy. Because of curve of its dividing movement, can design comfortable the best motion curve that closes at all sorts of yard, make the same score stability in motion thereby, fall a confusion of voices, lengthen the respect such as orgnaization service life to have good performance. Graph 3 it is the cam of dambered surface graduation that generates by 4 EB batten the graph of outline face illumination of tensor accumulating curved surface, its appearance is belt of one space helix. In factory of Qin Chuan machine tool the assistance of He Qingan company falls, measure with LK and UKM3 coordinate respectively machine, with radial, come back to be opposite to two kinds of methods the appearance of cam of dambered surface graduation undertook metrical. According to the measurement of above and error assess method, developed the error assess software of cam of dambered surface graduation with Visual C++ . Sampling design parameter sees subordinate list. The graph is shown 4 times for appearance the error graph on the corkscrewed yarn of R=57mm. This spare parts designs a requirement: Curvilinear error ± 0.

05mm, outline spends tolerancepublic errand to take for 0.

The two-way and equidistant configuration of 1mm. To the assess eventuate of this spare parts: The corkscrewed yarn outline of cam radius 57mm spends an error 0.

147mm, face outline spends an error 0.

165mm. Survey sample center of horn of graduation of part of stop of corner of dislocation of type of line of Xiang Qu of design parameter watch coming back is apart from dextrorotation of diameter of roller of height of roller of radius of index plate circumgyrate to be out of shape sine 120 ° 45 ° of 240 ° 108 ± 0.

012mm49.

2mm19mm  25-0.

005mm pursues 4 come back to curve of error of scanning corkscrewed yarn CNC Milling CNC Machining