神兜兜和他的朋友们

版权声明：转载时请以超链接形式标明文章原始出处和作者信息及本声明
http://chenzijian1987.blogbus.com/logs/34248849.html

A. Caballero-Ruiz et al. / Mechatronics 17 (2007) 231–243 241
tion. Acceptable results were obtained employing the fol-
lowing equations:pp
2 2
dx 1/4CxxX tCxyY tCxzZ tY cos tay tZcos taz ;
2 2pp
2 2
dy 1/4CyyY tCxyX tCyzZ tXcos tax tZcos taz ;
2 2pp
2 2
dz 1/4CzzZtCxzX tCyzY tXcos tax tY cos tay
2 2
e18T
where the constants Cxx, Cyy and Czz, represent positioning
errorsproducedbypartsofMMTsuchasgearboxes,home
position, lead screws, etc. Cxy, Cyz and Cxz represent errors
related with the straightness of each axis; and the constants
ax,ayandaz,representthedeviationanglesbetweentheaxes.
Fig. 15 shows how the error decreases when introducing
Fig. 14. Part of the B2 position set. new equations (Eq. (15)). For this model of deviations, the
errors in the corrected data decrease from 82 lm to 5.9 lm
and the robustness of the GA was acceptable. Five of sev-
ulated errors obtained by indirect evaluation [10]. eralexperimentsarepresentedinTable2and,thecorrected
nalyzing the 70 positions, we found an average error of centers and its errors are shown in Table 3.
3.5 lm. The values shown in Table 2 will be used to improve the
The implementation of the error Eqs. (13) and (14) for MMT behavior by means of a control system that includes
e correction of the experimental data was di?cult. The the error parameters, i.e. in order to compensate the
rder of the equations and the employed coe?cients make squareness, the constants ax, ay and az indicate that the
e algorithm converge to more than one solution with squareness in the X and Y axes is less than 0.006 rad, and
most the same optimization grade. This is because the in Z axis is less than 0.04 rad.
arameters are not independent and the solutions for the In Table 3, the deviation in the center found was less
A depend on which parameter is converging to its opti- than 20 lm. This result is better than the obtained with
al value in the first generations. In other words, the opti- the first error equations, which allowed the center of B2
ization process has branches which do not allow the tobedetectedwithadeviationupto100 lm.Theapproach
ptimal solution to be determined. For this reason, several for geometrical error analysis proposed in this paper repre-
periments with the modified error equations were made. sents an alternative to detect and compensate errors in order to establish the new error equations, the influence MMTs by means of control systems. In order to minimize
etween the components of the proposed error equations the deviation in the calculations of the center of B2, the
as determined. For example, the components for deter- improvement of error equations and the GA is needed.
ining the produced error by non constant thread in the That’s why the proposed method is valid to determine
ad screw and the first order components had a correla- the error sources in MMTs.
able 1
haracteristics of each position of B2
sition number B2 position (lm) Quadratic error Error (lm)
XYZ
10288.74 27432.90 14681.37 38909 21.4
10829.17 27410.46 15408.80 54686 25.4
12267.20 27541.36 16456.00 64690 27.6
12710.39 27511.44 16945.94 74224 29.6
14030.61 27565.67 17368.56 32353 19.5
14840.32 27646.08 17578.00 40172 21.7
16390.55 27589.98 17626.62 31697 19.3
16953.42 27474.04 17637.84 207968 49.5
18658.86 27591.85 17116.11 81438 30.9 19386.29 27720.88 16689.75 170327 44.8 20685.94 27670.39 15765.97 115352 36.9 21362.88 27879.83 14907.64 591308 83.4 22129.58 27999.51 13667.83 339525 35.8 22511.06 28136.02 12652.42 627448 85.9