神兜兜和他的朋友们

A. Caballero-Ruiz et al. / Mechatronics 17 (2007) 231–243 243
micro-machine tool during the error analysis and the esti- [11] Kussul E, Baidyk T, Ruiz-Huerta L, Caballero-Ruiz A, Velasco G
CNC micromachine tool: design & metrology problems. In: Zemliak
mation of the error parameters will made in less time.
A, Mastorakis N, editors. Advances in systems theory, mathematica
The results obtained in this research will be applied in
methods and applications, WSEAS Press; 2002. p. 93–7.
adaptive control systems to increase the precision in the
[12] MicroMachine Center. Application of micromachine technology
MMT without carrying out measurement of the work MicroMachine magazine (reference webpage: <http://
pieces during the manufacturing process and, in conse- www.mmc.or.jp/e/>); p. 7–20.
[13] Yu-Chong T. MEMS manufacturing at the Caltech micromachining
quence, it does not increase the manufacturing time. The
4
lab, M Workshopon Micro/Meso MechanicalManufacturing, USA
research presented can be used for industrial applications
2000. (Reference webpage: <http://www.mech.northwestern.edu/
where the machines tools are larger than the MMT pre-
MFG/AML/M4/M4-Files/Tai/index.htm>.)
sented in this work, but the method must be tested in sev- [14] Lauwers TB, Edmondson LZK, Hollis R. Progress in agile assembly
eral machines and conditions before this step. free-roaming planar motors. In: Proceedings of the 4th Internationa
Workshop on Microfactories, China; 2004. p. 7–10.
[15] Brand U, Kleine-Besten T, Schwenke H. Development of a specia
Acknowledgements
CMM for dimensional metrology on microsystem components
ASPE 15th Annual Meeting , USA; 2000. p. 542–46.
This work was supported by the Grants CONACYT- [16] Driesen W, Varidel T, Re′gnier S, Breguet J. Micro-manipulation by
2005-C02-51843/A-1. Thanks are also due to Mr. Mario adhesion with two collaborating mobile micro-robots. In: Proceed-
ings of the 4th International Workshop on Microfactories, China
Rodriguez-Segundo and Dr. Graciela Velasco-Herrera for
2004. p. 17–22.
their help during the project, to Dr. Gabriel Ascanio and
[17] Okazaki Y, Mishima N, Ashida K. Microfactory and micro-machine
Dr. Saul Santillan-Gutierrez for their comments and to
tools. Reported in The 1st Korea-Japan Conference on Positioning
Nora E. Reyes-Rocafuerte and Rita Coyne for the lan- Technology, Korea; 2002.
guage reviewing. [18] Mitsui K. Measurement and evaluation methods of micromachine
(Technical report). Micromachine Center, Micromachine Magazine
2000;33:16–7.
References
[19] Mitsui K. Basic research on a method for evaluating the geometrica
accuracy of microparts. Micromachine Center Micromachine Mag-
[1] Takayuki H. Future prospect of micro-machine, Technical article,
azine 1995;12:2.
Micromachine Center Japan; 1999. p. 6.
[20] Mitsui K, Shiramatsu T, Kawada M. Development of measurement
[2] Ishikawa Y, Kitahara T. Present and future of micromechatronics.
method for 3d shapes and dimensions of micro-components. ASPE
1997 International Symposium on Micromechatronics and Human
16th Annual Meeting, USA; 2002. p. 343–48.
Science, Japan; 1997. p. 13–20.
[21] Ogura I, Okazaki Y. Development of micro-probe for micro-CMM
[3] Kussul E, Rachkovski D, Baidyk T, Talayev S. Micromechanical
ASPE 16th Annual Meeting, USA; 2002. p. 349–52.
engineering: a basis for the low-cost manufacturing of mechanical
[22] Weck M. Handbook of machine tools, vol. 4. John Wiley & Sons
microdevices using microequipment. J Micromech Microeng
1984.
1996;6:410–25.
[23] ItoS,IijimaD,HayashiA,AoyamaH,YamanakaM.Micro-turning
[4] Trimmer WS. Micromechanics and MEMS, classic and seminal
system: a super small CNC precision lathe for microfactories. ASPE
papers to 1990. IEEE; 1996.
16th Annual Meeting, USA; 2002. p. 295–98.
[5] Kussul E, Baidyk T, Ruiz L, Caballero A, Velasco G, Makeyev O.
[24] Encyclopedia Britannica, Article 39170 (Reference web-
Techniques in the development of micromachine tool prototypes and
page:<www.britannica.com/eb/article-39170>).
their applications in microfactories. In: Leondes, Cornelius T, editor.
[25] Pahk HJ, Kim YS, Moon JH. A new technique for volumetric error
MEMS/NEMS Handbook – Techniques and Applications, vol. 3.
assessment of CNC machine tools incorporating the ball-bar
Springer Publications; 2006. p. 1–61. ISBN: 0-387-24520-0.
measurement and the 3d volumetric error model. Int J Mach Tools
[6] Kussul E, Baidyk T, Ruiz L, Caballero A, Velasco G. Scaling down
Manuf 1997;37(11):1583–96.
of microequipment parameters. Precision Eng 2006;30:211–22.
[26] ISO 230-2:1997. Determination of accuracy and repeatability of
[7] Okazaki Y, Kitahara T. Micro-lathe equipped with closed-loop
positioning numerically controlled axes. ISO; 1997.
numerical control. In: Proceedings of the 2nd International Work-
[27] ISO 10360-1. Geometrical product specifications (GPS) acceptance
shop on Microfactories, Switzerland; 2000. p. 87–90.
and verification tests for coordinate measurement machine (CMM)
[8] Fukuda T, Menz W. Handbook of sensors and actuators, micro-
ISO; 2000.
mechanical systems. Elsevier; 1998.
[28] ASME B5.54-1992. Methods for performance evaluation of com-
[9] Kussul E, Ruiz L, Caballero A, Kasatkina L, Baidyk T. CNC
puter numerically controlled machining centers. ANSI/ASME; 1993
machine tools for low-cost micro-devices manufacturing. The First
[29] ASME B89.4.1. Methods for performance evaluation of coordinate
International Conference on Mechatronics and Robotics, Russia
measurement machines an American National Standard. ANSI/
2000;1:98–103.
ASME; 1997.
10] Kussul E, Baidyk T, Ruiz-Huerta L, Caballero A, Velasco G,
[30] Goldberg David E. Genetic algorithms in search, optimization and
Kasatkina L. Development of micromachine tool prototypes for
machine learning. Addison–Wesley; 1989.
microfactories. J Micromech Microeng 2002;12:795–813.

42 A. Caballero-Ruiz et al. / Mechatronics 17 (2007) 231–243
Fig. 15. Plots of the corrected data and the theoretical data: (a) Calculations with Z axis constant; (b) Calculations with Y axis constant and (c)
calculations with X axis constant.
Table 2
Parameters of error equations
Cxx Cyy Czz Cxy Cyz Cxz ax ay az
0.015 0.0240.1042.39E071.41E074.95E070.0032 0.0032 0.034
0.014 0.0210.0084.71E07 2.27E073.62E070.0060 0.0017 0.036
0.015 0.0220.0084.24E07 1.75E072.46E070.0060 0.0013 0.037
0.017 0.0220.0083.97E07 3.31E075.84E080.0058 0.0014 0.037
0.016 0.0220.0073.98E07 3.31E072.33E070.0056 0.0032 0.037
0.015 0.0230.0083.57E07 9.32E083.06E070.0049 0.0018 0.036
Table 3 the motors to increase the feed rate and to reduce the time
Corrected centers and errors
employed in the manufacturing of every piece. For this
Corrected center (lm) Quadratic error Error (lm) case, the productivity is not a?ected.
XYZ An approach forgeometricalerror analysisinMMTsby
means of two ball gages to identify the errors associates to
12906.74 30067.73 10913.32 7036 5.93
12923.57 30050.90 10918.93 6386 5.65 an MMT was presented. The measurement process was
12921.70 30058.38 10911.45 6410 5.66 madeby electricalcontact and thedata processingtodeter-
12919.83 30058.38 10911.45 6600 5.74
mine the error parameters was based on a genetic algo-
12908.61 30062.12 10913.32 6510 5.70
rithm. Using this method, a general error of 35 lmina
12904.87 30069.60 10913.32 5680 5.32
specific region of a MMT workspace was determined.
Applying equations for the error compensation, the fitting
6. Conclusions of the experimental data to the theoretical data with an
error less than 6 lm was possible.This approach represents
Thebenefitofusingadaptivecontrolsystemstoimprove a low-cost alternative to evaluate micro-machine tools
the MMT precision was demonstrated. Using an adaptive against other commercial techniques such as interferome-
control system for the first prototype of a MMT, the man- ters. We propose to use the error parameters in future con-
ufacture of a micro-shaft with a diameter of 50 lm, length trol system to reduce the errors in the micro-machine tool
of 550 lm and a mean error of 8lm was possible. A draw- by means of software algorithms. Likewise, the results of
back of the presented control system is the manufacturing this research will help in the design of new micro-machine
time, which increased because of the measurement pro- tools. It is necessary to make further works in the estima-
cesses. It is possible to use the proposed adaptive control tion of the error equations in order to increase the robust-
system employing several micro-machining centers work- ness of the algorithm. Following this idea, the expected
ing in parallel mode or changing the operation mode of system will be able to include more components of the

40 A. Caballero-Ruiz et al. / Mechatronics 17 (2007) 231–243
* from the 51st generation to the 75th generation, the repeated 10,000 times and deviations presented in the cen-
mutation range was between18.8 and 18.8 lm; ter calculations were Ex < ±1.88 lm, Ey < ±1.88 lm y
* finally, from the 76th generation to the 100th genera- Ez < ±1.88 lm (see Fig. 12b). If each experimental data
tion, the mutation range was between1.8 and 1.8 lm. group is independently analyzed, it is easy to observe the
deviations with respect to the theoretical data (Fig. 13).
Fig. 12a shows the results of the GA implementation for These deviations are directly related to the MMT errors.
one of B2 position; the plot represents a correlation The algorithm was tested too for 14 position of B2 when
between the experimental data and the theoretical circles this ball was placed 17 mm from the MMT spindle to
that correspond to the experimental measurements. For establish the MMT error characteristics. The correspond-
this experimental data, the calculated center for B2 was ing points for the center of B2 and the characteristics for
X= 12831 lm, Y= 30168.3 lm and Z =11370.2 lm with each B2 position are presented in Fig. 14 and Table 1. This
a quadratic error of 448,069 motor steps, which is equiva- is a part of the final position set that will be analyzed in the
lent to an MMT error of 82 lm for that point. To deter- MMT evaluation. The maximum error was 85.9lmand
mine the robustness of the algorithm, the experiment was averageerror was35.68 lm.Thisresultissimilartothecal-
Fig. 12. (a) The experimental data and the theoretical points of the ball perimeter corresponding to the measurements and (b) deviations of the centers.
Fig. 13. MMT errors: (a) Measurements with Z axis constant; (b) Measurements with Y axis constant and (c) Measurements with X axis constant.

A. Caballero-Ruiz et al. / Mechatronics 17 (2007) 231–243 239
x
2 2 The chromosomes population is randomly created and is
dx 1/4 Cxx1X tCyxY tCzxZ tCxx2X sin t/x
p evaluated by an aptitude function defined by
rpp
mq?????????????????????????????????????????????????????????????????????????????? 2
tY cos tayx tZcos tazx ; 0 X 0 2 0 2 0 2
2 2 erri 1/4 eXliX0T teYliY0T teZliZ0T eRtrT
l1/41
y
2 2
dy 1/4 Cyy1Y tCxyX tCzyZ tCyy2Y sin t/y
16
p e T
r
e13T
0pp X 1/4 Xl tdxi;
li
tX cos taxy tZcos tazy ;
2 2 0 Yli 1/4 Yl tdyi; l 1/4 1;2;3;...;m; i 1/4 1;2;3;...;n e17T
z
2 2 0
dz 1/4 Czz1Z tCxzX tCyzY tCzz2Zsin t/z Zli 1/4 Zl tdzi;
p
rpp where erri is the quadratic error of the modified experimen-
tX cos taxz tY cos tayz ; 0 0 0
2 2 tal data Xli;Yli;Zli that is obtained by means of m experi-
mental data Xl, Yl and Zl a?ected by the error deviations
here the constants Cxx1, Cyy1, Czz1, Cxx2, Cyy2, Czz2, /x,
dx, dy and dz calculated from a population of ny and /z represent the translational errors; Cxx1, Cyy1
chromosomes.
nd Czz1 are the position error of the corresponding axis,
The GA generates a population of n chromosomes,
hich can be associated with mechanical parts such as
whose aptitude function is calculated. After that, the 20%
he gearboxes, the detection of home position, the straight-
of the population is considered as the fathers of the next
essoftheaxis,etc.andCxx2,Cyy2,Czz2,/x,/y and/z rep-
generation. A mutation is applied to the fathers to generate
esent the positional error corresponding to the produced
a new population of chromosomes, while the center of the
rrors by non constant thread in the lead screw and Pr is
sphere is recalculated taking into account the best chromo-
he lead of the lead screws. The constants Cyx, Czx, Cxy,
some of the current generation. The algorithm realizes azy, Cxz and Cyz represent how the straightness of comple-
defined number of generations to find the chromosome
mentary axes modify the errors the corresponding axis; in
set that presents the best fit for the aptitude function and
his case, this error can include pitch and yaw errors.Final-
selects it as thesolution ofthe problem.Therefore, thecon-
y, the constants ayx, azx, axy, azy, axz and ayz represent the
stants C , C , C , C , / , a , a , C , C , C , C , / ,
xx1 xx2 yx zx x yx zx yy1 yy2 xy zy y
eviation angles between the axes. The equations were pro-
a ,a ,C ,C ,C ,C ,/ ,a ,a canbeemployedinthe
xy zy zz1 zz2 xz yz z xz yz
osed after long time of study and experimentation with
deviations model to develop a control system to improve
he MMT presented in this paper.
the MMT function capabilities.
The experimental data are modified using the following
quation:
5.2. Experimental results
0
X 1/4 X tdx;
0
Y 1/4 Y tdy; e14T The proposed algorithms were experimentally tested
0 using two 5/16 in. (7.937 mm) stainless steel balls with dia-
Z 1/4 Z tdz;
metrical deviations lower than 0.6 lm. The balls are fixed
0 0 0
here X , Y , Z are the modified experimental data; X, Y, to shanks by epoxy glue and the electrical contact is pro- are the experimental data; and dx, dy, dz are the error duced by a wire that joins the ball and the shank. In the
eviation in the MMT. metrology process, a group of 233 measurements were con-
In order to determine the constants included in Eq. (13), sidered as the experimental test database for each B2 posi-
e use a similar algorithm to the algorithm used to find the tion. For the test of the algorithms, measurements for 70
enter of B2. In this case, the chromosome population was di?erent positions of B2 were made. These measurements
omposed by groups that contain all the constants pre- was obtained by rotating the B2 support using the spindle
ented in Eq. (14) as is shown in Eq. (15): along 14 di?erent positions and by moving the B2 support
along the Y axis in increments of 2 mm starting fromxx11;Cxx21;Cyx1;Czx1;/x1;ayx1;azx1;Cyy11;Cyy21;Cxy1;
11 mm from the spindle until 19 mm.zy1;/y1;axy1;azy1;Czz11;Czz21;Cxz1;Cyz1;/z1;axz1;ayz1:
In order to test the developed GA to calculate the centerchromosome 1; of B2, the best results were obtained with a chromosomexx12;Cxx22;Cyx2;Czx2;/x2;ayx2;azx2;Cyy12;Cyy22;Cxy2; population of 500 entities during 100 generations and the
mutation employed to create each next generation was dis-zy2;/y2;axy2;azy2;Czz12;Czz22;Cxz2;Cyz2;/z2;axz2;ayz2:
tributed in di?erent range of values as follows:chromosome 2;
.. ... ... ...
* From the 1st generation to the 15th generation, thexx1n;Cxx2n;Cyxn;Czxn;/xn;ayxn;azxn;Cyy1n;Cyy2n;Cxyn; mutation range was between3760 and 3760 lm;
* from the 16th generation to the 30th generation, thezyn;/yn;axyn;azyn;Czz1n;Czz2n;Cxzn;Cyzn;/zn;axzn;ayzn:
mutation range was between1880 and 1880 lm;chromosome n:
* from the 31st generation to the 50th generation, the
e15T
mutation range was between188 and 188 lm;

38 A. Caballero-Ruiz et al. / Mechatronics 17 (2007) 231–243
a) The MMT goes to its home position. ofB2).Thisevaluation ismadeapplyingthefollowingapti-
b) B1 moves to a position under B2, and then B1 moves tude function:
forward along Y axis until electrical contact with B2
m 2
Xq??????????????????????????????????????????????????????????????????????????????2 2 2
is made. Its position is recorded in a text file. erri 1/4 eXlX0iT teYlY0iT teZlZ0iT eRtrT
l1/41
c) B1 moves back a distance dY along Y axis, which
allows the error generated by backlash to be elimi- l 1/4 1;2;3;...;m; i 1/4 1;2;3;...;n e11T
nated. It moves then up a distance dZ.
where erri is the quadratic error that represents the adapt-
d) B1 moves forward again along Y axis until electrical
ability of each chromosome to the sphere defined by the
contact with B1 is made and the program records its
experimental data; Xl, Yl, Zl represent the coordinates of
position.
the contact points where B1 touched B2; m is the number
e) The steps from b to d are repeated along the Z axis
of experimental data; R is the radius of B1 and r is the ra-
(Fig. 10).
dius of B2.
In each generation, the aptitude function is calculated
Fig. 11 shows the setup for the evaluation method and a
for each chromosome and the k best chromosomes are
plot of the data obtained after a measurement process.
selected to produce the next generation of chromosomes.
In this case, we selected the mutation as genetic operator;
5.1. Determination of the center of B2 and its position errors
in other words, to produce the entities of a new generation,
the fathers are a?ected by a randomly mutation factor.
The obtained measurements for each ball position are
Each selected chromosome is considered as a father of
processed with a special algorithm to determine the ball
some of the next generation entities, where each father cre-
center and the position errors. There are numerical meth-
ates s =n/k sons.
ods to obtain the center of a sphere associated to several
points of its surface, i.e. least square method. In this X0eepkTthT 1/4 X0h trandheDXT;
research, we use a GA, which is a method of adaptive Y0eepkTthT 1/4 Y0h trandheDYT; p 1/4 1;2;...;es1T; h 1/4 1;2;3;...;k
search and optimization. The GA mimics some rules of Z0eepkTthT 1/4 Z0h trandheDZT;
the natural evolution to find the optimal solution of a
e12T
problem [30]. From a population of parameter vectors that
are obtained at random, the algorithm simulates the natu- where X0((p*k)+h), Y0((p*k)+h), Z0((p*k)+h) represent the
ral selection to find the best fit for an aptitude function. descendants of the previous generation, DX, DY, DZ are
In order to determine the errors of the MMT related to the mutation factor, and rand(u) is a random number in
the center of B2, a population of chromosomes is created, the range [0,u].
such a population is composed by a triad of values X0, Y0, ThepointsX0((p*k)+h),Y0((p*k)+h),Z0((p*k)+h) fromtheEq.
Z0 (Eq. (10)). Each chromosome represents the possible (12) and the k fathers of the current generation will con-
center of B2. form the next generation of chromosomes X0i, Y0i, Z0i.
The algorithm searches during a defined finite number of
X01;Y01;Z01chromosome 1
generation such values of X0i, Y0i, Z0i where the error is
X02;Y02;Z02chromosome 2 minimal. After a defined number of generations the chro-
e10T
... ... ... ... mosome, where Eq. (11) is minimal, is considered as the
center of B2 eX ;Y ;Z T.
0 0 0
X0n;Y0n;Z0nchromosome n;
After the first algorithm determines the center of B2, the
wheren represents the numberof chromosomes ofthe pop- equations that represent the model of deviations existing in
ulation. The population of the GA is randomly selected in the MMT are introduced to compensate the experimental
the beginning of the algorithm. The next step is to evaluate measurements. The error equations used in this algorithm
which chromosomes are near to the target point (the center are presented below:
Fig. 11. (a) Balls placement in the MMT workspace and (b) plot of the measurements.