The application of inertial navigation on machine tools
Citation for published version (APA):
Heuvelman, C. J. (1967). The application of inertial navigation on machine tools. (TH Eindhoven. Afd.
Werktuigbouwkunde, Laboratorium voor mechanische technologie en werkplaatstechniek : WT rapporten; Vol. WT0185). Technische Hogeschool Eindhoven.
Document status and date: Published: 01/01/1967
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techni'sche hogeschool eindhoven
laboratorrum voor mechanilche technologie en werkplaatstechnlek ,rapport Yan d. ..etie:
tit.1:
auteur(.):
l.eti.l.ider:
hoogleraar: Prof.4r. P.C. VeeD8tra
.aIMnyatting
The possiblllt7 of the application ot inertial AaYlsatioD on machiDe tool. has been studied. ~'. • Inertial navigatioD 18 ba.ed on the measur •• ent of the acceleratioD of the object for the purpose of obta1ainl ita position atter double intesra~io •• It tVD' O\lt that the inertial DaYip.tioa for
machine toolafat the pre.ent atate of the teohD1q.e.
, \
iayolye4
18
Dot7.'
attraotiY ••Note pre.eDted to . CIRP ... . Gro., j
o.
Harbor.,ruP.
1967._bIz.
o
van
, biz.rapport nr.
018,
coderin;:MS.
" trefwoord: Lenlht •• asure.eat datum: Sept.1967 aantal biz. ;e.chikt voor' publicatl. In:-The application of inertial navigation on machine tools Technological University
Eindhoven .. SwnmarY'
C .J. Heuvelman ~
The possibilitY' of the application of inertial navigation on machine tools has been studied. Inertial navigation is based on the measurement of the acceleration of the object for the purpose of obtaining its position after double integration. It turns out that the inertial navigation for machine tools at the present state of the technique involved is not yet very attractive.
Introduction
Generally, navigation mostly needs one or more fixed points as references as, for example, with ships and aircraft where radio baoons and stars serve this purpose. With machine tools it is
of course necessary to know the position of the tooltip witg
respect to the workpiece .. In practice, however, direct determinat-ion of this distance is not possible: mostly the position of the table on which the workpiece is placed with respect to the gu1dewars;has been measured. If the position of the tooltip with respect to the guideways is a fixed one and consequently known, the desired position is known. Owing to temperature effects, and to bending and vibrations of the machinefram., the position tooltip--slideways is not fixed at all and so serious -mistakes may be introducedo
With the navigation of ships and aircrafts remarkable results are
obtained when inertial navigation is used. The sensor, a relative small instrument. is placed in the object. It measures in a seismic
way the acceleration of the vehicle. Contrary to most other navigation systems no connection with a fixed point is required.
The question arises if inertial navigation is not possible with machine tools, so placing a small acceleration sensor very near to the tooltip and another on: the workpiece 0 The exact :posi't'i"on· of the tooltip
follows from the o~tput
of
these accelerometers •• For an answer to this question, a number of interfe~enee sources have to be examined. The most important ones are:(1) the influence of the gravitation on the measurement;
(3) the quality of the sensors and electronic equipment (drift. noise and linearity);
(4) the mutual influence of the accelerations with two or three coordinates: if the tooltip is moved along one coordinate, the accelerometers of the other$should not deliver any output.
For a first impression of the suitability of inertial naVigation with machine tools, the study was restricted to movements along one
coordinate, so point
4
was not examined. The remaining points will be discussed successivi~y.The influence of the gravitation
If an object is moved in a straight line with an acceleration aCt), the covered distance is T
SeT) =
1/
a(t)dt2•If aCt) i~ measured9 S can easily be computed. However, it is possible
that the horizontal (neutral) plane of the accelerometer makes an angle ~Cangle variation) with the plane perpendicular to the direction of the gravitation. Hence, the recorded acceleration is:
a ::: g sinoc.. ,
so after t seconds the apparently covered trajectory is S ::
t
at2 ::t
(g sino<. )t2.When a measuring time t=1 second is taken and a maximum misreading of 10,.pm is permitted, then
-6
sin<X..::: 2.10
so the maximum angle variation may not exceed
0<.
=
2 j'radian.It will be clear that this demand is difficult to meet.
There are several theoretical possibilities to diminish the influence of gravi tation by:
(1) mounting the accelerometers on a platform kept horizontal by gyro stabilizers;
(2) keeping such a platform horizontal by means of a servosystem controlled by a photoelectric autocollimator placed on a fixed point;
(3) measuring in advance the angle variations along the'g~ideways and subsequentc correcting for these variations.
The solution with gyro stabilizers is not very well possible, since there
are no suitable gyros available. Apart from this,high-quality gyros are very expensive. However, this method is very near to the ideal of measuring the tool position without any junction to a fixed point. The method with the autocollimator is possible, although the servosystem will be complicated.
Experiments were carried out with the third system: correction for the angle variations. These variations may not be t'oo large, and ~ust be reproducible and constant for a long period. If nott correction is not
very practicable.
Measurements carried out on several machines showed that the angle variations of most (good) gu.ideways are smaller than 20 Fad and well-reproducible (see appendix). '
The influence of the restricted bandwidth
Both the accelerometers, which are mass-spring systems of the second order, and the amplifiers and integrators have restricted amplitude-frequency characteristics. Since the determination of th~ position is obtained by double integration to the time. the restricted bandwidth must playa role. It can be shown that an error e in the position is
.3
made when the accelerometer moves at velocity v; this error is proportional to" the velocity:
e =-
2tf
v, where;Uis the relative damping and w the natural circle resonance-frequency of the accelerometer. When the table moves at a velocity of 50 mm per second, ~= 0.6 (critical damping) and W
=
600 radians per second(bandwidth 100 Hz), the error e
=
0~1 mm and absolutely not negligible. This means that inertial navigation is not very useful with continuous path machining, where the position of the tooltip must be known at any moment. Howevertcorrection for this error is possible with the aid of a velocity signal which can be derived after single integration of the acceleration signal. The error will be zero if the velocity is zero, only a very small error will be made just after stopping. It can be calculated that where the velocity is 50mm per second and the applied de-acceleration 1 m/s2, the positional error caused by the above mentioned accelerometer is less than 1~m just after stopping and only 50 me later the error is completely extinct.Proporties of the electronic equipment
The demands on the stability and linearity of the accelerometersand the integrators are very high. Inertial navigation is only useful if a
reasonable accuracy can be obtained. If a maximum inaccuracy of 10;um is allowed and if the measuring length is 1 meter, the relative inaccuracy of the compl~te equipment must be lower then 10 p.p.m •• The accelerometer used with the experiments (type 4310, Systron-Donner; Concord,Cali~) fulfils this requirement, but analogously working integrators generally cannot obtain this; so digitally working ones are required. However, digital integrators are complicated andt in spite of the increasing use
of integrated circuits, still expensive and rather slow. The analogous integrators are nevertheless used for the preliminary experiments. Apart from linearitY9 drift and hysteresis play an interfering role; they have the same effect as the appearance of angle variations. Generally, drift and hysteresis can be suppressed to a sufficient minimum.
Conclusions
Inertial navigation applied on machine tools is not yet very attractive owing to the high demands of keeping the accelerometers horizontal and of the linearity of the integrators. The difference of inertial navigation applied on machine tools and, for instance, with aircraft lies in the fact that with the latter the trajectories covered are much longer, so a much higher absolute inaccuracy is allowed. Linearity problems of the
integrators may be solved by means of digital equipment. It is not probable that better gyros will be developed for aircraft navigation and more
practicable gyros for machine tools are therefore not to be expected, since doppler navigation with lasers seems to become more attractive.
Reference
Parvin, R.H. Inertial NaVigation Systems D.v. Norstrand Company, inc. p.229D
+20 , ,tIrad
r:
~10 +5 ,tIrad 5 APPENDIX~
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100 200 300 position,'"mm
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position, mm
Upp.r t:1sur.: anll. Yar:1atioJ18 ot. the 10Dgitu4inal
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+:
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.. ' ,., ,. 200 .. 00-
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position, mmAngl. y.ariatiou of th.iu14 •• . , . ~t the C~~~tl 1I1l1lDa
_chia.
