Note: Descriptions are shown in the official language in which they were submitted.
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WO 97/31749 PCT/DE97/00303
METHOD AND DEVICE FOR COMPENSATING FOR DYNAMIC
MISALIGNMENTS IN CUTTING MACHINE TOOLS
Description
The invention relates to a method and a device for compensating for dynamic
mi~ nments in cutting machine tools. The compensation is intended to
compensate for misalignments in the relative movement direction between tool and0 workpiece, the so-called sensitivity direction, these misalignments occurring as a
deviation from a desired variable.
In order to be able to achieve high m~-~.hinin~ qualities with cutting machine tools,
as far as possible only small movement deviations from the ideal machining path of
15 the tool in relation to the workpiece should occur. However, in actual fact machine
vibrations, static machine deformations and thermally induced deformations causemovement deviations which lead to increases in the shape and roughness of the
machined surfaces.
2 o During the operation of cutting machines, vibrations are coupled into the machines,
for example via the drives, the gear mech~ni~m~) the bearings or the cutting action.
If, for example during longit~l-7in~l turning on a lathe, the distance between the axis
of rotation of the workpiece and the tool changes dynamically, this leads to an
increased surface roughness on the workpiece. The axial misalignment of an end
25 mill or a side grinding wheel in relation to the workpiece likewise leads to poorer
surfaces. During radial milling or during external circular grinding, a misalignment
of the axis of rotation of the tool in the direction of the surface normal to the
workpiece leads to poorer machining results.
3 o The vibrations may also affect a linear axis per se and cause a movement deviation
from the ideal desired movement. Thus, the vibrations of the linearly moved toolholder or workpiece holder in the infeed direction are brought about, for example,
during positioning operations or as a result of dynamic disturbance forces.
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One possibility for reducing the movement deviations resides in the constructional
machine design. Thus, an improvement can be achieved by means of increased
outlay in the mounting, the configuration of the gear meçh~ni~m and in the coupling
5 of the drives. However, the costs for such measures very rapidly reach values
which, measured against the achievable improvement, are no longer acceptable.
Further approaches to improving the accuracy consist in compensating for the
movement deviations. In this case, it would be possible, on the one hand, to reduce
10 the causes of disturbance by means of a control system. On the other hand, the
effect of the disturbance could be compensated for by a control system. However,in the case of the frequencies of up to l000 Hz, which occur typically in machines,
both these approaches come up against basic limits, since the measuring, computing
and infeed time is of the order of magnitude of one period of the vibration, and thus
15 steady-state control is not possible. For this reason, a further approach consists in
measuring the cause of the disturbance, in order to achieve a suitable compensatory
infeed at the point of action during the transmission time of the cause of the
disturbance at the point of action. The method is known as so-called echo
compensation. Since the measurement of the disturbances is in this case carried out
20 outside the actual process of machining the workpiece, the most precise model.cimul~tion of the process by the compensator system is necessary in order that the
compensation agrees with the real value of the movement deviation, both with
regard to its point in time and with regard to its level. The results of this method are
Im~ti~f~ctory. There is no decisive improvement in the surface finish on the
2 5 machined workpiece.
The invention is based on the object of finding a method and a device of the type
mentioned at the beginning with which a significantly more precise compensation
for the dynamic misalignments and hence, inter alia, a noticeable improvement in the
3 0 surface finish of workpieces can be achieved.
According to the invention, the object is achieved
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in that the disturbances which directly determine the misalignments at their point of
action between tool and workpiece are ascertained,
in that a mathematical process model is generated from the disturbances and used as
5 the basis for generating the nonstatistical components of the disturbances,
in that, on the basis of this process model, a preliminary estimate of the future
behavior of the disturbances occuring at the point of action is made,
10 and, in accordance with this future disturbance behavior, the mi~ nment in the
sensitivity direction is compensated for.
In a way that is preferred, according to the invention, it can be provided that the
compensation for the misalignment in the sensitivity direction is carried out by15 feeding in an additional actuator that acts in the sensitivity direction in the machine,
by feeding in an existing drive of the machine that acts in the sensitivity direction, or
by dynamically displacing in the sensitivity direction an additional auxiliary mass
that is arranged on the machine.
2 o With the method, real-time compensation of dynamic infiuences is available for the
first time. By contrast with previously known methods, no system properties of the
machine have to be known a priori for this. An infeed unit (actuator) that is
additionally fitted to the machine, the infeed unit of the machine which is present in
any case, or the movement of a dynamically displaced auxiliary mass changes the
25 distance in the sensitivity direction between the workpiece and tool holder at any
instant in such a way that the dynamic mi~ nment that otherwise occurs between
tool and workpiece in the sensitivity direction is balanced out.
The prediction is made possible by thé fact that the real misalignments that occur in
30 machine tools typically have, in the frequency domain, amplitude peaks at specific
frequencies.
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In a way that is preferred according to the invention, the misalignment is measured
directly as the disturbance. The misalignment may be measured, for example,
between workpiece and tool holder, while according to the invention it is
compensated for between workpiece and tool, for example by means of an
5 additional actuator that acts between tool and tool holder.
In a way that is likewise preferred according to the invention, the movements at the
tool holder, at the headstock and/or at the spindle can also be measured in the
sensitivity direction as the disturbances. This variant can be used in particular in the
10 case of lathes. Recourse can preferably be made to this method when direct
measurement is not possible or would lead to measurement errors.
In a way that is likewise preferred according to the invention, the force produced
between tool and workpiece during machining can also be measured as the
5 disturbance. In this case, it is possible, by using a number of force sensors, to
determine various components of the force: the passive force acting in the
sensitivity direction, the cutting force acting perpendicular to this and the advance
force acting perpendicular to both these. Information about the cutting depth and
hence the dynamic misalignment can be obtained from all the force components,
2 o since there is an approximately linear relationship between cutting depth and force.
If one or more force sensors are fitted in the force flow, it is necessary for the
misalignment signal resulting from the force signal to be corrected by the knowninfeed of the actuator, in order to infer the actual misalignment. The same is true for
25 the case in which the misalignment is measured directly, and the infeed of the
actuator or of the drive is in series with the measured misalignment signal.
The invention makes it possible to provide for the mathematical process model tohave an autoregressive character, or for the mathematical process model to operate
3 o in accordance with the moving average method. Likewise, a combination of the two
methods or the use of other known process models is possible. Such process models
are known, for example from speech signal processing, and are used there to reduce
the amount of tr~n~mi~.cion data.
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The invention makes it possible to provide for the mathematical process model tobe implemented as a telecommunications filter.
5 In order to make such a compensation possible in principle, the misalignment
occurring between tool and workpiece must be known by a certain prediction time
before its actual occurrence. According to the invention, the method can therefore
be implemented in such a way that the estimate leads by at least the total delay time
of the measuring, computing and infeed period. This minimllm prediction time
10 results from the fact that, for example, each active actuating device needs a certain
time after an actuating signal has been applied in order actually to reach the desired
actuating value. In addition, the measurement of the output signal and the
calculation of the ~ch1~ting signal also takes time.
15 In addition, in a way that is preferred according to the invention, provision can be
made for the infeed made on account of an ~stim~te to be measured and compared
with the actual misalignment, and for the difference to be used to adapt the
mathematical process model.
20 Instead of a measured value for the infeed carried out, in the case of a simplified
variant, it is also possible for the estimated value to be compared with the actual
mis~lignment, and for the difference to be used to adapt the mathematical process
model.
2 5 In addition, in a manner that is preferred in accordance with the invention, provision
may be made for the disturbance and the difference between the real and previously
estimated disturbance to be used to adapt the mathematical process model.
Two suitable procedures for feeding in the actuator or the infeed drive of the
30 machine, or for activating the auxiliary mass, are possible in accordance with the
invention. On the one hand, the infeed or activation can be controlled in such a way
that its action coincides with the real change, based on the estimate, of the
disturbance occurring at the point of action.
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This variant is used when machining is being carried out with a low chip thickness
and the aim of a high surface finish.
5 However, the invention may advantageously also be used for mastering a further problem:
During machining, machines predominantly vibrate at their inherent frequencies.
These are transmitted to the workpiece, primarily in the case of cutting processes
10 with high cutting powers, as waveforms of equal frequency. Cutting once more into
the previously generated wave, for example following one revolution of the
workpiece, leads to a further dynamic excitation of the machine. This effect is called
regenerative chatter. It depends essentially on the phase relationship between the
existing surface waveform and the tool vibration in the sensitivity direction. In order
5 to avoid regenerative chatter, it was hitherto possible only to reduce the cutting
power.
In order to avoid regenerative chatter, the infeed or the activation of the auxiliary
mass is controlled in such a way that its action occurs chronologically before the
20 real change, based on the estimate, of the disturbance occuring at the point of
action.
The delay, which is present during the chatter, between the tool vibration and the
surface waveform is compensated for by means of a prediction and a leading tool
25 infeed, so that the coupling in of energy can no longer occur. This enables active
phase shifting in order to avoid the regenerative chatter effect, which permits the
chip-removal power to be increased. This effect is made possible by the fact that the
method is able to predict the misalignment in the sensitivity direction, even for
longer time periods than the delay time of the measuring, computing and infeed
3 0 period.
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During infeed and positioning movements, dynamically induced movement
deviations of the linearly moved unit in the workpiece/tool system are compensated
for by the ideal infeed movement.
5 Going beyond the conventional control principle, use is in this case made of the fact
that the prediction constitutes a band-pass filter for the dominant frequency
components of the infeed error. By this means, components other than the dominant
frequency components of the infeed error are not coupled back to the drive. By
comparison with conventional control strategies, band-pass filtered feedback of this
10 type exhibits significantly increased effectiveness and stability. A particularly good
filter action can be achieved if, in this case, an infinite pulse response filter is used as
an adaptive filter for the prediction of the vibration.
When referred to an auxiliary mass damper, the prediction also constitutes a band-
5 pass filter for the dominant frequency components of the vibrating machinesubassembly. Provided with a suitable delay and gain, the prediction serves to damp
the dominant frequencies.
A device that is suitable for implementing the method is, according to the invention,
2 0 equipped with a measuring device for measuring the disturbances directly
determining the mi~lignments at the point of action,
and a computing device which is suitable for displaying a mathematical process
model, processes the measured disturbances, makes an estimate of the future
behavior of the disturbance occurring at the point of action and, in accordance with
25 the estimate, cyclically outputs a signal to compensate for the misalignment in the
sensitivity direction.
According to the invention, the device can be constructed in such a way that, inorder to compensate for the misalignment in the sensitivity direction, an actuator
30 that acts in the sensitivity direction is arranged in the tool/workpiece system in
addition to an existing drive that acts in the sensitivity direction.
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The actuator is preferably arranged between the workpiece holding device and themachine, in order in this way to be as close as possible to the point of action of the
misalignments.
5 If, for example in the case of a lathe, the sensitivity direction coincides with the
axial direction of the spindle, that is to say the workpiece is machined at the end,
then the actuator can also be arranged between workpiece and workpiece holding
device, between tool and tool holder or between the tool holder and the machine.
0 Various drive principles can be used for the actuator. Thus, the actuator can be
driven piezoelectrically or magnetostrictively. It may also be a hydraulic actuator or
an actuator based on the principle of a linear motor.
A suitable actuator is, in particular, an infeed device which, irrespective of the level
5 of the infeed, needs a constant infeed time and thus behaves like a frequency- independent delay element.
According to the invention, the device can also be constructed in such a way that, in
order to compensate for the mi~lignment in the sensitivity direction, at least one
20 auxiliary mass which can be displaced in the sensitivity direction by an actuator is
arranged on at least one of the machine components causing the misalignment
(auxiliary-mass damper).
The auxiliary mass is preferably driven electromagnetically or piezoelectrically.
This auxiliary-mass damper is seated, for example, on the tool holder and is
accelerated in the direction opposite to the predicted misalignment of the tool
holder. In the event of agreement between the phase and amplitude of the vibration
brought about in this way of the auxiliary-mass damper, it is in particular possible to
3 0 damp the dominant vibrations of the tool holder effectively.
Under certain preconditions, in order to compensate for the mi~ ;nment in the
sensitivity direction, it is also possible to use the infeed drive, which is present in
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any case, in this direction. This is preferably then a drive for which a linear drive is
used.
This variant can be used in particular in the case of so-called fast tools. In this case,
5 a linear drive is used to bring about an active tool infeed in a precision lathe. Fast-
tool devices are suitable for turning rotationally asymmetrical surfaces as well, for
example aspherical spectacle lenses. The cutting forces and the tool infeed excite
mechanical vibrations, which are superimposed on the desired infeed movement.
Without exerting any active influence on these vibrations, it is not possible to10 achieve adequate surface finishes. By means of the novel method, on the otherhand, it is possible for the surface roughness to be reduced to typically l O
nanometers, which represents only a fraction of the value reached hitherto. In this
case, the movement deviations can be measured using a vibration sensor which is
mounted directly on the moving part of the linear drive.
However, in the case of fast tools, the compensation is also possible with the aid of
an additional actuator mounted on the linear drive, preferably a piezoelectric
actuator.
2 o The measuring device can be, for example, a capacitive sensor suitable for
measuring relative displacements or a vibration sensor suitable for measuring
absolute displacements. It may also be realized by an interferometer.
The measuring device should preferably be arranged on the tool holder or on its
25 tool-receiving part or, also like an actuator, between workpiece holding device and
workpiece or machine or between tool holder and tool or machine.
If a direct arrangement of the measuring device is not possible, or if it would lead to
faulty measurements, because of the workpiece dimensions or shape, then,
30 according to the invention, it may also comprise a number of measurement pick-
ups, which depict the movements of the spindle, the headstock and the tool or
components of their movements.
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According to the invention, the measurement of the ~nisalignment is also possible by
means of force measurement. To this end, one or more force sensors may be
provided, which are arranged, for example, between tool and actuator.
The invention is to be explained in more detail below with reference to exemplary
embodiments. In the associated drawings:
Fig. l shows the schematic illustration of a lathe having an additional actuator driven by means of the method, according to the invention,
Fig. 2 shows the modeling in the case of the known echo method,
Fig. 3 shows, by comparison with this, the modeling in the novel method,
Eig. 4 shows a basic illustration of the novel method for predicting a movement
deviation on the basis of an autoregressive process model,
Fig. 5 shows an example of a tool/workpiece vibration in a precision lathe with an
uninterrupted cut, illustrated in the frequency domain,
Fig. 6 shows the basic illustration of an adaptive filter for the prediction in the case
of a vibration according to Fig. 5,
Fig. 7 shows a comparison of a real mi.~lignment with the precalculated values in
2 5 the case of a vibration corresponding to Fig. 5,
Fig. 8 shows a second example of a tool/workpiece vibration in a milling machine with interrupted cut, illustrated in the frequency domain,
~ o Fig. 9 shows a basic illustration of an adaptive filter for the prediction in the case of
a vibration according to Fig. 8,
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Fig. 10 shows a comparison of a real misalignment with the precalculated values in
the case of a vibration corresponding to Fig. 8,
Fig. 11 shows a basic illustration of the measured value processing in the case of
picking up measured values indirectly,
Fig. 12 shows the surface structure of a workpiece following normal machining,
Fig. 13 shows the surface structure of a workpiece following machining with the
novel method and
Fig. 14 shows the modeling in the case of the novel method when using force
measurement.
5 The exemplary embodiments relate to a variant having an additionally arranged
actuator.
The method will be explained first with reference to a lathe. Fig. 1 shows the basic
illustration of such a lathe, having a spindle l, in whose workpiece receiving part a
2 o workpiece 2 is clamped. The spindle l is mounted in a headstock 3 . The lathe tool 4
is held in a tool holder S, with the interposition of an actuator 6.
The distance between the workpiece 2 and the tool holder S is continuously
measured by a capacitive sensor 7. The diameter of the sensor surface, at a few
25 millimeters, is significantly larger than the cut width of the lathe tool 4 on the
workpiece 2. By this means, surface roughness on the workpiece 2 is not registered
on the round workpiece 2.
The coordinate system shows the possible movement directions of workpiece 2 and
30 lathe tool 4. In this case, x is the sensitivity direction, in which the workpiece 2
and/or the lathe tool 4 can move slightly toward each other or away from each
other on account of vibrations in the machine.
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The actuator 6 can move only in the x direction. In this example, it is intended to be
a piezoelectrically driven actuator 6, which is activated by means of the novel
method. The displacement of the lathe tool 4 by the actuator 6 takes place in the llm
range. To the extent that it is possible for the actuator to counteract, with identical
5 phase and amplitude, a change in the distance between workpiece 2 and lathe tool
4, the surface of the workpiece 2 will be improved.
Figures 2 and 3 show a comparison of the novel compensation method with the
previously known method of echo compensation. In the case of echo compensation,
10 the disturbances f(t) causing a misalignment are measured at their point of
production, well before their point of action. For example, a measurement is made
on the drives of a vibration which, as a result of the machine design, only occurs as
process output value at the lathe tool 4 after a certain phase shift in time.
5 This phase shift is used to process the measured signal for an infeed movement /~(t)
of the actuator 6, the latter needing a specific reaction time because of its inertia,
and this time, including the signal processing time, having to be less than the
propagation time of the vibration from its point of measurement to its point of
action. The infeed must then be carried out with phase and amplitude as far as
20 possible identical to the misalignment occurring at the workpiece. Because of the
difficulties in the precise modeling of the process, precise compensation is notpossible using the method.
By contrast, the novel method operates with the prediction of a misalignment value
25 ~(t), which is determined by modeling from the historical values of the measured
mi~lignment values x(ti). The feeding in of the actuator 6 is carried out in
accordance with the predicted value Ax(ti). The prediction compensates for the
influence of the delay as a result of the measuring, computing and actuator period.
30 Fig. 4 shows a model that is suitable for forming such a predicted value. Themis~lignment values x(tj) measured in the sampling interval T at the sampling
instants ti are processed in a mathematical process model 8, which generates thenonstatistical components of the misalignment values x(tj).
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Ir
A particularly simple implementation of the prediction results if the sampling
interval T of the signal x(t) as in the present exemplary embodiment, is selected to
be equal to the total delay time.
In the present case, this is an autoregressive process model.
The spectral distribution resulting from the process model 8 forms the input for the
process analysis 9, in which a predicted value x(tj+l) for the next sampling instant
10 ti+l is determined from this spectral distribution. This predicted value 'x~(tj+l) is used
to activate the actuator 6.
The sampling interval T is in this case kept sufficiently large to be equal to the total
delay time of the measuring, computing and actuator period. The more closely the15 predicted value /~(tj+l) agrees with the real mi~ nment value x(ti+l) that follows
the sampling instant tj, the smaller is the r~m~ining prediction error e(t). This error
is determined, in particular, by the stochastic components in the disturbance.
Fig. 5 shows the frequency spectrum of a typical tooVworkpiece vibration, such as
20 occurs in a lathe during the uninterrupted action of a lathe tool. In the present
example, machining was carried out at a speed of n=lO00 rev/min. A predicted
value was ascertained only for the respectively following sampling instant tj+l.
Fig. 6 shows the operating principle of the adaptive filter for this case. The filter
25 coefficients hk(i) are updated in each sampling interval by means of the least mean
square algorithm, the currently measured misalignment value x(t;) being processed.
In addition, in this example the respectively r~m~ining compensation error e(ti) is
also taken into account, being measured separately. In this way, it is possible to
compensate even for transient misalignments, which are caused, for example, by
3 o thermal processes on the tool and workpiece.
Fig. 7 shows the misalignment, measured in practice, on a lathe, the time series of
respectively eight sampling intervals T having been taken into account in the
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process model 8 and also in the process analysis 9. xrt;) is the actually measured
misalignment, /x~(tj) is the predicted value determined at each sampling instant, and
e(ti) is the remaining compensation error. In practice, 59% of the following
misalignments were compensated for.
As the upper part of the figure shows, the delay time of the actuator 6 was 0.45 ms,
the computing time was O.OS ms and the measuring time was 0.1 ms. From this, therequired prediction interval, equal to the sampling interval T, adds up to 0.6 ms.
This resulted in a frequency of about 1700 Hz, with which it was possible to
10 compensate for the relevant frequencies, of less than 500 Hz, which typically occur
in machine tools.
Figures 8-10 show an example of determining predicted values for a milling
machine. In the case of a milling machine, the continuously repeatedly interrupted
15 action of the cutting tool induces a frequency spectrum of the tooVworkpiece
vibrations which is in principle different from that in the case of a lathe, as is also
easy to see from a comparison of Fig. 8 and Fig. S. At a rotational speed of n =6000 rev/min, a basic frequency of fO = 100 Hz and corresponding harmonics occur.
20 The type of frequency spectrum permits a prediction of the vibration period
corresponding to the basic frequency and hence a combined short-term and long-
term prediction.
Fig. 9 shows the operating principle of the adaptive filter for a long-term prediction.
25 The filter coefficients b~;(i) are determined for one period of the basic frequency fO,
so that it is possible, within the period, to ascertain predicted values which lead the
actual misalignment value x(t;) by the delay value n.T, that is to say by one vibration
period N of the basic frequency fO, where
3 0 N = n.T = l/fo
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Fig. lO shows real measured mic~ 2nment values for a basic frequency of fO - lO00
Hz (rotational speed n = 6000 rev/min) and, once more, the curve of the predicted
values x(t) and the rçm~ining compensation error e(t).
5 The upper part of the figure shows once more the subdivision of the delay times, the
computing delay having the largest component in this example.
Until now, it has been assumed that the misalignment x(t;) is measured directly
between the workpiece and the tool. In the case of very small-area or offset
10 workpieces, for example, direct measurement is not possible. A misalignment is
therefore measured at those points which are ultimately responsible for the
misalignment occurring on the tooVworkpiece system. These are the spindle
concentric-running error in the headstock and the headstock vibration, which
together result in the workpiece vibration, and the vibration of the tool holder in
15 relation to the machine. Added together, all three result in the dynamic
misalignment which leads to the surface error on the workpiece during machining.
Fig. l l shows in schematic form the interaction of the various vibrations which lead
to a dynamic misalignment.
Figures 12 and 13 show diagrams of measured surfaces following the machining of
a workpiece on a lathe with and without the novel misalignment compensation.
Turning was carried out at a rotational speed of n=lO00 rev/min, a cutting radius of
0.3 mm and an advance of 20 Ilm/revolution. The comparison shows that a
25 reduction in surface roughness by about the factor 2 was achieved. Theoretical
analysis for other types of machine tools showed that, to some extent, further very
much higher reductions in the surface roughness will be achievable.
As an alternative to the direct measurement of the mic~lignment x(t), the
30 disturbance can also be measured by measuring the force F(t) produced during
machining between lathe tool 4 and workpiece 2. Fig. 14 shows the modeling for
this case. The force signal F(t) depicts, to a good approximation, the mi.c~lignment
x(t) between lathe tool 4 and workpiece 2 and/or between tool holder S and
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workpiece 2, since there is a largely linear relationship between force and cutting
depth. By means of the actuator 6, the lathe tool 4 is fed in using an infeed value
F(t) that is ascertained by means of modeling from the historical values of the
disturbance behavior. Since the measurement is carried out in the force flow, and
5 thus it is no longer the disturbance F(t) itself but the disturbance F'(t) modified by
the infeed of the actuator 6 that is measured, it is necessary, before the adaptation
of the filter, to correct the measured signal by the magnitude of the actuator infeed,
in order to depict the disturbance behavior. The infeed value F(t) corresponding to
the infeed of the actuator 6 is therefore subtracted from the force signal. The
10 resulting signal then reproduces the disturbance behavior.
