CA2248271A1

CA2248271A1 - Process and device for correcting dynamic misalignments in cutting machine tools

Info

Publication number: CA2248271A1
Application number: CA 2248271
Authority: CA
Inventors: Heinrich Ostendarp; Robert Hilbing
Original assignee: Individual
Current assignee: Fraunhofer Gesellschaft zur Forderung der Angewandten Forschung eV
Priority date: 1996-03-01
Filing date: 1997-02-18
Publication date: 1997-09-04
Also published as: WO1997031749A3; EP0883463A2; EP0883463B1; JP2000505578A; WO1997031749A2

Abstract

The aim of the process and associated device is a substantially more accurate correction of dynamic misalignments caused unavoidably by vibrations in the machine than is possible with known processes. In the process, the disturbances which directly determine the misalignments at the point of action between tool and workpiece are determined. A mathematical process model is generated from the disturbances and used to generate the non-statistical components of the disturbances. On the basis of the process model, a preliminary estimate is formulated of the future behaviour of the disturbance at the point of action and this is then used to correct the misalignment. The process can be used with machine tools to improve surface finish.

Description

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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.

t - 2 -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 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.

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.

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.

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.

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.

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 _ g _ 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.

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, 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).

CA 0224827l l998-08-28 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 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 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 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.

Claims

1. A method for compensating for dynamic misalignments in cutting machine tools, these misalignments occurring in the sensitivity direction between tool and workpiece as a deviation from a desired variable, wherein the disturbances which directly determine the misalignments at their point of action between tool and workpiece are ascertained, wherein a mathematical process model is generated from the disturbances and usedas the basis for generating the nonstatistical components of the disturbances, wherein, on the basis of this process model, a preliminary estimate of the future behavior of the disturbances occurring at the point of action is made, and, in accordance with this future disturbance behavior, the misalignment in the sensitivity direction is compensated for.

2. The method as claimed in claim 1, wherein the compensation for the misalignment in the sensitivity direction is carried out by feeding in an additional actuator that acts in the sensitivity direction in the machine.

3. The method as claimed in claim 1, wherein the compensation for the misalignment in the sensitivity direction is carried out by feeding in an existing drive of the machine that acts in the sensitivity direction.

4. The method as claimed in claim 1, wherein the compensation for the misalignment in the sensitivity direction is carried out by dynamically displacing in the sensitivity direction an additional auxiliary mass that is arranged on the machine.

5. The method as claimed in one of claims 1 to 4, wherein the misalignment is measured directly as the disturbance.

6. The method as claimed in one of claims 1 to 4, wherein the movements at the tool holder, at the headstock and/or at the spindle are measured in the sensitivity direction as the disturbances.

7. The method as claimed in one of claims 1 to 4, wherein the force produced between tool and workpiece during machining is measured as the disturbance.

8. The method as claimed in claim 7, wherein the forces between tool and workpiece are measured in the sensitivity direction and/or perpendicular to this.

9. The method as claimed in one of the preceding claims, wherein the mathematical process model has an autoregressive character.

10. The method as claimed in one of claims 1 to 8, wherein the mathematical process model operates in accordance with the moving average method.

11. The method as claimed in one of the preceding claims, wherein the mathematical process model is used in the form of a filter.

12. The method as claimed in one of the preceding claims, wherein the estimate leads by at least the total delay time of the measuring, computing and infeed period.

13. The method as claimed in one of the preceding claims, wherein the infeed that is made on account of an estimate is measured and compared with the actual misalignment, and the difference is used to adapt the mathematical process model.

14. The method as claimed in one of claims 1 to 12, wherein the estimated value is compared with the actual misalignment, and the difference is used to adapt the mathematical process model.

15. The method as claimed in one of claims 1 to 12, wherein the disturbance and the difference between the real and previously estimated disturbance are used to adapt the mathematical process model.

16. The method as claimed in one of the preceding claims, wherein the infeed or the activation of the auxiliary mass is controlled in such a way that its action coincides with the real change, based on the estimate, of the disturbanceoccurring at the point of action.

17. The method as claimed in one of claims 1 to 15, wherein the infeed or the activation of the auxiliary mass is controlled in such a way that its action occurs chronologically before the real change, based on the estimate, of the disturbance occurring at the point of action.

18. A device on a cutting machine tool having a workpiece holding device and a tool holder (5), for implementing the method as claimed in one of the preceding claims, defined by a measuring device (7) for measuring the disturbances (x(t)) directlydetermining the misalignments at the point of action, and a computing device (9)which is suitable for displaying a mathematical process model (8), processes themeasured disturbances (x i(t)), makes an estimate (x(t i+l)) of the future behavior of the disturbance (x(t)) occurring; at the point of action and, in accordance with the estimate (x(t i+l)), cyclically outputs a signal to compensate for the misalignment in the sensitivity direction (x).

19. The device as claimed in claim 18, wherein, in order to compensate for the misalignment in the sensitivity direction (x), an actuator (6) that acts in the sensitivity direction is arranged in the tool/workpiece system in addition to anexisting drive that acts in the sensitivity direction (x).

20. The device as claimed in claim 19, wherein the actuator (6) is arrangedbetween the workpiece holding device and the machine.

21. The device as claimed in claim 19, wherein the actuator (6) is arrangedbetween workpiece (2) and workpiece holding device.

22. The device as claimed in claim 19, wherein the actuator (6) is arrangedbetween tool (4) and tool holder (5).

23. The device as claimed in claim 19, wherein the actuator (6) is arrangedbetween the tool holder (5) and the machine.

24. The device as claimed in one of claims 19 to 23, wherein the actuator (6) is a piezoelectric actuator.

25. The device as claimed in one of claims 19 to 23, wherein the actuator (6) is a magnetostrictive actuator.

26. The device as claimed in one of claims 19 to 23, wherein the actuator (6) is a hydraulic actuator.

27. The device as claimed in one of claims 19 to 23, wherein the actuator (6) is a linear motor.

28. The device as claimed in claim 18, wherein, in order to compensate for the misalignment in the sensitivity direction (x), at least one 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.

29. The device as claimed in claim 28, wherein the auxiliary mass is drivenelectromagnetically.

30. The device as claimed in claim 28, wherein the auxiliary mass is drivenpiezoelectrically.

31. The device as claimed in one of claims 18 to 30, wherein the existing drive that acts in the sensitivity direction (x) is a linear drive.

32. The device as claimed in one of claims 18 to 31, wherein the measuring device (7) is a capacitive sensor suitable for measuring relative displacements.

33. The device as claimed in one of claims 18 to 31, wherein the measuring device (7) is a vibration sensor suitable for measuring absolute displacements.

34. The device as claimed in one of claims 18 to 31, wherein the measuring device (7) is an interferometer.

35. The device as claimed in one of claims 18 to 31, wherein the measuring device (7) comprises one or more force sensors.

36. The device as claimed in one of claims 18 to 35, wherein the measuring device (7) is arranged on the tool holder (5).

37. The device as claimed in claim 36, wherein the measuring device (7) is arranged on the tool-receiving part of the tool holder (5).

38. The device as claimed in one of claims 18 to 35, wherein the measuring device (7) is arranged between the workpiece holding device and the machine.

39. The device as claimed in one of claims 18 to 35, wherein the measuring device (7) is arranged between workpiece (2) and workpiece holding device.

40. The device as claimed in one of claims 18 to 35, wherein the measuring device (7) is arranged between tool (4) and tool holder (5).

41. The device as claimed in one of claims 18 to 35, wherein the measuring device (7) is arranged between tool holder (5) and the machine.

42. The device as claimed in one of claims 18 to 41, wherein the measuring device (7) comprises a number of measurement pick-ups, which depict the movements of the spindle (1), the headstock (3) and the tool (4) or components of their movements.