METHOD FOR ANALYSTING THE VIBRATIONAL BEHAVIOR OF A SYSTEM

Description

[0001] The invention relates to a method for analyzing the vibration behavior of a system consisting of at least one first and one second rolling stand, which are coupled to each other via a strip, e.g. made of metal, clamped into both rolling stands. Regarding the technological background

[0002] The core of the present invention relates to a particular vibration behavior of rolling mill stands, which is also referred to as chatter.

[0003] The term "chatter" refers to pronounced vibrations that can occur during the rolling of steel or aluminum strip. This phenomenon is known to occur in both hot and cold strip mills, and in both single-stand and multi-stand rolling mills. Chatter is particularly critical during the cold rolling of typically thin strips. Characteristic chatter vibrations are the so-called 3rd < Octave and 5th < Octave, named according to the position of the vibration frequency within the respective musical octave range (3rd octave: 110–220 Hz, 5th octave: 440–880 Hz). Depending on the intensity of the vibrations, the resulting problems range from reduced quality of the rolled products, such as thickness or surface finish, to damage to components, such as markings on rollers or bearings, and even strip breakage. Strip breakage means production downtime and potentially consequential damage to equipment and personnel. State of the art

[0004] It is known in the art to prevent chatter in rolling mills by providing suitable damping. With or without damping, undesirable chatter events can occur, particularly in systems consisting of at least two coupled rolling mills. It is essential to detect these events or provide timely warnings.

[0005] The technical article by Niroomand Mohammad Reza ET AL: "811. Frequency analysis of chatter vibrations in tandem rolling mills", May 14, 2012 (2012-05-14), pages 852-865, XP093106415, found on the Internet: URL:https: / / core.ac.uk / download / pdf / 323313225.pdf concerns the analysis of the vibration behavior of individual components of a rolling mill.

[0006] European patent application EP 3 903 953 A1 describes a method for detecting chatter in a cold rolling mill. Specifically, this method proposes to detect vibrations in the cold rolling mill using a sensor in the time domain and then to transform this time signal into the frequency domain for analysis. The method specifically provides for the detection of a chatter event if a peak in the amplitude spectrum of the signal exceeds a predefined threshold.

[0007] The technical article by Vaidya Vivek Anil et al.: "Analysis of Causes and Remedy of Chattering in the Aluminum Four Stand Tandem Cold Rolling Mill: A Case Study", JOURNAL OF THE INSTITUTION OF ENGINEERS (INDIA): SERIES C, SPRINGER INDIA, INDIA, Vol. 103, No. 1, September 23, 2021 (2021-09-23), pages 107-119, XP037709586, ISSN: 2250-0545, DOI: 10.1007 / S40032-021-00773-W discloses a method according to the preamble of claim 1.

[0008] The invention is based on the objective of further developing a known method for analyzing the vibration behavior of a system with regard to the occurrence of critical vibration situations (chatter events) in such a way that it becomes advantageously applicable to systems with several coupled rolling stands.

[0009] This problem is solved by the method according to claim 1. Accordingly, a chatter event for a system of at least two coupled rolling stands is detected when two conditions are met simultaneously: First, there must be a first peak in the first amplitude spectrum and at least one second peak in the second amplitude spectrum, both of which lie in a common frequency range (method steps e) and f)), and second, the first peak must additionally exceed a predetermined first amplitude threshold and the second peak must exceed a predetermined second amplitude threshold (method step g)). Only when at least these two conditions are met is the chatter event reliably detected according to the present invention. The first and second amplitude thresholds can be the same or different.

[0010] The terms "spectrum" and "amplitude spectrum" are used synonymously.

[0011] The dependent claims define various constellations or embodiments in which the two test criteria according to process step f) and according to process step g) are only partially fulfilled. In these cases, the chatter event is not yet reliably detectable; however, trends, i.e., temporal developments in the amplitude or frequency of the peaks in the amplitude spectra, are observed to determine whether they are developing towards fulfilling the two conditions according to process step f) and according to process step g). In these cases, the present invention provides that early warnings are issued.

[0012] According to a further embodiment of the invention, the detection of the chatter event or the timely warning thereof can be made subject to an additional condition, for example that - the correlation of the two signals in the time period is above the correlation threshold; and / or the natural frequencies of the first and / or the second rolling stand lie within the common frequency range and preferably also within the wider (narrower) common frequency range; and / or the frequency of the first peak and the frequency of the second peak lie within a further common frequency range that is narrower than the common frequency range; and / or an amplitude gradient determined according to the formula grad Pn = Pn t 2 − Pn t 1 / Δt for the first rolling stand n=1 lies above an individual gradient threshold, where: nRolling stand t1, t2Time period 1, Time period 2 ΔtTime difference t2-t1 = const. PnAmplitude of the peak for the rolling stand n1 and either the amplitude of the peaks of the amplitude spectrum of the second rolling stand has already been or is above the corresponding amplitude threshold during time periods 1, 2 and 3, or the gradient for the second rolling stand is also above an individual gradient threshold according to the formula.

[0013] Each of these criteria allows for an assessment of the similarity between the first and second amplitude spectra. The more similar the two spectra are, the more reliably the rattling event can be predicted or detected.

[0014] According to another embodiment, the first and / or the second amplitude spectrum is interpolated in the frequency domain before one of the test and / or comparison steps is performed. This interpolation allows for a more precise determination of the peak value as well as a more accurate determination of its frequency. This more precise determination of the amplitude and frequency of a peak, in turn, enables improved prediction or detection of the chatter event.

[0015] The detection of the chatter event and / or at least one of the warnings preceding it is preferably communicated to a system operator or to an automatic process control system. The information about the detection or the warning can, for example, be linked to a recommendation to slow down the system to prevent vibration build-up, i.e., undesirable resonance effects.

[0016] The method according to the invention can be used in both cold rolling mills and hot rolling mills.

[0017] The various methods mentioned in this description for detecting a chatter event or generating a corresponding early warning can be combined as desired to increase the accuracy of the prediction. Advantageously, the present invention provides for the simultaneous use of several different signals and criteria – optionally also in combination – to avoid false triggers while simultaneously lowering warning thresholds.

[0018] The aforementioned problem of the invention is further solved by a computer program product according to claim 10. The advantages of this solution correspond to the advantages mentioned above with reference to the claimed method.

[0019] The first and / or second sensor can be existing measuring equipment already present in the rolling stands, such as pressure transducers in the setting and bending cylinders, load cells, or, outside the rolling stands, thickness gauges for the metal strip. Equipment for analyzing these measurement signals may also already be available, eliminating the need for additional purchases. Using these sensors to carry out the method according to the invention has the advantage of incurring no additional costs. Furthermore, using other sensors in addition to these for carrying out the method according to the invention increases accuracy, again without additional costs. Such additional sensors and measuring equipment for recording the temporal vibration signals can, for example, be arranged in the intermediate stand area, i.e., between the first and second rolling stands.The additional sensors could include, for example, load cells or accelerometers. This additional measurement technology may incur extra costs.

[0020] When the inventive method is carried out in a system with active vibration damping in a rolling mill stand, vibrations in this stand are suppressed. This means that the peak amplitudes are sometimes small and the peak frequencies are not always discernible. Therefore, detecting the vibrations at the respective stand, as required for carrying out the inventive method, is not readily possible. In this case, this problem can be remedied by incorporating available information from the active vibration damping system, such as the system's control signal and its spectral analysis.

[0021] The first and second sensors for detecting the vibrations at the first and second rolling stands do not necessarily have to be mounted directly on the stands. For the implementation of the method according to the invention, it is sufficient if these sensors each generate a signal that represents the vibrations at the rolling stands, or from which the vibrations at the rolling stands can be derived.

[0022] The description includes a total of 14 figures, whereby Fig. 1 a schematic representation of the method according to the invention in the form of a flowchart; Fig. 2 the illustration of the transformation of time signals into the frequency domain; Fig. 3 + 4 the finding or defining of a common frequency range for a first and a second amplitude spectrum; Fig. 5 + 6 the use of a correlation of the first and second amplitude spectra to verify their similarity; Fig. 7 the observation of an increase in the amplitude of the first peak over time as a criterion for issuing an early warning of an impending rattle event; Fig. 8 the observation of an increase in the amplitude of the second peak as an early warning of an impending rattle event; Fig. 9 the observation of an increase in the amplitudes of both the first peak and the second peak as a scenario for an impending rattle event; Fig. 10 the observation of a shift in the frequency of the second peak over time into the common frequency range as a threatening scenario for a possible rattle event; Fig. 11 an interpolation of the spectrum of a signal in the frequency domain to improve the resolution of the maximum value of the amplitude and / or the frequency of a peak; Fig. 12the additional evaluation of the proximity of a peak's frequency to relevant natural frequencies of the respective rolling stands as a further criterion for detecting a chatter event; and Fig. 13 +14 the additional evaluation of a gradient of peak amplitudes in the amplitude spectrum of at least one rolling mill as a further criterion for the detection of a chatter event illustrated.

[0023] The invention is described in detail below with reference to the figures mentioned, in the form of exemplary embodiments. In all figures, identical technical elements are designated by the same reference numerals.

[0024] Fig. 1Figure 1 illustrates the inventive method for analyzing the vibration behavior of a system consisting of at least one first and one second rolling stand, both coupled to each other by a clamped strip, in particular a metal strip. The method comprises the following steps: a) detecting the vibrations at the first rolling stand n with a first sensor in the form of a first temporal vibration signal; and b) detecting the vibrations at the second rolling stand n+1 with a second sensor in the form of a second temporal vibration signal, simultaneously with the detection of the vibrations at the first rolling stand. The second rolling stand n+1 is arranged downstream of the first rolling stand n in the rolling direction of the strip.As mentioned earlier in the general part of the description, the sensors for detecting vibrations in the time domain, especially in a time interval, do not necessarily have to be attached to the rolling stands themselves; rather, it is sufficient if the sensors each generate a signal in a time interval that represents the vibrations at the respective rolling stand.

[0025] Following this signal acquisition in the time domain, the temporal sensor signals are transformed into the frequency domain, typically using a Fourier transform; see process steps c) and d) in claim 1.

[0026] Figure 2 This illustrates the transformation of oscillation signals from the time domain to the frequency domain. Specifically, the figure at the bottom left shows... Fig. 2The vibration behavior of a rolling mill stand n over a time interval is shown, and to the right of it, the corresponding amplitude spectrum can be seen. The amplitude spectrum here, by way of example or idealization, shows only a first peak P1, whose amplitude, again by way of example, lies below a predefined first amplitude threshold value A1. (Top left in) Figure 2The time-domain signal is shown, again as an example, which depicts the vibration behavior of the second rolling stand n+1 downstream of the first rolling stand n. To the right of this is the corresponding amplitude spectrum after a Fourier transform. This amplitude spectrum, again idealized, consists of only a single peak P2, whose amplitude is obviously smaller than a corresponding second amplitude threshold A2. The first amplitude threshold A1 and the second amplitude threshold A2 can be the same, but they do not have to be. Furthermore, a common frequency range 15 is defined for the two amplitude spectra, within which the respective peaks are to be compared.

[0027] The determination of the common frequency range 15 is carried out in accordance with Fig. 1and claim 1 in process step e). A subsequent first test step f) checks whether the first peak P1 and the second peak P2 each lie in the common frequency range 15; this test step is included in the Fig. 2 The example shown is to be affirmed. However, the maximum value or amplitude of the first peak P1 is below the corresponding first amplitude threshold A1, and the maximum value or amplitude of the second peak P2 is significantly below its corresponding second amplitude threshold A2; therefore, a second test step g) must be denied. In this respect, Figure 2 An example of a situation where no chatter event is detected according to the inventive method. The further procedure in this case is described below with reference to the Figures 7-9 as well as the Figure 13 and 14 described in more detail.

[0028] Fig. 3Figure 1 shows another example of how no chatter event is detected according to the inventive method. In this example, detection fails because only the first peak P1 of the first amplitude spectrum is visible in the defined common frequency range 15; see the lower figure. However, no second peak P2 of the second amplitude spectrum is visible in the common frequency range 15; see the upper figure. Fig. 3 The first test step f) is therefore not fulfilled here. Further proceedings in this case will be described with reference to Fig. 10 described.

[0029] Fig. 4 Finally, it shows the case where a rattle event is detected according to the inventive method. As in Fig. 4 This can be seen in particular when the following two conditions are met: 1. There is a common frequency range 15 in which both a first peak of the first amplitude spectrum (bottom figure) and a second peak of the second amplitude spectrum (see top figure in Fig. 4 ) lie; see test step f). In addition, the second condition of test step g) is fulfilled, namely that both the maximum value of the first peak P1 of the first amplitude spectrum lies above its associated amplitude threshold A1, and that the maximum value of the second peak P2 lies above its associated amplitude threshold A2.

[0030] Fig. 4This illustrates another condition, which, however, is not mandatory for the detection of the chatter event, but merely optional. This condition is that the frequencies of the first peak P1 and the second peak P2 not only both lie within the common frequency range 15, but also additionally within a further frequency range 17, which is even narrower than the common frequency range 15. The existence of this condition indicates sufficient agreement between the two spectra and, if applicable, supports the detection of the chatter event.

[0031] The Figures 5 and 6 Each consists of two superimposed images. The two superimposed images essentially correspond to the Figures 3 and 4 , apart from the further shared frequency range 17, which is in the Figures 5 and 6 is not shown.

[0032] In Fig. 5It can be seen that in the first lower amplitude spectrum, the maximum value of the first peak P1 lies above its corresponding first amplitude threshold A1. No peak in the upper second amplitude spectrum for the adjacent rolling stand n+1 lies within the common frequency range 15. This corresponds to a maximum dissimilarity between the two spectra in the common frequency range. The correlation coefficient, which illustrates the similarity of the superimposed amplitude spectra, is zero here, and thus below any potentially predefined correlation threshold. In the example according to Fig. 5 The test steps f) and g) are not fulfilled and, in addition, the optional correlation criterion, according to which the correlation of the two signals in time period 1 must be above the correlation threshold, is also not fulfilled.

[0033] The in Fig. 6 The embodiment shown differs from the one in the Fig. 5 The illustrated embodiment differs only in that, in this case, the second peak P2 of the second upper amplitude spectrum also lies within the common frequency range 15. In this case, there is maximum similarity between the two spectra, which is expressed as a correlation coefficient of 1. This correlation coefficient is above the correlation threshold KO and thus confirms the detection of a chatter event, as is generally the case with the presence of the first peak P1 and the second peak P2, each within the common frequency range 15 and each above their respective amplitude thresholds A1 and A2. Both test steps f) and g) as well as the optional correlation criterion are fulfilled.

[0034] The previously mentioned reference to the Fig. 2-6The described criteria for a high degree of similarity between the first and second amplitude spectra are merely optional conditions that should preferably be met in addition to test steps f) and g) to reliably detect a chatter event. If any of these conditions do not indicate a high degree of similarity between the first and second amplitude spectra, the detection of the chatter event will be subject to greater uncertainty than if a high degree of similarity is present. The same applies to the early warnings for the future occurrence of a chatter event provided by the method according to the invention.

[0035] The Figs. 7-9 illustrate three case scenarios according to the inventive method according to Fig. 1, where the first test step f) is always fulfilled, i.e., the first peak of the first amplitude spectrum and the second peak of the second amplitude spectrum always lie in the common frequency range 15. However, the second test step g) is not fulfilled – at least initially. In order to obtain an assessment of whether a chatter event is imminent in these cases as well, it is necessary to generate the first amplitude spectrum for the first rolling stand n and the second amplitude spectrum for the second rolling stand n+1 not only for a first time interval 1, but also at least for a second time interval 2 in each case. Figs. 7-9 Three spectra for different time periods 1, 2, and 3 are shown horizontally side by side. This comparison allows for the identification of any trends in the temporal development of the first peak P1 and / or the second peak P2. Time periods 1-3 in the Figures 7-10and 13 - 14 each denote different time periods of the temporal measurement signals underlying the spectra, following one another with or without a pause.

[0036] According to the second test step g), the method according to the invention provides that it is checked whether the first peak P1 and the second peak P2 are each above their respective amplitude thresholds A1 and A2. Fig. 7This applies to the spectra representing the first time interval only for the second spectrum, but not for the first spectrum. The maximum value or amplitude of the first peak P1 is significantly below the first amplitude threshold A1. Therefore, the test specification g) must be rejected in this case. The method according to the invention provides that, in this case, the amplitude spectra of the vibration signals for the first rolling stand are generated not only for the first time interval, but also for a second and optionally also for a third time interval. A comparison of the first amplitude spectrum for time interval 2 with the first amplitude spectrum for time interval 1 shows an increase in the amplitude of the first peak P1, although its amplitude is still below the corresponding first amplitude threshold A1.The first peak P1, together with peak P2, still lies within the common frequency range 15. The amplitude of the second peak P2 is still above the second amplitude threshold A2. However, because, as mentioned, the amplitude of the first peak P1 is still below the first amplitude threshold A1, a chatter event cannot yet be reliably detected. Due to the observed increase in the amplitude of the first peak P1 over time (first early indicator), for example, exceeding a first limit value G1, which is below the first amplitude threshold A1, an initial warning can be issued that critical chatter in the system could occur. This would be the case if the amplitude of the first peak P1 were to increase further over time and eventually exceed the corresponding first amplitude threshold A1, as shown in [reference]. Fig. 7for time period 3. For the situation as it appears in Fig. 7 For the third time period 3, as shown, the detection of the chatter event would be output or displayed according to the inventive method because the conditions according to the first test step f) and the second test step g) would both be fulfilled.

[0037] The issuance of the aforementioned first warning regarding the future occurrence of the rattle event can be made dependent on reaching a first threshold value G1. Only when this first threshold value G1, which is only slightly below the first amplitude threshold A1, is reached or exceeded, and when the amplitude of the first peak P1 is still below the first amplitude threshold A1, will the aforementioned first warning be issued. For the Fig. 8 The following explanations apply to the execution. Fig. 7 analog. In Fig. 8It is assumed that the amplitude of the first peak P1 is above its corresponding first amplitude threshold A1 in all three time periods, and that an increase in the second peak P2 is observed over time (second early indicator), until it exceeds the second amplitude threshold A2. Here, too, issuing an initial warning of a possible future rattle event can depend on whether the amplitude of the second peak P2 has already exceeded a second threshold G2, which is below the second amplitude threshold A2, but has not yet exceeded the second amplitude threshold A2 itself.

[0038] Fig. 9This illustrates a further embodiment in which, in the spectrum for time interval 1, the amplitude of the first peak P1 as well as the amplitude of the second peak P2 are each still below their respective amplitude thresholds A1 and A2, and preferably also below their limit values ​​G1 and G2. In this case, the spectra for the first rolling stand n and for the second rolling stand n+1 must again be determined and compared not only for the first time interval 1, but also for at least one second time interval 2. Fig. 9In the spectra for the second time period 2, an increase in amplitude is discernible for both the first peak P1 and the second peak P2, each in the direction of their respective amplitude thresholds A1 and A2. Therefore, in this case as well, an initial warning can be issued for a possible future rattle event, which will occur when the amplitudes of both the first peak P1 and the second peak P2 exceed their respective amplitude thresholds A1 and A2, as shown for time period 3.

[0039] With reference to the Figs. 7-9 As mentioned, the development of the amplitudes of peaks P1 and P2 over time was examined and, if necessary, an initial warning was issued.

[0040] Fig. 10In contrast, the temporal evolution of the frequency of a peak is illustrated, which can also serve to provide a (second) early warning regarding the possible future occurrence of a rattling event. In an initial situation, it shows Fig. 10 The first and second amplitude spectra are recorded for each time interval 1. It can be seen that only the first peak P1 lies within the common frequency range 15, while the second peak P2 lies outside the common frequency range 15. The frequency difference is Δ. The first test step f) would not be fulfilled here because the first peak P1 and the second peak P2 do not both lie within the common frequency range 15. In this case, it may be advisable to check whether the frequency of the second peak P2 changes over time and approaches the frequency of the first peak P1.

[0041] For this purpose, the first and second amplitude spectra are generated for a second time interval 2 in addition to time interval 1. A comparison of the second amplitude spectrum for time interval 1 and for time interval 2 shows a reduction in the frequency spacing Δ in time interval 2. With the frequency of the first peak in the first amplitude spectrum remaining unchanged, the frequency spacing in the second amplitude spectrum has now decreased to such an extent that the frequency of the second peak P2 lies within the common frequency range 15. Thus, the first test step f) is fulfilled. Since, moreover, both the amplitude of the first peak and the amplitude of the second peak are above their respective amplitude thresholds A1 and A2, the second test step g) is also fulfilled; therefore, the prerequisites for the detection of the chatter event are met.

[0042] Optionally, the first amplitude spectrum and the second amplitude spectrum can also be considered for a third time interval 3; see the two superimposed figures on the right in Fig. 10 . If, in this case, it is additionally determined that the first peak P1 and the second peak P2 lie not only within the common frequency range 15, but also within the even wider, narrower common frequency range 17, then this indicates a particularly high similarity of the spectra, the presence of which further supports the detection of the rattle event.

[0043] The Figures 7-10These figures merely show examples of how the amplitudes and / or frequencies of the peaks can evolve over time towards more critical situations that increase the likelihood of a chattering event occurring. Conversely, however, a constant or decreasing peak amplitude, or a constant or increasing frequency difference between the first and second peaks over time, does not change or reduce the probability of a chattering event occurring.

[0044] Fig. 11This illustrates a method for improving the resolution of the first and / or second amplitude spectrum. In reality, the first and / or second amplitude spectrum typically does not consist of a single peak, as depicted for simplicity in the preceding figures, but rather of a multitude of peaks P1(f-1), P1, P2(f+1). That is, the first peak P1 with frequency f and / or the second peak P2 typically have neighboring peaks in their immediate frequency environment with slightly lower frequencies f-1 and / or slightly higher frequencies f+1. Interpolating these amplitude spectra can, for example, lead to a change or correction of the amplitude and / or frequency of the respective first and / or second peak, as is the case for the first peak P1 in Figure 11This is illustrated. The amplitude and frequency of the first interpolated peak P1' are considered more precise than the frequency and amplitude of the non-interpolated first peak P1. Therefore, the method according to the invention provides that the first and / or second amplitude spectrum is preferably interpolated before one of the test and / or comparison steps is carried out. These test or comparison steps are then carried out with the amplitudes and frequencies of the interpolated peaks P1'; see the first optional intermediate step in Fig. 1 .

[0045] The detection of the chatter event and / or at least one of the early warnings for a future occurrence of the chatter event are output to an operator of the system and / or to an automatic process control system according to the method of the invention. The output of this information may include a recommendation to slow down the system in order to prevent further escalation or the occurrence of the chatter event. This applies in particular if the frequency of at least one of the peaks is less than a predetermined frequency difference from at least one of the natural frequencies of the rolling stands.

[0046] Possible scenarios related to this topic are described in Fig. 12 depicted. The illustration in Fig. 12The lower left shows the first amplitude spectrum for the first rolling stand n for a first time interval 1. Above it is the second amplitude spectrum for the second rolling stand n+1 for the same first time interval 1. It can be seen that both the first peak P1 of the first amplitude spectrum and the second peak P2 of the second amplitude spectrum each fulfill the conditions of the first test step f) and the second test step g). That is, both peaks P1 and P2 lie within the common frequency range 15 and their amplitudes are each above their respective amplitude thresholds A1 and A2. Thus, according to the method according to the invention, the prerequisites for the detection of the chatter event would actually be fulfilled. This is all the more true because both the first peak P1 and the second peak P2 lie within the further common frequency range 17 and thus exhibit an even greater degree of agreement.

[0047] However, the two spectra for time interval 1 also show that both a natural frequency EF1 of the first rolling stand n and a natural frequency EF2 of the second rolling stand n+1 lie outside the wider and narrower common frequency ranges 17, respectively. Based on this, the detection of the chatter event, as generally observed here, could be qualified and called into question. That is, the situation could be considered not so critical with regard to the occurrence of the chatter event, because the peaks still have a sufficient frequency difference from the natural frequencies EF1 and EF2 of the rolling stands.

[0048] For the right half of the Fig. 12 The same description applies as for the left half of the Fig. 12with the following differences: The spectra shown on the right refer to a different, second time interval 2, and it can be seen that the natural frequency EF2 of the second rolling stand n+1 falls, for example, within the wider common frequency range 17 of the first and second peaks P1 and P2. In this case, the original detection of the chatter event is affirmed and confirmed, since the immediate proximity of the frequency of the second peak P2 to the critical natural frequency EF2 of the second rolling stand can lead to an undesirable amplification of the vibrations or to undesirable resonance effects.

[0049] The Figure 13 and 14Each of these illustrates the amplitude gradient as a further criterion that, in addition to the two mandatory criteria according to procedural steps f) and g), can be used – optionally also in combination with one or more of the other previously described criteria – as an indicator of the future occurrence of a rattle event. Specifically, this criterion checks whether the (temporal) gradient of the amplitudes of two peaks in amplitude spectra over different time periods lies above a gradient threshold value or not.

[0050] In other words, the gradient criterion compares the amplitudes Pn of the peaks in an amplitude spectrum at a current time interval (t = t₂) with the amplitudes of the peaks in an amplitude spectrum from a previous time interval (t = t₁) at a specific, predetermined time difference (t₂ - t₁ = Δt = const.) for a rolling mill stand n. This allows for a gradient evaluation of the amplitudes as follows: grad Pn = Pn t 2 − Pn t 1 / Δt

[0051] If the calculated gradient is above a gradient threshold value Gn, this is interpreted as an additional indication of the possible occurrence of a chatter event, at least at the rolling stand n; and vice versa. According to the invention, a positive gradient evaluation then triggers an advance warning to the operator or the automatic control unit of the rolling stand that an amplitude exceedance is to be expected in the future at at least this rolling stand.

[0052] Fig. 13The gradient evaluation is illustrated using the rolling stand n and a downstream rolling stand n+1. For both rolling stands, the peak amplitudes within time intervals 1 and 2 are, as examples, below the respective amplitude thresholds A1 and A2. The gradient evaluation is performed separately for the rolling stand n=1 and for the rolling stand n+1=2 according to formula (1). For both rolling stands, the determined gradient grad P1 and grad P2 are above the individually assigned gradient thresholds G1 and G2, respectively (in Fig. 13 (not shown). This suggests that in a future time interval 3, the amplitudes of the peaks of the amplitude spectra for both rolling stands will be above their individual amplitude thresholds A1 and A2, respectively. The occurrence of these expected events is shown in the right-hand figures in Fig. 13 .

[0053] Fig. 14The gradient evaluation is illustrated using only the rolling stand n as an example. For the neighboring rolling stand n+1, it was assumed for simplicity that the amplitudes of the peaks in the amplitude spectra over time periods 1, 2, and 3 are always above the corresponding amplitude threshold A2. Therefore, only a gradient evaluation for rolling stand n is required. For rolling stand n, the amplitudes of the peaks within time periods 1 and 2 are below the respective amplitude threshold A1. The gradient evaluation is performed according to formula (1) for rolling stand n=1. For rolling stand n, the determined gradient grad P1 is above the gradient threshold (in Fig. 14(not shown). This suggests that in a future time interval 3, the amplitude of the peaks of the amplitude spectrum for the rolling stand n will also be above the individual amplitude threshold A1. The occurrence of this expected event is shown in the lower right figure in Fig. 14 The upper right image in Fig. 14 shows that the amplitude of the peak in the amplitude spectrum for the neighboring rolling stand n+1 is still above the amplitude threshold A2 even over the later time period 3. Reference symbol list

[0054] A1 First amplitude threshold A2 Second amplitude threshold 15 Common frequency range 17 Narrower common frequency range EF1 Natural frequency of the first rolling stand EF2 Natural frequency of the second rolling stand G1 First limit value G2 Second limit value KO Correlation threshold First rolling stand n +1 Second rolling stand P1 First peak P1' First interpolated peak P1 (f-1) Neighbor peak with a lower frequency than P1 P1 (f+1) Neighbor peak with a higher frequency than P1 P2 Second peak Δ Frequency difference / Frequency spacing t 1 Time interval 1 t 2 Time interval 2

Claims

1. Method of analysing the vibration behaviour of a system consisting of at least one first roll stand and at least one second roll stand, which are coupled together by way of a strip, particularly a metal strip, clamped in place in the two roll stands, comprising the following steps: a) detecting the vibrations at the first roll stand by a first sensor in the form of a first vibration signal over time; b) detecting the vibrations at the second roll stand by a second sensor in the form of a second vibration signal over time simultaneously with detection of the vibrations of the first roll stand; c) transforming the first vibration signal in a first time segment into the frequency domain, resulting in a first amplitude spectrum for the first time segment; characterised by d) transforming the second vibration signal in the first time segment into the frequency domain, resulting in a second amplitude spectrum for the first time segment; e) determining a common frequency range in which the first amplitude spectrum and the second amplitude spectrum are compared with one another; f) checking whether there are at least one first peak in the first amplitude spectrum and at least one second peak in the second amplitude spectrum which both lie in the common frequency range; g) checking whether the first peak exceeds a predetermined first amplitude threshold value (A1) and the second peak exceeds a second predetermined amplitude threshold value (A2); and h) detecting occurrence of a chatter event if the two checking steps f) and g) are each answered in the affirmative.

2. Method according to claim 1, characterised by the following steps if the checking step f) is answered in the affirmative, but the checking step g) answered in the negative because the first peak (P1) lies below the first amplitude threshold value (A1): - transforming at least one second time segment of the first vibration signal into the frequency domain, resulting in the first amplitude spectrum for at least the second time segment; - comparing the peaks of the first amplitude spectrum in the common frequency range (15) for the first time segment and for at least the second time segment with one another with regard to whether a rise in the amplitude of the peak for the second time segment by comparison with the amplitude of the peak of the first time segment, preferably above a lower limit value (G1) below the first amplitude threshold value (A1), is recognisable as first early indicator; and - issuing a first advance warning that critical chatter of the system could arise if the first early indicator is given and the second peak in the common frequency range for at least one of the considered time segments, preferably for all considered time segments, lies above the second amplitude threshold value (A2).

3. Method according to any one of the preceding claims, characterised by the following steps if the checking step f) is answered in the affirmative, but the checking step g) is answered in the negative because the second peak (P2) lies below the second amplitude threshold value (A2); - transforming at least one second time segment of the second vibration signal into the frequency domain, resulting in the second amplitude spectrum for at least the second time segment; - comparing the peaks (P2) of the second amplitude spectrum in the common frequency range (15) for the first time segment and for at least the second time segment with one another with regard to whether a rise in the amplitude of the peak (P2) for the second time segment by comparison with the amplitude of the peak (P2) for the first time segment, preferably above a lower limit value (G2) below the second amplitude threshold value (A2), is recognisable as second early indicator; and - issuing a first advance warning that critical chatter of the system could rise if the second early indicator is given and the first peak in the common frequency range for at least one of the considered time segments, preferably for all of the considered time segments, lies above the first amplitude threshold value (A1).

4. Method according to claim 2 and 3, characterised by the following steps if the checking step f) is answered in the affirmative, but the checking step g) is answered in the negative because the first peak (P1) lies below the first amplitude threshold value (A1) and the second peak (P2) below the second amplitude threshold value (A2); - carrying out the two transformation steps and the two comparison steps according to claim 2 and claim 3; and - issuing a first advance warning that critical chatter of the system could arise if the early indicator is given in each of the two comparison steps.

5. Method according to any one of the preceding claims, characterised by the following steps if the checking step f) is answered in the negative because the first peak (P1) and / or the second peak (P2) lies or lie outside the common frequency range (15): - transforming at least one second time segment of the at least one relevant vibration signal into the frequency domain, resulting in the relevant amplitude spectrum for at least the second time segment; - comparing the peaks of the relevant amplitude spectrum in the common frequency range (15) for the first time segment and for at least the second time segment with one another with regard to whether a displacement of the frequency of the peak for the second time segment by comparison with the frequency of the peak for the first time segment has taken place in a defined area around the common frequency range (15); and - issuing a second advance warning that critical chatter of the system could arise if the frequency of the relevant peak has run into the area of the common frequency range (15) and if in addition the checking step g) is answered in the affirmative.

6. Method according to any one of the preceding claims, characterised in that detection of the chatter event or issue of the first or second advance warning takes place only if in addition: - the correlation of the two signals in the time segment lies above the correlation threshold value (KO); and / or - the natural frequencies of the first roll stand (EF1) and / or the second roll stand (EF2) lie within the common frequency range (15) and preferably also within the further (narrower) common frequency range (17); and / or - the frequency of the first peak (P1) and the frequency of the second peak (P2) lie within a further common frequency range (17) which is narrower than the common frequency range (15); and / or - an amplitude gradient determined in accordance with the equation grad Pn = Pn t 2 − Pn t 1 / Δt for the first roll stand n = 1 lies above an individual gradient threshold value (G1), wherein: n roll stand t1, t2 time segment 1, time segment 2 Δt time difference t2 - t1 = const. Pn amplitude of the peak for the roll stand n1 and either the amplitude of the peaks of the amplitude spectrum of the second roll stand (P2) was positioned or lies above the associated amplitude threshold value (A2) already during the time segments 1, 2 and 3 or the gradient for the second roll stand according to the equation (1) also lies above an individual gradient threshold value (G2).

7. Method according to any one of the preceding claims, characterised in that the first and / or the second amplitude spectrum before carrying out one of the checking steps and / or one of the comparison steps is or are interpolated into the frequency range.

8. Method according to any one of the preceding claims, characterised in that detection of the chatter event and / or at least one of the advance warnings is issued to an operator of the system or an automatic process control of the system, for example with the recommendation to slow down the system particularly if at least the frequency of one of the peaks is separated from at least one of the natural frequencies of the roll stands by less than a predetermined frequency separation.

9. Method according to any one of the preceding claims, characterised in that each of the first roll stand and the second roll stand is a cold-rolling stand.

10. Computer program product which can be downloaded directly into the internal memory of a digital computer and comprises software code segments by which the steps in accordance with at least one of the preceding method claims are executed when the product is run on the computer.