CHATTER DETECTION USING PRINCIPAL COMPONENT ANALYSIS IN COLD ROLLING MILL

Most cold rolling mills are prone to chatter problem. Chatter marks are often observed on the strip surface in cold rolling mill leading to downgrade and rejection of rolled material. Chatter impact product quality as well as productivity of mill. In absence of online chatter detection no corrective action can be taken immediately and whole campaign gets affected. Most conventional approach for online chatter detection is by using vibration measurement of mill stands in time & frequency domain. Present work proposes two approaches to detect chatter in cold rolling mill using a statistical technique called Principal Component Analysis (PCA). In this paper two methods are used for chatter detection. First method applies PCA on Fast Fourier Transform (FFT) to differentiate between chatter and non-chatter condition. Second method applies PCA on statistical parameters calculated from raw vibration data to detect chatter.


INTRODUCTION
In cold roll mill alternate dark & bright bands are often observed on rolled strip surface along the length of the coil perpendicular to rolling direction.These bands on strip surface are called chatter mark defect shown in Fig. 1.Pitch of these bands varies from 10 to 40 mm.Like most cold rolling mills Pickling Line Tandem Cold Rolling Mill (PLTCM), Tata steel, Jamshedpur is also prone to chatter problem.PLTCM is 5 Stand 6 high Universal Crown mill with annual production capacity of 2 million tons.Chatter mark defects are often observed on the strip surface leading to down grade and rejection of coils.Chattering impacts product quality as well as hampers production due to frequent strip breakages.In absence of online detection system chatter defects are caught after one week of actual rolling at inspection stations just before dispatching coils to the customers.So, no corrective action can be taken immediately and the whole campaign is affected.A project has been initiated by Automation Division for developing an Online Chatter Detection system in PLTCM.
A considerable amount of research has been done on the chatter generation phenomenon in rolling mills.It is well established; chattering is caused by mill vibrations called third octave & fifth octave [1].The terms third octave & fifth octave relate to definition of musical frequency ranges and were used historically to distinguish two problems.Third octave vibrations are in the frequency range of 100Hz to 200 Hz.It is due to self-excitation of one of the natural frequency components of mill stand due to changes in rolling condition like friction, emulsion heat dissipating properties, etc.Under resonance mill vibrate with larger amplitude leading to large periodic thickness gauge variation in the strip.Its severity increases with mill speed.If mill speed is not decreased vibration amplitude increases rapidly leading to strip breakage.Sometimes it significantly hampers productivity of the mill by limiting the top speed of the mill.A good amount of work has been done for chatter detection in rolling processes.In reference [1] T. Farley explains the phenomenon of third octave and fifth octave chatter observed in cold rolling mills and their causes.Some authors used theoretical approach to study chatter using simulations.The objective of these simulations is to find effects of various rolling parameters on the stable rolling limit.In [2] J. Tlusty explained third octave chatter in detail.Tandem mill was simulated to study the effect of rolling speed, strip width, friction coefficient, and tuned dampers on third octave chatter.Similarly, in [3] electric drive & control system parameter was investigated to find a stable rolling region in domain of electrical drive parameters.
According to some authors rolls, gears and other mill part vibration kinematics frequencies are a source of chatter generation.They stated that chatter marks on the roll and strip surface are the result of resonance in the mill due to an integer number of defect wavelength along the roll circumference.These models are represented in references [4,5,6].In references [7, 8] contact friction and emulsion instability is considered as a source of vibrations.During the emulsion breakdown heat generated in metallic deformation is not properly dissipated.This heat energy is dissipated in the form of large vertical vibration amplitudes of work rolls in mill stand.Some authors [9,10,11] successfully investigated the roll grinding process influence on the strip chatter marks and mill vibration.They showed the exact relation between usually invisible roll surface defects after grinding and chatter vibrations in the rolling mill.Some companies supply passive & active vibration dampers that can be installed in mill stands to dissipate vibrations [12].As reported by designers such devices allow increasing mill speed by 25-30%.However, some structural modification in required in a mill which is not always feasible.Some authors have used vibration measurement & analysis for chatter detection.At Arcelor Mardyck cold rolling mill, online chatter detection system is developed for third octave using vibration measurement at mill stands [13].In reference [14] time varying kurtosis of vibration measurement is used for chatter detection.
Principal Component Analysis (PCA) can be used for differentiating healthy and unhealthy conditions by capturing small differences in the data set for two conditions.PCA is used in fault detection using vibration data in reference [15,16].In present paper PCA is applied in vibration measurement for chatter detection.

PRINCIPAL COMPONENT ANALYSIS
Principal Component Analysis (PCA) is a statistical tool for variables reduction and analysis.
It is used to obtain a smaller number of artificial variables from the large number of observed variables that will account for most of the variations in observed variables in the data set.The number of artificial variables called principal components are less than or equal to original observed variables.The first component extracted in a principal component analysis accounts for a maximal amount of total variance in the observed variables.Under typical conditions, the first component will be correlated with at least some of the observed variables.The second component extracted will have two important characteristics.First, this component will account for a maximal amount of variance in the data set that was not accounted for by the first component.Again, under typical conditions, second component will be correlated with some of the observed variables that did not display strong correlations with component 1.The second characteristic of the second component is that it will be uncorrelated with the first component i.e. orthogonal.The remaining components that are extracted in the analysis, display the same two characteristics: each component accounts for a maximal amount of variance in the observed variables that was not accounted for by the preceding components, and is uncorrelated with all of the preceding components.PCA capture variables which have the highest impact on variance within the data set and this forms the basis of chatter detection.
This paper involves the use of two methods for chatter detection.First method uses Fast Fourier Transform (FFT) data for chatter detection.PCA is applied to distinguish FFT pattern between chatter and non-chatter condition.In second method 10 statistical parameters are calculated using high frequency raw vibration data.PCA is applied to these 10 parameters to distinguish between chatter and non-chatter condition.

DATA ACQUISITION
Accelerometers are installed on mill housing on Operator Side (OS) in mill Stand #2, #3, #4, # 5 as shown in Fig. 2. As sensor installed on stand#2 was giving small vibration amplitude, a sensor on stand #1 was not installed.For chatter detection, vibration measurement in Stand#3, #4, #5 is important.The vibration measurement is done at a sampling frequency of 10 KHz.The raw vibration data from sensors on mill stand are transmitted through fibre optic cable to controller PC in the control room.In controller PC raw data is processed & data are saved in database in the workstation.Workstation is connected to the Centralised Condition Monitoring System (CCMS) on which HMI (Web Application) is hosted for online chatter monitoring.See Fig. 3 for complete system architecture of chatter detection system.

CHATTER DETECTION
Two methods are used for chatter detection.First method uses FFT data for chatter detection while the second method uses 10 statistical parameters for chatter detection .PCA is used in both methods to distinguish between chatter and non-chatter condition.As chatter marks can come from any stand of mill each stand is investigated separately.

Chatter detection using FFT data
Raw vibration data is collected for 14 coils with chatter marks and 43 non-chatter coils for Stand#2, Stand#3, Stand#4, and Stand #5 at 10 KHz when the mill is running at constant speed.All the 57 coils are of similar grade and sections.FFT is performed on raw data using a Hanning window with frequency resolution of 1 Hz.Graph in Fig. 4 1.For example F20 is calculated by summing FFT amplitude in the frequency range 0 Hz to 20 Hz.After grouping FFT data of 43 non chatter coils in 14 variables, the data set is centered and PCA is applied.The Hotelling T 2 value is calculated using equation 1 to compare chatter and non-chatter coils.Table 2 shows 10 principal components (PC 1 , PC 2 , PC 3 , PC 4 , PC 5 , PC 6 , PC 7 , PC 8 , PC 9 , PC 10 ) derived from 43 non-chatter coils FFT data for Stand#5.Variables F20, F100, F200 etc. are described in Table 1.Top 6 principal components are taken in Hoteling T 2 score calculations as it covers 90 % of the variance.The Hotelling T 2 score is calculated for each 43 non-chatter coils.For comparison data set of chatter coils is centered by subtracting each variable of every coil (14 chatter coils) by mean of the corresponding variable (F20, F100, F200...) of non chatter coils.After this Hotelling T 2 scores for 14 chatter coils is calculated.The comparison is shown in Fig. 5 for non-chatter and chatter coils for Stand#5.In graph shown in Fig. 5 Coil1 to Coil43 are non -chatter coils (green diamonds), Coil44 to Coil57 (red squares) are chatter coils.For better visualization and comparison logarithmic scale is used.Similar comparison is shown in Fig. 6 for Stand#4.
The graph is Fig. 5 clearly distinguishes between chatter and non-chatter coils for Stand#5.For Stand#4 in Fig. 6 there in no such distinction between chatter and non-chatter coils.For Stand#3 and Stand#2 results are similar to Stand#4 and not shown here.Generally in PLTCM, chatter comes from Stand#4 or Stand#5.This shows that for these 14 coils chatter marks are generated in Stand#5.

Chatter detection using Statistical Parameters
Raw vibration data is collected for 14 chatter coils and 43 non-chatter coils for Stand#2, Stand#3, Stand#4, and Stand #5 at 10 KHz when the mill is running at constant speed.The raw data is filtered using Butterworth fourth order low pass filter with cutoff frequency of 1300 Hz.One second raw vibration data is used to calculate 10 parameters, as given in Table 3.It is made sure that when the sample is taken mill is steady and running at top speed.This is done to capture steady state condition and avoid any transient.PCA is applied to these 10 parameters for 43 non-chatter coils.Table 4 shows four principal components ((PC 1 , PC 2 , PC 3 , PC 4 ) derived for stand#5.Top 3 principal components (PC 1 , PC 2 , and PC 3 ) are taken in Hoteling T 2 score calculations as it covers 90 % of the variation.The Hotelling T 2 score is calculated for each 43 non-chatter coils.For comparison data set of chatter coils is centered by subtracting each variable of every coil (14 chatter coils) by mean of the corresponding variable (RMS, Kurt, Skew ...) of non chatter coils.After this Hotelling T 2 scores for 14 chatter coils is calculated.Fig. 7 shows 3D plot of chatter and nonchatters along PC 1 , PC 2 , and PC 3 axis for Stand#5.Also Hotelling T 2 score comparison is shown in Fig. 8 for non-chatter and chatter coils for Stand#5.Similar comparison is shown in Fig. 9 for Stand#4.
The graph is Fig. 7 and Fig. 8 clearly differentiate between chatter and non-chatter coils for Stand#5.For Stand#4 there in no such distinction between chatter and non-chatter coils shown in Fig. 9.This shows that chatter in these 14 coils is generated in Stand #5.For Stand#3 and Stand#2 results are similar to Stand#4 and not shown here.

RESU
This w for chatte is Fig. 5

Fig. 1 .
Fig. 1.Chatter marks on strip surface along the length perpendicular to rolling direction (RD) Fifth octave vibrations are forced vibration in the frequency range of 600 Hz to 1200 Hz.It is due resonance in mill stands excited from some external source.Chatter marks are generated on backup rolls & printed via work rolls on the surface of the strip with spacing between 10mm to 40 mm.Typical sources of fifth octave vibrations are defective gear teeth, roll bearings and drive couplings.Another major source of these vibrations is periodic submicron level defects developed on roll surface

Fig. 2 .
Fig. 2. Schematic diagram of sensor installation on mill stand shows the frequency spectrum of chatter and non-chatter coil.Spikes with large amplitude are visible in range 0 20 Hz.Spikes are visible in different frequency ranges as shown in Fig. 4. No vibration is visible above 1300 Hz.Therefore, frequency range is limited from 0 Hz to 1300 Hz for analysis.

Fig. 4 .
Fig. 4. Frequency spectrum of chatter and non-chatter coil Applying PCA on 1300 variables gave a large number of Principal Components (PC).To simplify, 1300 variables are clubbed into 14 new variables by grouping based on frequency spectrum shown in Fig. 4. 14 new groups are formed by summing FFT amplitude deviation of 1,2,3..n principal components respectively.
Fig. 5. Comparison between non-chatter and chatter coils for Stand#5 using FFT data

Table 1 .
Grouping of Variables

Table 3 .
List of Statistical Parameters