Chatter detection techniques using microphone Edouard Rivi´ ere∗ ,V. Stalon∗ , O. Van den Abeele∗ , Enrico Filippi∗ , Pierre Dehombreux∗ ∗ Facult´ e Polytechnique de Mons, Service de G´ enie m´ ecanique Rue du Joncquois, 53 - 7000 Mons email:
[email protected],
[email protected],
[email protected] Abstract— In milling operations, chatter vibration is one of the main factors that lower the productivity. This phenomenon is responsible of poor surface quality and increases cutting forces. Higher efforts tend to accelerate tool wear and can lead to tool breakage. Two main fields of research try to improve control of the process: prediction and on line detection. Prediction techniques simulate behavior of the machining system and try to anticipate vibratory behavior in order to compute optimal parameters for a given operation (spindle speed, depth of cut,...). On line detection techniques try to detect instability using sensors (force sensor, accelerometer, microphone,...) and signal processing. On line detection often needs fewer data about the studied system (sometimes restricted to current spindle speed) and can give important information for control techniques. In this paper, three chatter detection techniques are presented and experimentally tested. The first one is based on the measured signal level, the second one studies the frequency content of the signal and the last one uses the variance of the signal sampled at a once per revolution rate. Each method is initially applied to a signal given by numerical simulation of the milling process. Ideal signal and signal disturbed by a random white noise are studied. This first step validates the three detection methods. These techniques are then used to analyze signals from milling operations tests. We used a microphone as chatter detection sensor, which can easily measure a signal without disturbing the system. Machined workpiece is clamped in a very simple structure designed to be as close as possible from a single degree of freedom system. This simplifies the frequency content of the signal and thus makes detection easier.
Our goal is to develop simple and low-cost techniques easily usable by small companies facing that kind of problems. On line detection techniques can then be used as starting point to control machining process in-line (see for example [5], [6], [7], [8]). Our first reflexion is based on the best suitable sensor for chatter detection. Then three different analysis method would be tested on simulated and real machining tests. II. Selection of sensor Detection techniques are based on a signal measured inline during machining process. A. Force sensor Cutting forces can be measured to detect chatter, but also to monitor tool wear and tool breakage. There are two main types of force sensor in milling : dynamometric table on which the blank is attach and rotating dynamometers hodling the tool and rotating with the spindle. Some other techniques can be used to determine efforts in milling, using current intensity that leads to power thus to torque.
Those three techniques are easy to implement and give accurate results for chatter detection as far as the threshold between stable and unstable is carefully chosen. Keywords— Chatter detection, sensor, microphone
I. Forewords
I
N milling operations, self excited vibrations (also called ’chatter’) is one of the main factor that limits productivity. The consequences of this phenomenon is poor quality of surface, higher cutting forces implying higher wear of the tool or even tool breakage. Many researchs were made in that field. The aim is to find stable zones where the metal removal rate is high and stability acceptable. Two main solutions were proposed : prediction using analytic or dynamic simulation and on line techniques. Simulation tends to predict the behavior of the system to determine optimal parameters (spindle speed, depth of cut,...). These techniques need a high level of expertise and sometimes expensive hardware. Software for simulation of machining process exist (For example Cutpro[1] developed by Malinc Labs). On line techniques monitor milling process and try to detect when the instability limit is reached. Many authors used several techniques to reach that objective ([2], [3],[4]).
Fig. 1. Kistler dynamometer for cutting forces measurement Such types of sensor are very useful, but they have limitations: • while machining less resistant material, efforts are low so the sensitivity must be high to detect these efforts; • while using small immersion (i.e. in finishing operation), efforts and the time spent to cut is also low and could be insufficient to detect chatter; • the bandwidth of the sensor must be as high as possible to allow accurate measurement (a typical sensor has a bandwidth of 1000 Hz); • using rotating dynamometer increases tool overhang and modify the dynamics of the unit spindle/toolholder/tool.
B. Accelerometer The mounting of an accelerometer is easy but its location must be carefully chosen. Indeed, if the sensor is close to a vibration node, signal amplitude would be very low. During the milling process, nodes can move, so it is very difficult to predict an optimal location. Accelerometer and displacement sensors are subject to alteration of the signal due to sensitivity to displacement. It is also very difficult to put accelerometer on a rotating part. C. Microphone Smith[9] found that the acoustic pressure emitted by a structure during machining is proportional to the displacement of the tool. It is thus possible to use a microphone as sensor to predict chatter instability. While in condition of stable cut, dominant frequencies are spindle speed (and harmonics) and tooth passing frequency. When instability is reached, some other frequencies appear[10]. The detection of peak at frequency different from spindle speed or tooth passing frequency is a way to detect chatter. The use of a microphone is simple and does not imply positioning problems as the other types of sensors. It must be noted that ambient condition (environmental noise, reflection, near field) can distort the signal.
Fig. 2. Frequency analysis of sound pressure, stable case (from [11] )
Fig. 3. Frequency analysis of sound pressure, unstable case (from [11] )
Microphone is already used in commercial software such as Accord Mill[12] and Harmonizer[13]. III. Chatter detection technique The rest of this paper is dedicated to the detection of chatter using a microphone. The microphone was chosen because of its fairly low cost and the simplicity of implementation. The methods described in this paper are applied to signal given by a microphone, but they are also suitable for displacement, acceleration or effort signal. The method used to detect chatter can be used to detect tool breakage[14]. The studied methods are based upon signal level, frequency content of the signal and variance of the signal sampled once per revolution. Two or more techniques can be combined to reduce the disadvantages and to benefit from the advantages. A. Level-based methods The simplest technique to detect chatter is to fix a threshold for the acoustic pressure emitted by the operation. Above this level, we consider that chatter occurs. The main handicap of this method is the way of choosing an adequate threshold. Two kinds of methods are shown in the literature. The simplest compares the amplitude of the acoustic pressure to a measure made in stable condition. This technique is dependent on working condition. In some other cases, the frequency of the highest peak is compared to the mean of the low frequency spectrum multiplied by a scalar factor (6 to 10 times). If the amplitude goes over this threshold, chatter is detected. Figure 2 and 3 shows typical signal for stable and instable signal. The dominant peak is visible. This technique is fairly simple, but the scalar factor that determines the threshold is difficult to establish. B. Frequency of the highest peak Another technique consists in the analysis of the frequency of the highest peak given by the frequency spectrum of the signal. Frequency content of the signal is different while machining in stable or unstable condition. Stable signal is mainly composed of tooth passing frequency and spindle speed peaks and harmonics. Some other peaks can result from ambient noise. Unstable signal contains frequencies close to dominant eigenfrequency of the structure which is often called ’chatter frequency’. The acoustic pressure measurement is transformed in frequency chart using fast Fourier transformation (FFT). The peaks corresponding to the stable frequencies (tooth passing frequency and spindle speed) are removed from the signal. This method needs more information about the machining condition (spindle speed and number of teeth) and requires more computations. On the other hand, it permits to know the frequency of the dominant chatter frequency. This information can be useful for some control techniques.
C. Statistical detection In order to reduce the amount of data processing, several authors developed statistical methods. Delio[3] proposes a method based in the measurement of acoustic pressure at a once per revolution rate. In stable cut, the tool moves at the same frequency as the spindle. Its position is the same for each rotation (see figure 4). While chatter occurs, the frequency of the vibration is different and the tool tends to have an elliptical movement (see figure5). Sampling can use synchronization with spindle speed or signal given by infrared sensor detecting a reflective mark on the spindle. The variance of the sample σ 2 is computed according to PN 2 2 i=1 xi − xm 2 (1) σ = N −1 where N is the size of the sample, xi the data and xm the mean value given by : xm =
PN
i=1
xi
(2)
N
This method needs simplest computing, and the amount of data is smaller. Disadvantage lies in the missing information of the chatter frequency and the need of fixing a threshold for chatter. IV. Validation test case using dynamic simulation Techniques shown in previous section were at first tested on signals given by dynamic simulation of milling (method described in [15]). The studied system is described hereafter: • single flute cylindrical mill with zero helix angle; • constant spindle speed of 3500 RPM; • half immersion downmilling with several axial depth of cut (0, 1; 0, 2; 0, 4; 0, 6; 0, 8; 1; 1, 2; 1, 4; 1, 6; 1, 8; 2; 3; 4; 5 mm); • flexible workpiece perpendicularly to the feed direction modeled as single degree of freedom (’mass-springdamper’) f = 100 Hz, k=10 kN/m; ξ =0, 4%. Stability lobes computed with the analytical method[16] are shown in figures 6 and 7.
By fixing a threshold for the variance, it is possible to determine when chatter occurs.
35
Axial depth of cut (mm)
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0 −0.5 0.5 Displacement (µm)
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Fig. 6. Stability lobes for the simulated system
Fig. 4. Displacement and sampling of the signal once per revolution, stable case 5 4.5
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Fig. 7. Zoom at 3500 RPM Fig. 5. Displacement and sampling of the signal once per revolution, unstable case A. Signal identification The method is transposable to acoustic pressure detection by sampling once per revolution acoustic pressure and computing variance of the signal. While the variance exceeds a threshold, chatter is detected.
The time domain simulation produces temporal evolution of the different signals (displacement, efforts,...). It is thus possible to examine the signal closely to determine if the system is stable or unstable. Figure 8 shows the
0.02 0.015 0.01 displacement (mm)
value. Our simulation would allow us to find a threshold comparing stable case (0,1 mm depth of cut) to the last stable simulation (0,8 mm depth of cut). White noise does not significantly influence the computation. The ratio between dominant peak amplitude is about 8. We would use this value for the experimental validation later on. 0.06
Amplitude of the dominant peak (m)
displacement evolution for a stable case. The amplitude of the vibration is constant after transient period of time. Figure 9 is the first depth of cut where the system becomes unstable (vibration amplitude is growing instead of reaching a steady state). The amplitude growth would only be limited by the fact that tooth jumps out of the material. The limit between stable and unstable case is thus between 0, 8 and 1 mm.
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Fig. 8. Axial depth of cut = 0,1 mm, stable case
Fig. 10. Evolution of the amplitude of the highest peak: original signal (plain) and signal with white noise (dashed)
C. Frequency content identification While the depth of cut is small, the signal is stable and the dominant frequency is the second harmonic of tooth passing frequency. As the depth of cut grows, chatter frequency (close to natural frequency of the system) becomes more and more important. We can achieve instability while dominant frequency is different from an harmonic of tooth passing frequency. The results are given in table I.
0.02 0.015
displacement (mm)
0.01 0.005 0 −0.005 −0.01 −0.015 −0.02 0
2
4
6
8
10
time (s)
Fig. 9. Axial depth of cut = 1 mm, unstable case Two time series are studied : the first one is the raw signal given by dynamic simulation, the second one is is the superimposition of a random white noise to the original signal in order to distort the ’perfect’ signals. The amplitude of the white noise is 5 % of the maximum amplitude of the original signal. Both results are analyzed using fast Fourier transformation method using a script written in Matlab. Hanning windowing is used before frequency analysis. B. Level-based method In this method, the amplitude of the dominant peak in the frequency spectrum of the signal is computed. This amplitude is a monotonic increasing function of axial depth of cut. The instability is assessed using a threshold on that
ADOC (mm) 0,1 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8 2 3 4 5
Frequency (Hz) 116,7 116,7 116,7 116,7 116,7 100,5 100,5 100,5 100,5 100,6 100,6 100,7 100,8 100,9
TABLE I Dominant frequency of the simulated signal
The limit of stability is at 0,8 mm, which is in agreement with the observation of the signal. There is no significant
difference between original signal and signal with white noise. D. Statistical method As for the level-based method, this technique requires a threshold to assess instability. The evolution of the variance of the signal sampled once per revolution is available in figure 11. Original signal and disturbed signal follow the same trend, but the difference is more significant. Threshold is fixed as the ratio between variance at 0,1 mm depth of cut and variance at 0,8 mm depth of cut. We would then use this value of about 10 for this threshold during experimental validation.
performed at three different spindle speeds (1200, 1500 and 1800 RPM) and axial depths of cut ranging from 0, 3 mm to 1, 5 mm. This paper presents the results obtained while analyzing the 1200 RPM series.
0.02 0.018 0.016
2
variance of the signal (mm )
Fig. 12. Experimental setup
0.014 0.012
A. Level-based method
0.01
The method is tested at 1200 RPM. Amplitude of the highest peak is compared to a threshold to assess stability. The threshold is chosen as eight time the maximum amplitude in an ambient noise measurement i.e. 7, 818 mV. The results are listed in table II and plotted in figure 13.
0.008 0.006 0.004 0.002 0 0
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ADOC (mm) 0,3 0,5 0,75 1 1,25 1,5
Fig. 11. Evolution of the variance of the signal sampled once per revolution : original signal (plain) and signal with white noise (dashed)
E. Summary of the methods on simulated signal
V. Validation testcase Detection methods presented in this paper were tested in real conditions. Several machining tests were performed on a Maho MH500EZ milling machine. Experiments consist in slotting and half immersion up and downmilling of steel test pieces. In order to simplify the dynamic behavior of the system, the test pieces were clamped on a flexible structure that has been designed to be as close as possible from a single degree of freedom system (natural frequency 120, 4 Hz, damping ratio 0, 38%). We used a 3-fluted cylindrical carbide tool with no helix angle. The signal was recorded using a microphone (Bruel & Kjaer 2236) to measure acoustic pressure and an accelerometer mounted on the fixture. Tests were
TABLE II Amplitude of the highest peak, experimental validation
18 16 14 Amplitude (mV)
Simulated signal is analyzed using three methods of detection. The comparison between direct observation of the signal and evolution of instability indicators is good : • chatter frequency becomes dominant while signal becomes unstable; • slope of the chart amplitude of the highest peak - axial depth of cut (or variance - axial depth of cut) increases while instability is reached; • threshold value of 8 for amplitude method and 10 for variance method are in good agreement with the literature.
Amplitude (mV) 3,8 4,2 5,6 10,1 12,7 16,1
12 10 8
Treshold
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1.2
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Fig. 13. Evolution of signal amplitude versus axial depth of cut The limit for stable condition is between 0,75 and 1 mm. This is in good agreement with the observation where
roughness is dramatically worse for the testpieces machined with a depth of cut higher than 0,75mm. The same methods was tested with the signal from the accelerometer, the results are the same. This method is well adapted for this kind of detection.
The method assesses that the system is unstable when the chatter frequency dominates the signal. Table III lists the dominant frequency for each case. So here instability is detected a bit earlier than with the previous method. C. Statistical method
B. Frequency content identification Again FFT of the signal for the 1200 RPM series is performed, but here the frequency of the highest peak is detected. The figures 14 and 15 show results at 0, 3 and 1, 5 mm depth of cut. For small depth of cut, signal is, as predicted, dominated by the harmonic of tooth passing period. While the depth of cut is high, chatter frequency becomes dominant.
0.016
Amplitude (V)
0.014 0.012
Previous methods need computation of FFT, so if the frequency range considered is high, many point are needed and computing time can be inappropriate for a real-time analysis. Methods based on the variance of the signal sampled once by revolution are good and allow precise detection with few calculations. Figure 16 shows the evolution of that variance computed for the same measure as in the previous example. Threshold is fixed at 14·10−4V so the limit between stable and unstable case is between 0, 75 and 1mm. This is coherent with the conclusions of the other methods. We can also notice that, as observed in simulated example, the slope of the curve is increasing while chatter occurs.
Tooth passing period
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Fig. 14. FFT of the signal, 1200 RPM, ADOC=0,3 mm
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Fig. 16. Evolution of the variance
0.012 Tooth passing period
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VI. Conclusion
0.006 0.004 0.002 0 0
50
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150 200 250 Frequency (Hz)
300
350
400
Fig. 15. FFT of the signal, 1200 RPM, ADOC=1,5 mm
ADOC (mm) 0,3 0,5 0,75 1 1,25 1,5
Dominant frequency (Hz) 119,7 119,7 150,4 150,4 150,4 150,4
TABLE III Dominant frequency of the signal, experimental validation
In this article, three methods to detect chatter vibration during machining using a microphone are studied and tested. First of all, the methods are tested on signals given by dynamic simulation. The techniques tested over two data sets are studied : the raw signal from the simulation and the same signal disturbed by a random white noise. For both case, we can see that the detection technique give good results. Threshold between stable and unstable conditions can be established during this phase. Then the same methods are tested on real machining tests performed on steel testpieces clamped on a flexible structure. The results are in good agreement with the observation. Each method has its own advantages and disadvantages. • amplitude-based method is one of the most common method. The difficulty lies in the threshold needed to assess instability. It must be carefully chosen to ensure good precision; • frequency identification method does not need threshold an can give useful information to proceed active control.
This method however needs some information about the actual machining condition (spindle speed for example). • variance method needs less computation than the other methods. It can be more suitable for real-time control, but again a threshold is needed to assess instability. Detection techniques using a microphone can be a good starting point to monitor vibratory behavior during machining. References [1] [2] [3]
[4] [5] [6]
[7] [8] [9] [10] [11] [12] [13] [14] [15]
[16]
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