Semi-active Control of Chatter in Boring Based on

proposes a new semi-active control method to suppress chatter, which is based on a ..... [GAM 91] GAMOTA, D.R., FILISKO, F. E., Dynamic mechanical studies of.
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Semi-active Control of Chatter in Boring Based on Electrorheological Fluids Wang Min Fei Yenyuan Yang Jianwu School of Mechanical and Electric Engineering Beijing Polytechnic University [email protected] ABSTRACT. In the machining system of the boring, the cantilever boring bar is the least rigid component. Chatter is always around the natural frequencies of boring bars. This paper proposes a new semi-active control method to suppress chatter, which is based on a novel design for a tunable-stiffness boring bar containing an electrorheological(ER) fluid. ER fluids are one kind of smart materials, undergo a phase change when subjected to an external electrical field, and this change is reversible and swift. The characteristic of ER fluids permits the global stiffness and energy-dissipation properties of the boring bar to be tuned in processes. Using this boring bar chatter can be suppressed by continuously varying the stiffness of the bar in process after chatter is detected. It is shown experimentally that the effect on chatter suppression is obvious and chatter can be avoided if the chatter can be detected timely. KEY WORDS: Chatter control. Electrorheological fluid. Regenerative chatter.

1.Introduction The machining Chatter is an intense vibration between cutting tools and workpieces which has been investigated by numerous researchers including Tobias[TOB 65], Merritt[MER 65], Sexton[SEX 78], Rivin[RIV 92], Smith[SIM 92], and others. It falls into two categories, forced and self-excited chatter. Usually the forced chatter is not a problem in machining shops. However, self-excited chatter is a serious problem, because its amplitude increases with the progress of cutting. Furthermore, there are two kinds of self-excited chatter, regenerative chatter and mode-coupling chatter. Most chatter occurring in practical machining operations is regenerative chatter[TOB 65]. It is caused by the undulation of the workpiece surface, and the frequency of regenerative chatter is always around the natural frequency of machining systems[RIV 92]. In boring, cantilever boring bar has the lowest inherent stiffness and limits machining regimes due to the development of chatter vibration. The occurrence of chatter invariably results in a degradation of surface accuracy, tool life. As a result, on-line recognition and suppression of chatter in boring has become a very important research task. Generally, the former methods of chatter suppression can be categorized into active ones and passive ones. In this paper a semi-active control method is presented to suppress chatter in boring. This method overcomes the minus of the active methods and the passive methods, and is with adaptability and reliability. The success of this method is ascribed to a new design of the boring bar, which contains

an electrorheological fluid and is with a tunable-stiffness. The global stiffness of the bar can be varied rapidly by changing the electric field strength exerted on the ER fluid. By computer simulation, it has been proven that the occurring conditions of the regenerative chatter don’t exist in boring if the natural frequency of the boring bar is continuously varied. Consequently, the chatter can be suppressed by using of this new concept. Based on the tunable-stiffness boring bar, this concept has been carried out in our experiments and results are satisfied. 2.Theory background Regenerative chatter is a modulated vibration, which results from the interaction of the dynamic of the cutting process and the structure dynamic of the machine tool. Fig.1 shows the control block diagram of machine tool chatter[TAR 97]. The uncut

hm(s)

+

+ +

h(s) -

Gc(s)

F(s)

y(s) Rs(s)

Primary feedback Time delay Regenerative feedback µe

-Ts

Fig.1 Control block diagram of machine tool chatter chip thickness h(s) is composed of the mean uncut chip thickness hm(s), the vibration of cutting tool y(s) and the workpiece surface undulation left by the previous tool pass y(s)e-Ts. Where T is the time for one revolution of the tool or workpiece in boring operations. µ is overlap factor indicating the degree of influence of vibration marks on the machined surface left by the previous pass on the chip thickness. The uncut chip thickness h(s) is fed into the cutting process to produce the cutting force F(s) acting on the cutting tool. The transfer function of the cutting process Gc(s) can be expressed as: G c (s ) = k d b

[1]

Where kd is cutting force coefficient relating force to chip area, b is the width of cut, which is proportional to the depth of cut in boring. According to the Nyquist stability criterion, the control system for machine tool chatter is at the stability limit when the gain of the open loop transfer function has the critical value of –1. Therefor, the value of the cut width b at the stability limit is expressed as blim =

−1 k d R s ( jω c )(1 − µ e −



)

[2]

Where ? c is the chatter frequency, and f =? T is the phase between the tool motion and the surface undulation left by the previous tool pass. For the sake of simplification, let us choose µ=1 since this value is the most pessimistic for chatter. Because blim is a real positive value, blim can be given by: blim =

−1 2k d Re[ R s ( jω c )]

[3]

Where b is the width of cut, which is proportional to the depth of cut in boring, ? c is the chatter frequency, kd is cutting force coefficient relating force to chip area, Re[Rs(j? )] is the real part of the dynamic compliance of the machining structure. Since boring bars of L/D>5 have relatively low stiffness, the influence of a usually rigid machine tool structure is very small and can be neglected. It has definitely been established by numerous studies that the chatter of boring bars

c

k m

Fd Fig.2.Dynamic model of boring bar always develop at their lowest natural frequency[RIV 92]. Accordingly, the dynamic model of the boring bar was assumed to be a single-degree-of-freedom lumped parameter system whose stiffness and mass are the effective stiffness and mass of the bar reduced to the point of attachment of cutting insert. Fig.2 shows the schematic diagram of the dynamic model of boring bar. Where m is effective mass of bar, k, c are its structural stiffness and damping. Fd is the dynamic cutting force. According to Fig.2. the dynamic compliance of the structure, Rs(j? ) is expressed as: R s ( jω ) =

1 (k − mω 2 ) + jcω

[4]

Where m is effective mass of boring bar, k, c are its structural stiffness and

e

d

b’

Cut width

c

k3

k2

k1 Chatter frequency Fig.3. Stability chart (k1, k2 and k3 are three lobe corresponding different values of stiffness)

damping. Based on equation (3) and (4), the relationship between the chatter frequency, the value of b at the stability limit, and the structural stiffness k is shown in Fig.2. In Fig.3, every lobe is respectively obtained from different structure dynamic. Along with the structural stiffness increasing, the lobes shift from low frequencies to high frequencies. The area under the lobes, namely the area dissipating energy, corresponds to stable cutting and free of chatter. On the other hand, the area above the lobes, namely the area storing energy, corresponds to unstable cutting and occurrence of chatter. In boring, because of the low rigidity of boring bar the chatter is difficult to be avoided even if the cut depth is very small. For a certain cut width b’, the chatter frequencies are always the value corresponding the points of intersection of the stability lobes and the line representing the cut width, which are closer to natural frequency of boring bars. It can be found that the chatter is possible to be suppressed by varying the structural stiffness. For example, if the chatter occurs at the point e, the point e can be located in the area dissipating energy when the lobe shifts from k2 to k3 by increasing the stiffness. Once the stability lobe has shifted, the chatter vibration immediately starts to attenuate. If the chatter occurs at the point d again, the point d can also be located in the area dissipating energy when the lobe shifts from k3 to k1 by decreasing the stiffness, thus the chatter can also be suppressed. If the lobe continually shifts between k3 and k1, the amplitude of vibration between tool and workpiece can’t increase with the progress of cutting. Therefore, the chatter can be avoided. 3.Design of tunable stiffness boring bar The construction of the boring bar is shown in Fig.4. For the application of ER fluid a pair of electrodes is necessary. The positive electrode is fixed to the bar. The supporting sleeve is used as the negative electrode and connected to the ground. The width of the gap between two electrodes is 0.5 millimeter. An insulator is placed between the positive electrode and the bar. ER fluid is sealed into housing between two electrodes with two O-rings. The segment of L2 is mounted into the tool post. The L1/D of the boring bar equals 6. Supporting sleeve

Positive electrode

L2

O-ring

Insulator

Bar

Insert

L1 Fig.4. Tunable-stiffness boring bar

Electrorheological fluids are suspensions of fine particles serving as the dispersed phase in a non-conducting base liquid[GAM 91][STA 96]. When an electric field is applied to the fluids, particle chains form as shown in the Fig.5, and the fluid becomes a semisolid. This transition is reversible and can be achieved in a few milliseconds[STA 96]. The deformation modes of ER fluids are dependent on applied electrical field strength and strain amplitude. This phenomenon permits the global stiffness and energy-dissipation properties of the bar to be tuned rapidly on line. In experiments, two electric field strength, 0kV/mm and 2kV/mm, were chosen to vary the stiffness of the boring bar. Under two electric fields the resonant Field direction

Zero field

The field of 2kV/mm

Fig.5. the micro-structure change of the ER fluid under two different electric fields The ration of amplification 1:240 frequency of the boring bar changed drastically when the bar was oscillated by an impact. This indicates that the effect of different electric field exerted on the ER fluid on the change of the structure stiffness is very evident. 4.Experimental set-up The schematic diagram of the experimental set-up is shown in Fig. 6. A series of experiments were carried out on a CA6140 engine lathe. The workpiece was clamped in jaws while the boring bar mounted cantilevered in tool post. In this experiment, the supervisory processing is performed using a Legend 233MHz computer. The computer is equipped with an HY-6070 General Purpose Data Acquisition Board and the software developed to monitor and control cutting Voltage Control Command Computer Charge Vibration Amplifier Signal

High Voltage Source

Accelerometer Workpiece

Commanded Voltage

Bar Insert

Fig.6. Schematic diagram of the experimental set-up

Tool Post

processes. The horizontal vibration signal was detected by the accelerometer at the free end of the bar. The output channel of the data acquisition board is analog voltage signal sent to a GYW-010 high voltage source, which exerts the commanded voltage to the ER fluid in the bar. The commanded voltage is with a square voltage variation between 0kV and 2kV and frequency of 2 Hz. The system software is developed using C++ language. The software consists of three sections: the system initialization, the chatter detection and the chatter suppression. 5.Experimental results

Acceleration(m/s2)

5.1 Effect of the method on chatter suppression In this experiment, cutting process was performed with a spindle speed of 200 rpm, a feed per revolution of 0.1 mm and cut depth of 0.2mm. After cutting for several seconds, the start of the voltage variation quickly reduced the vibration amplitude to a low value in less than one second as illustrated in Fig. 7. Fig. 8 shows the acceleration signal three-dimensional spectrum. It can be seen that the chatter frequency of 262 Hz in the spectrum gradually dies away after the voltage variation starts to be exerted. 5.2 Results of on-line chatter control

Magnitude

Time (millisecond) Fig.7.Acceleration signal

Frequency(Hz)

Time (millisecond)

Fig.8. Acceleration spectrum In section 5.1, the validity of continuously varying stiffness method has been proven. However, it is not necessary to apply a variable voltage to the ER fluid when

Acceleration(m/s2)

the cutting process is stable. So, this chatter suppression method should be combined with the art of the chatter detection. The voltage signal should be applied according to the result of sampled vibration signal analysis. In this control system a Radial Basis Function(RBF) Neural Networks[HUM 95] is used to on-line recognize the probability distributions of the acceleration signal sampled from the end of the boring bar. Based on the analysis of the signal probability distribution the chatter omen can be derived in processes. Once the chatter omen is detected the continuously varying voltage in a certain range will be applied to prevent the chatter forming. In our experiments this control system has been

Control start

2 0 -2 0

500

1000

1500

2000

2500

3000

3500

4000

Time (millisecond) Fig.9. the acceleration record during the running of the control system

proven to have the capability in keeping the cutting process stable under different cutting conditions. Next, the implementing result of the control system is given, which is performed with a spindle speed of 200 rpm, a feed per revolution of 0.10 mm and a cut depth of 0.50mm. Fig.9 shows the vibration record during the running of this control system. Fig.10 shows the three-dimensional acceleration spectrum corresponding to the time domain vibration signal shown in Fig.10. It can be seen that the frequency domain vibration signal can be clearly divided into two portions with the progress of cutting process. In the first portion, the cutting process gradually transits from stable cutting to unstable cutting, while the frequency component of 262Hz gradually stands out in the spectrum. In the second portion, contrarily, the cutting process shifts from unstable cutting to the stable cutting, while the chatter frequency gradually dies away in the spectrum. However, the time domain acceleration is with not obviously increasing amplitude during the whole course of the cutting process. This indicates that the control system timely detects the chatter omen, and successfully prevents the chatter coming into being.

10 5 0 0

4000 100

3000 200

Frequency(Hz)

2000

300 1000

400 500

Time (millisecond)

0

Fig.10. the three-dimensional acceleration spectrum 6.Conclusion Based on a novel design for a tunable-stiffness boring bar, this paper has presented a new semi-active control system for chatter avoidance in boring. According to the research of J. S. Sexton[SEX 78], the stabilizing effect from continuously varying spindle speed arise in the way that the tool is not excited at a constant frequency near the natural frequency but at a continuously varying frequency. Therefore the new control method is more direct and simple compared with cutting under continuously varying spindle speed. It will be useful for some machining process in case the inherent stiffness of machining structures can’t be sufficiently improved due to the limitation of the cutting conditions. References: [TOB 65] TOBIAS, S. A., Machine Tool Vibration, Blackie and Son, London, 1965 [MER 65] MERRIT, H. E., “Theory of self-excited machine-tool chatter,” Journal of Engineering for Industry,(Vol. 87, November), pp447-454, 1965 [SEX 78] SEXTON, J. S., STONE, B. J., “The stability of machining with continuously varying spindle speed”, Annals of CIRP, Vol.27, No.1, pp21-326, 1978 [RIV 92] RIVIN, E. I., KANG, H., “Enhancement of dynamic stablity of cantilever tooling structures,” Int. J. Mach. Tools manufact., Vol. 32, No. 4, pp539-561, 1992 [SIM 92] SMITH, S., DELIO, T., “Sensor-based chatter detection and avoidance by spindle speed selection”, ASME Journal of dynamic systems, measurement, and control, Vol.114, pp.486-492, 1992 [TAR 97] TARNG, Y. S., LEE, E. C., “A Critical Investigation of the Phase Shift Between the Inner and Outer Modulation for the Control of Machine Tool Chatter”, Int.J.Mach.Tools Manufact.Vol.37, No.12, pp.1661-1672, 1997 [GAM 91] GAMOTA, D.R., FILISKO, F. E., Dynamic mechanical studies of electrorheological materials: Moderate frequencies, J. Rheol., Vol.35, No.3, pp.399-425, 1991 [STA 96] STANWAY, R., SPROSTON, J. L., AND EI-WAHED, A. K., “Applications of electro-rheological fluids in vibration control: a survey,” Smart Materials and Structures,

Vol.5, pp.463-482, 1996 [HUM 95] HUMMELS, D. M., “Adaptive Detection of Small Sinusoidal Signals in NonGaussion Noise Using an RBF Neural Network”, IEEE Trans. Neural Networks, Vol.6, No.1, pp214-219, 1995