An experimental detection and suppression of chatter vibration in modern milling machines Tomasz Kucharski, Krzysztof Kalinski Technical University of Gdansk, Department of Mechanical Engineering Narutowicza 11/12, 80-952 Gdansk, Poland ABSTRACT. A main purpose of this paper is to present an experimental implementation of methodology of chatter suppression in modern milling machines. Due to great concentration of operations being observed, an investigation of vibration control strategies, which are based upon application of expensive spindle speed control systems, is reasonable with respect to economics. The problem of matching the spindle speed to optimal phase shift between inner and outer modulation of the cutting layer is generalised. In case of varying cutting conditions, a bang-bang strategy appeared successful. KEY WORDS: dynamics, machine tools, control, measurement, computers

1. Introduction The problems of milling dynamics during the cutting process have been the subject of the research project. The relative vibration of tool-workpiece during cutting process, in the case of certain conditions, may lead to a loss of stability and generate self-excited vibration, which is called: chatter. To counteract it a several strategies of tool-workpiece vibration control has been examined. As a result of the investigation two strategies have been employed. The first one is based upon the spindle speed regulation by matching to optimal phase shift between two subsequent passes of tool edges [LIA 96, KAL 99]. A state of vibration is monitored by special computer system, which generates a spindle speed control command. The second one is based upon the spindle speed bang-bang control [KAL 00]. Our previous experiments evidenced that cutting with periodically changing spindle speed prevents generation of the chatter vibration in a wide range of speed values. Recommended peak-values of the pulse spindle speed are 10 - 15 % of desired ones, and pulse frequencies – up to 5 Hz [SOL 97, ALT 92]. The strategies selected guarantee high productivity and increased depths of cutting.

2. Features of the research object A vertical milling centre VMC FADAL 4020HT ( made in USA ) has been chosen as an object of the research. It seems to be a modern milling machine (Fig. 1), in case of which an investigation of implementation of vibration control strategies is fully reasonable. Though it satisfies conditions, they concern: dynamic properties of the carrying system. A feature of modern machine tools is rigid carrying system whose influence on dynamics of the cutting process is meagre; dynamic properties of the main driving system. Small inertia of the system is required, which puts in principal position structures with short kinematic chains and motor installed directly on the spindle (so called: electrospindles). Leading producers of machine tools offer such solutions as above. In case of the VMC FADAL, its main driving system is composed of: contemporary vector asynchronous motor with optimal phase regulation, two-speed belt transmission and short, rigid spindle; production process, in which, due to a danger of the chatter occurrence, some problems with technological criteria (e.g. surface quality, tool life, productivity) being satisfied, are observed. The phenomena may occur during the milling by using long tools (end mills, ball end mills) and drilling deep holes (at drill diameter being increased). Any, more simple rules of the counteraction (e.g. diversification of edges’ pitch) cannot be considered in this case; possibility of utilising the standard control system CNC of the machine tool. It should be noted that a great concentration of operations is observed in the milling centre. Therefore, an investigation of vibration control strategies, which are based upon application of expensive spindle speed control systems, is reasonable with respect to economics. Let us consider, when the chatter vibration occurs during machining process. Former experimental investigation of the cutting process, performed on the VMC FADAL using short end mill, evidenced a lack of chatter vibration, even at extremely significant values (up to 15 mm) of the cutting depth. However when a face milling process by a slender end mill is a subject of consideration the high level of chatter vibration can be observed. The slender end mill NOMA 206.016 W-W, which is purposed for high-speed cutting has been used in mentioned experiment. It should be noted that the cutting using slender tools is observed in modern machining centres very frequently. A technological reason lies in necessity of making difficulty accessible hobbings (e.g. die pockets) [HOC 97]. It is usually treated as finishing work, so that the depths of milling can reach even a few millimetres. Big depths of cut can also be met during manufacturing of the first row (it is very inconvenient situation). The milling centre model [KAL 99, KAL 00] has been performed basing upon following assumptions: several subsystems, which perform desired relative motions, are separated from the machine tool structure: the spindle together with the tool fixed in the holder,

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and the table with the workpiece. Thus, because of more rigid structure of the VMC FADAL the rule seems to be obvious; only a flexibility of the slender tool has been considered. The other elements of the structure, including also the main driving system, are idealised as rigid.

Fig. 1. Vertical milling centre FADAL Several milling tests have been carried out on a VMC FADAL to evaluate dynamics of spindle drive with in-house CNC. Assuming variation of spindle speed as ideal step function the real responses have been measured. The results of chosen tests are

shown in Fig.2. The switching time-interval has been selected as follows 0.5, 0.125 and 0.0875 sec. The experimental results prove that standard control system CNC of the machine tool can be used for the spindle speed bang-bang control. Spindle speed [rev/min]

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Time [s] Spindle speed [rev/min]

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Time [s] Spindle speed [rev/min]

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Time [s] Fig.2.

Real step responses of the spindle speed when bang-bang control is used; a) the switching time-interval 0.25 sec. (~1 Hz pulse), b) the switching time-interval 0.125 sec. (~1.7 Hz pulse),c) the switching time-interval 0.0875 sec (~2.3 Hz pulse).

3. Experimental set-up and instrumentation The experimental set-up consists of the 3300 Transducer System. Together, the 3300 Bently probe, tension cable, Proximitor, amplifier and filter make up a proximity transducer system for use to measure the transverse vibration of end mill and for measuring the spindle speed. A personal computer, equipped with a 16channel data harvester board and a digital signal processing board, was used. The standard control system CNC of VMC FADAL is utilising and a personal computer is used as controller. The spindle speed parameters are sent from the personal computer to the standard control system CNC via RS-232 serial connection. The experimental set-up for the verification of the theoretical investigation uses a special software package of MATLAB/SIMULINK. The computer programmes allow to monitoring vibration by measurement of the tool displacement signal and then spectral analysis and identification of resonant peak (or a few peaks). It makes possibility for automatic chatter detection and suppression of chatter vibration.

4. A generalised spindle speed regulation by matching to optimal phase shift The strategy of tool-workpiece vibration control, by matching to optimal phase shift between two subsequent passes of tool edges can be easy employed. A state of transverse vibration can be monitored by computer system, which generates a spindle speed control command in real time. Let us consider the speed control strategy performance in real vibrating system. The performance of tuning optimal spindle speed of the machine tool does not require any knowledge on the mass-spring system structure and dynamic properties of the cutting process. It can be realised: - manually - using standard control system of the machine tool, - on-line – by a special closed-loop control system. Following procedure concerns both the cases above: - monitoring of vibration by measurement of the tool displacement; - spectral analysis and identification of resonant peak with frequency fα (or a few peaks); - in case of generalised approach application - matching the spindle speed nα based upon equation [KAL 99]:

znα fα = 60 0.25 + m

(1)

where: z - number of teeth on the cutter, fα - observed chatter frequency, nα - optimal spindle speed, which corresponds to vibration with frequency fα. m=1,2,3,...

Application of this approach requires separation of chatter resonance with frequency fα, whose amplitude is dominant in the spectrum of displacements. In practice, time required for identification of chatter resonant peaks is about 1 s. and is so short as to adjust corrected value of the spindle speed before the end of the cutting process. The evaluation of chatter resonance can be made in the first pass of tools through workpiece or specimen. This information is obtained using FFT numerical analyser observing the time response at the end mill point. The next several passes of tools through workpiece are made while the optimal spindle speed of the machine tool is applied. To illustrate and to appreciate this approach let us analyse results of experiments. Calculation of RMS level has been treated to quantify the vibration level. The RMS value is the most relevant measure of amplitude because it both takes the time history of the vibration into account and gives an amplitude value, which is directly related to the energy content, and therefore the destructive abilities of the vibration. This one indicates the vibration influence on an accelerated tool wear. Considering several experiments the following data is introduced: initial spindle speed n0=3000 rev/min , feed per tooth fz = 0.1 mm, number of indexible inserts of the mill (cover material: TiN) z=2, mill diameter D=16 mm, widths of cutting B1 =8 mm, length of cutting Lw=15 mm, main cutting angle κr =90°. A milling with the depth of ap=0.1 mm is a stable case of cutting. Except the zones of the entrance and of the exit, which are characterised by dominant influence of unsteady free vibrations, the vibration peak value is maintained about 70 µm (Fig. 3a). The RMS value for time-interval from 1.2 to 4 sec. is 0.034mm. The frequency response plot (Fig. 3b) shows only these resonant peaks, which correspond to static component of the spectrum (i.e. frequency=0), and component with frequency of entering an edge into material (about 100 Hz). Presumed chatter resonant peaks are almost unnoticeable. A cutting with the depth being increased (i.e. ap=0.15 mm) yields a loss of stability and appearance of strong chatter vibration. In a range of two-edge cutting a level of vibration reached about 200 µm (Fig. 4a). The RMS value for time-interval from 1.5 to 3 sec. is 0.067mm. Based upon an observation of the amplitude spectrum (fig. 4b) main resonant frequency values f1= 686.19 Hz and f2= 787.10 Hz have been determined. An application of the generalised approach towards the first resonance allowed us to determine improved values of the spindle speed. Results of analysis for undeveloped chatter vibration are shown in Fig 5. The RMS value for timeinterval from 0.7 to 1 sec. is 0.042mm. The results obtained for optimal spindle speed nα= 3294 rev/min are shown in Fig.6 and Fig. 7. The results obtained for optimal spindle speed nα= 2491 rev/min are shown in Fig.8 and Fig. 9. Based upon the results of experiments, we can conclude that abilities of the strategy described are limited. The efficiency of one can be observed only for short time of machining process, when the chatter vibration is undeveloped. The developed chatter vibration can not be suppressed using this strategy.

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Fig 3. Stable case of cutting; a) time response of the end mill, b) frequency response

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Fig. 4. Unstable response of the end mill - no surveillance – developed chatter vibration.( n0=3000 rev/min, fz=0.2 mm, ap=0.15 mm, fc =686.19 Hz) a) time plot, b) frequency curve

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Fig 5.

Unstable response of the end mill - no surveillance – undeveloped chatter vibration ( n0=3000 rev/min, fz=0.2 mm, ap=0.15 mm, fc =686.19 Hz) a) time plot, b) frequency curve

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Fig 6.

Unstable response of the end mill - surveillance– developed chatter vibration (n=3294 rev/min., fz=0.2 mm, ap=0.15 mm, fc = 735.03 Hz ) a) time plot, b) frequency curve

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Fig. 7. Unstable response of the end mill - surveillance – undeveloped chatter vibration (n=3294 rev/min., fz=0.2 mm, ap=0.15 mm, fc = 735.03 Hz) a) time plot, b) frequency curve

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Fig. 8. Unstable response of the end mill - surveillance – developed chatter vibration., (n=2495 rev/min fz=0.2 mm, ap=0.15 mm, fc = 727.70 Hz) a) time plot, b) frequency curve

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Fig. 9. Unstable response of the end mill - surveillance – undeveloped chatter vibration (n=2495 rev/min., fz=0.2 mm, ap=0.15 mm, fc = 749.68 Hz) a) time plot, b) frequency curve

5. Strategy of suppression of chatter vibration by programmed spindle speed bang-bang Before starting a machining process, it is recommended for slender mill, we have to simulate the cutting process using computer in order to appreciate a possibility of chatter behaviour and to evaluate depths of cutting or feed per tooth. When computer prediction of the chatter frequency basing upon data of tool geometry and its mechanical properties is provided, the strategy of tool-workpiece vibration surveillance by spindle speed bang-bang control can be activated. In this case a state of transverse vibration is monitored by computer system. As it was mentioned in section 3 the proximity transducer system is used to measure the transverse vibration of end mill in experimental investigation. However, vibration and noise are closely related. Noise is simply part of vibration energy of a structure transformed into air pressure variations. Most noise and vibration problems are related to resonant phenomena. Therefore, measurements of noise for selected frequency domain (near chatter resonant peak) allows to indicate a level of chatter vibration and hence the microphone detector of chatter vibration is recommended for industry applications. When criteria values of the chatter factors have been exceeded, a control system, whose performance is based upon a bang-bang spindle speed variation, is started on. To illustrate and to assess this approach let us analyse results of experiments. A cutting with the depth ap=0.2 mm yields a loss of stability and appearance of strong chatter vibration. In a range of two-edge cutting a level of vibration reached about 0.290 mm (Fig. 10a). The RMS value for time-interval from 1.5 to 2 sec. is 0.117 mm. Based upon an observation of the amplitude spectrum (fig. 10b), the dominant resonant frequency values f1= 686.19 Hz (peak 0.087mm) and f2= 787.10 Hz (peak 0.051mm) have been detected. The high level of chatter vibration caused the inserts of the mill being damaged. To suppress the chatter vibration, the spindle speed control bang-bang has been employed. The results of surveillance of the chatter vibration, when the spindle speed bang-bang control has been employed, are shown in Fig. 11. In this case, the pulse spindle speed is used as it is shown in Fig.2a. In the next example, the pulse spindle speed is used as it is shown in Fig.2b. The results of surveillance of the chatter vibration, when the spindle speed bangbang control has been employed, are shown in Fig. 12. In the last example, the pulse spindle speed is used as it is shown in Fig.2c, and the results of surveillance of the chatter vibration are shown in Fig. 13. Based upon the results of experiments, we can conclude that abilities of the strategy described are satisfying. The efficiency of the one can be observed during all time of the machining. The peak-value of resonant chatter vibration is reduced about three times. The RMS values are decreased as well. These ones reach the level 0.091 mm. It should be noted, the best results are obtained in the last example.

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Fig. 10. Unstable case of cutting; a) time response of the end mill, b) frequency response

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Fig 11. Unstable response of the end mill under surveillance, a) time plot, b) frequency curve

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Fig 12. Unstable response of the end mill under surveillance, a) time plot, b) frequency curve

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Fig 13. Unstable response of the end mill under surveillance, a) time plot, b) frequency curve

Conclusion The aim of this paper, which was depended upon assessment of abilities of two strategies of tool-workpiece chatter vibration surveillance, has been performed. The strategies described in the paper for control of vibration are observed during real machining operations. The first strategy, which is based on matching the spindle speed to optimal phase shift between two subsequent passes of tool edges, is limited for applications. The efficiency of one can be observed only for short time of machining process (~0.5 sec), when the chatter vibration is undeveloped. The developed chatter vibration can not be suppressed using this strategy. The strategy of suppression of the chatter vibration by programmed spindle speed bang-bang can be applied with more success. The efficiency of one can be observed in all time of machining process. The peak-value of resonant chatter vibration is reduced about three times. The RMS values are decreased as well. It should be noted that the results are obtained using small fund; the standard control system CNC of the machine tool VMC FADAL is employed. This cheap approach can be easily applied for industry. The efficiency of this strategy can be improved when the special control system CNC of the machine tool is installed. This approach will be considered for investigation in the future. ACKNOWLEDGEMENTS The research was supported by the Polish Committee for Scientific Research, Grant No. 7 T07D 042-14. References [LIA 96] LIAO, Y.S., YOUNG, Y.C., “A new on-line spindle speed regulation strategy for chatter control”, Int. J. Mach. Tools Manufac., vol. 36, no 5, p. 651-660, 1996. [KAL 99] KALINSKI, K., “On one method of the tool-workpiece vibration control during cutting process”, Advances in Technology of the Machines and Equipment, vol. 23, no 3, p. 17-42, 1999. [KAL 00] KALINSKI, K., KUCHARSKI, T., “Computer prediction of the toolworkpiece vibration surveillance in modern milling operations”, II International Seminar on Improving Machine Tool Performance, 2000. [SOL 97] SOLIMAN, E., ISMAIL, F., “Chatter suppression by adaptive speed modulation”, Int. J. Mach. Tools Manufact., vol. 37, no 3, p. 355-369, 1997. [ALT 92] ALTINTAS, Y., CHAN, P.K., “In-process detection and suppression of chatter in milling”. Int. J. Mach. Tools Manufact., vol. 32, no 3, p. 329-347, 1992. [HOC 97] HOCK, S., “High speed cutting (HSC) in die and mould manufacture”. Proceedings of I French and German Conference on High Speed Machining p. 274-283, 1997.