Technique for online controlling the cutting process stability

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1 Indian Journal of Engineering & Materials Sciences Vol. 21, June 2014, pp Technique for online controlling the cutting process stability Alexandru Epureanu, Vasile Marinescu, Ionut C Constantin, Mihaela Banu & Gabriel R Frumusanu* Manufacturing Engineering Department, Dunarea de Jos University, Galati, Romania Received 21 August 2013; accepted 11 February 2014 Nowadays techniques for online controlling the cutting process stability are based on the use of a sensor, in order to identify the occurrence of self-excited relative vibration between tool and part. A disadvantage of these techniques is that dynamic stability control system reacts only after passing over the stability limit, and the self-excited vibrations have already appeared. Hence, any reaction to the instability occurrence is delayed. This paper presents a novel technique for dynamic stability online control in cutting processes. According to it, the current operating point of the machining system is not only permanently brought into the stability domain, for maintaining the process stable, but also kept near the stability limit, for reaching the maximum level of productivity. The new technique has the following advantages: (i) provides to permanently use the entire processing capacity of the machining system, in optimal terms of dynamic stability; (ii) in the designing stage, allows to satisfy the specific requirements of both dedicated and flexible machining systems. The equipment required for implementing it can be designed as independent unit that can be attached to a machining system, or as integrated unit on a CNC machining system. The paper includes tests proving the possibility of applying the technique for turning processes stability control. Keywords: Chatter, Stability, Machining system dynamics, Cutting process, Online control Stability is one of the key factors limiting the cutting process intensity. The lack of process stability leads to the occurrence of unwanted high amplitude vibrations between the part and cutting tool. Instability also leads to appearance of surfaces with inadequate quality 1 and, at the same time, causes premature tool and machine tool wear. Usually, the dynamic stability control is based on machining system offline modeling 2-4 followed by a control algorithm implementation 5. Frequently, the models encountered in literature are based on some simplifying assumptions that limit their accuracy. More specific, for example, Gilsinn and Balachandran 6 have built a model for the turning process using boring bars with diamond round nosed tools, in order to predict chatter appearance. Another model, with two feedback loops, was also developed in the case of the boring process 7. In the same line, Budak and Ozlu 8 have developed a stability multidimensional model for turning processes, which takes into account the three-dimensional motion of the cutting tool. Moreover, these models are often requiring additional information about the tool or about the part, difficult to get in practice. In online control of cutting dynamic stability, a recently *Corresponding author ( gabriel.frumusanu@ugal.ro) proposed method uses of a sensor to identify the occurrence of self-excited relative vibration between tool and part, followed by cyclical changes in cutting speed, with appropriate frequency and amplitude, until chatter disappears. Suleiman and Ismail 9 proposed a system, which does not identify the system lobes stability by analytical approach, but selects the optimal speed by increasing the spindle speed until chatter appears. The main disadvantage of these methods is that the dynamic stability control system reacts only after the stability limit has been over-passed and, consequently, after the self-excited vibrations already appeared, and thus any reaction to instability occurrence is always delayed. Another disadvantage is that while the system operating point is placed inside the cutting process stability domain, the dynamic stability control system is not actually controlling the cutting process, no matter if by moving the operating point closer to the stability limit then the productivity could be significantly increased. As both dynamic stability limit, and position of operating point within the dynamic stability domain are widely varying along the cutting tool path, most of the times this potential increase of productivity remains unused.

2 278 INDIAN J. ENG. MATER. SCI., JUNE 2014 Problem Formulation The technical problem approached in this paper is to provide a technique for online controlling the cutting process dynamic stability. By applying it during the cutting process, more of the machining system capacity will be used, while maintaining the process stability, even when the worked part dimensions and material and/or machining system characteristics vary in time and space. In an earlier study 10, we developed a method for finding indicators that reveal the moments when the current operating point of a machining system comes close to the stability limit, based on simultaneous online monitoring of two signals (proportional to the cutting force, respective to the acceleration during tool/part relative motion). Here, by carrying forward these researches, we present a technique for implementing the method in order to realize the online control of cutting process stability. The technique is based on successive discrete adjustments of the cutting speed, with different increments when increasing or decreasing it, having as purpose to keep permanently the system operating point as closer as possible to the stability limit. Method for Assessing the System Operating Point Position Relative to the Stability Limit In order to assess the current position of the machining system operating point relative to the dynamic stability limit, the proposed method 10 lays on simultaneously monitoring a couple of signals coming from two sensors. The first signal, considered as proportional to the cutting force value, will be further called force-signal. The second signal, which can be considered proportional to acceleration in the tool/part relative motion, will be further called acceleration-signal. These signals are recorded as a couple of time series and transmitted to an embedded control system. Force and acceleration signals are processed by this control system, according to the following algorithm: Step I Elimination of the time slow-varying component, separately for each signal; Step II Scaling of the two filtered signals; Step III Application of the Fourier transform to both signals; Step IV Establishment of the operating point position, relative to the dynamic stability limit, by analyzing the Fourier transforms corresponding to the two signals. The analysis from the last step is based on the observation that if the cutting process is unstable, then the natural frequency of the machining system can be clearly distinguished, for both force and acceleration signals, while when the cutting process is stable, the two signals differently highlight the machining system natural frequency. More specific, the force signal shows no dominant frequencies inside the stability domain, while the acceleration signal divides the stability domain in two sub-domains: a first one, which will be called the sensitive stability domain and another, which we will further name the insensitive stability domain. The sensitive stability domain is near the stability limit and it is characterized by the fact that the machining system natural frequency is better marked in the acceleration signal FFT if the process is closer to this limit. The insensitive stability domain is the rest of the stability domain and, in its case, both signals FFT do not show the natural frequency of the machining system. In conclusion, after analyzing the two signals, one may establish where is the current position of the cutting process operating point, considering that: (i) if both signals show a natural frequency of the machining system, then the process is in the instability domain; (ii) if the force signal does not indicate any natural frequency, while the acceleration signal does, then the process is in the sensitive stability domain, closer to the stability limit when the amplitude of acceleration signal FFT (corresponding to the system natural frequency) is higher; and (iii) if the two signals either do not indicate the system natural frequency, then the process is in the insensitive stability domain. Figure 1 presents the position of the stability limit, here the surface , in the space of usual values for the cutting process parameters - namely the cutting speed (with values between minimum v m and maximum v M ), the chip thickness (0... a M ), and the chips width (0... b M ). Above the stability limit, there is the instability domain. Below this limit is placed the stability domain, composed by the sensitive stability domain (whose thickness is marked in the figure), located near the surface , and the insensitive stability domain, composed by the remaining stability domain. The method proposed for assessing the system operating point position relative to the stability limit was experimentally tested in the case of a lathe. The considered lathe has only one significant natural frequency. When the current operating point belongs to the instability domain, i.e., at rotation speeds of 500 rpm or higher, the system s natural frequency can

3 EPUREANU et al: TECHNIQUE FOR ONLINE CONTROLLING THE CUTTING PROCESS STABILITY 279 be clearly distinguished for both force and acceleration signals (Fig. 2 (c,d)). If the current operating point belongs to the stability domain, i.e., for rotation speeds below 500 rpm, the two signals differently highlight the natural frequency of the machining system. Thus, the force signal does not reveal anything (Fig. 2b), for the whole stability domain, while the acceleration signal divides the stability domain in two above-mentioned zones. Fig. 1 The stability limit position The sensitive stability domain (i.e. when the rotation speed is 300 rpm) shows the natural frequency on acceleration signal FFT (see Fig. 2a), while inside the insensitive stability domain, acceleration signal FFT does not show anything, either. In diagrams from Fig. 2 (a) and (c), 0.1 V on vertical axis are corresponding to an acceleration of 9.81 m/s 2. The method for assessing the system operating point position relative to the stability limit can be applied for online controlling the dynamic stability depending on the possibilities available on the machining system, already existing or specifically created in this purpose. In many practical cases, the chip width, the cutting speed, and sometimes the chip thickness are the most suitable candidates for dynamic stability control variables. For example, Fig. 3 presents the intersection between the space of possible values for chip thickness, a, chip width, b, and cutting speed, v, with two planes P and Q. The plane P is normal to chip thickness axis in a 0 and intersects the stability limit surface after 7-C-8-T-9 line. The plane Q is normal to cutting speed axis in v 0 and intersects the stability limit surface after 10-C-11 line. Let us consider the P plane and a cutting process where chip thickness and chip width remain constant at their programmed values, namely a 0 and b 0, while Fig. 2 FFT transforms (a) acceleration signal at 300 rpm, (b) force signal at 300 rpm, (c) acceleration signal at 500 rpm and (d) force signal at 500 rpm

4 280 INDIAN J. ENG. MATER. SCI., JUNE 2014 cutting speed is assigned as stability control variable. During the stability online control, the current operating point of the machining system moves along RSTU line, located in this plane. If we intend to maximize the process productivity, then the operating point should be located on the ST segment, as close as possible to the point T. If both force and acceleration signals are showing the natural frequency of the machining system, then the current operating point is on TU segment, which belongs to the instability domain. If so, then the cutting speed should be reduced in order to bring the operating point on TS segment, where force signal shows no natural frequency of the machining system but the natural frequency is clearly marked on acceleration signal. If none of the two signals indicates the natural frequency, then the current operating point is on RS segment and the cutting speed should be increased until the acceleration signal clearly shows its maximum natural frequency, while the force signal one does not show it. Thus, the operating point reaches the ST segment, near the point T. In the lower zone of the plane P there are presented the variation diagrams for both acceleration and force signals FFT amplitudes, A a respective A f, corresponding to the exemplified stability control action. A similar example can be considered if, the operating point route during the stability control is the ABCD line, from Q plane. In this case, the control variable is the chip width, b, while the chip thickness and cutting speed remains constant, at their programmed values a 0 and v 0. Control Model of the New Technique for Online Stability Control A new technique for online controlling the cutting process stability was conceived on the base of the above presented method for assessing the system operating point position relative to the stability limit. It works by following a discrete control model, which consists in successive adjustments of the cutting speed v, performed in order to keep permanently the system operating point in the sensitive stability domain. The control model supposes a radical initial reaction, to change definitely the system state (obviously, when a change is necessary). We should notice that the change might have two senses: from instability domain towards sensitive stability domain, or from insensitive stability domain (but with low productivity) towards sensitive stability domain. The initial reaction is followed then by other successive reactions of smaller and equal magnitudes, performed in order to explore the sensitive stability domain and to keep the operating point inside it, for reaching the maximum productivity that the machining system is able to give. The control model flowchart is presented in (Fig. 4). The control model parameters are the limits L 1, L 2, and four multipliers λ 1... λ 4. L 1 means a conventional value that, once passed-under by the amplitude of acceleration signal FFT, A a, the system operating point is considered inside the stability insensitive domain. L 2 is another conventional value, which if is passed-over by the amplitude of force signal FFT, A f, Fig. 3 The operation point position relative to the stability limit (experimental) Fig. 4 The control model flowchart

5 EPUREANU et al: TECHNIQUE FOR ONLINE CONTROLLING THE CUTTING PROCESS STABILITY 281 the system operating point is considered outside the stability domain. The λ 1... λ 4 multipliers are used for cutting speed v adjustment. Among them, λ 1 and λ 2 are sub unitary and they are applied to reduce the speed; λ 1 is smaller than λ 2 because λ 1 gives the initial, radical reaction, and λ 2 the eventual subsequent reactions. Multipliers λ 3 and λ 4 are supra unitary. Their application increases the cutting speed and λ 3 > λ 4, because λ 3 corresponds to the initial reaction, while λ 4 to the successive others. Both force and acceleration signals are periodically assessed during the cutting process (after a preset time interval or after a preset number of principal motion cycles), according to the method presented in the previous section (steps I... IV). The resulted values of amplitudes A f and A a are then successively compared to the limits L 2 and L 1, respectively. As long as A f value remains lower than L 2 and A a value is, concomitantly, higher than L 1, the control system should not change anything, because in this case, the system is stable and its operating point is in the sensitive stability domain (the machining process productivity is quasi-maximum). If at a given moment A f value is found greater than L 2, meaning chatter imminence, then the cutting speed is reduced to a value calculated by applying to the current one a multiplier smaller than 1. This action aims, obviously, to avoid the instability occurrence and according to the reasoning of above, there are two intervention levels: if A f previous value was smaller than L 2, then λ 1 multiplier is used, while if previous A f value was also higher than L 2, then λ 2 is applied. On contrary, when A a value drops below L 1, meaning a too low productivity, a similar type of reaction takes place, but in opposite direction, by using one of the other two multipliers, namely λ 3 or λ 4, for increasing the cutting speed, hence the productivity. The algorithm chooses which among λ 1 and λ 2 (respectively among λ 3 and λ 4 ) multipliers should be used at a given time, according to the upper presented details, with the help of two binary auxiliary variables, k and l. The current value of k equal to 1 means that the initial cutting speed reduction was already applied since A f passed over L 2 for the last time, while if the current value is 0, this thing did not happen. Similarly, the current value of l equal to 1 means that the initial cutting speed increase did take place after A a last drop below L 1, while if the current value is 0 another in-row increase was not previously applied. Regarding the conventional limits L 1, L 2 and the multipliers λ 1... λ 4, their precise values do not play a very important role and should be adopted based on experiments, depending on how coarse we want to control the system stability. Experimental Testing of the New Stability Control Technique An experimental program was performed in order to prove the applicability and the efficiency of the online stability control technique that we suggested. The technique was applied in the case of a turning process. Cylindrical parts made from steel (Fig. 5) were machined on a middle-size CNC lathe, provided with a special control system enabling to continuously modify the spindle rotation speed, according to the commands received from an external computer. The tool programmed path had sinusoidal shape (defined by A amplitude and ω pulsation). The phase angle was modified by 180 between consecutive tool passes. Thus, the thickness of material layer to be detached, has been continuously varied between t = t 2A and t = t 2A (1) min max + This variation had the purpose to force the cutting process transition from stable to unstable and vice-versa, during the same operation. In relation (1), t means tool displacement into radial direction, between two consecutive turnings. We exercised the application of the stability control technique at the frontier between the sensitive stability domain and the instability domain. This can be done by using only the force signal. Thus, when A f passed over the limit L 2, part rotation speed was diminished according to the presented control model (see Fig. 4), while if the process proved (became) stable, then the rotation speed was increased (again), up to a superior limit imposed by safety reasons. The results obtained for such an experimental application of the technique are illustrated in Fig. 6. Fig. 5 The machined part shape and dimensions

6 282 INDIAN J. ENG. MATER. SCI., JUNE 2014 Fig. 6 Results for the experimental application of the new stability control technique Here one can see three variation diagrams. The first one, entitled A f free, gives the evolution of the force signal FFT amplitude when the process took place without any intervention of the stability control system and chatter did occur. The second, A f controlled, refers to the force signal FFT amplitude when the part was machined in similar conditions, but the stability was controlled as above-mentioned (L 2 = 1.5, λ 1 = 0.7, λ 2 = 0.85); as it can be noticed, the process was thereby kept in the sensitive stability domain. The third, lambda, means the current value of the correction coefficient applied to the nominal value of the cutting speed (in this case, 60 m/min); for a better observation, this diagram was elevated with 30 unities above its real position. Conclusions In this paper, a new approach for online controlling the cutting process stability is proposed. It provides to use entirely the machining system processing capacity, as far as it is considered conditioned by the dynamic stability. The control technique derived from the new approach can be applied for any machining system whose dynamic instability is represented by tool/part self-excited vibrations, allowing a near-optimal control of the machining system stability. It is based on successive discrete adjustments of the cutting speed, with different increasing/decreasing increments, having as purpose to keep permanently the system operating point as closer as possible to the stability limit. The supposed control system requires a small number of settings to be adjusted, for adapting it to the particularities of a given machining system. The most important factor with impact on the control system performance is the appropriate selection of the cutting speed multipliers. In the performed experiment, the vibration amplitude was reduced with 80-85%. An advantage of the new control technique is the fact that the equipment required by its implementation is suitable to meet the requirements of both dedicated and flexible machining systems. Acknowledgements The authors gratefully acknowledge the financial support of the Romanian Ministry of Education and Research through grant PN_II_ID_794/2008. References 1 Praveen Raj P, Elaya Perumal A & Ramu P, Indian J Eng Mater Sci, 19(2) (2012) Totis G, Int J Mach Tools Manuf, 49 (2009) Wan M, Zhang W H, Dang J W & Yang Y, Int J Mach Tools Manuf, 50 (2010) Khorasani A M, Aghchai A J, Khorram A, Int J Adv Manuf Technol, 55 (2011) Giriraj B, Gandhinadhan R, Prabhu Raja V & Vijayaraghavan T, Indian J Eng Mater Sci, 15(4) (2008) Gilsinn D E & Balachandran B, J Manuf Sci E - T ASME, 123(4) (2001) Horodinca M, Carata E, Seghedin N E, Boca M, Chitariu D & Filipoaia C, Int J Mod Manuf Technol, III(2) (2011) Budak E & Ozlu E, Ann CIRP, 56(1) (2007) Soliman E & Ismail F, J Manuf Sci E - T ASME, 120(4) (1998) Marinescu V, Epureanu A, Constantin I C, Banu M & Marin F B, The Annals of Dunărea de Jos University, Fascicle V Technologies in Machine Building, Year XXVII (XXXII) (2010)

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