Bendahhou, Abdessamad

Zentner, Lena

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58th  ILMENAU SCIENTIFIC COLLOQUIUM Technische Universität Ilmenau, 08 – 12 September 2014 URN: urn:nbn:de:gbv:ilm1-2014iwk:3 ©2014 - TU IlmenauMeasurement Tools and Strategies to improve stability in Metal cutting Bendahhou, A; Zenter, L.* *Ilmenau University of Technology, Faculty of Mechanical Engineering, P.O. Box 100565,98684 Ilmenau, Department of Mechanism Technology, E-mail: abdessamad.bendahhou@tu-ilmenau.de ABSTRACT The prediction of appropriate cutting parameters to reduce cycle time and maintain product quality is major challenge in manufacturing industries. Regenerative chatter is a well known issue caused by the dynamic characteristics of tool, workpiece and spindle configuration resulting in self exited vibrations and unstable process output. In this paper CutPro is used to avoid chatter for different tool-holder settings and predict stable cutting parameters. The influences on the systems’ dynamic characteristics are analysed using modal analysis of data from impact tests on various tool-holder combinations. The results show the influence of tool holder mass and length on structural flexibility and achievable predicted depths of cut. Index Terms - Stability Lobes, Vibration Analysis, Metal Cutting INTRODUCTION Automotive Industry Manufacturers pursuing for flexible and cheap ways to increase output and product quality. Stable processes guarantee reduced cycle times and excellent product features at low cost and minimum of waste. To realize proper outcome, Manufacturers looking for innovative solutions to observe, measure and improve production processes in line. A useful instrument for on-demand measuring of tooling machines, which has been established in the last years, is the Modal Analysis. The largest reduction in milling quality occurs from a regenerative phenomenon called “Chatter Vibration” [1]. The vibration is the reason of poor surface and a loss of productivity. It produces more costs because of increasing tool and machine wear. Since the conception of modern manufacturing and CNC machining, several investigations have sought to deal with Chatter Vibration. A result of these researches is the Stability Lobe Diagram, which is one of the leading models to select optimum machine parameters. The approach in this paper is to improve process stability with Modal Analysis and Vibration testing. Taylor started a century ago with investigation to improve the process of cutting metal [1]. The first scientists, who developed a predictive model for stable process conditions and begin research in chatter vibration, was Tobias [2] and Tlusty [3]. They discovered that the main source of self-excitation, regeneration, is the dynamics of the machine tool-workpiece system and the feedback between the subsequent cuts on the same cutting surface. They used an orthogonal chatter model, which based on average directional milling coefficients and average number of teeth in cut. To describe the milling process accurately several parameters, as the rotating tool, multiple cutting teeth, periodical cutting forces or chip-load directions are missing in that model. Sridhar et al. [4] researched also the chatter stability. They achieved an elimination of the periodic and time delay terms in the stability model by using a systems state transition matrix. Minis et al. and Yanushevsky [5, 6] introduced a two-degree-freedom cutter model with point URN (Paper): urn:nbn:de:gbv:ilm1-2014iwk-057:0©2014 - TU Ilmenau  2 contact. To predict stability limits they took the Nyquist criterion into account. Lee et al. [7, 8] replaced the time varying directional coefficients by a constant with the mean value method. The analytic approach from Altintas and Budak [9] is that the average value in the Fourier series expansion of the time varying coefficients was adopted. Many other researches use this approach. Later, Altintas and Budak [10, 11] also started researches, which include the harmonic terms. The outcome of the investigation was that the multi-frequency solution results are nearly the same as the in single frequency solution. In this paper the feasibility of Modal Analysis and Vibration testing for an a priori predication of process stability and chatter avoidance is proven in an industrial environment. In this context frequency based approaches using impact testing and spindle acceleration measurements are taken into account. Sensible strategies for tooling machine measurement and simulation of stability lobes are evaluated with respect to contemporary production issues. Trails to calculate stability lobes by fitting them under consideration of a few cutting trials are accomplished as well. This requires less time to acquire data and predict stable cutting parameters.  ANALYTICAL MODEL  The following chapter introduces the physical and mathematical background to understand the subsequent results. In this instance the stability model based on Atlintas und Budak [9] will be summarized. Fig. 1 shows the differential forces in the milling process. Milling cutter and workpiece have two orthogonal modal directions allowing the cutter to move in the x-y plane.  The periodic milling forces induce dynamic displacements, which cause a wavy surface on the workpiece. Every tooth in cut leaves a wave on the surface, which is interleaved by a likely shaped path of the following tooth. The phase shift between two following teeth in cut causes a modulation of chip thickness inducing subsequent vibration into the system.   Fig. 1 - Differential forces in the milling process [9, 10, 11]  The phase shift is summarized in the modulated chip thickness which can be express as:                                                     ft is the feed per tooth. ϕj = (j-1) ϕp+Ωt (Ω rotional speed) is the angular immersion of the tooth (j) for a cutter with constant pitch angle ϕp = 2π/N (N number of teeth).            and (          are the dynamic displacements in the chip thickness direction due of the cutter and workpiece at the current and previous tooth passes.                                                     j is the angular position. c and w stands for cutter and workpiece. xp and yp are the dynamic displacements in global axis. After neglecting the static part in (1), which is can be eliminated in the chatter analysis, is the dynamic chip thickness defined as:                                                              where                                                                                      The dynamic cutting force on a tooth in tangential (     and radial (     direction is defined as:  hjWorkpieceby kyyXbxkxVibration marks left by tooth (j)Vibration marks leftby tooth (j-1)φjΩTooth (j)Tooth (j-1)dFtjdFrj νjujXφj(t)y(t)©2014 - TU Ilmenau  3                                                        The axial depth of cut is defined as a. Kt and Kr are the cutting force coefficients. In global directions and after substitution hj the cutting forces can be expressed as:                                                                           where axy are the directional coefficients and depend on the angular position. This makes Eq. (6) time varying:                                                                       [A(t)] is periodic at the tooth passing frequency ω = NΩ. For the solution of periodic systems Fourier series expansion is applied. Altintas and Budak [10, 11] revealed that only the average term in the fourier series expansion of [A(t)] is sufficient for the solution. In that case the directional coeffients of [A(t)] are shaped as                                                                                                                                                                [10, 11]. Considering Eq. (8), Eq. (7) reduces to:                                                                         [A0] is a time invariant cutting coefficient matrix. The dynamic displacement vector in Eq. (9) can be solved from the FRF (frequency response function) and the dynamic forces. By replacing the response and the delay terms the following term is obtained:                                                       {F} constitutes the amplitude of the dynamic cutting force {F(t)} and [G(iωc)] is the transfer function matrix, which identified at cutter – workpiece contact zone,                                                                           where Gxx(iω) and Gyy(iω) are direct transfer functions in x and y directions. Gyx(iω) and Gxy(iω) are the cross transfer functions. Eq. (10) has a non-trivial solution only its determinant is zero,                                                                     [I] is the unit matrix and Eq. (13) defines the oriented transfer matrix.                                                                               The eigenvalue Λ can easily be calculated from Eq. (12) numerically and is obtained as:                                                             If two orthogonal degrees of freedom in feed (X) and normal (Y) directions are considered (Gyx and Gxy are neglected) an analytical solution is possible:                                                             where                                                                              The numerical solution of Eq. (12) will give eigenvalues with complex and real parts, Λ = ΛR + iΛI. The axial depth of cut (a) has a real value. After substituting the eigenvalue and       =        i       in Eq. (14), the complex part of the equation vanishes:                                                                           This equation can be used to obtain a relation between the chatter frequency and the spindle speed [9, 10, 11]:  ©2014 - TU Ilmenau  4                                                                                                Where   is the phase difference between the inner and outer undulations, k is an integer corresponding to the number of vibration waves within a tooth period and n is the spindle speed (rpm). After eliminating the imaginary part in (14) the final expression for chatter free axial depth of cut is:                                                                      Hence for a given chatter frequency ωc the eigenvalues are obtained from (12), which permit the critical depth of cut to be computed (19) and finally the spindle speed using (16) for the different number of vibration waves, k. This procedure is frequent for various chatter frequencies around the structures dominant modes. The stability lobe diagram for a milling system is obtained. The diagrams will be used to locate the maximum chatter free cutting depths and spindle speeds.    EXPERIMENTS  1.1 Measurement setup  To identify how Tool-Mass und -Length affects transfer functions, analytical stability Lobes impact tests were conducted on two evenly matched cutters mounted in different tool holder extensions.    Fig. 2 – Tool holder geometry: 1 cutting tool, 2 tool holder extension, 3 Spindle, 4 clamping  The first configuration by using extension C achieves an overall tool length of 340 mm and mass of 7.5 kg. To reach an aggregated tool length of 380 mm extension A is mounted on B with a total mass of 12 kg as seen in Fig. 2. Additional information on tool and holder extension parameters is shown in Table 1.   Table 1. Cutting tool and extension parameters Tool parameters     Cutter type End mill    Diameter (mm)      40  Helix angle 40° Tool length (mm) 140  Relief angle 7° Evenly spaced Flutes 3  Rake angle 14° Extension parameters A  B C Diameter (mm)      63  100 63 Length (mm) 100  140 200  The impact tests were performed using a Kistler type 9722A500 Impulse hammer and a Kistler 8776A50 type accelerometer. To capture signal data a National Instruments 9234 Data acquisition card is used. The Acquisition device is connected to a storage Device and Signals are processed by simulation tool CutPro. In order to identify the Static flexibility of any given tool, -holder, spindle-assembly the tool tip gets excited by the impact of an impulse hammer. The inducted vibrations are measured and processed by an accelerometer as shown in Fig. 3.    Fig. 3 – Measurement chain  1.2 Results  The frequency response function as seen in equation 10 equals the ratio of the measured output over the input.                                                                                 CBA 340 mm380 mm4132Hammer(Exciter)Piezoelectric crystalelement(Force-sensing element)Accelerometer(Pickup)Data acquisitioncardFStorage DeviceSimulation©2014 - TU Ilmenau  5  where        is the vibration vector at a present time [12].                                                                           And        equals the vector of the applied impact Forces. The FRF’s processed by CutPro depending on the obtained acceleration und Force data, transferred by the impulse hammer, are used to compare the different Tool holders concerning static structural Flexibility as well as the simulated Stability lobes.  Figure Fig. 4 shows the real and imaginary part of the transfer function obtained in feed direction of the tested tool-holder combinations.   Fig. 4 – Real- and imaginary part  The slight difference in Amplitude of Real- and Imaginary-part points at a higher overall stiffness in the 380 mm configuration. The maximum negative peak of the Real-part is in both cases around a frequency of 274 Hz. At this frequency the system will tend to chatter most likely. Figure Fig. 5 shows the Structural flexibility (Modulus of FRF in μm/N) and the Phase shift (Phase in °).    Fig. 5 – Structural flexibility and Phase response  The highest peak of both curves is at a frequency of 360 Hz differing in Amplitude about 0,3 μm/N. The Phase response differs in Phase and Frequency. The highest phase shift is reached by the 380 mm configuration at a frequency of 1820 Hz.     Fig. 6 – Nyquist Plot  -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 100 600 1.100 1.600 2.100 2.600 Real,  μm/N Frequency, Hz 380 mm 340 mm -0,9 -0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 100 600 1.100 1.600 2.100 2.600 Imaginary, μm/N Frequency, Hz 380 mm 340 mm 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 100 600 1.100 1.600 2.100 2.600 Modulus of FRF, µm/N Frequency, Hz 380 mm 340 mm -200 -150 -100 -50 0 50 100 0 500 1.000 1.500 2.000 2.500 3.000 Phase, ° Frequency, Hz 380 mm 340 mm -0,9 -0,8 -0,7 -0,6 -0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 Im Re 380 mm 340 mm ©2014 - TU Ilmenau  6 Fig. 6 confirms the higher static structural flexibility of the 340 mm configuration making this system act softer in comparison to the 380 mm configuration.  The lower stiffness can be reduced on the lack mass in shape of the missing tool holder B. The highest overall negative value noticed in the Nyquist Plot shows a higher chatter affinity of the 340 mm configuration.   Fig. 7 – Predicted stability lobes  Considering the simulated stability lobes (Fig. 7), the additional dominant peak noticed at 1280 Hz in the 380 mm configuration, seen in Fig. 5, might be correlated with the additional sectioning between holder extension A and B. This is having a negative influence on the reachable depths of cut as seen in Fig. 7. An extract of the simulation parameters applied in CutPro to predict stable cutting parameters are summarized in Table 2. .  Table 2. Extract of simulation parameters Analytical Stability Lobes        Edge radius (mm)       0.02      Flank wear (mm)             0.05      Spindle direction  Clockwise      Milling mode  Up-milling Cutting parameters          Feedrate (mm/flute)             0.09      Radial width of cut (mm)        1    SUMMARY AND OUTLOOK  The conducted measurements  show slight differences in the prediction of stability lobes due to the variation of tool-holder mass and length. It is show that even though the 380 mm configuration is stiffer, it reaches lower depth of cut over the available spindle speed spectrum. An experimental validation of the predicted cutting parameters has to be done with respect to trade-offs in terms of output loss, cost per part and Quality reduction in series production.  In future tasks the dynamic spindle-holder-tool flexibility should be taken into account to compare results and evaluate the influence on cutting stability. Moreover additional Measurements should be conducted to identify further influencing factors on cutting stability in industrial environments.  The analysis of additional tool-holder configurations can provide useful data for prospective tool layouts as well as improvements for an effective construction.    ACKNOWLEDGMENT  The Author would like to thank the Manufacturing Automation Laboratory (Yusuf Altintas from University of British Columbia and Martin Herrmann) for technical Support.   REFERENCES  [1]  F.W. Taylor: “On the art of cutting metals.”, Transactions of the American Society of Mechanical Engineers, 28, pp. 31 - 350, 1907 [2]  S.A. Tobias, W. Fishwick: “A Theory of Regenerative Chatter.”, The Engineer London, 1958 [3]  J.Tlusty, M. Polacek: “The Stability of Machine Tools Against Self Excited Vibrations in Machining.”, International Research in Production Engineering ASME, pp. 465 – 474, 1965 [4]  R. Sridhar, R.E. Hohn, G.W. Long: “General Formulation of the Milling Process Equation.”, ASME Journal of Engineering for Industry, pp. 317 – 324, 1968 [5]  I. Minis, T. Yanushevsky: “A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling.”, ASME Journal of Engineering for Industry, 115, pp. 1 - 8, 1993 0 5 10 15 20 25 30 35 40 0 2855 5355 7855 10355 12855 15355 Depths of cut, mm Frequency, Hz 380 mm 340 mm ©2014 - TU Ilmenau  7 [6]  I. Minis, T. Yanushevsky, R. Tembo, R. Hocken: “Analysis of Linear and Nonlinear Chatter in Milling.”, Annals of the CIRP, 39,  pp. 459 – 462, 1990 [7]  A.C. Lee, C.S. Liu: “Analysis of the Chatter ‘Vibration in the End Milling Process.”, International Journal of Machine Tool Design and Research, 31(4), pp. 471 – 479, 1991 [8]  A.C. Lee, C.S. Liu, S.T. Chiang: “Analysis of the Chatter Vibration in a Cutter – Workpiece System.”, International Journal of Machine Tool Design and Research, 31(2), pp. 221 – 234, 1991 [9]  Y. Altintas, E. Budak: “Analytical Prediction of Stability Lobes in Milling.”, Annals of the CIRP, 44(1), pp. 357  362, 1995 [10] E. Budak, Y. Altintas: “Analytical Prediction of Chatter Stability in Milling – Part1: General Formulation.”, Transactions of the ASME, 120, pp. 22 – 30, 1998 [11] E. Budak, Y. Altintas: “Analytical Prediction of Chatter Stability in Milling – Part2: Application of the General Formulation to Common Milling Systems.”, solvingTransactions of the ASME, 120, pp. 31- 36, 1998 [12] Y. Altintas, Manufacturing Automation, Cambridge University Press, New York, NY 10013-2473, USA (2012)   CONTACTS  Dipl.-Ing. A. Bendahhou abdessamad.bendahhou@tu-ilmenau.de Prof. Dr.-Ing. habil. L. Zentner  lena.zentner@tu-ilmenau.de  

Measurement tools and strategies to improve stability in metal cutting

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Measurement tools and strategies to improve stability in metal cutting

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