Analysis and Prediction of Dynamic Disturbances of the BTA Deep Hole Drilling Process

Transcription

1 Analysis and Prediction of Dynamic Disturbances of the BTA Deep Hole Drilling Process K. Weinert, O. Webber, M. Hüsken, J. Mehnen, W. Theis Department of Machining Technology, University of Dortmund, Germany Institut für Neuroinformatik, Ruhr-Universität Bochum, Germany Lehrstuhl für Computergestützte Statistik, University of Dortmund, Germany {mehnen, webber, Abstract: The BTA deep hole drilling method was developed for machining holes with a high length-to-diameter ratio, good surface finish and straightness. The dynamic properties of the slender tool-boring bar combination necessary for producing this type of geometry significantly influence the overall process dynamics and lead to characteristic disturbances. These disturbances can be classified as chatter vibration or spiralling. Statistical design of experiments has been employed to determine the influence of process parameters on the workpiece quality. Surface quality and roundness profiles have been determined. Time series of drilling torque, feed force and structure- and airborne sound were recorded during the experiments. This data has been analyzed with the longterm goal of intelligent control in mind. A model describing the longterm development of chatter vibration is presented. Keywords: Machining, Dynamic system, BTA deep hole drilling. 1 Introduction Guiding pad 2 Drill bush Inlet for cutting fluid Deep hole drilling methods are used for producing holes with a high length-to-diameter ratio, good surface finish and straightness. For drilling holes with a diameter of 2 mm and above, the BTA (Boring and Trepanning Association) deep hole machining principle is usually employed [5]. The working principle is shown in figure 1. In contrast to conventional twist drills, deep hole tools have an asymmetric cutting edge arrangement, resulting in a nonzero radial component of the cutting force. Through the radial component of the cutting force and the guiding pads indicated in figure 1, a self guiding effect of the tool within the bore hole is achieved. This leads to a very low deviation of the bore hole axis from the ideal straight line. Another improvement over conventional drilling tools is the forced removal of the generated chips by the cutting fluid supplied at a high flow rate. These two aspects are prerequisites for deep hole drilling. The machining of bore holes with a high length-todiameter ratio implies the use of slender tool-boring bar assemblies featuring low static and dynamic stiffness properties. This in turn leads to the process being susceptible to dynamic disturbances such as chatter vibration and spiralling. The defects of form and surface quality constitute a significant impairment of the workpiece. As the deep drilling process is often used during the last production phases of expensive workpieces, process reliability is of prime importance. To achieve an optimal process design with the aim of reducing the risk of workpiece damage, a detailed analysis of the process dynamics is necessary. The work presented in this paper has been carried out as part of a project aimed at modeling the BTA deep hole drilling process, with special emphasis on dynamic aspects. The longterm goal is online-prediction of dynamic disturbances, which in future may be used as a basis for intelligent control of the process. Statistical design of experiments has been applied to investigate the correlation between the input parameters of the process and quality aspects of the resulting workpiece. During the associated experiments, time series of different process Chip mouth Brazed tip Guiding pad 1 Drill head BTA thread Boring bar Pressure head Figure 1: Working principle of BTA deep hole drilling [5]. quantities have been recorded in order to investigate the development and the characteristics of the dynamic disturbances. The investigation so far mainly focused on chatter vibration and the corresponding results are presented in this paper. The experiments were carried out on a system without additional damping in order to be able to observe the unrestrained system dynamics. Current work in progress includes experiments with the addition of a Lanchester damper and the investigation of spiralling. This paper will first give a short introduction to the above mentioned dynamic disturbances and describe the experimental setup used for the project. Following on to this, the results from the statistical experimental design, the times series analysis, and the modeling approach for the development of chatter vibration will be presented. 2 Dynamic Disturbances Chatter in deep hole drilling is a form of self excited, mainly torsional vibration of the tool-boring bar assembly. Its effect on the workpiece is usually restricted to radial chatter marks at the bottom of the bore hole as shown in figure 2. In extreme cases, chatter vibration may also lead to marks on the cylindrical surface of the bore hole wall. The effects on the tool are more severe. The high dynamic content of the cutting forces leads to excessive

2 wear of the cutting parts and guiding pads. Unpredictable breakage of the cutting parts may damage the workpiece or the BTA tool. Based on the observation of out-of-phase torsional and longitudinal vibration during chatter, Thai [8] traces this type of behavior of the BTA deep drilling process back to the principle of coupled states. From the high dynamic content of the process torque, he furthermore derives the periodic disengagement of the cutting parts from the workpiece. Cutting inserts Guiding pads Figure 4: The BTA-tool used for the investigations. Figure 2: Radial chatter marks. Another form of dynamic instability leads to a multilobe-shaped deviation of the cross section of the hole from absolute roundness. The pattern is helically propagated along the bore hole (figure 3), which is why the effect has become known as spiralling. In order to explain the tool motion necessary for producing multi-lobeshaped cross sections, previous researchers have usually referred to investigations performed in the context of reaming. Here, it has been shown, that multi-lobeshaped holes may result from a circular movement of the center of the rotating tool around the ideal center of the bore hole. The number of points of contact of the rotating tool with the workpiece hereby determines the number of lobes of the cross section [6]. Stockert [7] differentiates between three types of spiralling according to their occurrence: At the start of the process, reproducibly at the same drilling depth and seemingly at random. Investigations of Gessesse et. al. [2] have shown a connection between the bending modes of the boring bar and spiralling for the second type of occurrence. Figure 3: Effects of spiralling on the bore hole wall. 3 Experimental Setup The experiments were carried out on a CNC BTA deep hole drilling machine Type Giana GGB 56 with a bed length of 1.4 m, maximum spindle speed of 16 1/min, maximum feed rate of 57 mm/min and a maximum spindle power of 13 kw. The workpiece material used was C 6. A commercially available multi-edge BTA solid boring tool has been employed. It is equipped with three guiding pads and two cutting inserts and has a nominal external diameter of 6 mm. Due to signal lines having to be lead away from the boring bar (see below), the experiments were carried out with stationary tool and rotating workpiece. For the purpose of modeling the dynamics of BTA deep hole drilling, time series of quantities characterizing the process have to be recorded. Chatter and spiralling can be detected in the variation of the cutting and friction forces acting upon the cutting parts and guiding pads respectively. Previous investigations have demonstrated the difficulty of this type of measurement, due to, among other things, the restricted space available. Therefore, the process forces were measured in terms of feed force and drilling torque transmitted via the boring bar. For this purpose, the strain gauges HBM Type XY11 6/12 and HBM Type XY21 6/12 were applied to the clamped end of the bar. Drive unit Acceleration sensors Rotating workpiece BTA tool Microphone Oil supply device Acceleration sensor Boring bar Feed Machine bed Figure 5: Experminental Setup. Drive unit Strain gauges for forces and moments Airborne and structure-borne sound from several locations on the machine structure were also recorded. A diagram showing the experimental setup is given in figure 5. The analysis presented in this paper focuses on the torque data, which has proven to be the most expressive. In order to aid the interpretation of the process dynamics, the torsional modes of the tool-boring bar assembly were identified. For this purpose, the mounted tool was rotationally excited by impact offset from the center axis. The torsional response of the system was determined by evaluating the difference of the output of two acceleration sensors measuring in tangential direction and mounted diametrically opposed to each other on the boring head. By averaging the power spectra of five response measurements a spectrum was calculated from which the frequencies belonging to the first six torsional modes were identified. 4 Statistical experimental design Experimental design is a powerful tool to ensure the best possible parameter estimates for a given model with few experiments. Typically, only very simple linear or quadratic functions are used as models as long as there is no further knowledge concerning the functional form by which the influencing factors are connected to the response. A statistical experimental design defines a set of points in the space of operational values of the influencing factors, where experiments should be carried out in order to be able to estimate the given model as accurately as possible. Here we have chosen to use a quadratic function in three influencing factors, namely the cutting speed v c, the feed f and the oil flow rate V. These factors had turned

3 out to be the most important influences on roughness, roundness and tool-wear in work of V.P. Astakhov and Al- Ata [1]. The quadratic model reads: R = µ + β 1f + β 2v c + β 3 V + β 12fv c + β 13f V (1) +β 23v c V + β 11f 2 + β 22v 2 c + β 33 V 2 + ε (2) µ = const, und ε N (, σ 2 ε) (3) To be able to estimate this model a central-composite design was chosen with parameter α = 2 and seven repetitions in the center (Box and Draper [1]). The design is depicted in a projection into the possible values of cutting speed and feed in figure 6. As can be seen from this figure, one of the advantages of this design is the fact that only one influencing factor at a time is set to an extreme value in the outlying experiments. cutting speed v c 3 m/min limit due to generation of long chips maximum rotational speed manufacturers recommendation for BTA-tool botek type 22, Ø=6 mm limit due to maximum power of the motor (P =konst.) c limit due to the maximal mechanical stress of the cutting edges parameters according limit due to generation to VDI 329 of built up edges,5,1,15,2,25,3 mm/u,35,4 feed f Figure 6: The experimental design indicated by the black dots in the space of the possible values of v c and f. The values in table 1 were chosen as extreme values for the three influencing factors. f v c V min max Table 1: Extreme values of the influencing parameters. Finally to allow for a possible influence of the wear of the cutting edge, the experiments were arranged in blocks by the number of experiments carried out on each cutting insert. Therefore, seven inserts were used and the observations were blocked into three groups. 5 Results from the statistical analysis of quality measures During the experiments, phases with different process dynamics were observed. These in turn lead to corresponding sections of the workpiece, which also showed different characteristics. For all quality measures we therefore defined a weighted mean to obtain one value per experiment, which reflects the different surfaces from the observed phases of the process appropriately. It weighs the measurement from each homogeneous part of the hole by the length of the corresponding section: wr = lstart 5cm Rstart + l good 5cm R good (4) + l chatt. 5cm R chatt. + l extr.ch. 5cm R extr.ch. (5) Start stands for the first part of the drilling process until the guiding pads are completely contained in the hole. Good means a part where no chatter marks are visible. And finally two different sorts of chatter have been observed, the usual which leaves chatter marks in the surface and an extreme form leading to the formation of a pattern along the bore hole wall which may be described as high frequency spiralling. Since the complete model described above led to no satisfying fit for none of the used quality measures, a stepwise regression was performed by a function in the statistical software package R [3] to select the best possible model. This selection was done with the Akaike Information criterium as objective. The AIC is defined as AIC = 2 log L + 2p, where L denotes the likelihood function and p the number of estimated parameters in the model. The AIC should be minimized by the chosen model. A second measure of goodness of fit is the R 2 adj, which measures the correlation between the fitted values and the observations and should be near Roughness For the two selected measures of roughness (mean roughness depth (R z) and roughness average (R a)) the following models were selected as optimal: For mean roughness depth (R z): µ + β 11f 2 + β 22v 2 c + β 33 V 2 + β 1f + β 2v c (6) +β 3 V + β 12fv c + β 13f V + β 23v c V (7) with R 2 adj =.77 and AIC = For roughness average (R a): µ + β 11f 2 + β 22v 2 c + β 33 V 2 + β 1f + β 2v c (8) +β 3 V + β 12fv c + β 13f V (9) with R 2 adj =.83 and AIC = 9.84 Furthermore it was tested whether the usage of the blocks as a random parameter could improve the found models, but it turned out that this only added to the number of parameters in the model and did not reduce the variability. Since the better fit is reached for R a this model was also fitted for R z to make the results comparable and it turned out that this only slightly affected the fit (R 2 adj =.76 and AIC = 3.87). So these models were used to calculate the optimal values for the influencing factors. The result can be seen in figure 7. The optimum is realized at one of the borders of the chosen experimental region and it would be common practice to move the experimental region now in that direction. But since the values were already chosen quite extreme, it appears more appropriate to move on to the usage of the Lanchester damper. 5.2 Roundness Again the full model showed a bad fit and so again the best model was searched for by a stepwise regression. The result including the coefficients of the terms scaled for the original factor values is: wround = f.176v c (1) V v c V (11) and has an R 2 adj =.53 and AIC = Those values are not satisfying but the residuals display no hint of further structure and therefore so far unreflected influences, as can be seen in figure 8.

4 Estimated gwra for f vs. v_c v_c Estimated gwra for v_c vs. V V third variable fixed at: V= v_c third variable fixed at: f=.12 f V Estimated gwra for f vs. V f third variable fixed at: v_c=88.16 Minimum found at: f =.12 v_c = V = 2 Predicted gwra value: % confidence interval: [.2549,.2979] Figure 7: Contourplots with optimum for roughness average.5 Residuals..5 Residuals vs Fitted WV 1 WV 1 Standardized residuals Normal Q Q plot WV 21 WV 21a WV 21 WV 21a Fitted values Theoretical Quantiles Figure 8: Residual- and Normalplot of the model for roundness (a) Experiment 1: torque (Nm) torque (Nm) ,1 mm,1 mm (b) Experiment 2: torque (Nm) Figure 9: Evolution of the torque in two typical drilling experiments. 6 Time Series Analysis and Modeling In the following we present an analysis of the data of two typical measurements out of 22 conducted experiments and provide a mathematical model for the transition from stable drilling to chatter. 6.1 Recorded Time Series During the drilling experiments, the time series of six quantities are recorded with a sampling rate of ν = 2 Hz. We only use the most expressive data, i.e. the signals of the torque sensor, for our analysis. Figure 9 (a) and (b) depict two typical results of the measurements, both conducted with the same machine parameter values: feed f =.185 mm, cutting speed v c = 9 m, and min oil flow rate V = 3 l, i. e. in the centre of the design in figure 6. As the boring tool moves with a velocity min v = v cf/(2πr) 1.47 mm along the workpiece, the whole s drilling process takes almost six minutes. In the observations different phases can be distinguished. Prior to the actual drilling process (depth< mm) the workpiece is rotating relative to the BTA tool without actually being in contact with it. Hence, the torque data fluctuates randomly around the common mean. As at a depth of mm the workpiece and the BTA tool come into contact, the torque rapidly increases to approximately 21 Nm and keeps fluctuating. During the next 35 mm the tool is guided in the starting bushing. After leaving the bushing we observe different be- haviour in the two experiments, although both of them are conducted with the same machine parameter values. In the first experiment (figure 9 (a)) stable drilling continues, the distribution of the measured data is almost Gaussian with a very low amount of additional structure (see upper inset in figure 9 (a)). After about 3 mm chatter starts, identifiable by the rapid but smooth increase of the torque (lower diagram in figure 9 (a)); after the transition the observed time series is very smooth and periodic (lower inset in figure 9 (a)). In the second experiment (figure 9 (b)) chatter starts right after leaving the bushing; after 28 mm a change of the structure of chatter seems to have occurred, as the amplitude of the torque rapidly increased. In both experiments after 5 mm the BTA tool leaves the workpiece and the torque decreases to the starting value of Nm. 6.2 Spectral Analysis The analysis of the power spectra, see figure 1, allows a much deeper insight into the nature of the drilling process. Only a low number of different frequencies, mostly related to the rotational eigenfrequencies of the boring bare, seem to play an important role: In our 22 experiments these are 234 Hz (the lowest eigenfrequency is approximately 24 Hz), 73 Hz, and 1183 Hz, which are close to the odd numbered harmonics of 234 Hz. Chatter is only observed with a periodicity according to one of these three frequencies. In the two presented experiments, basically three

5 a) Stable drilling: (b) Chatter with 73 Hz: (c) Chatter with 1183 Hz: Figure 1: Typical power spectra in different phases of the drilling process: (a) stable drilling measured in experiment 1 at a depth of 1 mm, (b) chatter with 73 Hz, measured in experiment 1 at 4 mm and very similar to the spectrum in experiment 2 at the same depth, and (c) chatter with 1183 Hz, measured in experiment 2 after 1 mm. (a) Experiment 1: 73 ± 5 Hz 1183 ± 5 Hz (a) Experiment 2: 73 ± 5 Hz 1183 ± 5 Hz Figure 11: Evolution of the at certain frequencies. states are discriminable by means of the power spectrum. Although during stable operation, see figure 1 (a), no frequency is dominating the spectrum, slight peaks are discernible among others at 73 Hz and 1183 Hz. In the state of chatter (figure 1 (b) and (c)) one of the above mentioned frequencies and the associated harmonics, in particular the odd numbered ones, are significantly enhanced. After approximately 3 mm both of the presented experiments are in the state of 73 Hz chatter, the second drilling process operates between 35 mm and the 73 Hz chatter in the 1183 Hz chatter state. Chatter at different frequencies seems to be of slightly different nature. In all of our 22 experiments we did not observe any transition from 73 Hz chatter to any other chatter state as well as no transition from 234 Hz to 1183 Hz chatter. In this sense, 73 Hz chatter seems to be the most stable, 1183 Hz the less stable state. However, right after leaving the starting bushing it is much more likely to enter the 1183 Hz chatter state then any other one. The transitions from stable drilling to chatter as well as from one chatter state to another one are not as sudden, as it might seem from figure 9, but are a result of a long-term process over minutes. This can be seen from the evolution of the at 73 Hz and 1183 Hz, given in figure 11. In both experiments after 35 mm, i.e. right after leaving the starting bushing, the at 73 Hz starts to increase exponentially with increasing depth or increasing time, respectively, for approximately 3 minutes; after reaching a threshold of approximately 1 5 to, the drilling process switches to the 73 Hz chatter state. At the same time the spectral power at 1183 Hz behaves very different in the two experiments. After leaving the starting bushing the spectral power strongly increases. However, in the first experiment it directly starts to decrease again slowly, while in the second one it further increases and stabilizes at 1 9. As both experiments have been conducted with the same machine parameter values, the result indicates a strong probabilistic influence to the machine behaviour, i.e. the choice of stable and chatter states. However, the long-term increase also indicates a systematic one, which is subject of the model presented in the next section. 6.3 Modeling Approaches Providing a model for the observed phenomena will help to deepen the understanding of the process as well as to find strategies for controlling the process in a stable domain. The above analysis indicates the major importance of only a low number of characteristic frequencies. Based on this we present a purely phenomenological model for the temporal evolution of the deviation x(t) from the mean value of the torque, capable of describing the transition from stable operation to chatter. The description is based on the van der Pol-equation [9] d 2 x(t) dt 2 + ε ( a 2 x(t) 2) dx(t) dt + ω 2 x(t) =. (12) The sign of ε has a strong impact on the behaviour of the solutions. For ε >, the fixed point x = is an attractor of (12), i.e. the dynamic system tends to approach this value with increasing time. For ε < the fixed point at x = is instable and the systems has a stable limit cycle. In lowest approximation of the solution of this limit cycle, we get a periodic solution with frequency ω/2π, amplitude 2a, and only the odd numbered harmonics contributing to the power spectrum. As the different kinds of solutions of (12) qualitatively coincide with the experimentally observed states in the drilling process, we suggest to model transitions from stable drilling to chatter by means of a bifurcation in (12): ε = ε(t) = ε (bif) ( t (bif) t ) ; ε (bif) >. (13) A time or depth dependency in the model seems plausible, as during the drilling process certain conditions like the quality of the drilling tool or the position of the tool changes and therefore might lead to a change of the dynamic of the whole system. Finally, we add two sources of noise. First the process itself is assumed to be noisy: d 2 x(t) dt 2 + ε(t) ( a 2 x(t) 2) dx(t) dt + ω 2 x(t) = ξ (mod.) t (14) Here, ξ (mod.) t is white noise with mean and standard deviation σ (mod.). As such noise is very likely to occur in the

6 x (m.) (t)+21 (Nm) x(t) (m.) +21 (Nm) Figure 12: Simulation results for the torque. process, e.g. due to inhomogeneities in the workpiece or unsystematic disturbances of the machine, the model has to be able to cope with such perturbations. To compare the model output with the experimental measurements we include additive noise ξ (meas.) t with standard deviation σ (meas.) in the measurement process: x (m.) (t) = x(t) + ξ (meas.) t (15) The model (14) is simulated by means of a second order method for stochastic differential equations [4] for a certain choice of the model parameters. The comparison with the experimental results in figure 9 (a) exhibits strong qualitative and quantitative matches, only the slow increase of the amplitude of the oscillation after the transition to chatter is not modeled. The main features of the power spectra of the simulation results, in particularly the shape of the long time increase of the spectral energy at 73 Hz in figure 13 (b) coincide with the experimental measurements. 7 Conclusion and Outlook The results from the statistical experimental design provide an overview of how the process parameters are connected to quality aspects of the workpiece. With the help of time series analysis, different process states can be classified. Their temporal development can be described, modeled and predicted. The presented simulation results encourage to use (14) as a starting point for modeling more of the above mentioned effects, in particular the interactions and resulting transitions between the different chatter modes. Moreover, the relation between the model parameter and machine parameter must be established to increase the usefulness of such a model for controlling the drilling process. Future investigations will also include analysis and modeling of the spiralling effect in order to provide a sound and complete basis for designing a control strategy. Acknowledgments We would like to thank the DFG, grant SFB 475, for financial support. (a) Power spectra: at 1 mm at 4 mm (b) Spectral power at 73 ± 5 Hz: Figure 13: Power spectra of the simulation results from figure 12. References [1] Box, G. and Draper, N.: Empirical Model-Building and Response Surfaces. Wiley & Sons, New York, [2] Gessesse, Y. B., Latinovic, V. N., and Osman, M. O. M.: On the problem of spiralling in BTA deephole machining. Transactions of the ASME, Journal of Engineering for Industry, 116 (1994)p [3] Ihaka, R. and Gentleman, R.: R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, 5 (1996) 3, p [4] Milshtein, G. N.: A method of second-order accuracy integration of stochastic differential equations. Theory of Probability and its Applications, 23 (1978) 2, p [5] N.N.: VDI-Richtlinie 321: Tiefbohrverfahren. VDI Düsseldorf, Juni [6] Pfleghar, F.: Verbesserung der Bohrungsqualität beim Arbeiten mit Einlippen-Tiefbohrwerkzeugen. Berichte des Instituts für Werkzeugmaschinen der Universität Stuttgart. Technischer Verlag Günter Grossmann GmbH, Stuttgart-Veihingen, 1. edition, [7] Stockert, R.: Beitrag zur optimalen Auslegung von Tiefbohrwerkzeugen. Dissertation, Universität Dortmund, [8] Thai, T. P.: Beitrag zur Untersuchung der Selbsterregten Schwingungen von Tiefbohrwerkzeugen. Dissertation, Universität Dortmund, [9] van der Pol, B.: On relaxation-oscillations. Philosophical Magazine, 7 (1926) 2, p [1] V.P. Astakhov, M. O. and Al-Ata, M.: Statistical design of experiments in metal cutting part one & two. Journal of Testing and Evaluation, 25 (1997) 3, p