翻译原文-颤振检测监测主轴驱动电流.PDF

Int J Adv Manuf Technol (1997)13:27-34 1997 Springer-Verlag London Limited The btemational Journal of Advanced manufacturing IechnoloiI Chatter Detection by Monitoring Spindle Drive Current E. Soliman and F. Ismail Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada The purpose of this work is to investigate a new method for detecting chatter in milling. In this method, the spindle drive current signal of a vertical milling machine is used for monitor- ing process instability. Both simulations and experimental work are conducted. Results show that current signals can transm# chatter frequencies reliably. The sensitivity of the current signal to slight process instability is assessed. A statistical indicator, the R-value is used to evaluate this sensitivity, Statistical analysis of experimental data shows that the R-value is insensi- tive to variations in speed, feed and geometry of cut. Also, experiments show that slight variations in the process instability results in a significant increase in the R-value. Keywords: Chatter; Machining; Monitoring 1. Introduction Monitoring and control of machining processes are crucial tasks for any automated manufacturing system. The main moni- toring tasks include tool-wear and tool-breakage detection, and sensing the onset of process instability, namely chatter. This paper focuses on chatter detection in milling operations. Monitoring of a machining process depends heavily on the type of sensor used and its location, as well as on the data- processing techniques employed. Excellent reviews are avail- able in the literature (e.g. 1,2) that discuss the general requirements of these sensors. Regarding chatter detection, Delio et al. 3 compared different sensors and concluded that monitoring the audio signal using a microphone was the most promising method; it covered a wide frequency range, and was not sensitive to the geometry of cut. They acknowledged, however, the effect of background noise on the audio signal and proposed some techniques to alleviate the problem. Recently, electrical current signals have been used for moni- toring machining processes. This is because current sensors meet many of the requirements of good sensors. For example, they are cheap, reliable and durable, also, they are remote Correspondence and offprint requests to: Professor F. Ismail, Depart- ment of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada. from the machining area and therefore less susceptible to the harsh cutting conditions. Stein and Shin 4 studied the sensitivity of the current signal of the field-controlled d.c. spindle drive of a CNC lathe to variations in the cutting force. A system bandwidth of approximately 2 Hz was obtained. Altintas 5 used the arma- ture current of the d.c. motor of the feed drive of a CNC vertical milling machine for predicting the cutting forces and tool breakage. The author reported a 20 Hz frequency band- width for the current sensor. Matsushima et al. 6 used the spindle drive current signal for detecting tool breakage in turning. The bandwidth of the current signal was less than 10 Hz. The narrow bandwidth of the spindle drive in turning and the feed drive in milling can be attributed to the large inertia of the moving parts; the machine table in milling and the power transmission elements and the spindle-workpiece system in turning. This narrow bandwidth imposes a serious restriction on the use of the current signals of these drives lor detecting machining chatter which usually develops at higher frequencies. Stein et al. 7 evaluated the d.c. servo feed drive of a CNC lathe as a force sensor, The authors pointed out that while the bandwidth of the velocity loop was about 80 Hz, the torque loop was very sensitive to disturbances in the cutting force. The current sensor response to a step input in the cutting force was similar to that of a first-order system with a time constant of 2 ms. This corresponds to a frequency bandwidth of about 500 Hz. The authors stated that the dynamic characteristics of the silicon control rectifier of the motor control circuit played an important role in determining the bandwidth of the current loop. This means that an improved design of such rectifiers may enhance the bandwidth of the current signal to cover the range of chatter frequencies which can be as high as 4 kHz. Fortunately, a particular class of machine tools, that includes large powerful machines, chatters at frequencies below 500 Hz. Nevertheless, the potential of increased bandwidth in the cur- rent signal was the prime motivation behind the current work. Although our system is quite different from that of Stein, and the bandwidth of our system was significantly lower than the chatter frequency, the attenuated signal was still able to detect the development of chatter reliably. The experimental set-up is described, followed by a presen- tation of an approximate model of this set-up. The objective 28 E. Soliman and F. Ismail Table 1. Modal parameters of the Rambaudi milling machine. Modal parameters X-direction Y-direction Mode 1 Mode 2 Mode 3 Mode 4 Frequency (Hz) 345 435 342 394 Damping ratio (%) 5.28 5.11 6.52 6.54 Stiffness (N mm -) 115982 163944 129386 150276 Mass (kg) 24.3 22.4 28.2 34.5 of this model is to give insight into the dynamics of the system and to help explain the experimental evidence. The reliability of the current signal for detecting chatter in milling is assessed in Section 4 using “statistical design of exper- iments“. It will be shown that in all the cutting tests conducted, the current signal manifested the development of chatter very clearly. 2. System Description The machine under consideration is a home retrofitted CNC Rambaudi Versamill milling machine. Modal analysis testing has shown that the machine structure could be modelled as one with two degrees of freedom in each of the machine principal X and Y directions 8. The measured modal para- meters at the end of the tool are given in Table 1. The spindle drive system is shown schematically in Fig. 1. It comprises a motor driving module, a power supply module, a three-phase permanent magnet synchronous motor and a pulley-belt system. The drive module controls the motor speed via a d.c. command signal. The speed command signal ranges between 0 and 10 V and the motor speed 0r, (rad s -) can be obtained from: (m = “/x speed command (1) Where “y (rads -l V -) is a scaling factor that can have a maximum value of 20.9122 which corresponds to a maximum M a i n s Drive modale Motor speed of 1997 r.p.m. In this work, the maximum value of / is used to obtain a maximum range of the spindle speed. The power supply module provides power to the motor through a three-phase high-voltage mains. The maximum con- tinuous power rating of the drive module is 1.2 kW. The peak shunt power is 40 kW. The motor generates a maximum torque of 50 Nm. The pulley-belt system consists of two aluminium pulleys and a timing belt (Goodyear 700h200). The trans- mission ratio is 1.6 to 1 from the motor to the spindle which corresponds to a maximum spindle speed of 1248 r.p.m. The spindle drive in Fig. 1 is a feedback system where the reference input is the speed command and the feedback signal is the motor speed. The motor speed is measured using an encoder built inside the motor casing. Both the command and the feedback signals are fed into the unit Gve which comprises a rectifier, rectifier logic and current amplifier. These compo- nents generate a d.c. current, L for driving the motor at the speed specified by the command signal. The function of the unit GVL is to ensure that the motor speed follows the command speed. The unit Gw dictates the bandwidth of the velocity loop. The current, /, together with the encoder output are fed into the unit GeL which comprises a current inverter and inverter logic. These components generate a three-phase current signal, lp, which is fed into the motor windings to generate the motor torque Tm. The function of the unit GeL is to ensure that the motor provides the required torque for driving the load, TL. The unit GeL, together with the pulley-belt system and the motor, determine the bandwidth of the torque (current) loop. 3. Modelling and Simulation of the Spindle Drive The spindle drive current signal can only be used for monitor- ing the process instability if the spindle drive is capable of transmitting the high frequencies at which chatter develops. Therefore, it is necessary to examine the dynamic character- istics of this drive, and in particular its frequency bandwidth. In order to accomplish this task an approximate model for the spindle drive is constructed. The numerical results from this model will be used in interpreting the experimental evidence. For the system in Fig. 1, the pulley-belt system is modelled first. A free body diagram of the pulley-belt system is shown in Fig. 2. The pulleys are assumed to be rigid with rigid T. T clin) Fig. 1. Schematic diagram of the spindle drive system. Fig. 2. Free body diagram of the pulley-belt system. Chatter Detection by Monitoring Spindle Drive Current 29 supports. The damping at the pulley supports is assumed to be negligible. The belt is assumed to be a light elastic lumped member. Also, the belt material is assumed to dissipate energy owing to hysteresis losses. Considering these assumptions, the governing equations of the pulley-belt system can be written as: Jmrm = T., - (F, - Fz)r (2) J.6 = (F; - F) R - T (3) F, - F = M (4) F2 -/2 = M Y (5) where arm and J are the inertias of the motor and the machine spindle respectively, K is the belt stiffness, “q is the hysteresis loss factor of the belt material, and M is the belt mass. R and r are the radii of spindle pulley and motor pulley, respectively. 0 m and 0 are angular displacements, while /m and TL are the motor torque and toad torque, respectively. FI, F, F2 and F; are the forces in the belt while 2 is the acceleration of mass M/2. The motor inertia is supplied by the manufacturer. The spindle inertia is calculated based on the geometry and material of the machine spindle. The belt stiffness and mass are supplied by the manufacturer. The values of these parameters are given in Table 2. The tension in the belt, the belt stretch and the angular displacements of the pulleys can be correlated as follows: F, = (8 + r0 - R0s) K(I + il) (6) F2 = (3 - r0m + R0s) K(I + iq) (7) where 8 represents the preload of the belt, and + (r0- R0) 0. Combining euations (2) to (7) and using the Laplace transform, we get Om(s)O m - T m = c(s)0 s Qs(s)0s + T L = (y.(s)0 m where, Qm(s) = JmS 2 + 2r2K(l + ixl) Q(s) = (J + R2M)s 2 + 2R2K(I + il) a(s) = 2rRK(I + iq) (8) (9) (10) (11) (12) The power supply and drive modules, GVL and GeL , respect- ively, have sophisticated electronic circuits; the modelling and Table 2. Parameters of the spindle drive system. Parameter Value Jm 0.00938 kg m 2 J 0.028 kg m 2 K 2283067 N m - 11 0.12 M lkg H 5.8 amp s21rad K 171 K 117 K 1.4 N m/amp R 0.08 m r 0.05 m a 0.008 l/s simulation of which is beyond the scope of this work. Neverthe- less, a simple model for simulating the general characteristics of these modules was suggested by the manufacturer 9. That model, however, considers the stiffness of the motor shaft as the main factor that determines the system natural frequencies. For the spindle drive system under consideration, the belt stiffness is much lower than the motor shaft stiffness and consequently it is the belt that represents the main source of flexibility in the system. Therefore, the model suggested by the motor manufacturer was modified in order to incorporate the pulley-belt system dynamics. A block diagram of the modified system is given in Fig. 3. Simplifying the block diagram of Fig. 3, the transfer function GL = I/TL is written as: -ot(s)H(s + a)(Kps + Ki) GI = o2(s) _ Q,(s)H(s + a)(Kps + Ki)K, - Qm(s)Qs(s) (13) Also, the transfer function Ga = sOrespeed command is given by: G2 = Qs(s)(gps + Ki)Kt Qm(s)Q(s) + Qs(s)(Kps + Ki)KtH(s + a) - a2(s) (14) where, Kp and K are the gains of the PI controller in Fig. 3, H and a represent the dynamics of the motor speed encoder and K t is the motor current torque factor. Kp and Kt are selected using Nichols-Ziegler rules 10 and H, a and K, are supplied by the manufacturer. The values of these parameters are also given in Table 2. G and G2 represent the dynamic characteristics of the current and velocity loops, respectively. Using the parameters in Table 2, the simulated G is shown in Fig. 4(a). It shows that the current loop has a natural frequency at 167 Hz. This frequency is mainly associated with the pulley-belt system. According to Fig. 4(a), should chatter develop at one of the measured higher frequencies of Table 1, the cunent signal at these frequencies would be attenuated by as much as 20 dB. Fortunately, as will be presented later, the experimental results showed that the chatter frequencies were not attenuated as much. Also the chatter indicator used was quite sensitive even to this reduced signal. The frequency response of G2 is simulated in Fig. 4(b). It shows that the velocity, loop has a cut-off frequency of 10 Hz. This is much lower than the cut-off frequency of the current signal. This result is similar to those obtained by Stein et al. Speed commd “ H s (s+a) i A e. - Current I Fig. 3. Block diagram of the spindle drive system. 30 1:2 Soliman and F. lsmail (a) 20 . , “= o “ -20 -40 I0 (b) 60 g 4O 20 0 . l i0 ooo Exp. - - Sim. l0 s 10 Frequency Hzl -20 . . . . . . . . . . . . . . . 10 101 10 = Frequency Fktz Fig, 4, Frequency response of the spindle drive system; (a) simulated current loop, (b) simulated and measured velocity loop. 7 and by Altintas 5. In order to test the bandwidth of the velocity loop experimentally, the motor was commanded to operate at a sinusoidally modulated speed. The amplitudes of speed modulation were always set below 10% of the motor mean speed to ensure a safe operation of the motor. Two mean motor speeds were used; 800 and 1280 r.p.m. They correspond to 500 and 800 r.p.m, mean spindle speeds, respect- ively. The speed modulation frequency was incremented in each test until the motor could not follow the modulations in the commanded speed. At each frequency the transfer function from the commanded speed to the actual motor speed was calculated and averaged for the two speeds. The results of this exercise are shown in Fig. 4(b). From the figure, it can be seen that the measured bandwidth of the velocity loop is about 12 Hz which is reasonably close to the simulation results. This agreement in bandwidth, albeit not a very close one, will be taken as a measure of credibility of the developed model. It will help explain the results from the cutting tests described next. 4. Sensitivity of the Current Signal to Process Instability The sensitivity of the current signal, or any signal that rep- resents a machining process, to chatter can be expl, essed in terms of three factors. The first one is the ability of the signal to transmit information related to process instability. For example, the ability of the signal to carry chatter frequencies without serious amplitude or phase distortions. The second factor is a measure, or a signal processing procedure, that is capable of extracting chatter information from the signal. This measure must be able to reflect process instability“ without being sensitive to variations in the cutting parameters. This condition is important as it prevents false chatter indications when there are abnormal cutting conditions such as transients when the feed or the cutting speed is changed. The third factor is the sensitivity of such a measure to process instability. In other words, this measure must instantly indicate any instability in the cutting process and then it must show how much the process is above the stability limit. This condition becomes very important if this measure is used for on-line control of chatter where the control action is proportional to the degree of process instability. Comparing the high- and low-frequency components of the monitored signal is a fundamental means for detecting process instability. Altintas and Chan 11 calculated the ratio of high- and low-frequency components of the acoustic emission from the milling process. They compared this ratio with different threshold values in order to detect process instability. No justification was given to the setting of these thresholds, Ismail and Kubica 12 calculated the ratio of the second moments of the high- and low-frequency components of the cutting force signal measured over one spindle revolution. They denoted this ratio, the R-value, and it was calculated from: /( (dynamic_c_utt!ng force)2t R-value = E (static cutting force) 2 (15) They used a threshold value of 0.2. They set this threshold value based on qualitative observations of the workpiece sur- face features. The feasibility of using the spindle drive current signal for monitoring process instability is addressed experimentally in the next two sections. The sensitivity of the R-value calculated from the current signal to process instability and to variations in the cutting parameters was examined using analysis of variance. Only one aspect of the sensitivity of the R-value to process instability is considered; this is its ability to detect slight process instability. The relation between the R-value and the degree of process instability is left for future work. 5. Design of Experiments There are several parameters which affect the stability of the milling process, the main ones being the geometry of cut, cutting speed, feedrate and depth of cut. The effects of these parameters on the R-value provide a base for examining the feasibility of using the current signal for chatter detection