Monitoring of drill fracture from the current measurement of a three-phase induction motor

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Int. J. Maeh. Tools Manufact.Vol. 36, No. 6, pp. 729-738, 1996 Copyright© 1996ElsevierScienceLtd Printed in Great Britain. All rightsreserved 0890--6955/96515.00+ .00

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0890-6955(95)00052-6 MONITORING OF DRILL FRACTURE FROM THE CURRENT MEASUREMENT OF A THREE-PHASE INDUCTION MOTOR H. S. LIU,t B. Y. LEEr and Y. S. TARNG~t (Received 29 July 1994; in final form 21 April 1995) Abstract--The use of three-phase induction motor current to detect tool fracture in drilling operations is presented in this :paper. The basic principles of three-phase induction motors are briefly described and then an equivalent circuit diagram of induction motors is given. Based on the equivalent circuit diagram, the square stator current of induction motors is approximately proportional to the electromagnetic torque developed by the motor. Since the occurrence of tool fracture will cause the variations in the motor torque, measurement of t]~e stator current appears to be an indirect technique for sensing tool fracture. Experimental results have shown that drill fracture can be clearly recognized from the stator current of a three-phase induction spindle motor system. Copyright © 1996 Elsevier Science Ltd

1.

INTRODUCTION

Three-phase induction motors are the most popular electrical motors and are used extensively in industry. However, in the past, three-phase induction motors with the constraints on fixed-voltage, fixed-frequency alternating-current (a.c.) power supplies were inferior to direct-current (d.c.) motors in structure and control performance [ 1]. The situation ihas begun to change rapidly since the fast development of semiconductor power electronics on variable-voltage, variable-frequency a.c. power supplies [1, 2]. As a result, three-phase induction motors have begun to replace d.c. motors in many applications, for example, the spindle motor of machine tools. Even though power monitoring of a three-phase induction spindle motor system has been evaluated [3], little research has been reported using three-phase induction spindle motor systems as sensors for monitoring tool conditions in machining. In practice, there are sew:ral merits of choosing spindle motor systems as sensors for monitoring tool conditions in machining. This is because spindle motor systems are already built in machine tools. Therefore, the cost of sensor investment can be greatly reduced and the mounting of the sensor does not interfere with the operations of machine tools, etc. In the present paper, the use of three-phase induction spindle motor current to monitor tool fracture in drilling operations is studied. Based on the equivalent circuit of three-phase induction motors, the square stator current of induction motors is approximately proportional to the electromagnetic torque developed by the motor. It is known that the occurrence of tool fracture will cause the variations in the motor torque. Therefore, in this paper, measurement of the stator current has been proposed as an indirect technique for monitoring tool fracture. In reality, the stator current is not so sensitive to the motor torque variations due to the limited bandwidth. However, the response time for monitoring tool fracture is still acceptable based on the sensitivity analysis. In the following, the principles of a three-phase induction motor [4-6] are briefly discussed. The relationship between the induced torque and the stator current is derived using the equivalent circuit diagram of induction motors. Then, monitoring of drill fracture by the stator current of the induction spindle motor system is proposed and

tDepartment of Mechanical Manufacture Engineering, National Yunlin Polytechnic Institute, Yunlin, Taiwan, 63208, R.O.C. ~Department of Mechanical Engineering, National Taiwan Institute of Technology, Taipei, Taiwan, 10672, R.O.C. 729

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H.S. Liu et

al.

supported with experimental results. Finally, the paper concludes with a summary of the present work. 2. PRINCIPLESOF A THREE-PHASE INDUCTION MOTOR In general, a three-phase induction motor consists of two main components: a stationary stator and a revolving rotor. The rotor is separated from the stator by a small air gap. As shown in Fig. 1, a three-phase (a, b, c) set of voltages is applied to the stator and then a three-phase set of currents (Ia, Ib, and Ic) is flowing. These currents produce a rotating magnetic field with four alternate N - S poles. Therefore, the motor in Fig. 1 is called a three-phase four-pole induction motor. The rotation speed of the magnetic field which is also called the synchronous speed ns (rpm) can be expressed as: 120f ns = - P

(1)

where f is the frequency of stator in hertz In reality, the rotor rotation speed, i.e. is always slightly less than the synchronous of the synchronous speed is defined as the ns and rotor speed n, that is: S-

and p is the number of poles per phase. the rotation speed of an induction motor, speed ns. The slip s expressed as a percent difference between the synchronous speed

ns - n - -

(2)

ns

Figure 2 illustrates how electrical energy is converted into mechanical energy in an induction motor. First, electrical power Pin flOWS from the line into the three-phase stator. Owing to the stator copper losses, a portion of electrical power P~¢~is dissipated as heat in the windings. The other portion of electrical power Pil is dissipated as heat in the stator core due to the iron losses. Therefore, the remaining electrical power Pag is carried across the air gap and transferred to the rotor by electromagnetic induction. Another portion of electrical power Prcl is dissipated as heat because of the rotor copper losses. Finally, the remaining electrical power Pm is available in the form of mechanical power. In practice, mechanical power available to drive the load is slightly

Phase

'bJse

-----" I a O" h & ~ =I "I cO

e

StAtor

Gap

Fig. 1. A three-phase four-pole induction motor.

MonitoringDrill Fracturefrom Current Measurement

731

Windage And Friction Loss Starer Copper Iron Loss Loss ,OP~. ~ PU ~P~t Rotor Copper Loss ~p Mechanical Power Electrical Power / ! ~ To St~tor __~ II

Power Enzetrioal l~

Supplied To Rotor

Fig. 2. Powerflowdiagramof an inductionmotor [4]. less than Pm due to windage and friction losses P ~ . The rotor copper losses Prc~related to the rotor input power P~s can be expressed as:

Prc!= S Pag.

(3)

Based on the above discussion, the mechanical power can be expressed as: P m = P~,~ -

er¢l

=

(4)

(1 - s) Pag.

Combining equations (2) and (4), the motor torque Tm developed by the mechanical power can then be expressed as: 60 (1 - s) P ~ eag s) ns = 9.55 -n S

ern

(5)

Tm = 2--~n/60 = 2-~ (1

To gain a better understanding of the characteristics of an induction motor, a perphase equivalent circuit diagram of the induction motor is shown in Fig. 3. The power Pag transferred across the air gap from the stator can then be expressed as: Pag = q J~ R2

(6)

$

where q is the number of phases (q = 3), 12 is the rotor current and R2 is the rotor winding resistance. Substituting equation (6) into (5), the motor torque Tm developed by the mechanical power can be rewritten as:

Stator II

VI

R1

Rotor iX1

Rm

I2

iX2

<

._~

Fig. 3. Per-phaseequivalentcircuitof an inductionmotor [7].

~S

H. S, Liu et al.

732 Current Sensor

s blc 3-Phase I

I

C/V

Induction

Converter

Motor GearTrain 5:1

Voltage Amplifierl D

CNC-Maehinin6 I Center Controller

rFeedi l} ~l l1Spindle

Filter

-[

A/DI

~l DT2828 #

Fig. 4. Schematic diagram for the experimental set-up.

ARE Tm = 28.65 - -

(7)

s ns

In reality, the rotor current/2 is very difficult or impossible to measure directly on the induction motor. Fortunately, it is easy to measure the stator current 11. The rotor current 12 can then be determined from the stator current I1 by using the following equation: E1 I2 -

Z2 -

V1 Z4/(Z1 + Z4) Z2

-

Z4 V1 Z4 Z2 Z1 + Z4 - Z 2 11

(8)

where Z1 = R1 + iX1; Z2 = R2/s + iX2; Z 3 : jXmRm/(jXm + R m ) ; 2 4 Z 2 2 3 / ( Z 2 dZ3) where V~ is the stator input voltage; R~ is the stator winding resistance; X1 is the stator leakage inductance; X2 is the rotor leakage inductance; R~ is the equivalent resistance for the iron losses and windage and friction losses; and Xm is the magnetizing inductance. Based on equations (7) and (8), it shows that the square stator current (/211)of the induction motor is proportional to the electromagnetic torque Tm developed by the motor. =

3.

MONITORING OF DRILL FRACTURE BY THE STATOR CURRENT

It is well known that tool fracture is a very complex cutting phenomenon involving chemical, physical, and mechanical processes. Once tool fracture occurs, tool cutting edges with chipping, breakage, or severe deformation lose their usefulness. If the broken cutting edges are still in use, a larger motor torque will be generated by the spindle drive system due to an excessive cutting force acting on the broken cutting edges. In other words, to protect the workpiece, the tool and machine, tool fracture must be immediately detected. As discussed in the preceding section, the stator current of the induction spindle motor increases with the motor torque. In this paper, the use of the stator current of the induction spindle motor to monitor tool fracture has been proposed.

Monitoring Drill Fracture from Current Measurement

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A

rod

1_ b) I~I

R

Fig. 5. (a)

3.1.

R(

R

Four-diode bridge rectifier; (b) second-order Butterworth low-pass filter (R~ = 10 kll; R~ = 5.86 kll; R = 7.95 kfl; C = 0.1 p,F; corner frequency = 166 Hz).

Experimental set-up

The schematic diagram of the experimental set-up is shown in Fig. 4. A series of experiments were carried out on a CNC machining center (Yeong Chin YCM-VMC60A) using a 12 mm x 140 mm (diameter x length) twist drill for the machining of $45C steel plates. A three-phase four-pole induction spindle motor (Mitsubishi SJ7.5K-A) was installed in the machining center with a gear ratio of five between the (dB) 50.00 :::::

-'-'-'-": ::;::

I ,< --~

.oo :

800 1000

0.00

M o "~ - 5 0 . 0 0 r~ -100.00

. . . . . . . .

0.01

i

,

0.1

,

,,.,,,i

. . . . . . . .

1

.

i

10

,

,

,.,,,

100

Frequency(Hz) Fig. 6. Transfer function between the demodulated stator current and the cutting torque with several spindle speeds.

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H . S . Liu et al.

motor and spindle. Then, the rotor speed n is equal to five times the spindle speed. For an induction motor, the stator currents (Ia, Ib, and Ic) (Fig. 1) have the same peak-to-peak amplitude but are displaced in time by a phase angle of 120°. Therefore, only one of the stator current signals was measured by a current-to-voltage (C/V) sensor (LEM Module LA 50-P) and recorded on a PC workstation through a data acquisition board (DT2828) with a sampling rate of 1000 Hz. The instantaneous stator

(A)

60.00

I

o.oo - ~

-60.00

0.00

12.00

T~me(sec)

b)

(A) 60.00

o k

.-A

0.00

q b

o

12.00

Time(sec)

(A)

C

60.00

=

0.00

-60.00

O,

Time(see)

12.00

Fig. 7. Instantaneous stator current, rectified stator current, and demodulated stator current with tool fracture (spindle speed = 1000 rpm; feedrate = 240 mm/min; drill diameter = 12 ram; work material: $45C).

Monitoring Drill Fracture from Current Measurement

735

Fig. 8. Photograph of the fractured drill (the cutting parameters as shown in Fig. 7).

current signal is an a.c. signal with a frequency of stator f [equation (1)]. In the experiments, the amplitude of the instantaneous stator current was chosen as the sensing signal for monitoring tool fracture. To obtain the amplitude of the instantaneous stator current signal, the instantaneous stator current signal was demodulated by a bridge rectifier and a low-pass filter (Fig. 4). The circuit diagrams of the bridge rectifier and low-pass filter are shown in Fig. 5. The corner frequency of the low-pass filter is approximately equal to the frequency of the stator f. For example, a spindle speed of 1000 rpm corresponds to a rotor speed of n = 5000 rpm. Assuming that the rotor speed n is very close to the synchronous speed ns, the frequency of the stator f -~ 166 Hz can be obtained by using equation (1). To perfon~l the sensitivity analysis for the demodulated stator current signal, a dynamometer (Kistler 9271A) was mounted under the workpiece. The dynamometer signal was transmitted through the charge amplifier (Kistler 5007) from which the

00.00

A .< SO.O0

0.00 0.00

Time(sec) Fig. 9. Three-dimensional demodulated stator current signal (the cutting parameters as shown in Fig. 7).

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H.S. Liu et al.

torque signal was obtained and also recorded the PC workstation. The transfer function between the demodulated stator current and torque with different spindle speeds is shown in Fig. 6. The transfer function indicates the frequency response on the demodulated stator current as variable torques are acting on the cutting tool. It shows that the bandwidth is not wide and a higher spindle speed can enhance the frequency response a little. The corresponding time constant is close to 0.2 sec. Therefore, once tool fracture occurs, the use of the demodulated stator current to detect the tool fracture event will have a little time delay. Basically, the time delay is still acceptable for the detection of tool fracture. 3.2.

Experimental results and discussion

Figure 7 shows the result of a drilling test in the tenth drilling cycle with a spindle speed of 1000 rpm and a feed of 240 mm/min. Figure 7(a) displays the instantaneous stator current signal. A constant peak-to-peak instantaneous stator current signal was recorded when the spindle was free run. Once the drill started to engage the workpiece at 2.5 sec, the current signal gradually increased. The peak-to-peak instantaneous stator current signal became constant again when the drill head fully entered the workpiece.

(a) 60.00

0.00

-60.00

7.60

O.q

14 ~0

Time(sec)

(b)

Fig. 10. (a) Demodulated stator current with tool fracture; (b) photograph of the fractured drill (spindle speed = 1000 rpm; feedrate = 200 mm/min; drill diameter = 12 ram; work material: $45C).

Monitoring Drill Fracture from Current Measurement

737

(a) 60.00

0.00

-60.00

0

Time(nee)

7,1

(b)

Fig. 11. (a) Demodulated stator current with tool fracture; (b) photograph of the fractured drill (spindle speed = 1200 rpm; fee&ate = 220 mm/min; drill diameter = 12 mm; work material: $45C).

However, a large deviation in the instantaneous stator current signal occurred at 10.4 see due to tool fracture. The photograph of the fractured drill is shown in Fig. 8. It is found that the instantaneous stator current signal decreased, then immediately increased to a large value at the occurrence of drill fracture. This is because the drill and workpiece may lose contact at the instant of drill fracture. As a result, the instantaneous stator current signal decreases. However, the broken drill still proceeds at a given feed rate so that the drill and workpiece may contact again. A larger instantaneous stator current signal is then generated due to the broken drill still in cutting. Figure 7(b) displays the instantaneous stator current signal passing through the bridge rectifier. It is shown that the absolute value of the instantaneous stator current is obtained after rectification. The rectified current signal was further filtered by the low-pass filter to extract the amplitude of the instantaneous stator current. Figure 7(c) displays the rectified stator current signal passing through the low-pass filter. It is deafly shown that drill fracture can be detected by setting a threshold on the demodulated stator current signal in Fig. 7(c). The three-dimensional (3D) demodulated current signal in this drilling test is shown in Fig. 9. The demodulated stator current signal without drill fracture from the first cycle to the ninth cycle is demonstrated. Catastrophic drill fracture suddenly occurred in the tenth drilling cycle. In the following cuts, cutting parameters in drilling operations were changed to verify

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H.S. Liu et al.

the feasibility of monitoring drill fracture by the demodulated stator current signal. Figure 10 shows the experimental result for the other drilling test using a spindle speed of 1000 rpm and a feed of 200 mm/min. The demodulated stator current signal and the photograph of the fractured drill are shown in Figs 10(a) and (b), respectively. Drill fracture was clearly detected at 12.2 sec [Fig. 10(a)]. Figure 11 shows the experimental result for another drilling test using a spindle speed of 1200 rpm and a feed of 220 mm/min. A similar result for the detection of tool fracture from the demodulated stator current signal is illustrated. 4. CONCLUSIONS

In this paper, an inexpensive and reliable technique for the detection of drill fracture in drilling operations has been developed. The stator current of three-phase induction motors is used to monitor the variations of motor torque due to drill fracture. It is found that the stator current is not so sensitive to the motor torque variations because of the limited bandwidth. However, the response time for the tool fracture detection is still acceptable. To extract drill fracture features from the stator current, the instantaneous stator current is demodulated by a bridge rectifier and a low-pass filter. Drill fracture can be clearly detected by setting a threshold on the demodulated stator current signal. Experiments have also shown the effectiveness of the proposed method for monitoring drill fracture using different drilling conditions. Acknowledgements--The authors wish to express sincere appreciation to the reviewers for their helpful comments in improving the manuscript. REFERENCES [1] S. Yamamura, AC Motors for High-Performance Applications. Marcel Dekker, New York (1986). [2] A. E. Fitzgerald, C. Kingsley, Jr. and S. D. Umans, Electric Machinery. McGraw-Hill, New York (1983). [3] J. L. Stein and C. H. Wang, Analysis of power monitoring on AC induction drive systems, ASME J. Dyn. Systems, Measurement Control 112, 239-248 (1990). [4] T. Wildi, Electrical Machines, Drives, and Power Systems. Prentice-Hall, Englewood Cliffs, NJ (1991). [5] A. F. Kip, Fundamentals of Electricity and Magnetism. McGraw-Hill, New York (1969). [6] B. K. Bose, Power Electronics and AC Drives. Prentice-Hall, Englewood Cliffs, NJ (1987). [7] S. J. Chapman, Electric Machinery Fundamentals..McGraw-Hill, New York (1985).