ELSEVIER Journal of fvlalcrials Processmg Tcchwlogy 70 (1997) 279 284

Monitoring of tool fracture in end milling using induction motor current

B.Y. Lee a, H.S. Liu a, Y.S. Tarng b+*

Abstract

This paper describes the use of induction motor current to moni!or tool fracture in end milling operations. The principles of induction motors are studied in this paper to estabhsh the re!dtionship between the motor current and the motor torque. It is shown that the square of the stator current. of induction motor5 is approximately proportional to the motor torque. Since the occurrence of tool fracture will cause variations in :he motor torque, measurement of the stator current appears to be an indirect technique for monitoring tool fracture.. A sensitivity analysis of the stator current to the occurrence of tool fracture is also reported. Finally, experimental results under varying cutting conditions have been presented to demonstrate the effectiveness of this approach for the detection of tool fracture in end milling operations. Q 1997 Elsevier Science .%A.

Keywords: Induction motor: Tool fracture: End milling

1. Introduction

* Corresponding author. Fax: f 886 2 7376160.

0924-0136/9’i/Sl7.00 0 I997 Elsevier Science S.A. All rights reserved.

PJI SO924-0136(97)OOOp,2-4

unavoidable due to the excessive cutting force. In real- ity, the induction spindle motor current is not so sensi- tive to the cutting-force variations because of the limited bandwidth. However, based on sensitivity anal- ysis, the response time for tool fracture detection is still acceptable. Therefore, in this paper, measurement of the stator current has been proposed as an indirect technique for monitoring tool fracture.

In what follows, the principles of a three-phase in- duction motor [3,4] are discussed. The relationship between the motor torque and stator current is then d&ved. A sensitivity analysis of the stator current to the occurrence of tool fracture is also studied. Experi-

mental results for monitoring tool fracture under vary- ing cutting conditions using the stator current are presented. Finally, a summary of the present work is given.

2. Principles of an induction motor

In general. an induction motor consists of two main components: a stationary stator and a revolving rotor. There are many windings with resistances and induc-

EIeoMcaI To Stator

Windage And Friction Loss

Rotor Copper Loss

Fig. 1. Power-flow diagram of an induction motor [SJ.

tances on the stator and rotor. The rotor is separated from the stator by a small air gap. A three-phase set of voltages is applied to the stator causing a three-phase set of currents to flow. These currents produce a rotat- ing magnetic field with several alternate N-S poles. The rotation speed of the magnetic field, which is also called the synchronous speed ns (rpm), can he expressed as:

phase stator. Owing to the stator copper losses, a portion of the electrical power, Ps,,, is dissipated as heat in the windings, whilst another portion of the electrical power, P,,, is dissipated as heat in the stator core due to iron losses. Therefore, the remaining electrical power, Pug, is carried across the air gap and transferred to the rotor by electromagnetic induction, as mentioned e&r- lier. Another portion of the electrical power, P,,, is dissipated as heat because of the rotor copper losses. Finally, the remaining electrical power, P,,,, is available in the form of mechanical power. In practice, the mechanical power available to drive the load is slightly less than f’,,, due to windage and friction losses, Pti The rotor copper losses, P,,, related to the rotor input power Pa, can he expressed as:

P,, = spas (3)

Based on the above discussion, the mechanical power can be expressed as.

p, = p*, - prc, (4)

P,=(l -S)P., (5)

Combining Eqs. (2) and (S), the motor torque, T,,,, developed by the mechanical power can then be ex- pressed as:

P P T =2=955L!E

In 2nn/60 . Ns

3. Equivalent circuit of an induction motor

To gain a better understanding of the characteristics of an induction motor, an equivalent circuit diagram [5,6] of the induction motor is studied. Fig. 2 presents a per-phase equivalent circuit of the induction motor, showing that the power Pas transferred across the air gap from the stator can be expressed as:

281

Fig. 2. Per-phase equlvalenc circuil of an inductnon mokx [6].

Pug = 41: $ (7)

where q is the number of phases (q = 3); Iz is the rotor current; and Rz is the rotor winding resistance.

Substituting Eq. (7) into Eq. (6). the motor torque r,,, developed by the mechanical power can be rewritten as:

In reality, the rotor current, I?. is very difficult or impossible to measure directly on the induction motor. Fortunately, it is easy to make measurement of the stator current, I,. The rotor current Iz can then be determined from the stator current I, by using the following equation:

V,Z,l(Z, + Z‘l) Z4 VI -_ z2

Z, * =Y2z,+z,-z, ’ (9)

Current

I

i c/v

Converter

Voltage Am lifier

* Rectifier

in which Z, = RI + jX,; Z, = R,/s + jX,; Z3 = jX,,,R,/ CjX,,, -t R,); Z, = ZzZ3/(Zz + Z,) where V, is the stator Input voltage; R, is the stator winding resistance; X, is the stator leakage inductance; Xz is the rotor leakage inductance; R, is the equivalent resistance for the iron losses and windage and friction losses: and X,,, is the magnetizing inductance.

Based on Eqs. (8) and (9), it is seen that the square of the stator current (I:) of the induction motor is propor- tional to the electromagnetic torque T,,, developed by the motor. Since the occurrence of tool fracture will cause cutting-force and torque variations, in this paper

the square of the stator current is chosen as the sensing signal for the monitoring of tool fraczre.

4. Experimental set-up

A schematic diagram of the experimental set-up is shown in Fig. 3. A number of experiments were carried out on a CNC machining center (First MCV-641) using an end mill of 12 mm diameter for the machining of the S45C steel workpiece. A three-phase eight-pole induc- tion spindle motor (Fanuc 68) was installed in the machining center with a gear ratio of two between the motor and the spindle, thus the rotor speed n is equal to twice the spindle spzed. For an induction motor, each stator current has the same peak-to-peak ampli- tude, but is displaced in time by a phase angle of 120”. Therefore, only one of stator current signals was mea- sured by a current-to-voltage (C/v) sensor (LEM Mod-

J-Phase Indnction , Motor Belt Train

Fig. 3. Schematic diagram for the experimental set-up.

282 B. Y. Lee et al. /Journal of Materials Processing Technology 70 (1997) 279-284

geometry with feed change is shown in Fig. 5(a), whilst Fie. 5(b) shows the instantaneous stator current signal o& the’whole cutting period. A constant peak-to-peak instantaneous stator current sianal was recorded when the sdndle was free running. once the end mill started to engage the workpiece at 2.0 s, the instantaneous statorc&ent signal-gradually increased. The peak-to-

(dB) l”.oo I

Frequency(&)

Fig. 4. ‘lknsfer function betwezn the square of the stator the cutting force on the tool (spindle speed I 300 rpm).

current and

ule LA 50-P) and recorded on a PC-386 workstation through a data acquisition board (DT2828) with a sampling rate of 300 Hz. Since the instantaneous stator current signal is an AC signal with the frequency of the stator, f (Eq. (l)), further signal processing is required to extract the square of the stator current signal for tool fracture monitoring. In the experiments, the square of the stator current signal is obtained by demodulating the instantaneous stator current, then multiplying it by itself. The demodulation process is accomplished by using a bridge rectifier and a low-pass filter. In order to perform the sensitivity analysis for the square of the stator current signal, a dynamometer (Kistler 9265A2) was mounted under the workpiece. The dynamometer signal was transmitted through a charge amplifier (Kistler 5007) from which the cutting force signal was obtained and also recorded in the PC workstation.

5. Experimental results and discussion

The transfer function between the square of the stator current and the cutting force is shown in Fig. 4. The transfer function indicates the frequency response of the square of the stator current as variable cutting forces act on the cutting tool, and shows that the frequency response decreases dramatically after about 20 Hz. Alihough the bandwidth is not very wide, it is still good enough for monitoring tool fracture in end milling. In the following, a number of cutting tests have been conducted to verify tool fracture monitoring using the square of the stator current. Fig. 5 shows cutting test results with a spindle speed of 300 rpm and an axial depth of cut of 8 mm. The corresponding cutting

peak instantaneous stator cuirent signal became con- stant aeain when the end mill fullv entered the workdece. A larger constant ueak-to-neak instanta- neoud stator current signal at&eared -again with a change of feed from 40 to 120-mm min-‘. However, tool fracture suddenly occurred at 59.6 s. It is shown that the variation of the instantaneous stator current signal due to tool fracture is not so obvious (Fig. 5(b)). Through the signal modulation and multiplication, the square of the stator current signal is used to monitor the occurrence of tool fracture (Fig. 5(c)). It is shown that a large deviation in the square of the stator current signal occurred at 59.6 s due to tool fracture. A pho- tograph of the fractured end mill is shown in Fig. 6.

Fig. 7 shows the cutting test result with a feed of 80 min ‘I and an axial depth of cut of 5 mm. The change

(A) b) *o.w

1 1

Fig. 5. Cutting geometry. instantaneous stator current, and square of the stator current, with tool fracture. (Spindle speed=300 rpm: feed=40, I20 mm min-‘: axial depth of cut = 8 mm: end-mill diameter = 12 mm; work material: S45C.)

Fig. 6. Photograph of the fractured end mill. (The are as for Fig. 5.)

of cutting geometry with change of spindle speed is shown in Fig. 7(a). The instantaneous stator current signal and the square of the stator current signal are also shown, in Fig. 7(b) and (c), respectively. End mill fracture was detected clearly at 47.0 s (Fig. 7(c)). Fig. 8(a) shows the change of cutting geometry with change

Fig. 7. Cutting geometry, instantaneous stator current, and square of the stator current with tool fracture. (Spindle speed = 300. 600 rpm: feed = 80 mm min- ‘; axial depth of GUI = 5 mm; end-mill diame- ter = I2 mm; work material: S45C.)

Fig. 8. Cutting geometry, instantaneous stator current. and square of the stator current with tool fracrure. (Spindle speed=300 rpm: feed = HJ mm min - ‘; axial depth of cut = 3, 5. 9 mm; end mill diameter = I2 mm; work material: !WC.)

of axial dspth of cut, a spindle speed of 300 rpm and a feed of 60 mm min - ’ being selected for this test. It was found that tool fracture appeared at 62.6 s. It seems that the difference of the instantaneous stator current signal between the end mill with and without fracture is not obvious (Fig. 8(b)). However, tool-fracture features can still be identified clearly by the square of the stator current signal (Fig. 8(c)).

In the foregoing discussion, the use of the square of the stator current signal to sense tool fracture in end- milling operations with variations in feed, spindle speed, and axial depth of cut, is illustrated.

6. Conclusion

To protect the workpiece, the tool and the machine, tool fracture must be detected immediately. In this paper, an inexpensive, reliable, and sensitive technique for monitoring tool fracture in end milling has been proposed, based on the Occurrence of tool fracture with variation in cutting force and torque. It is shown that the square of the stator current of induction motors is

284 B. Y. Lee e! al. /Journal of Materials Processing Technology 70 (1997) 279-284

a suitable signal to indicate the variations in cutting force and torque due to the occurrence of tool frac- ture in end-milling operations. Experiments have confirmed the effectiveness of the proposed method for monitoring tool fracture under varying cutting conditions.

[I] M.A. Mannan. S. Broms, Monitoring and adaptive control of

cutting process by means of motor power and current measure- ments, Ann. CARP 38 (I) (1989) 347-350.

[2] J.L. Stein, C.H. Wang, Analysis of power monitoring on AC induction drive systems, ASME J. Dyn. Syst. Meas. Control 112 (1990) 239-248.

[3] S. Yamamura, AC Motors for High-Performance Applications, Marcel Dekker, New York, 1986.

[4) A.E. Fitzgerald, C. Kingsley Jr.. SD. Umans, Electric Machin- ery. McGraw-Hill. New York. 1983.

[S] T. Wildi. Electrical Machines, Drives, and Power Systems, Pren- tice-Hall, Englewood Cliffs, New Jersey, 1991.

[6] B.K. Bose, Power Electronics and AC Drives Prentice-Hall, Englewomi ClitTs, New Jersey, 1987.