A N ULTRASONIC MACHINE TOOL DATUM

S.W, Tehon and C.R. Roberts General Electric Company, Electronics Lahoratory

Syracuse, New York 13201

A I3 ST RA CT

The GE Machine Tool Monitor (MTM), a proto- type NC lathe control system, is based on the accurate establishment of the positions of cutting tools and work part surfaces. An ultrasonic Datum has been developed that provides reference sur- faces which precisely locate the cutting edge of a tool in the machine coordinates. MTM includes an ultrasonic accelerometer, mounted a t the lathe tu r r e t , used in the system cutting mode to monitor work rate and detect tool breakage. The datum, a steel bar vibrating at 50 kHz, is used in the tool sett ing mode and in testing the MTM status. For coordinate location, the tool i s brought up to touch i t s vibrating surface, and the accelerometer imme- diately senses 50 kHz vibrations. Since displace- ments of the datum surface a re only a few micro- inches, location is extremely accurate.

1 ntroduction

T h e Machine Tool Monitor system incorporates an ultrasonic detector. with sensitivity to machine vibrations in the 50 kilohertz frequency region, for the purpose of detecting abnormal cutting operation such as chatter due to chipping of the tool bit. For the purposes of automated machine control. each cutting operation must be measured from accurately known position references, re- quiring recalibration of position for each change in the cutting tool surface. The Datum, described in t h i s paper, provides the means for precise location of that surface. It is an accurately machined steel ba r , square in cross section, vibrating with an amplitude of the order of a few microinches and a frequency of 50 kHz. I t i s mounted so that its sur face lies on the reference axis of the machine. When a cutting tool is brought up to that surface, a t the instant of contact 50 kHz vibrations a re carried through the tool into the machine, and hence to the ultrasonic detector, indicating that t he cutting surface is within microinches of the reference axis. Since the Datum is square, two accurately located faces can he used to locate an X-axis and a Y-axis, individually.

The first type of Datum built was a 2-inch long ba r . its length chosen to resonate with free ends in lengthwise motion a t 50 kHz. The natural motion a t resonance for the half-wave length used is symmetrical about the midlength, the ends moving in and out in synchronism. Piezoelectric trans- ducers were attached near the stationary node a t

468 - 1985 ULTRASONICS SYMPOSIUM

this midlength, providing electrical means for driving and detecting the resonant motion.

Shortly after placing the half-wave Datum in use, we were requested to supply a modified model, this new type to be substantially longer but still to operate a t 50 k H z . Th i s was built in the form of a 4-inch long har , designed to be operated in the second harmonic, a t 50 kHz. of i t s funda- mental 25 kHz length resonance. In this overtone mode, the stationary nodes a re a t a quar te r of the b a r length from each end, the pattern of vibration being a full wavelength from end to end.

Pa t te rns of Motion

T h e basic motion for which both types of Datum a r e designed is vibration parallel to the length of t he har. With both ends free, resonances occur a t each frequency for which the bar length is an integral multiple of a half wavelength, a t the speed of sound in the bar. I n a thin steel bar , sound travels a t 5050 m/s. For a resonance at 50 k H z . with half period of 10 microseconds, possible lengths a re multiples of 5 . 0 5 centimeters -- ap- proximately 2 , 4 , 6 , ---, inches.

Figure 1 illustrates motion in the 2-inch and 4- inch bars a t four instants during one cycle. Variation with position, and with time, is sinusoi- dal. At t i m e s when the bar is shorter than its normal length, the nodal regions become apprecia- bly thicker, and a t times when the bar is elongated they a re thinner. Only the exact center point i n a nodal region remains stationary a t all times.

The resonant free-free bar therefore has no external surfaces entirely free from vibration motion, and in that sense is a suitable source of reference surface vibration as a datum. However, t he re a re no external stationary points by which the bar could be rigidly mounted in the machine reference system. Since the ba r is steel, no mounting materials could clamp the surface motion, being a t best of comparable stiffness. and any suppor t system for the ba r will necessarily share in the vibrations, modifying this idealized pattern of b a r motion. Since an approach to stiff clamps i s desirable from the viewpoint of holding the datum rigidly in i ts reference position, we incorporated a steel flange, built as part of the element, girdling the bar about a nodal point. This i s a symmetrical mount, so the interacting forces do not tend to convert the bar vibrations into assymetrical hend- ing moments.

0090-560718510000-0468 $1.00 0 1985 IEEE

H A L F - W A V E :

1 1 4 " SQUARE

1 3"

I t 1 "

I

00

L a 900

I 1800 -1 c--c

t

270'

Figure 1. Vibrations for half-wavelength ( / 2 ) and full- wavelength ( X resonant bars

The mounting flange does interact with motion in the bar. A s a result , the total s t ruc ture with flange shows a multitude of spurious resonances tha t do not exist in a simple bar. A s long a s the excitation for the datum is a 50 kHz sinusoid, tuned precisely to the exact frequency of longitu- dinal resonance, then the surface motion is very close to that for the free-free bar. The presence of unwanted resonant modes has most effect i n the construction of the excitation source, which must sense the proper frequency and provide the driv- ing forces, avoiding the spurious resonances.

Datum Construction

Each bar is square in cross section, .250" by ,250". I t s mounting flange, a 1-inch square plate used for bolting the datum into the lathe, i s .125" thick, and i s centered about a nodal section of ba r length. The bar and flange, machined from one piece of steel, are given a thin nickel plating for protection against corrosion. The nickel also provides a hard, wear-resistant working surface.

Each transducer is a PZT-4 ceramic chip .020" thick. measuring .250" by .500", poled in thick- ness between surface electrodes. Four chips are mounted on the faces of the datum bar, adjacent to the flange in a region of high vibration strain. a s shown in Figure 2. Solder and conducting epoxy have both been used satisfactorily for bonding; the datum tends to exhibit much higher resonant Q with solder bonds.

In order to reduce the number and intensity of spurious resonances, the geometry is symmetrical about the length of the bar , purposely minimizing

X DATU^

2 DATUM

V Figure 2. Datum Bar construction, with mounting

flanges and ceramic t ransducer chips

any tendency to excite flexural vibrations. Two t ransducers on opposing faces a re driven electri- cally in parallel, and the other two provide an output voltage as a monitor of longitudinal strain. The transducers a re all oriented with positive poling faces outward, so opposing-face transduc- e r s couple additively to longitudinal vibrations and cancel for flexural motion. Th i s orientation pro- duces l R O o phase shift between input and output voltages a t 50 kHz.

Frequency Response Chara der i s t ics

T h e t ransfer characteristic from voltage applied a t the drive transducers to voltage induced by vibration in the readout transducers exhibits the mechanical resonances of the datum, including the effects of mounting flange, bonded transducer chips, and attached wire leads and solder. The magnitudes of drive and readout voltage are both functions of frequency, vibration damping and circuit impedances, but the readout voltage peaks when the vibration amplitude peaks. Therefore, t he plotted t ransfer characteristic is a map of resonances in the composite bar.

Figure 3 is a plot of output voltage amplitude ve r sus frequency, taken with a network analyzer sweeping slowly across the band from 0 to 100 kHz, for a half-wave datum. The fundamental resonance is at 52 kHz.

Figure 4 is the plot for a full-wave bar. The fundamental resonance response, a t 26 kHz, i s reduced in amplitude by the flange, which is not located in the nodal region for this resonance. T h e second harmonic exhibits a strong 40 dB rise in amplitude, essentially unaffected by the flange in this nodal region.

In addition to the longitudinal resonances a t roughly 25, 50. 75 and 100 kHz, there a re flexural resonances with overtones appearing throughout t h e frequency range. These tend to be weak, occurring only because there are imperfections in t h e desired symmetry, in both drive and readout

1985 ULTRASONICS SYMPOSIUM - 469

planes of flexural motion. Phase shift a t resonance due to longitudinal motion i s 180°, and phase shift due to flexural resonance is Oo. Stray electrical capacitance between input and output adds a quadra ture component of output voltage, which i s not desirable from the viewpoint of oscillator sta- bility.

Simplified Equivalent Circuit

Although there a re many possible modes of

I I I I U 20 U0 6 C 8 0 1

K H z

Figure 3 . Frequency response of a half- wavelength Datum Bar

I ' n I~

oo 20 3 0 60 80

K H z

Figure 4. Frequency response of a full-wavelength Datum Bar

mechanical resonance for the datum s t ruc tures , t he choice of mounting flanges and t ransducer locations has been made to emphasize, a s well a s possible, t he 50 kHz longitudinal mode. For design of the associated electronic oscillator circuits, it is useful t o have an "equivalent" circuit representation of t he 50 kHz behavior, including input and output impedances, t ransfer impedance that exhibits the resonance, and s t ray capacitive coupling between input and output terminals.

Since the 50 kHz response predominates in the band of frequencies around resonance. a simple se t of measurements determines the component values, in the equivalent circuit illustrated in Figure 5 . The capacitances and CO2 a r e the low frequency values of input and output trans- ducer capacitance; since very little cur ren t f lows through the L R C and C' branches except near resonance, they a r e simply the terminal capaci- tances measured a t any convenient frequency away from resonance.

4- C '

; 1 I D E A L

Figure 5 . Equivalent circuit representing Datum Bar performance near 50 kHz

With and CO2 determined, the next s tep is to determine L, R and C in the motional branch. T o find R. terminate the output transducer in a small value of resistance RL such tha t

a t the resonant frequency f = w o / 2 n : 5 0 x I d . 0

Then drive the input t ransducer with voltage from a laboratory oscillator, adjusting frequency to produce maximum signal across R L . This i s the precise frequency f o., and the ratio of input to output signal voltages is

E i n - - - 1 + RIRL E o u t

Having determined f and the voltage ratio, ad- jus t frequency to the adjacent half power fre- quencies 5 and fi . T h e quality factor of the motional branch is

f0

f2 - f1 Q = - .

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From these measured values, the component values are calculated:

L = QR/wO

1 c = - 2

O L 0

Finally. the value of the stray capacitance C can be found by measuring the value of frequency f a , lying just below 50 kHz, for which the transmission is minimum. At this frequency, C resonates i n parallel with the resonant branch RLC. The series combination of C and -C (nega- tive because of the 180° phase shift through mechanical coupling) is antiresonant with L:

2 1 / L ( I / c - I / c '1 = w a

C CY=--

1 - ( f a / f o IL

Typical values for a long Datum whose trans- ducers were attached using conducting epoxy as bonding agent:

Col = Co2 = 1500 pf = 51.920 kHz

f2 = 52.090 kHz fi = 51.750 k H z

E i n / E o u t = 1.251.005 = 250 f o r R L = 50 ohms

fa = 49.290 kHz

For these values,

Q = 153 R = 1 2 , 4 5 0 ohms L = 5.84 henrys C = 1.609 pf C' = 1 6 . 3 pf

Later versions of the Datum used solder i n place of epoxy for attaching the transducers. They generally have much higher values of Q. often as high as 2000.

Oscillator and Indicator Circuit

Since the equivalent circuit predicts the per- formance of the Datum Post reasonably well for frequencies near the desired resonance, it was used as the basis for design of the electronic circuit employed as active feedback, to make the Datum self exciting at its natural resonant fre- quency. With a nominal impedance of 1000 ohms

the phase shifts, a s predicted by the equivalent circuit, by 180 degrees at resonance. Thus, an oscillator can be formed by coupling back from the readout transducers to the input transducers through an amplifier with zero degrees phase shift. Figure 6 shows the amplifier circuit. Signal transmission through the Datum Post is coupled from the output to the inverting input of the operational amplifier.

Figure 6 . Circuit for Datum oscillator and output indicator

The critical components in the circuit are those for impedance matching and resonance selection. Since several false resonances are possible in the Datum Post, they must be carefully avoided by these critical components. This can be achieved by careful matching of the bias circuits of the opera- tional amplifier and either using an active device with limited gain-bandwidth product, or using a frequency selective circuit in part of the feedback network.

In our early development, use of limited gain- bandwidth was satisfactory. However, in opera- tional tests it was found that higher amplitudes of motion were desirable. Rather than change ampli- fiers, we simply added a series inductance in the network to provide series resonance with the transducer capacitance, resulting in increased amplifier current and an increase in vibration amplitude by about 9 to 10 dB. This approach also stabilizes the response region, so the desired resonance is assured. This has been so successful that care must be taken not to exceed the op amp specifications on dissipation.

An added feature is the use of an LED indica- tor, which is excited from the oscillator circuit. I f operation of the Datum should fail for any reason. the LED is extinguished.

Co n d us ion

The ultrasonic Datum Bar i s a precise reference for locating cutting edges of tools in an automated lathe system. It has the advantage that each tool is the probe used for measuring i ts location in the machine coordinate system.

1985 ULTRASONICS SYMPOSIUM - 471