Parameters of Ultrasonic Radiation Used to Measure the Dimensions of Parts
Abstract Generated abstract
This paper discusses the selection of ultrasonic radiation parameters for noncontact measurement of part dimensions during machining. It presents a two-stage ultrasonic location method combining coarse wavelength-based measurement with precise phase measurement, and derives formulas for choosing wavelength, frequency, pulse duration, pulse repetition period, maximum measuring distance, and receiver sensitivity conditions. A worked example for a barium titanate emitter in air gives parameters for measuring diameters up to 315 mm with an absolute accuracy of 0.01 mm, including temperature compensation for changes in sound velocity. The paper thereby provides a practical calculation procedure for designing an ultrasonic dimensional monitoring device.
Full Text
PARAMETERS OF ULTRASONIC RADIATION USED FOR MEASURING THE DIMENSIONS OF PARTS
L. M. Anan'ev, F. K. Voloshnikov
(Presented by the scientific seminar of the Research Institute of Nuclear Physics, Electronics, and Automation at TPI)
Monitoring the dimensions of parts by the method of ultrasonic location makes it possible to measure parts on metal-cutting machines during their machining, without stopping the machine and without mechanical contact between the measuring device and the part being inspected.
For these purposes ultrasound is needed, emitted by radio pulses having a stable repetition frequency and duty cycle.
The block diagram of such a device may have various variants depending on the specific task (the required measurement accuracy, the range of dimensions of the parts being measured, and the material of the emitter and receiver). An example of such a block diagram is given in Fig. 1.
The parameters of ultrasonic oscillations may be selected, for example, according to the following method:
the measurement principle is two-stage: coarse and precise measurements. The coarse measurement gives the size of the part with an accuracy up to one whole wavelength of the ultrasonic radiation; the precise measurement measures the phase of reflection of the ultrasonic wave from the measured surface and supplements the coarse measurement. Thus, the specified absolute measurement accuracy determines the wavelength \(\lambda\) of the ultrasonic oscillations.
\[ \lambda = \frac{\Delta D}{\Delta \lambda \%}\cdot 100, \]
where \(\Delta D\) is the absolute measurement accuracy,
\(\Delta \lambda\) is the possible accuracy of measuring the phase between the emitted and reflected ultrasound,
whence the ultrasound frequency is
\[ f = \frac{V}{\lambda}, \]
where \(V\) is the velocity of propagation of ultrasound.
The result obtained should be checked for the condition that there is no dispersion of the ultrasound velocity, according to the inequality
\[ f < 10^5 \text{ kHz}. \]
The minimum duration of the pulse of ultrasonic oscillations is found from the condition that measurement is possible at the maximum dimensions of the part.
\[ t_{\mathrm{p}}= \frac{X_{\mathrm{b}}-\dfrac{D_{\max}}{2}}{V}, \]
where \(X_{\mathrm{b}}\) is the maximum distance from the emitter to the surface being inspected,
\(D_{\max}\) is the maximum diameter of the part.
The distance \(X_{\mathrm{b}}\) depends on the attenuation of ultrasonic oscillations in the surrounding medium and can be found from the expression:
\[ X_{\mathrm{b}}=-\frac{\lambda \lg \dfrac{J_x}{J_0}}{4\alpha^* \lg e}, \]
where \(J_x\) is the minimum value of ultrasonic power to which the ultrasonic receiver responds;
\(J_0\) is the magnitude of the ultrasonic radiation power at which the emitter is capable of operating for a long time without overheating;
\(\alpha^*\) is the coefficient of ultrasonic absorption in the surrounding medium.
The investigation period of ultrasonic pulses \(T\) is selected from the condition of complete attenuation of the ultrasonic wave in the interval between pulses according to the equation
\[ T \geq N \frac{2X_{\mathrm{b}}}{V}, \]
where \(N\) is a coefficient taking into account the increase in scattering that is necessary for complete attenuation of the ultrasound; it is calculated from the expression:
\[ N= \frac{\lg \dfrac{J_{x\mathrm{p}}}{J_0}} {\lg \dfrac{J_x}{J_0}} = \frac{\lg J_{x\mathrm{p}}-\lg J_0}{\lg J_x-\lg J_0}. \]
The quantity \(J_{x\mathrm{p}}\) defines the sensitivity threshold of the receiver and is related to \(J_x\) by the relation:
\[ J_{x\mathrm{p}}=\frac{J_x}{m}, \]
where \(m\) is a coefficient guaranteeing the absence of reception.
For a specific example of a barium titanate emitter
\((J_0=2\ \text{W/cm}^2,\ J_x=2.5\cdot10^{-2}\ \text{W/cm}^2,\ m=100)\), in an air medium \((\alpha^*=29.1\cdot10^{-4})\), with maximum part diameter \(D=315\ \text{mm}\) and an absolutely specified accuracy \(\Delta D=0.01\ \text{mm}\) at a relative phase-measurement accuracy \(\Delta\lambda=1\%\), we have \(\lambda=1\ \text{mm}\), \(f=340\ \text{kHz}\), \(X_{\mathrm{b}}=200\ \text{mm}\).
\[ t_{\mathrm{p}}=\frac{1}{34000}\ \text{s}\ (\simeq 30\ \mu\text{s}), \]
\[ T=\frac{1}{170}\ \text{s}\ (\simeq 5880\ \mu\text{s}). \]
In view of the fact that the ultrasound velocity \(V\) changes under the influence of fluctuations in the temperature of the surrounding air according to the dependence
\[ V = V_{20^\circ}\left(1 + 0.0018\,\Delta t^\circ\mathrm{C}\right), \]
the measured time interval will change accordingly,
\[ t_{\text{meas}} = \frac{X}{V} = \frac{X}{V_{20^\circ}\left(1 + 0.0018\,\Delta t^\circ\mathrm{C}\right)}. \]
To compensate for this influence, it is necessary to introduce into the anode resistance of trigger 4 a thermistor \(R\), which will change the current passing through indicator \(A_1\) according to the same law, but in the opposite direction; then, introducing the scale factor \(A\), we shall have
Fig. 1. Block diagram of the device: 1—ultrasonic transmitter-receiver; 2—forming circuit, v—input, c and d—outputs; 3—sinusoidal-oscillation generator, a and o—its outputs; 4—trigger, g and i—outputs; 5—trigger, \(\alpha\) and \(\beta\)—inputs; 6—rectangular-pulse generator with large duty factor and low frequency, e—input, g and l—outputs; 7—time selector; p—input, m—input, n—output; 8—receiver, s—input, k and \(\Theta\)—outputs; \(A_1\), \(A_2\)—current indicators; \(R\)—temperature compensator (thermistor); 9—part being measured.
\[ t_{\text{meas}} = A J_{\text{cp}} = \frac{A J_{\text{cp},20^\circ}\left(1 + 0.0018\,\Delta t^\circ\mathrm{C}\right)} {1 + 0.0018\,\Delta t^\circ\mathrm{C}}, \]
\[ t_{\text{meas}} = A J_{\text{cp},20^\circ}, \]
where \(J_{\text{cp},20^\circ}\) is the mean current in indicator \(A_1\) at a temperature of \(20^\circ\mathrm{C}\).
The specific example considered illustrates the operation of the device with the indicated ultrasonic parameters. The operating characteristics for this example will be as follows:
a) range of diameters measured by the device — \(0 \div 315\) mm;
b) absolute measurement accuracy — 0.01 mm;
c) minimum distance to the surface being inspected — 20 mm;
d) maximum distance to the surface being inspected — 200 mm;
d) the minimum surface width monitored by the sensor (along the axis of the rotating part) is 0.3 mm, which is achieved by introducing focusing.
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