INSTRUMENT FOR MEASURING LOW-FREQUENCY VIBRATIONS

G. S. ZHARTOVSKII, G. P. TSELISHCHEV

(Presented by the Department of Mining Machines, Mine Transport, and Mining Mechanics)

The operation of many machines and mechanisms, including impact-action mechanisms, is accompanied by intense low-frequency vibrations, during which the magnitude of the overloads reaches 10 \(g\) and more. The problem of measuring vibrations with such overloads and with a frequency range approximately from 10 to 60–70 Hz can be solved by means of seismic transducers operating in vibrometer mode, i.e., possessing a resonance frequency no higher than ten hertz. However, in cases where transducers of increased reliability are required, capable of operating under conditions of random impacts, jolts, etc., it is better to use the accelerometric (pre-resonance) mode. In this case the sensitivity of the transducer is sharply reduced, since in this mode it is inversely proportional to the square of the natural frequency. Piezoelectric transducers, sufficiently reliable mechanically, are difficult to use for solving this problem, since in most piezoaccelerometers the lower limiting frequency lies within the range 30–60 Hz. Correction of the frequency characteristic and double integration of the signal may require bulky electronic equipment, which is not always acceptable under shop-floor conditions. Therefore, for the development of a vibrometer with measurement limits for vibration-displacement amplitude of 0.01–1.0 mm, a magnetoelectric transducer with a pendulum suspension on an elastic hinge of the “spring cross” type was used, with the following data: natural frequency of the seismic system \(f_0 = 138\) Hz, velocity sensitivity \(S_v = 8\ \text{mV}/\text{mm Hz}\), damping ratio \(\beta = 0.05\). Thus, the output signal of the transducer, practically up to 55 Hz, is proportional to the third power of the vibration frequency. In order for it to be constant at an unchanged value of the vibration-displacement amplitude, triple integration is necessary. It is known that during integration the output signal is attenuated; therefore it must be amplified so that subsequent measurements can be made with a pointer instrument. The transducer is made in a housing of hard aluminum alloy. The transducer is fastened to the object by a thread in the boss of the housing. A closed magnetic system and a shielded cord 3 m long protect the converter coil from external magnetic fields.

The basic electrical circuit of the instrument is shown in Fig. 1. The signal from the transducer is fed to two integrating \(RC\) circuits, while the third circuit is connected at the output of the amplifier, since the attenuation of the signal during

Fig. 1. Schematic electrical circuit of the instrument

in triple integration is so considerable that the useful signal already becomes comparable with the noise level of the amplifier tubes. As the integrating resistance of the first circuit, the resistance of the sensor coil is used. To match the input resistance of the second circuit with the maximum output resistance of the first, the value \(R_1\) was chosen to be \(3.6\ \text{k}\Omega\). After the two circuits the signal is amplified by three stages of an amplifier assembled with 6N2P and 6Zh4P tubes. In order that the high-ohmic output of the third stage not be shunted by the low-ohmic load of the third integrating circuit, coupling is carried out by means of a cathode follower assembled with a 6P14P tube, which has a sufficiently high transconductance (\(S = 11\ \text{mA/V}\)) and a large grid-characteristic range. The latter is especially important, since the signal level at the grid reaches \(30\ \text{V}\). In order to weaken negative current feedback as much as possible, in the first three stages the automatic-bias resistances \(R_4\), \(R_6\), and \(R_{11}\) are shunted by large-capacitance capacitors \(C_3\), \(C_6\), and \(C_8\). To weaken the mutual influence of the stages, and also to smooth the ripple of the anode supply voltage, filters \(R_7C_4\) and \(R_{20}C_{15}\) are included in the circuit.

The third integrating circuit \(R_{18}C_{12}\), by adding an inductance \(L_1\) in parallel with the resistance \(R_{18}\), performs the role of a correcting link that raises the frequency response of the amplifier at low frequencies, beginning at approximately \(15\ \text{Hz}\) and below. Correction of the frequency response is obtained because the circuit \(L_1C_{12}\) has a resonance frequency lying in the region of the lower limit of the measuring frequency range.

The coupling between the registering link and the output of the amplifier is carried out through a cathode follower assembled on one half of a 6N2P tube. The registering link consists of semiconductor diodes \(D_2\) and \(D_3\), large-capacitance capacitors \(C_{13}\), \(C_{14}\), limiting resistance \(R_{19}\), and an M-24 pointer instrument, and is assembled according to the circuit of a double “parallel” detector having opposite polarities of the output signals. In a “parallel” detector the output voltage is proportional to the peak value of the measured signal if the time constant of the circuit \(\tau = R_{19}C_{13}\) is much greater than the period of the signal. The difference of the output voltages (the instrument current is proportional to it) will be equal to the peak-to-peak value of the input signal, if each output voltage of the “parallel” detectors is equal respectively to the positive and negative values of the peak magnitude of the signal.

Fig. 2. Amplitude-frequency characteristic of the instrument

The instrument is designed for a mains voltage of \(220\ \text{V}\); its power-supply unit consists of a transformer, a full-wave rectifier using D-211 semiconductor diodes, a series of smoothing filters, and gas-discharge voltage stabilizers SG1P and SG3P. The entire range of vibration-displacement measurement is divided into two limits: \(0.01\text{–}0.1\ \text{mm}\) and \(0.1\text{–}1.0\ \text{mm}\). This is accomplished by stepwise regulation of the gain coefficient by resistances \(R_8\) and \(R_9\).

The amplitude-frequency characteristic of the electronic unit together with the sensor is shown in Fig. 2. As is evident from the characteristic,

in the frequency range of 10–60 Hz its nonuniformity is 10–8%. The rise of the characteristic beginning at 55 Hz is explained by the fact that the sensor is underdamped; therefore, the cubic dependence of the sensor output signal at a constant vibration displacement is maintained approximately up to 55 Hz, while at higher frequencies the signal begins to increase more intensely. It should be noted that damping of the sensor occurs not only due to eddy currents induced in the coil frame, but also due to the shunting effect of the winding by the capacitance \(C_1\); however, the higher the natural frequency, the more difficult it is to damp the system, since the degree of damping of the sensor is inversely proportional to the first power of the natural frequency.

Experimental verification of the operability of the instrument, a photograph of the general appearance of which is shown in Fig. 3, showed that the instrument

Fig. 3. General view of the instrument with vibration sensor

stably provides the guaranteed accuracy of vibration-displacement measurements within \(\pm 10\%\) and is sufficiently simple to operate. In order to make it possible to observe the form of the measured process, an output to an electronic oscilloscope is provided on the front panel of the instrument. The instrument is of the portable type. Its weight is approximately 5 kg.