Induction Method for Measuring the Starting Torque of Instrument Ball Bearings

E. F. Kolotii

(Presented by the scientific seminar of the Faculty of Automation and Computer Engineering)

When measuring the starting torque of instrument ball bearings, a gradually increasing torque is applied to the moving part, consisting of a flywheel fitted onto the outer ring of the bearing [1]. To create such a torque, it is proposed to use an induction mechanism with a traveling magnetic field, similar to that used in electric-energy meters. As is known, the rotating torque of an induction measuring mechanism is equal to [2, 4]

\[ M_{\mathrm{э}} = k f \Phi_1 \Phi_2 \sin \psi, \tag{1} \]

where \(k\) is the coefficient of proportionality;
\(f\) is the alternating-current frequency;
\(\psi\) is the phase difference between the magnetic fluxes \(\Phi_1\) and \(\Phi_2\).

Figure 1 shows a diagram of a device with an induction mechanism for measuring the starting torque of ball bearings. By means of the starting circuit 1, a generator of linearly increasing voltage 2 is brought into operation; at its output a gradually increasing voltage \(U_{\mathrm{г}}\) appears (Fig. 2). This voltage acts on modulator 3, which supplies an alternating voltage \(U_{\mathrm{м}}\), whose amplitude increases in accordance with the increase in the voltage of 2. Through the matching transformer \(T_{\mathrm{р}}\), the voltage from the output of the modulator is applied to windings \(w_{\mathrm{г}}\) and \(w_{\mathrm{и}}\) of the induction measuring mechanism, which

Fig. 1. Diagram of a device with an induction mechanism for measuring starting torque

Fig. 2. Time diagrams of voltages.

develops the torque \(M_\beta\), applied to the moving part and increasing in accordance with the growth of the amplitude at the modulator output. The readings of ammeter \(A\), connected into the circuit of one of the windings of the induction mechanism, increase during the time \(t_1\), until the torque \(M_\beta\) exceeds somewhat the starting torque of the bearing. In this case, under the action of the difference of torques \(\Delta M = M_\beta - M_{\mathrm{tr}}\), the moving part turns through a certain angle, which causes the fixing device 4 with a photoresistor to operate and further growth of the voltage at the output of generator 2 to cease (instant \(t_1\)). From the ammeter readings, the value of the starting torque of the ball bearing is determined. To obtain the value of the starting torque for a different mutual position of the bearing rings, it is necessary to rotate one ring (in this case the inner one) relative to the other through an angle determined by the technical specifications for the given type of bearing (for example, through \(36^\circ\)), and to start the measuring circuit again. For sorting bearings according to starting torques under mass-production conditions, all these operations (starting the measuring circuit, fixing and resetting the ammeter readings, rotating the inner ring of the bearing through a specified angle, signaling rejection) are readily automated.

Because the windings of the induction mechanism are supplied from a single transformer, the condition is fulfilled

\[ I_1 = \kappa_1 I_2, \]

where \(I_1\) and \(I_2\) are the currents in windings \(w_r\) and \(w_u\) of the induction mechanism;
\(\kappa_1\) is the proportionality coefficient.

Taking into account that, for the induction mechanism, \(\Phi_1 \equiv I_1\) and \(\Phi_2 \equiv I_2\), equality (1) may be rewritten in the following form:

\[ M_\beta = \kappa_2 f I_1^2 \sin \psi . \tag{2} \]

It follows from this that the scale of an instrument measuring the current in one of the windings of the induction mechanism, when calibrated in units of torque, is quadratic (expanded at the beginning and compressed at the end). This circumstance is very important when measuring very small starting torques, since the sensitivity of such an instrument when measuring small torques is considerably higher than when measuring larger torques.

The error of such a device for measuring starting torque consists mainly of the error of the method [1], the error in converting \(I_1\) into \(M_\beta\), and the error of the indicating instrument.

The error in converting \(I_1\) into \(M_\beta\) is determined by the instability of the characteristics of the induction mechanism, as well as by the instability of the frequency of the supply alternating voltage and by fluctuations of the ambient temperature.

The basic error of induction mechanisms is about 0.5% [3]; however, their temperature error reaches 1% per \(10^\circ\mathrm{C}\). Therefore, to obtain accurate operation of the induction transducer it is necessary to maintain a constant temperature in the room where the starting torque of bearings is measured.

It follows from expression (2) that the frequency error of the induction transducer is completely determined by the instability of the frequency of the supply voltage.

To obtain high accuracy in measuring the starting torque by means of an induction transducer, it is necessary, in addition to introducing temperature and frequency stabilization, also to take into account the error-

ness of the measurement method. In this case, the total measurement error when using a class 0.5 indicating instrument can be brought down to 1%.

References

1. E. F. Kolotii, I. G. Leshchenko. On the question of measuring the starting torque of instrument ball bearings. (The article is included in this collection.)
2. A. V. Fremke. Telemeasurements. Gosenergoizdat, Moscow–Leningrad, 1958.
3. M. M. Fetisov. New automatic compensation instruments for measuring nonelectrical quantities. Part I, LDNTI, Leningrad, 1960.
4. P. N. Goryunov, S. M. Pigin, N. N. Shumilovskii. Electrical Counters. Gosenergoizdat, Moscow–Leningrad, 1951.