A New Method for Recording the Torque–Speed Curve of a Squirrel-Cage Motor

I. G. Kuleev

Recording the curve of the dependence of rotational torque on the number of revolutions of a squirrel-cage motor in the so-called unstable part of this curve presents certain difficulties. There are several methods by which it can be obtained. Engineer Kiklievich uses a series generator as the load of an induction motor. The resisting (rotating) torque of the series generator is proportional to the cube of the number of revolutions; as a result of this, on the unstable part of the curve the induction motor, coupled to the series generator, rotates steadily (Fig. 1).

This method has the disadvantage that, at speeds below 120 rpm, it is not possible to record the curve.

Kluge and Linke measured the force transmitted to the shaft during the acceleration of an electrical machine by means of piezoquartz, whose emf, amplified many times, was transmitted to an oscillograph. The disadvantage of this method is that the amplifier circuit may introduce significant distortions. A simpler and more reliable method is the one proposed by the author, in which a machine with independent excitation (H) is used as the load (Fig. 2).

Fig. 1

The torque of an electrical machine is

\[ M \equiv E I_a \]

Fig. 2

With constant flux, which is the case for a motor with independent excitation,

\[ M \equiv n I_a \]

It follows from this that, when the rotational speed changes, the change in torque takes place along a straight line whose slope depends on the armature-current intensity.

For stable operation of the machine it is necessary that the following conditions be satisfied.

1. The motor characteristic \(M_d=\psi(n_d)\) and the load characteristic \(M_n=f(n_n)\) intersect at the point corresponding to the speed at which it is desired to maintain the motor.

Fig. 3

1. For \(n_n<n\): \(M_d>M_n\).

2. For \(n_n>n\): \(M_d<M_n\).

If the listed conditions are satisfied, then the slightest deviation of the unit speed from \(n\) leads to the creation of an excess torque equal to

\[ M_d-M_n, \]

returning the system to its initial state (Fig. 3). By increasing \(r\) and the excitation current of machine (III), it is easy to attain fulfillment of the above conditions for stable operation.

Indeed, when the excitation current of machine (III) is increased, its EMF will increase. The armature current of machines (N) and (III) will decrease, since

\[ I_{\mathrm{я}}=\frac{U_{\mathrm{н}}-E_{\mathrm{ш}}}{r+r_{\mathrm{ш}}}. \]

Here \(U_{\mathrm{н}}\) is the voltage of machine (N), \(E_{\mathrm{ш}}\) is the EMF of machine (III), and \((r_{\mathrm{ш}})\) is the resistance of the armature winding of machine (III).

The asynchronous motor, owing to the reduction of the load, will increase its speed. The EMF and the voltage of machine (N) will increase. An equilibrium state will be established at larger torques of the asynchronous motor and of machine (N).

Figure 4 gives the curves of the change in torque of the asynchronous motor AD—31/6 when operating in the motor mode and in the electromagnetic-brake mode, obtained by the author’s method.

When the curves were taken, the machine windings were connected according to the circuit (Fig. 2). The excitation current of machine (N) was maintained constant. The current intensity in its armature was varied by changing the resistance \((r)\) and the excitation current of machine (III). When the excitation current of machine (III) is increased, its voltage increases. The current in the armature circuit of the machines is constantly decreasing, because the voltages are directed oppositely. Machine (III) is a consumer of the energy of machine (N). If, under these conditions, to the current flowing in the armature of machine (N) one adds the no-load current under the same operating conditions of the machine (at the same speed and excitation current), then the magnitude of the resultant current will be proportional to the torque developed by motor AD.

The curve of torque versus speed was taken both for the motor mode and for the electromagnetic-brake mode (Fig. 4).

The curve for the motor mode was taken as follows: a reduced voltage was applied to the stator winding of motor AD, the excitation of machine (III) was removed, and machine (N) at this time was closed on the resistance \((r+r_{\mathrm{ш}})\). The asynchronous motor AD,

connected by a belt to machine (H), rotated steadily at the minimum speed (30–40 rpm). When the excitation current of machine (III) was increased, the asynchronous motor accelerated to a higher speed, at which it likewise rotated steadily.

Operation of the machine in the electromagnetic-brake mode was carried out as follows: machine (H), using the energy of machine (III), rotated in the same direction, while the asynchronous motor, owing to the fact that two terminals of the stator were interchanged, attempted to rotate in the opposite direction; however, machine (H), operating in the motor mode, rotated it in its former direction, i.e., the rotor rotated against the stator field. Keeping the magnitude of the excitation current of machine (H) unchanged, by varying the excitation current of machine (III) the asynchronous motor was rotated at various speeds, beginning with 30–40 rpm and up to the normal speed.

Fig. 4

The curve of the armature current of machine (H) at no load as a function of the number of revolutions was obtained as follows: with the belt removed, machine (H) was given such an excitation that it operated in the motor mode. Keeping the excitation current constant, a reduced voltage was applied to it; then, by increasing the voltage, the number of revolutions was gradually increased to the normal value.

LITERATURE

1. Elektrichestvo, No. 2, 1941.
2. VDI, 1929, p. 1311, and 1930, p. 887.