DYNAMIC PROPERTIES OF ELECTRICAL MACHINE COMMUTATORS

L. Ya. Zinner, A. I. Skorospeshkin, A. I. Proshin

(Recommended by the seminar of the departments of electrical machines and general electrical engineering)

From the practice of adjusting direct-current machines it is known that commutation conditions depend on the state of the working surface of the commutator [1, 2].

Until recently there have been no sufficiently concrete data on the degree to which mechanical factors influence commutation. This is explained by the absence of sufficiently accurate instruments that make it possible to measure very small disturbances of the commutator surface when operating at elevated rotational speeds.

In the present work we give information concerning a semiconductor profilometer developed by us [2, 3] and the results of investigations carried out on machines of the “P” series.

The schematic diagram of the profilometer is shown in Fig. 1.

The principal element of the profilometer is the measuring cell, which is a high-frequency transformer bridge, Tr1, with tight inductive coupling between two ratio arms. A capacitive transducer, which is a point probe, is connected between the balancing capacitance and the inductive arm. The measuring cell is supplied with a high-frequency voltage of 3 V, at a frequency of 1 MHz, from a generator assembled on transistors T1, T2 (P403) and connected into the diagonal of the bridge. When the distance from the commutator surface to the capacitive probe changes, the balance of the bridge is disturbed and an emf proportional to the change in the gap is induced in the measuring winding.

The unbalance emf, through the emitter follower T3 (P403), is fed to the input of the measuring circuit, consisting of the resonant amplifier stage T4 (P403), an amplitude detector, a carrier-frequency filter, and a three-stage video amplifier T5, T6, T7 (P403). Thus, the carrier frequency of the generator, amplitude-modulated by the commutator segments, is subsequently amplified in the resonant amplifier, detected, and at the output of the video amplifier, by means of a cathode-ray oscilloscope, a characteristic pattern is observed that reflects the condition of the commutator surface.

To check the operating modes of the individual functional elements of the circuit and to monitor the overall runout of the commutator statically, a millivoltmeter T8—T11 (P403), M24, is introduced into the circuit; it is intended for measuring sinusoidal voltages in the range 0.5—1.5 MHz and has four measurement ranges: 0—10 mV, 0—100 mV, 0—300 mV, 0—3 V. The input resistance of the millivoltmeter is not less than 100 kΩ, and the measurement accuracy on all ranges is no worse than 3%.

Fig. 1. Schematic diagram of the profilometer.

Power for the profilometer is supplied by a voltage of 15 V from a semiconductor stabilizer \(T_{12}\)—\(T_{13}\) (P4D, P13).

The profilometer is constructed in the form of two separate units. Fig. 2 shows the external appearance of the instrument. The remote unit, containing a high-frequency generator, a measuring bridge, and a capacitive probe, is mounted on a solid textolite plate.

Fig. 2. External view of the profilometer.

When it is necessary to measure the profile of a commutator, the remote unit is fastened to the machine window; then, with the aid of a micrometer, the required gap is set and the measuring bridge is balanced.

In order to reduce circuit error, all stages are provided with feedback, which substantially reduces temperature drift.

During testing of the instrument under factory conditions it was established that the profilometer has:

1) high sensitivity to small changes in the commutator surface, which makes it possible to measure the protrusion of individual bars or groups of bars down to \(1\,\mu\text{m}\);

2) high resolving power with respect to the width of the lamella, which eliminates error when inspecting commutators of various designs.

Thus, the developed profilometer makes it possible, with sufficient accuracy, to monitor changes in the shape of commutator surfaces at any rotational speeds and may find application both in studying the influence of mechanical factors on commutation and directly in factory practice in designing new types of commutators.

In the course of experimental testing of the profilometer on a number of machines of the P series, the authors investigated the dynamic behavior of commutators. On the basis of the experimental data obtained, it was possible to establish the nature and frequency range of the disturbances transmitted to the brush by the commutator during dynamic interaction.

In the general case, the dynamic state of the commutator surface is determined by the following interrelated factors:

a) clearance in the bearings and diametral scatter in the dimensions of the balls;

b) elastic deformation of the shaft;

c) the force of unilateral magnetic attraction;

d) ovality of the commutator surface and its initial eccentricity;

e) elastic deformation of the commutator at high rotational speeds.

Let us consider the influence of the above-listed components on the behavior of the commutator in dynamics.

Clearance in the bearings can have a substantial influence on the increase in the total runout of the commutator in dynamics when sliding bearings are used, as occurs in high-power machines [4], where, as the rotational speed of the armature increases, the radial clearance is taken up. In this case the character of the change in eccentricity with increasing rotational speed is described by the expression:

\[ \gamma = \sqrt{ R^{2}-\left(\frac{\delta}{2}\right)^{2}\sin^{2}\varphi } - R + \delta \sin^{2}\frac{\varphi}{2}, \tag{1} \]

where \(R\) is the radius of the outer bearing race;

\(\delta\) is the radial clearance of the bearing;

\(\varphi\) is the angle determined by the direction of the resultant of the armature weight and the centrifugal force of unbalance.

The maximum value of the eccentricity is \(e_{\max}=\delta\); however, in practice \(e \ll \delta\), since the clearance, owing to the hydrostatic support of the oil in the bearing, is always taken up to a quite definite value, and with a further increase in speed no increase in eccentricity occurs. In the case of a well-balanced machine, no change in runout due to the taking-up of the radial clearance should occur at all.

For low-power machines using rolling bearings, the change in commutator runout due to taking-up of the radial clearance occurs within still narrower limits, with a frequency equal to the rotational frequency of the shaft and an amplitude of 5–10 µm.

Studies carried out on machines of frame sizes 3–5 showed that sinusoidal oscillations, having a quasi-random character both with respect to frequency and with respect to amplitude, are superimposed on the developed profile of the commutator. The frequency of these oscillations is determined by the rotational frequency of the armature and by the speed of displacement of the balls in the bearing race. In the speed range up to 2000 rpm, their frequency for the machines studied is approximately an order of magnitude higher than the rotational speed of the shaft, and the maximum amplitude of the oscillations is 1–2 µm (Fig. 3, a). With increasing rotational speed they are damped (Fig. 3, b), which is explained by the damping action of the lubricant layer.

Elastic deformation of the shaft, which occurs in practically any machine and is caused by the weight of the armature, the unbalanced mass of the armature, and the force of unilateral magnetic attraction, can lead to a considerable increase in the total runout of the commutator at high rotational speeds. The latter is the more obvious, the more poorly balanced the machine is. However, even in the case of ideal balancing, an increase in the dynamic runout of the commutator is observed due to elastic deformation of the shaft under the action of the armature weight and the force of unilateral magnetic attraction.

In the presence of initial eccentricity due to unbalance of the armature, initial bending of the shaft from the force of gravity, and the force of unilateral magnetic attraction, the motion of the center of gravity of a shaft with a concentrated mass is described by the following equations [5]:

Fig. 3. Profilograms of the commutator of machine П-51.
a) 1500 rpm,
b) 3000 rpm.

\[ m\frac{d^{2}x}{dt^{2}}+\mu\frac{dx}{dt}+kx=ke\cos\varphi, \tag{2} \]

\[ m\frac{d^{2}y}{dt^{2}}+\mu\frac{dy}{dt}+ky=ke\sin\varphi-(mg+P_{\delta}), \tag{3} \]

where

\(m\) — concentrated mass of the armature,
\(k\) — shaft stiffness coefficient,
\(x, y\) — coordinates of the center of gravity of the mass,
\(\varphi\) — angle of rotation of the shaft,
\(e\) — eccentricity of the mass,
\(\mu\) — friction force proportional to the rotational speed of the shaft,
\(P_{\delta}\) — force of one-sided magnetic attraction.

As is easy to see, the force \((mg+P_{\delta})\) creates a deflection equal to

\[ y=\frac{mg+P_{\delta}}{k}, \]

and the coordinate in equations (2) and (3) will be

\[ y_{1}=y+\frac{mg+P_{\delta}}{k}. \]

Shifting the origin of coordinates along the \(y\)-axis by the amount \(\dfrac{mg+P_{\delta}}{k}\), we obtain

\[ m\frac{d^{2}x}{dt^{2}}+\mu\frac{dx}{dt}+kx=ke\cos\varphi, \tag{4} \]

\[ m\frac{d^{2}y_{1}}{dt^{2}}+\mu\frac{dy_{1}}{dt^{2}}+ky_{1}=ke\sin\varphi. \tag{5} \]

The solution of these equations gives the relations describing the motion of the commutator in two mutually perpendicular planes

\[ x_{k}= \frac{ b\left[ek\sin(\omega t-\alpha)-\dfrac{P_{\delta}}{k}\sqrt{(k-m\omega^{2})^{2}+\mu^{2}\omega^{2}}\sin\psi\right] }{ a\sqrt{(k-m\omega^{2})^{2}+\mu^{2}\omega^{2}} }, \tag{6} \]

\[ y_k = \frac{ b\left[ ek\cos(\omega t-\alpha) -\frac{1}{k}(mq+P_\delta)\sqrt{(k-m\omega^2)^2+\mu^2\omega^2}\cos\psi \right] }{ a\sqrt{(k-m\omega^2)^2+\mu^2\omega^2} }, \tag{7} \]

where \(b\) is the distance from the measured commutator track to the left support,

\(a\) is the distance from the center of mass to the left support,

\(\psi\) is the angle determining the direction of action of the force \(P_\delta\),

\[ \alpha=\operatorname{arctg}\frac{\mu\omega}{k-m\omega^2} \tag{8} \]

As is seen from (6, 7), the motion of the commutator proceeds according to a complex law that cannot be approximated by a sinusoid, as has been assumed in works [6, 7]. The assumption that the forcing force applied to the brush from the commutator side is sinusoidal is valid in the case when the armature is completely balanced, which is practically not achieved in any machine (Figs. 4, 5).

Fig. 4. Profilograms of the commutator of machine P-42.
a) 2000 rpm,
b) 3000 rpm,
c) 4000 rpm.

The ovality and eccentricity of the commutator, caused by noncylindricity of the surface and by misalignment of the commutator, do not exert any substantial influence on the current-collection process because of their low-frequency character. As is not difficult to show, in the case when ovality and eccentricity are displaced along the circumference of the commutator by half a period, the frequency of the disturbing force acting on the brushes is equal to twice the rotational frequency of the armature, and the brush, at a pressure of \(250\ \text{g}/\text{cm}^2\), has time to follow the changes in the commutator surface.

The latter is valid for machines in which the total runout of the commutator does not exceed \(25\text{--}30\ \mu\text{k}\), and for machines operating at spee-

speeds not exceeding 3–4 thousand rpm. Large values of runout and speed, all other conditions being equal, lead to a sharp deterioration of commutation.

Summarizing the foregoing, it should be noted that during operation of the machine a case may occur in which all the components act in one direction and the total runout, while remaining low-frequency, increases sharply in amplitude, reaching values of 50–60 μ, which entails a deterioration of commutation.

Fig. 5. Profilograms of the commutator of the PBS-32 machine.
a) 2000 rpm,
b) 3000 rpm,
c) 4000 rpm,
d) 5000 rpm.

In the general case, the disturbances transmitted to the brushes by the commutator have a frequency two to three times higher than the rotational frequency of the shaft, which often leads to deterioration of commutation, especially in those cases when the disturbance amplitudes and the rotational speed are high. However, as studies carried out on actual machines show, with

In a well-balanced armature, the change in the total runout of the commutator occurs within comparatively narrow limits, and its influence on commutation is insignificant, except for those limiting cases discussed above.

In our view, the greatest influence on the commutation process is exerted by the elastic and inelastic deformations of the commutator, which, as is known, may be of two kinds: elastic deflection and stretching of the commutator, manifested in a slight increase in diameter as the rotational speed increases; and elastic disturbances caused by nonuniformity of the forces holding the segments, which may cause permanent steps to form on the commutator surface. The latter type of disturbance is the most harmful, since in all cases the continuity of the brush–commutator contact is disrupted.

In order to determine the degree of influence of the various components on the behavior of commutators under dynamic conditions, we investigated a number of machines. Figure 4 (a, b, c) presents profilograms of the commutator of machine II-42, taken at speeds of 2, 3, and 4 thousand rpm.

For convenience in processing the profilograms and synchronizing the oscilloscope, foil 10 μ thick was glued to one of the segments. The two extreme marks on the oscillograms in Fig. 4 correspond to the signal from the foil and serve as the scale of the displacements of the commutator surface relative to the sensor plates.

As can be seen from Fig. 4, a, at rotational speeds up to 2000 rpm the commutator surface is not subject to any changes; the total runout is 5 μ and represents the initial eccentricity of the commutator. At this stage the machine is characterized by satisfactory commutation, with barely noticeable sparking under the brushes.

As the rotational speed increases, the working surface of the commutator is sharply disturbed (Fig. 4, b, c), both in the direction of increasing total runout and in the direction of increasing microrelief, which is accompanied by deterioration of commutation. At a speed of 4000 rpm, the total runout of the commutator is 10 μ, and the difference between individual sections of the commutator is 2–3 μ.

Still more illustrative in this respect are the oscillograms of the commutator surface of machine PBS-32 (Fig. 5, a, b, c, d), taken respectively at 2, 3, 4, and 5 thousand rpm. The static runout of the commutator was 20 μ, and measurements made with a minimeter and a profilometer gave good agreement of results.

With a smooth change in the rotational speed of the armature from 2 to 5 thousand rpm, the commutator surface, as can be seen from Fig. 5, undergoes noticeable changes, which is simultaneously accompanied by an intensive increase in sparking of the machine. Of interest is the fact that the change in the commutator surface with increasing speed obeys a definite regularity, consisting in the fact that, for each increment of speed by 1000 rpm, the amplitude value of the runout increases by a quite definite amount.

The latter indicates that, at high rotational speeds, the commutator undergoes considerable deformation.

For the commutator in Fig. 5, the character of the increase in runout is described by the numerical series

\[ A_0 = B + 2B + 3B + \ldots + nB, \tag{9} \]

where

\[ \begin{aligned} A_0 &\text{— initial value of the runout,}\\ B &\text{— a constant quantity characterizing the change in runout between}\\ &\quad \text{two adjacent values of speed,}\\ 1, 2, 3 \ldots n &\text{— successive values of speed.} \end{aligned} \]

At a certain value \(n_{\mathrm{cr}}\), destruction of the commutator occurs.

From analysis of the profilograms obtained it becomes obvious that the disturbance of commutation in the given case is due exclusively to elastic deformation of the commutator, which leads to the formation on its surface of steps with an amplitude of up to 36–40 μ and with durations of the leading and trailing fronts \(\tau_{\mathrm{p}}=0.0012\) sec, \(\tau_{\mathrm{z}}=0.0009\) sec, which the brush is unable to follow.

Indeed, in order for a brush raised to the height of a step to return to its initial level, a time equal to 0.003 sec is required. During this time the commutator, rotating at a speed of 4000 rpm, has time to turn through \(1/4\) revolution, and, consequently, for \(1/4\) revolution the brush hovers above the surface of the commutator.

On the basis of the foregoing, the interaction of the brush with the commutator in the presence of deformation has the character of a short-time dynamic impact, as a result of which the brush receives an acceleration in the radial direction. The magnitude of the acceleration and of the radial rebound can be determined, if the shape of the step, its height, and the time of interaction are known, from the following expressions:

a) for the case when the step has the form of a half-wave of a sinusoid,

\[ a=\frac{2.46\lambda\omega^{2}R^{2}}{l^{2}}, \tag{10} \]

\[ h=\frac{2.46\lambda\omega^{2}R^{2}-a_{1}l^{2}}{l^{2}}t^{2}; \tag{11} \]

b) for the case when the step has a sawtooth form,

\[ a=\frac{7.85\lambda\omega^{2}R^{2}}{l^{2}}, \tag{12} \]

\[ h=\frac{7.85\lambda\omega^{2}R^{2}-a_{1}l^{2}}{l^{2}}t^{2}; \tag{13} \]

c) for the case when the leading front of the step varies according to an exponential law,

\[ a=\frac{19.7\lambda\omega^{2}R^{2}}{l^{2}}, \tag{14} \]

\[ h=\frac{19.7\lambda\omega^{2}R^{2}-a_{1}l^{2}}{l^{2}}t_{2}, \tag{15} \]

where

\(a\) — acceleration imparted to the brush by the step on the surface of the commutator;
\(h\) — height of the brush rebound;
\(\lambda\) — maximum height of the step;
\(\omega\) — rotational speed of the commutator;
\(l\) — length of the leading front of the protrusion;
\(t\) — time of interaction of the brush with the step;
\(a_{1}\) — acceleration of the brush by the spring.

In the general case the character of the dynamic interaction of the brush with a protruding plate or group of plates may be described by the equation [8]:

\[ h(t)=N\sin\frac{\pi}{T}t\exp\left[-\frac{\pi}{T\operatorname{tg}\frac{\pi}{k_{1}}}\left(\frac{T}{k_{1}}-t\right)\right], \tag{16} \]

where

\[ N=\frac{h_{\max}}{\sin \frac{\pi}{k_1}}, \]

\(T\) is the duration of the action,

\[ k_1=k_0+1, \]

\[ k_0=\frac{\tau_{\mathrm{sp}}}{\tau_{\mathrm{n}}}, \]

\(\tau_{\mathrm{n}}\) is the time of rise of the function from zero to the maximum,
\(\tau_{\mathrm{sp}}\) is the time of fall from the maximum to zero,
\(t\) is the current time coordinate.

The behavior of the brush assembly under dynamic action from the commutator can most simply be established by modeling the process. By varying the values of \(h_{\max}\) and \(k\), it is thus possible to determine the rebound magnitude, the amplitude, and the frequency of oscillations of the brush upon collision.

\[ h=\psi[h_{\max},\, k,\, V], \tag{17} \]

where \(V\) is the linear velocity of the projection.

Simulation of the impact (15) can be carried out with the aid of a rectangular-pulse generator or an LRC generator that supplies an exponential signal to the load.

By changing the parameters of the generator, the experimental conditions can readily be varied.

The investigations carried out make it possible to draw the following conclusions:

1. The profilometer developed, providing high sensitivity and resolving power, makes it possible to measure changes in the commutator surface of \(1\ \mu\text{m}\) and greater.

2. The dynamic runout of the commutator has a complex character, not amenable to sinusoidal approximation, and may reach a value of \(50\text{–}60\ \mu\text{m}\).

3. The greatest influence on the process of current collection is exerted by the elastic deformation of the commutator itself, which has a high-frequency character with an amplitude up to \(45\text{–}50\ \mu\text{m}\).

4. The interaction of the brush with the commutator in high-speed machines has the character of a short-duration dynamic impact.

References

1. M. F. Karasev. Commutation of DC Commutator Machines. GEI, 1961.

2. A. I. Skorospeshkin, L. Ya. Zinner, A. I. Proshin. An instrument for investigating mechanical factors in commutator electrical machines. Izv. TPI, vol. 160, 1967.

3. L. Ya. Zinner, A. I. Skorospeshkin. A bridge instrument for investigating the dynamics of commutators of electrical machines. Izv. TPI, vol. 160, 1967.

4. K. K. Namitokov, V. G. Brezhinsky, B. B. Kats. Eccentricity of commutators of DC electrical machines in dynamics. Elektrotekhnika, No. 4, 1965.

5. S. P. Timoshenko. Oscillations in Engineering. Fizmatgiz, 1959.

6. N. A. Pavelko. On vibration of the brush assembly. Vestnik elektropromyshlennosti, No. 7, 1962.

7. A. V. Lozhkin, G. S. Zhartovsky. Vibration of the brush assembly of commutator electrical machines. Elektrotekhnika, No. 10, 1966.

8. B. A. Glagovsky, E. S. Evsiovich, A. A. Khait, V. A. Yashin. On generating functions describing intense short-duration actions. Trudy VNII AGSh, No. 3, 1966.