METHOD FOR DETERMINING THE REDUCTION OF THE COMMUTATION PERIOD AS A FUNCTION OF THE PARAMETERS OF THE COMMUTATOR–BRUSH ASSEMBLY

E. K. Strelbitskii, V. S. Stukach, A. Ya. Tsirulik

(Presented by the scientific seminar of the Departments of Electrical Machines and Apparatus and General Electrical Engineering)

At the Department of Electrical Machines of TPI, the reduction of the commutation period was studied as a function of the degree of scatter of the mechanical parameters of the commutator–brush assembly. The random delay in the beginning of commutation at the leading edge \(x_1\) and the random advance in the end of the commutation period at the trailing edge \(x_2\) enter into the equation for the residual flux linkage [1].

Fig. 1. Diagram of brush contact with the commutator: A — point at which contact arises at the leading edge of the brush; B — point at which contact ceases at the trailing edge of the brush

As is seen from Fig. 1,

\[ x_1=x_1' + \Delta t_k, \qquad x_2=x_2' + \Delta t_k + v_u, \]

where \(x_1'\) and \(x_2'\) are due to the rounding of the edges of the brush and the commutator bar, the instability of the moment of the beginning and end of contact under the influence of microroughness of the surfaces of the commutator and brushes, under the influence of vibrations, etc.;

\(v_u\) — width of the interlamellar slot;

\(\Delta t_k\) — technological deviations of the commutator pitch. The parameters \(v_u\) and \(\Delta t_k\) can be determined statistically by measurements for different types of commutators and different levels of production technology. The parameters \(x_1'\) and \(x_2'\) must be determined for different grades of brushes and typical designs of brush holders as functions of differences in bar levels, commutator eccentricity, contact

pressure, the circumferential speed of rotation of the commutator, the temperature of the commutator, the humidity of the medium, etc.

With a brush overlap greater than unity, \(x_1'\) and \(x_2'\) will be functions of several steps, since several bars are located under the brush. Such functions must be determined for the following cases:

1) for \(0 < b_{\mathrm{sh}} < t_{\mathrm{k}} + b_{\mathrm{u}}\)

\[ x_1' = f(\Delta_1); \qquad x_2' = f_2(\Delta_1); \tag{2} \]

2) for \(t_{\mathrm{k}} + b_{\mathrm{u}} < b_{\mathrm{sh}} < 2t_{\mathrm{k}} + b_{\mathrm{u}}\)

\[ x_1' = f_1(\Delta_1,\Delta_2); \qquad x_2' = f_2(\Delta_1,\Delta_2); \tag{3} \]

3) for \(2t_{\mathrm{k}} + b_{\mathrm{u}} < b_{\mathrm{sh}} < 3t_{\mathrm{k}} + b_{\mathrm{u}}\)

\[ x_1' = f_1(\Delta_1,\Delta_2,\Delta_3); \qquad x_2' = f_2(\Delta_1,\Delta_2,\Delta_3) \quad \text{etc.} \tag{4} \]

Here

\[ \begin{aligned} b_{\mathrm{sh}} &\text{— brush width;}\\ \Delta_1 &\text{— difference in the levels of adjacent bars at the beginning}\\ &\text{\quad (when determining \(f_1\)) and at the end}\\ &\text{\quad (when determining \(f_2\)) of contact between the brush}\\ &\text{\quad and the bar;}\\ \Delta^2,\Delta^3,\ldots &\text{— the subsequent steps, in order, located}\\ &\text{\quad under the brush.} \end{aligned} \]

We shall consider a step positive if the bar following in the direction of brush motion is higher than the preceding one. We shall measure \(x_1'\) and \(x_2'\) in fractions of the commutator pitch.

Analytical determination of the dependences \(f_1\) and \(f_2\) is not possible because of the large number of input parameters and the random nature of their manifestation. These dependences can be determined experimentally, using mathematical methods of planning an experimental search and regression methods for processing the results [2].

To measure \(x_1'\) and \(x_2'\) dynamically, the following method was developed and used. The measuring brush MB (Fig. 2) is installed

Fig. 2. Diagram for measuring the reduction of the commutation period

on the entering edge (when measuring \(x_1'\)) or on the leaving edge (when measuring \(x_2'\)) of the main brush. The edges of the main and auxiliary brushes coincide exactly. If the working brush is in contact with a bar, then the pulse of the voltage drop under the brush is fed to the input of the oscillograph. At the same time, a high-frequency voltage from a high-frequency generator HFG (4–6 MHz) is fed to the oscillograph input. When the MB is on a commutator bar, the HFG is shunted, and on the oscillograph screen one can see the commutator sweep (Fig. 3), measure the actual values of the commutator pitch and the width of the interbar slot, and determine the statistics of the technological scatter of these parameters. To increase the measurement accuracy, the measuring brush is rigidly clamped in the movable part of a special brush holder, while the device itself

Fig. 3. Oscillogram of the commutator sweep

the movable part of it can rotate to ensure contact pressure on a backlash-free axis (on centers). This eliminates uncertainty in the position of the measuring brush.

The parameters \(x_1'\) and \(x_2'\), on the time scale, correspond to the shift between the high-frequency pulse that determines the geometric position of the working brush relative to the segment, and the voltage pulse between the brush and the segment at the occurrence and at the interruption of contact (Fig. 4, a and 4, b). In view of the short duration of the processes (several micro-

Fig. 4. Oscillographic measurement of the shortening of the commutation period:
a) on the entering edge of the brush; b) on the leaving edge of the brush

seconds), very rigid synchronization of the oscilloscope is required. This is accomplished by a precise mechanical sensor DS and by the SPS synchronization-signal conversion circuit. At the same time the strobotachometer ST is synchronized; with its aid the number of the segment being observed can be seen. By rotating the synchronization sensor, it is possible to survey and photograph the signals from all segments of the commutator.

As an example, let us consider a method for determining the dependence of \(x_2'\) on the magnitude of the level differences of the commutator segments at various pressures on the EG74 brush. The experiment was carried out on a P32 machine at an armature rotation speed of 1610 rpm. The commutator was turned by means of a device directly in the machine, in its own bearings, in order to eliminate the effect of eccentricity. The level differences of the segments \(\Delta\) were planed according to a central composite rotatable design of the second order for three variables: \((\Delta_1, \Delta_2\) and \(\Delta_3)\), case 3, expression (4) [2]. The formation of the segment differences on the commutator was accom-

was carried out by the galvanic method, as described in paper [3]. The design matrix and the values of \(x_2'\) in millimeters are given for different pressures in Table 1.

Table 1

The intervals for varying the input parameters were selected with allowance for the actual technological scatter of the level differences of commutator bars for machines of the P1-6 frame-size series and are presented in Table 2 in \(\mu\text{m}\).

Table 2

We specify the form of the dependence \(x_2' = f_2(\Delta_1,\Delta_2,\Delta_3)\) by a second-degree polynomial:

\[ x_2' = b_0 + \sum_{i=1}^{3} b_i \Delta_i + \sum_{i=1}^{3} b_{ii}\Delta_i^2 + \sum_{i<j}^{3} b_{ij}\Delta_i\Delta_i . \tag{5} \]

Table 3 presents the coefficients of equation (5), obtained on the basis of processing the data of Table 2. The quantity \(x_2'\) is expressed in fractions of the commutator pitch.

Table 3

Since the multiple correlation coefficient \(R\) is close to unity, equation (5) describes the experiment with sufficient adequacy.

Figure 5 gives the dependences of the coefficients of equation (5) on the magnitude of the pressure on the brush (brush cross section \(10 \times 12\) mm).

Fig. 5. Dependence of the coefficients of equation (5) on the magnitude of the pressure on the brush

Similarly, one can find the dependences of \(x_1'\) and \(x_2'\) on the plate-to-plate steps at other rotational speeds, at another commutator temperature, and under other environmental conditions. All new variables must be varied according to a definite plan in accordance with the requirements of the theory of experimental design [2]. Then a universal dependence can be obtained for the instability of contact at the entering and leaving edges of the brush on technological deviations in the parameters of the commutator-brush assembly and on operating conditions.

Conclusions

1. A method has been developed for the direct measurement of the magnitude of the reduction of the commutation period caused by contact instability at the leading and trailing edges of the brush.

2. An experimental-statistical procedure has been proposed for determining the dependence of the magnitude of the reduction of the commutation period on technological deviations.

References

1. E. K. Strelbitskii, V. S. Stukach, A. Ya. Tsirulik. Accounting for the influence of technology on commutation in the design of direct-current machines. Izvestiya TPI, vol. 190, 1968.

2. V. V. Nalimov, N. A. Chernova. Statistical Methods for Planning Extremal Experiments. “Nauka,” Moscow, 1965.

3. A. I. Skorospeshkin, L. Ya. Zinner, E. K. Damm. A method for modeling commutator profiles for investigating the influence of the condition of the commutator surface on the electrical and mechanical characteristics of the brush contact. Izvestiya TPI, vol. 190, 1968.