ON ACCOUNTING FOR THE INFLUENCE OF TECHNOLOGICAL AND MECHANICAL FACTORS ON THE WIDTH OF THE SPARKLESS COMMUTATION ZONE

V. S. Tsirulik

(Presented by the scientific seminar of the Department of Electrical Machines)

For a quantitative assessment of the commutation properties of a direct-current machine, the method of sparkless zones is most often used. Attempts are being made to develop methods for analytically calculating the width of the sparkless-operation zone by solving systems of equations for commutating circuits and by approximate methods [1]. In the proposed procedures, the geometry of the magnetic system of the machine and of the commutator-brush apparatus is considered ideal, and the influence of mechanics on the operation of the brush contact is not taken into account.

It is known, however, that the indicated factors are always present and always lead to a narrowing of the actual zone of sparkless commutation as compared with the calculated value of its width. In the present article a method is proposed for the quantitative determination of the influence of technological and mechanical factors on the width of the zone.

Let us denote the width of the sparkless commutation zone (s.c.z.), expressed in calculated units (for example, in units of the current of the auxiliary-pole winding), by the symbol $\beta$. The actual width of the s.c.z. is equal to

\[ \beta=\beta_{\mathrm{T}}-\Delta\beta, \tag{1} \]

where

$\beta_{\mathrm{T}}$ — the theoretical width of the zone;

$\Delta\beta$ — the deviation of the actual width of the s.c.z. from the theoretical value, caused by the influence of technology and mechanics.

The deviations $\Delta\beta$ can be found by statistical processing of experimental data on determining the width of commutator s.c.z.’s, taken separately for each commutator bar corresponding to a section completing commutation of the slot (in machines with non-stepped windings) [2].

Since the deviations $\Delta\beta$ can be of only one sign (the influence of mechanics can only narrow the s.c.z., but cannot widen it), the probability density of the distribution of the widths of the s.c.z.’s of the bars may have the approximate form shown in Fig. 1, a. It is clear from the figure that if, for a certain series of machines, for typical technology and typical operating conditions, one constructs the empirical probability-distribution law for the width of the bar s.c.z.’s, then the maximum value of $\beta$ in this distribution is, in the limit, an estimate of the theoretical wid-

...the sparkless-commutation zones of machines of the given series in the absence of the influence of mechanics, while the minimum \(\beta\) corresponds to the actual width of the sparkless-commutation zone of the machines. From the constructed distribution one should determine the theoretical value of the width of the sparkless-commutation zone.

For a more accurate determination of the mean value of the actual width of the sparkless-commutation zone \(\overline{\beta}\), one should construct an empirical distribution law for the series over a sufficiently large number of machines (Fig. 1, b).

The mean value \(\overline{\Delta\beta}\), characterizing the narrowing of the sparkless-commutation zone due to the influence of technological and mechanical factors, is determined from the expression

Fig. 1. Distribution of the width of the sparkless-commutation zone for individual commutator segments (a) and for the commutator as a whole (b)

Fig. 2. Distribution of the width of the lamellar zones of sparkless operation of PN-28.5 (a) and PN-145 (b) machines

\[ \overline{\Delta\beta}=\beta_{\mathrm{T}}-\overline{\beta}. \tag{2} \]

This value is valid for a definite technology and operating conditions. It can be used in calculating the actual mean width of the sparkless-commutation zone of machines at the design stage by the formula

\[ \overline{\beta}=\beta_{\mathrm{p}}-\overline{\Delta\beta}, \tag{3} \]

where

\(\beta_{\mathrm{p}}\) is the calculated value of the width of the sparkless-commutation zone, determined by one method or another. It is more convenient to transform expression (3) into the form

\[ \overline{\beta}=\beta_{\mathrm{p}}\cdot\left(1-\frac{\overline{\Delta\beta}}{\beta_{\mathrm{p}}}\right)=\beta_{\mathrm{p}}\cdot k. \tag{4} \]

Here

\[ k=\left(1-\frac{\overline{\Delta\beta}}{\beta_{\mathrm{p}}}\right) \]

is the coefficient of reduction of the width of the sparkless-commutation zone under the influence of technological and mechanical factors. Obviously, the more stable the operation of the sliding contact in the mechanical respect, the smaller \(k\) is.

Figure 2 shows histograms of the distribution of the width of the lamellar sparkless-commutation zones for PN-145 and PN-28.5 machines, constructed from the data of [2]. On the abscissa axis are relative units (r.u.). From these figures the coefficient \(k\) is equal, respectively, to 0.335 and 0.35.

Conclusion

A method has been proposed that makes it possible to quantitatively determine the influence of technological and mechanical factors on the narrowing of the sparkless commutation zone of DC machines and to take this narrowing into account when calculating the zone.

References

1. V. V. Pruss-Zhukovskii. On an approximate description of the sparkless zones of DC machines. Elektrichestvo, 1972, No. 10.

2. V. I. Timoshina. Analysis of commutation by the method of collector sparkless zones. Optimal commutation of DC machines. Scientific Proceedings of OMIIT, vol. 122, Omsk, 1971.