Selection of the Geometry of Pole Tips of Claw-Pole Rotors of Electrical Machines

N. K. Sergeev

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

In designing highly utilized electrical machines with a claw-pole rotor, it is very important to check the geometry of the pole tips, established as a result of the electromagnetic calculation, for conformity with the mechanical loads caused by the action of inertial forces. The previously proposed methods for strength calculations of such rotors [1, 2] make it possible to calculate the stresses in dangerous sections and the total deflection measured at the free end of the cantilever projections (pole tips) of the rotor, and also to compare the values obtained with the maximum permissible ones. Taking into account the great capabilities of modern computing technology, the method for calculating the strength of pole tips was programmed for the M-20 electronic digital computer. This made it possible to perform calculations for many design variants differing from one another in outside diameter, height at the base and length of the pole tip, as well as in various combinations of the central angles $\alpha_k$ and $\alpha_0$. The calculation results for the most widely used designs were employed in analyzing the influence of individual geometric parameters on the magnitude of the maximum deflection, the stress at the clamping point of the pole tip, and the resultant of the inertial forces, and were compiled into nomograms, one of which is shown in Fig. 1.

Let us dwell in more detail on the structure of the nomograms and give the necessary explanations for their use in engineering practice. As is known, the principal parameters determining the geometry of the rotor pole tips are the following:

a) the outside radius — $r$;
b) the inside radius and central angle at the free end of the pole tip — $r_0$, $\alpha_0$;
c) the inside radius and central angle at the clamping point (at the base) of the pole tip — $r_k$, $\alpha_k$;
d) the length of the pole tip — $l$.

Thus, we obtain six quantities, a change in each of which leads to a change in the strength characteristics and weight of the pole tip. The latter also determines the stress–strain state of the ring part subjected to the action of tensile forces and bending moment.

For convenience in using the nomograms, it is expedient to group them according to three principal parameters that are constant for each nomogram separately: the outside radius, the thickness at the base $\Delta = r_0 - r_k$, and the central angle $\alpha_k$. The variable parameters included in the nomograms are the central angle $\alpha_0$ and the length of the pole tip—

Fig. 1. Nomogram for selecting the geometry of the pole tips of claw-pole rotors:

—◇— — calculation of deflections — $\ln(y/\omega^2)$;

—△— — calculation of stresses — $\ln(\sigma/\omega^2)$;

—◐— — calculation of the resultant inertial forces — $\ln(P/\omega^2)$

of tip $l$. The variation of the listed parameters in each nomogram, as well as in passing from one nomogram to another, is carried out with a certain step, which is established depending on the range of the quantities being varied and on the desired degree of accuracy in selecting the optimal variant. In this connection it should be borne in mind that excessively small step values entail a sharp increase in the number of nomograms and substantially complicate working with them. In addition, intermediate variants can be obtained by extrapolation.

The quantities calculated in the nomograms include the maximum values of the normal stress at the base of the pole tip — $\ln(\sigma/\omega^2)$, the maximum deflection at the free end — $\ln(y/\omega^2)$, and the resultant of the nonuniformly distributed load of the rotating pole tip — $\ln(P/\omega^2)$. All these quantities are referred to the square of the angular velocity and are expressed in natural loga-

graphs. Having determined, as a result of the electromagnetic calculation of the machine, the geometry of several variants of the claw-pole rotor, we construct a nomogram with the corresponding calculated parameters and determine the maximum values of deflection, stress, and the resultant nonuniformly distributed inertial load for the specified rotational speed. Comparing these values with the permissible ones and using the data of the electromagnetic calculations and Fig. 2, we choose the variant optimal in terms of electromagnetic and mechanical loads, after which we proceed to the design of the ring part of the claw-pole rotor. The principal criteria in assessing the strength and rigidity of the structure are the yield strength of the material and the magnitude of the air gap.

Fig. 2. Dependence of deflections, stresses, and resultant inertial forces, referred to the square of the angular velocity, on various geometric parameters of the rotor:
a — on the outside radius; b — on the length; c — on the central angle at the clamping point;
d — on the central angle at the free end of the pole tip.

The inverse solution of the problem is also possible. In this case the initial quantities are the maximum permissible values of deflection, stress, and the resultant nonuniformly distributed load, as well as the outside radius, the height at the base of the tip, and the angle $\alpha_k$. The length of the pole tip $l$ and the angle $\alpha_0$ are then determined from the nomogram and compared with the data obtained as a result of the electromagnetic calculation.

Conclusions

The nomograms developed make it possible, at the design stage or during the modernization of existing electrical machines, to quickly select the geometry of the pole tips of a claw-pole rotor that is the most rational with respect to energy and weight indicators, and to obtain the necessary information on the degree of its mechanical loading under the action of inertial forces.

References

1. G. D. Del, N. K. Sergeev, F. Kh. Tomilov. Calculation for the strength and rigidity of claw-pole rotors. In: Devices for low-power electrical supply and electric drive, vol. 2, Electrical machines and apparatus, Energiya Publishing House, 1970.

2. G. D. Del, N. K. Sergeev, A. S. Solyanik, F. Kh. Tomilov, D. V. Khan. Strength and rigidity of claw-pole rotors under elastic deformation. In: Electrical apparatus, vol. 2, Electrical machines, Energiya Publishing House, 1971.