DESIGN FEATURES OF ELECTRIC MOTORS WITH A BUILT-IN DC BRAKE ELECTROMAGNET

V. S. Grinberg, E. M. Guselnikov, E. V. Kononenko

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

Increasing labor productivity requires a reduction in unproductive working time, the amount of which is determined to a considerable extent by the time required for starting and stopping mechanisms. In emergency situations arising as a result of a sudden interruption in the supply of electric power or for other reasons, the stopping time of mechanisms is of great importance from the standpoint of safety engineering. Therefore, for the normal operation of many types of electric drives, it is necessary to equip electric motors with reliably operating mechanical spring brakes that ensure, at the required moment, rapid stopping of the machine or mechanism. Compared with electrical braking, the mechanical method of braking makes it possible sharply to increase the number of operating cycles of the electric motor per hour, to improve its thermal conditions, to reduce significantly the amount of starting equipment, and to simplify the motor control circuit \[1\].

A compact and convenient drive of this type is represented by electric motors with a built-in DC brake electromagnet. These electric motors are structurally simple and technologically advantageous in comparison with other types of brake motors \[2\].

However, a disadvantage of these electric motors is the considerable pickup time of the brake electromagnet when switched on, due, in particular, to the fact that the magnetic circuit of the electromagnet is not laminated for technological reasons (the electromagnet winding 1 (Fig. 1) is located in a special bearing end shield 2 of the electric motor).

A considerable pickup time of the brake electromagnet leads to acceleration of the electric motor with the friction linings 3 (Fig. 1) of the braking device not released, to a slowing of the motor start, to deterioration of the thermal conditions (especially with a high frequency of switching), and to increased wear of the friction linings. Therefore, the pickup time of the built-in electromagnet is one of the main parameters of a brake electric motor, on which the durability of the brake motor, the weight of copper in the electromagnet winding, and the power consumed by it also depend.

When selecting the permissible value of the pickup time of the brake electromagnet, it is necessary to relate it to the starting time of the electric motor. The starting process of a brake electric motor may be divided in time into three stages. The first stage is characterized by the fact that the shaft of the elec—

Fig. 1. Schematic representation of designs of electric motors with a built-in DC brake electromagnet:
a) with an electromagnet built into the bearing shield; b) with an electromagnet attached to the bearing shield

the electric motor is braked. In this case, the relationship between the torques applied to the shaft is as follows:

\[ M \leqslant M_c + M_t, \tag{1} \]

where

\[ \begin{aligned} M &\text{— transient electromagnetic torque of the electric motor;}\\ M_t &\text{— braking torque;}\\ M_c &\text{— resistance torque.} \end{aligned} \]

As the magnetic flux increases, the tractive force of the DC electromagnet increases, while the braking torque \(M_t\) decreases. At the instant when the value of the transient electromagnetic torque of the electric motor exceeds the sum of the resistance torque \(M_c\) and the braking torque \(M_t\), the second stage of starting begins, during which the electric motor begins to rotate while the friction linings are not yet disengaged. The equation for the second stage of starting is

\[ M - M_c - M_t = J \frac{d\omega}{dt}, \tag{2} \]

where \(J \dfrac{d\omega}{dt}\) is the dynamic torque.

During this stage the braking torque \(M_t\) continues to decrease, and at the instant of release \((t = t_{\mathrm{tr}})\) of the electromagnet armature 4, the electric-motor shaft 5 (Fig. 1) is completely released from braking. The equation of the third stage \((t \geqslant t_{\mathrm{tr}})\) does not differ from the starting equation of a conventional electric motor

\[ M - M_c = J \frac{d\omega}{dt}. \tag{3} \]

It follows from the above that the release time of the brake electromagnet affects the transient electromechanical processes of the electric motor at the beginning of starting (the first and second stages). In this case, an increase in the release time \(t_{\mathrm{tr}}\) beyond a certain permissible value \(t_{\mathrm{tr\,dop}}\) leads to rapid wear of the friction linings.

Analysis of catalog data and experimental studies carried out at SKBEM in Tomsk on prototype brake electric motors of the 4A series with shaft-center heights from 56 to 132 mm showed that, in order to achieve the required service life of the friction linings of asynchronous brake electric motors (1–2 million operations), the permissible values of the pickup time \(t_{\text{tr dop}}\) should not exceed 0.05–0.12 s (Fig. 2). Here, the larger permissible values of pickup time apply to electric motors with greater shaft-center heights (Fig. 3).

Fig. 2. Dependences of the pickup time of built-in brake electromagnets on the copper weight of their windings

The pickup time \(t_{\text{tr}}\) when a DC brake electromagnet is switched on, under generally accepted assumptions, is written in the form [3]

\[ t_{\text{tr}} = T \ln \frac{F}{F - F_{\text{sr}}}, \tag{4} \]

where

\(T\) — the time constant of the electromagnet at the initial air gap \(\delta\);

\(F\) — the ampere-turns of the electromagnet;

\(F_{\text{sr}}\) — the operating ampere-turns.

In this case the time constant of the electromagnet \(T\) can be represented as:

\[ T = \frac{G_{\delta}\cdot F^{2}}{P}, \tag{5} \]

where

\(G_{\delta}\) — the permeance at the initial air gap,

\(P\) — the power consumed by the electromagnet.

We shall write the operating ampere-turns \(F_{\text{sr}}\) in the form [4]

\[ F_{\text{sr}} = \sqrt{\frac{2P_{\text{pr}}\cdot \delta}{G_{\delta}}}, \tag{6} \]

where \(P_{\mathrm{pr}}\) is the opposing force, which is determined by the braking torque \(M_{\mathrm{t}}\) and the parameters of the brake system,

\[ P_{\mathrm{pr}}=\frac{M_{\mathrm{t}}}{\mu_{\mathrm{t}} k_i R_{\mathrm{t}}}, \tag{7} \]

where

\[ \begin{aligned} \mu_{\mathrm{t}}&\text{ is the coefficient of friction of the friction-surface material;}\\ k_i&\text{ is the number of pairs of friction surfaces;}\\ R_{\mathrm{t}}&\text{ is the friction radius of the friction surfaces.} \end{aligned} \]

The value of the braking torque \(M_{\mathrm{t}}\) is found from the specified ratio

\[ k_{\mathrm{m}}=\frac{M_{\mathrm{t}}}{M_{\mathrm{n}}} \]

of the braking torque to the nominal torque of the electric motor,

\[ M_{\mathrm{t}}=k_{\mathrm{m}}\cdot M_{\mathrm{n}} . \tag{8} \]

Substituting (7) into (6), taking (8) into account, we obtain an expression for the ampere-turns required for operation of the brake electromagnet in terms of the nominal torque of the electric motor and the parameters of the brake system:

\[ F_{\mathrm{cp}}= \sqrt{\frac{2\cdot k_{\mathrm{m}}\cdot \delta \cdot M_{\mathrm{n}}} {\mu_{\mathrm{t}} k_i R_{\mathrm{t}}\cdot G_\delta}} . \tag{9} \]

The weight of copper \(Q\) of the electromagnet may be written in the form

\[ Q=\gamma\cdot \rho \cdot l_{\mathrm{v}}^{2}\frac{F^{2}}{P}, \tag{10} \]

where

\[ \begin{aligned} \gamma&\text{ is the specific weight of copper;}\\ \rho&\text{ is the specific resistance of copper;}\\ l_{\mathrm{v}}&\text{ is the mean length of a coil turn.} \end{aligned} \]

Hence the ampere-turns of the electromagnet are

\[ F=\frac{1}{l_{\mathrm{v}}}\cdot \sqrt{\frac{P\cdot Q}{\gamma\cdot \rho}} . \tag{11} \]

Substituting (5) and (9) into (4), taking (11) into account, after simple transformations we obtain

\[ t_{\mathrm{tr}}= \frac{G_\delta\cdot Q}{\gamma\cdot \rho\cdot l_{\mathrm{v}}^{2}} \cdot \ln \frac{1} {1-l_{\mathrm{v}}\sqrt{ \frac{2\gamma\cdot \rho\cdot k_{\mathrm{m}}\cdot \delta M_{\mathrm{n}}} {\mu_{\mathrm{t}} k_i R_{\mathrm{t}} G_\delta\cdot P\cdot Q} }} . \tag{12} \]

As is evident from (12), the starting time depends on the geometric dimensions \((\delta, l_{\mathrm{v}}, R_{\mathrm{t}}, G_\delta)\) and the parameters of the brake device \((\mu_{\mathrm{t}}, k_i, k_{\mathrm{m}})\), on the copper weight \((Q)\) of the electromagnet and the power \((P)\) consumed by it, and also on the nominal torque \((M_{\mathrm{n}})\) of the electric motor.

For a particular frame size (axis of rotation) of the electric motor and the chosen structural arrangement (Fig. 1), the geometric dimensions of the electromagnet at the air-gap surface vary within small limits \((l_{\mathrm{v}}, G_\delta \approx \mathrm{const})\), while the values \(\delta, R_{\mathrm{t}}, \mu_{\mathrm{t}}, k_i, k_{\mathrm{m}}, M_{\mathrm{n}}\), for the purpose of unifying the brake system, are taken as constant in design. Therefore, the starting time is determined mainly by the copper consumption \(Q\) and the power \(P\) consumed by the electromagnet.

Brake electric motors can be designed according to two basic structural arrangements [5]: with the electromagnet built into the bearing shield (Fig. 1, a) or with the electromagnet attached to it (Fig. 1, b).

With the first structural arrangement it is possible to create a simple, technologically convenient design of a brake electric motor, but the cooling conditions of the electromagnet in this case substantially limit the consum—

... the power \(P\) consumed by it. Under the second scheme, the design of the braking electric motor becomes more complicated, but the power \(P\) permissible under heating conditions can be increased as a result of better cooling.

From (12), the minimum weight of copper required for operation of the electromagnet is

\[ Q_{\min} = \frac{2 \cdot \gamma \cdot \rho \cdot l_{\mathrm{B}}^{2} \delta \cdot k_{\mathrm{M}} \cdot M_{\mathrm{n}}} {P \cdot \mu_{\mathrm{T}} \cdot k_{i} R_{\mathrm{T}} \cdot G_{\delta}} \text{.} \tag{13} \]

Taking the foregoing into account, by assigning values of the copper weight \(Q > Q_{\min}\), it is possible to find, for a specific motor size, the dependence \(t_{\mathrm{tr}} = f(Q)\) at the maximum permissible values of the electromagnet power \(P_{\mathrm{dop}}\), which are determined by the adopted structural scheme of the braking device.

Figure 2 presents calculated dependences of the response time as a function of the copper weight of the electromagnet for asynchronous braking electric motors of the 4A series with a shaft height of \(132\ \mathrm{mm}\), for two structural versions of the braking device: curve 1 corresponds to the structural scheme in Fig. 1,a and to the power permissible under heating conditions \(P_{\mathrm{dop}1} = 55\ \mathrm{W}\); curve 2 corresponds to the structural scheme in Fig. 1,b and to the permissible power \(P_{\mathrm{dop}2} = 85\ \mathrm{W}\). An analogous dependence is also given here (curve 3) for a braking electric motor with a shaft height of \(56\ \mathrm{mm}\), made according to the scheme in Fig. 1,a \((P_{\mathrm{dop}3} = 20\ \mathrm{W})\).

The dependences shown in Fig. 2 indicate that increasing the copper weight beyond the value \(G_{\mathrm{opt}}\) does not lead to any further decrease in the response time. A comparison of curves 1 and 2 shows that increasing the permissible power of the electromagnet \(P_{\mathrm{dop}}\) makes it possible to reduce not only the response time, but also the copper consumption of the electromagnet. Nevertheless, for electric motors with a shaft height of \(132\ \mathrm{mm}\), the permissible response time \(t_{\mathrm{tr\,dop}}\) is unattainable for both structural versions of the braking device and the indicated values of permissible electromagnet power. In such cases, a reduction in response time can be achieved by supplying high power to the electromagnet only during operation, i.e., by forcing the operation of the electromagnet.

Figure 3 gives averaged dependences of calculated values of the minimum response time as a function of the shaft height \(h\) of 4A-series electric motors; curve 1 in this figure corresponds to the structural scheme of Fig. 1,a, and curve 2 to the structural scheme

Fig. 3. Dependences of the minimum response time of built-in brake electromagnets on the shaft height of electric motors.

Fig. 1, b. From Fig. 3 it can be seen that, for 4A-series electric motors with shaft-axis heights of 56–63 mm, the required value of the operating time \(t_{\text{tr dop}}\) can be obtained with the simplified design arrangement of Fig. 1, a; for electric motors with shaft-axis heights of 71–90 mm, with the more complex design arrangement of Fig. 1, b; while for motors with shaft-axis heights greater than 90 mm the required operating time \(t_{\text{tr dop}}\) cannot be achieved without forcing the actuation of the electromagnet. Therefore, brake electric motors with shaft-axis heights greater than 90 mm should be designed according to the design variants of Fig. 1, a, with a control circuit providing forcing of the electromagnet. The rational design version of brake electric motors with shaft-axis heights below 100 mm should be selected on the basis of a techno-economic comparison of the designs of brake electric motors, taking into account their manufacturing cost, service life, and also the reliability of the braking device and of the electromagnet control circuit.

Thus, when designing electric motors with built-in DC brake electromagnets, it is necessary to take into account a number of factors that are absent in the independent design of ordinary electric motors and DC brake electromagnets—in particular, the influence of transient processes in the electromagnet on transient processes in the electric motor, and the influence of the design arrangement of the brake electric motor on the maximum speed of response, as well as on the weight characteristics of the built-in electromagnet.

REFERENCES

1. Yu. N. Molchanov. Electric motors with a built-in electromagnetic brake. AC electric machines. Moscow, Informelektro, 1969.

2. E. M. Gusel’nikov, B. S. Tsukerman. Self-braking electric motors. Energiya, 1971.

3. B. K. Bul’, G. V. Butkevich et al. Fundamentals of the theory of electrical apparatus. Vysshaya shkola, 1970.

4. A. K. Ter-Akopov. Dynamics of fast-acting electromagnets. Energiya, 1965.

5. W. Baumann. Bauarten und Eigenschaften electromagnetish gelufteter Bremsen an Stoppmotoren, Konstruktion, 21 (1969), Heft 4, S. 137—147.