Calculation of the Magnetic Circuit of Self-Braking Electric Motors with Electromagnetic Inserts
Abstract Generated abstract
The paper addresses the magnetic circuit calculation of self-braking electric motors in which electromagnetic inserts are released by the motor’s own stator magnetic field rather than by a separate brake winding. Using an equivalent magnetic circuit, the authors analyze a prototype based on a 4A132M4 induction motor for varying lengths of the main and braking stator parts and varying working air gaps. The study derives a flux distribution coefficient relating the main-part flux to the ratio of stator section lengths, compares it with experimental data, and examines how the braking-part saturation coefficient decreases as the insert air gap increases. A simplified calculation procedure is proposed for design use, including practical assumptions for saturation coefficients and air-gap correction factors.
Full Text
CALCULATION OF THE MAGNETIC CIRCUIT OF SELF-BRAKING ELECTRIC MOTORS WITH ELECTROMAGNETIC INSERTS
L. K. Burulko, E. M. Guselnikov, N. M. Malyshenko
Presented by the scientific seminar of the Departments of Electrical Machines and General Electrical Engineering
Increasing the productivity of mechanisms is associated mainly with increasing the speed and reducing the idle time of the actuating motor. Therefore, with each passing year electric motors for rapid and precise stopping, equipped with braking devices, are becoming increasingly important.
One of the promising electric motors in this respect is the self-braking electric motor (SBM) with electromagnetic inserts on the rotor or stator.
Unlike braking electric motors [1, 2], in which a special winding is provided to control the braking device, in an SBM the brake is controlled by means of the magnetic flux of the electric motor itself. Thus, the magnetic field of the stator is used both to create the torque and to create the releasing force of the brake. Such use of the stator magnetic field is due to the design features of the stator or rotor of the SBM [1].
Fig. 1. a) Magnetic system of a self-braking electric motor with an insert on the stator;
b) configuration of the slot of the braking part.
Figure 1a shows the construction of the magnetic system of an electric motor with an electromagnetic insert on the stator. The stator of such an electric motor consists of two parts: the main part 1 and the braking part 2, separated by a nonmagnetic spacer. The core of the main part of the stator is made in the usual manner. The core of the braking part consists of separate packets with axial stacking. The width of a packet is equal to the width of a tooth of the main part, in connection with which the shape of the slot of the braking part has the form shown in Fig. 1b. The stator winding is placed in the slots of the main and braking parts, combining them into a single system. When voltage is applied to the stator winding, a magnetic flux is produced, part of which, $\Phi_o$, closes through the rotor and the main part of the stator, while the other part of the flux, $\Phi_t$, closes through the rotor and the braking part of the stator. The indicated construction of the braking part of the stator contributes to the fact that the magnetic flux $\Phi_t$ is forced to close through the electromagnetic insert 3 as through the stator yoke, thereby creating electromagnetic forces that ensure attraction of the insert-armature.
Since both fluxes $\Phi_o$ and $\Phi_t$ are caused by one and the same magnetomotive force and together constitute the total magnetic flux of the motor, the magnetic circuit can be represented by the following analogous electrical equivalent circuit (Fig. 2).
In the equivalent circuit the following are denoted:
Fig. 2. Equivalent circuit of the magnetic circuit of self-braking electric motors with electromagnetic inserts on the stator
$R_c, R_{zc}, R_{\delta o}, R_{zp}, R_p$ — magnetic reluctances of sections of the magnetic circuit of the main part of the stator and rotor;
$R_t, R_{zt}, R_{\delta t2}, R_{\delta t1}, R_{zpt}, R_{pt}$ — magnetic reluctances of sections of the magnetic circuit of the braking part of the stator, the rotor, and the electromagnetic insert;
$\sum F$ — total magnetomotive force of the electric motor;
$\Phi$ — total magnetic flux;
$\Phi_o$ — magnetic flux in the main part of the electric motor;
$\Phi_t$ — magnetic flux in the braking part of the electric motor.
The magnetic circuit of such an electric motor proves to be nonuniform along the length of the machine, since the magnetic reluctances for the fluxes $\Phi_o$ and $\Phi_t$ are not the same, which makes it difficult to perform the electromagnetic calculation and to determine the tractive forces arising in the air gap $\delta_{t2}$.
To determine the distribution of induction in the air gap between the stator and the rotor along the length of the electric motor and to determine the method for calculating the magnetic circuit, verification calculations of the magnetic circuit were carried out for a motor with an electromagnetic insert on the stator (Fig. 1a), for different ratios of the lengths of the main and braking parts and for different gaps \(\delta_{\mathrm{t}2}\). The calculations were performed for a prototype manufactured on the basis of the 4A132M4 induction motor.
In calculating the magnetic circuit, the magnetic core was divided into two parts in accordance with the equivalent circuit (Fig. 2); in this case, the dividing line of the rotor was considered to be located opposite the middle of the nonmagnetic stator spacer separating it into the main and braking parts.
For several values of induction in the air gap between the stator and the rotor of the main and braking parts, the magnetization curves \(\Phi_{\mathrm{o}}(\sum F_{\mathrm{o}})\) and \(\Phi_{\mathrm{t}}(\sum F_{\mathrm{t}})\) were calculated and plotted; then, by adding the obtained characteristics, the curve of the total magnetic flux \(\Phi(\sum F)\) was constructed. From the known magnetomotive force, the values of the magnetic fluxes \(\Phi\), \(\Phi_{\mathrm{o}}\), and \(\Phi_{\mathrm{t}}\) were established for different lengths of the braking part of the stator and different gaps \(\delta_{\mathrm{t}2}\).
The results of the analysis performed showed that:
- The ratio of the magnetic fluxes of the main motor to the total flux is
\[ k = \frac{\Phi_{\mathrm{o}}}{\Phi} = \frac{l_{\mathrm{o}}}{l_{\mathrm{o}} + l_{\mathrm{t}}}, \tag{1} \]
where \(k\) is the magnetic-flux distribution coefficient;
\(l_{\mathrm{o}}\) is the length of the main part of the stator;
\(l_{\mathrm{t}}\) is the length of the braking part of the stator.
The dependence obtained is represented graphically by characteristic 1 in Fig. 3. In Fig. 3, in addition to the calculated one, the dependence
\[ \frac{\Phi_{\mathrm{o}}}{\Phi} = f\!\left(\frac{l_{\mathrm{o}}}{l_{\delta}}\right), \]
obtained as a result of experimental studies by the SKB of the “Sibelektromotor” plant [1], is presented. From a comparison of these characteristics it is evident that the calculated and experimental curves practically coincide.
Fig. 3. Experimental and calculated dependences for inserts drawn up to the end face of the stator.
- An increase in the air gap \(\delta_{\mathrm{t}2}\) is accompanied by a decrease in the magnetic flux of the braking part, which in turn leads to a decrease in the saturation coefficient of the magnetic circuit of the braking part, which was defined as
\[ k_{\mu \mathrm{t}}=\frac{\sum F_{\mathrm{t}}}{F_{\delta \mathrm{t}1}+F_{\delta \mathrm{t}2}} . \tag{2} \]
The curves \(k_{\mu \mathrm{t}}(\delta_{\mathrm{t}2})\) are shown in Fig. 4. Analysis of these dependences shows that the saturation coefficient of the magnetic circuit of the braking part decreases sharply with an increase in the air gap \(\delta_{\mathrm{t}2}\). When the length of the braking part of the stator is reduced, this coefficient increases somewhat.
- The saturation coefficient in the main part of the stator does not depend on the magnitude of the air gap \(\delta_{\mathrm{t}2}\), but it increases somewhat in comparison with the saturation coefficient calculated for the magnetic circuit of the base motor. The increase in the coefficient \(k_{\mu \mathrm{o}}\) is 15% compared with \(k_{\mu}\) of the motor of the basic version 4A132M4.
Fig. 4. Dependences of the saturation coefficient \(k_{\mu \mathrm{t}}\) of the braking part of the stator on the working air gap:
1 — for \(l_{\mathrm{t}}=25\) mm, 2 — for \(l_{\mathrm{t}}=15\) mm, 3 — for \(l_{\mathrm{t}}=0.5\) mm
Using the results of the analysis, the procedure for calculating the magnetic circuit of a self-braking electric motor can be determined as follows.
From the initial data, the total magnetic flux \(\Phi\) [3] is calculated; then, by specifying the ratio of the length of the main part of the stator to its full length, one can determine the magnetic-flux distribution coefficient and, correspondingly, the fluxes \(\Phi_{\mathrm{o}}\) and \(\Phi_{\mathrm{t}}\) in the main and braking parts of the stator.
Since the sum of the magnetomotive forces attributable to the main part of the machine is equal to the sum of the magnetomotive forces attributable to the braking part (Fig. 2), it is sufficient to perform the magnetic-circuit calculation only for the main part. To determine the saturation coefficient of the magnetic circuit of the braking part, the inductions and magnetomotive forces attributable to the air gaps \(\delta_{\mathrm{t}1}\) and \(\delta_{\mathrm{t}2}\) should additionally be calculated. In this case, the increase in the air gap \(\delta_{\mathrm{t}1}\) is taken into account by the coefficient
\[ k_{\delta \mathrm{t}1}=k_{\delta \mathrm{t}}\cdot k_{\delta \mathrm{r}}, \qquad \text{where} \tag{3} \]
\(k_{\delta \mathrm{r}}\) — coefficient accounting for the increase in the gap due to the toothed surface of the rotor;
\(k_{\delta \mathrm{t}}\) — coefficient accounting for the increase in the gap due to the toothed surface of the braking part of the stator.
The coefficient \(k_{\delta \mathrm{t}}\) will be higher than the analogous coefficient determined for the main part of the stator, because of the larger slot opening. The increase in the air gap \(\delta_{\mathrm{t}2}\) depends only on the toothed surface of the end face of the braking part of the stator; moreover, the slot opening is not a constant quantity. In this connection, it is proposed to determine the air-gap coefficient as follows:
\[ k_{\delta \mathrm{t}2}=\frac{t_{z\mathrm{t}}+10\cdot \delta_{\mathrm{t}2}}{t_{z\mathrm{t}}-b_{sc}+10\cdot \delta_{\mathrm{t}2}}, \tag{4} \]
where
\[ t_{zT}=\frac{\pi(D_a-h_T)}{z_1} \]
is the average slot pitch of the end face of the braking part of the stator (Fig. 1b);
\(h_T\) is the height of the end face of the braking part of the stator (Fig. 1b);
\[ b_{sc}=\frac{\pi(D_a-h_T)-b_{z1}\cdot z_1}{z_1} \]
is the average slot opening in the end part of the stator on the side of the electromagnetic insert.
The height of the end face of the braking part is determined by the formula
\[ h_T=\frac{(D_a-D)-2h_p}{2}, \tag{5} \]
where \(h_p\) is the height of the stator slot;
\(D_a\) is the outer diameter of the stator stack;
\(D\) is the inner diameter of the stator stack.
On the basis of the results of the investigations, the following conclusions may be drawn:
- The variation of the flux ratios \(\Phi_0/\Phi\) with the ratios of lengths
\[ \frac{l_0}{l_0+l_T} \]
for self-braking electric motors with inserts on the stator and rotor is the same.
-
The saturation coefficients in the braking parts decrease sharply with an increase in the air gap \(\delta_{T2}\); therefore, in approximate calculations they may be taken as constant and equal to \(1.1 \div 1.2\), and for the main part \(k_{\mu 0}=1.15\,k_{\mu}\) of the base motor.
-
The proposed method for calculating the magnetic circuit, using the calculated dependence of the flux distribution along the length of the machine, makes it possible to simplify the calculation considerably and can be used in calculations and design of self-braking electric motors.
REFERENCES
-
E. M. Guselnikov, B. S. Tsukerman. Self-braking electric motors. Moscow, “Energiya,” 1971.
-
Yu. M. Molchanov. Electric motors with a built-in electromagnetic brake. Moscow, “Informelektro,” 1969.
-
N. V. Vinogradov, F. A. Goryainov, P. S. Sergeev. Design of electrical machines. Moscow, “Energiya,” 1969.