Direct current machine

DC machines are electric machines that operate on direct current and can be used both as motors and generators. They are characterised by precise controllability of speed and torque, making them ideal for applications with variable speed and load. DC machines have high starting torque and allow easy reversal of the direction of rotation. They are often used in electric vehicles, industrial control systems and battery-powered devices.

1 Digression: Principle of the electric motor

First, the principles presented in Module 6 will be reviewed. Figure 1 shows three diagrams that summarise how an electric motor works. The basic structure of an electric motor consists of a stationary part, called the stator, and a rotating part, called the rotor. The three figures show a conductor coil in a horseshoe magnet. The horseshoe magnet forms the stator and a conductor coil that can move around its own axis represents the rotor. The first diagram illustrates the isolated course of the magnetic field lines of the horseshoe magnet. They run vertically from the north to the south pole within the horseshoe magnet. The second diagram shows the isolated course of the magnetic field lines of the current-carrying conductor loop. The flow of current creates two opposing eddy fields at the conductor loop. The third diagram shows the interaction between the horseshoe magnet (stator field) and the current-carrying conductor loop (rotor field). The two fields overlap. The Lorentz force resulting from the overlap causes the conductor loop to rotate according to the right-hand rule. Electromagnetic energy is converted into mechanical energy.

The Lorentz force can be calculated using the formula familiar from Module 6: \begin {equation} F =B\cdot I\cdot \ell \cdot N \end {equation}

Power of a direct current machine A direct current motor has a magnetic flux density of \(B=0.8\,\mathrm {T}\) in the air gap. There are a total of \(N=400\) armature wires under the poles, through which a current of \(I=10\,\mathrm {A}\) flows. The effective conductor length is \(\ell =150\,\mathrm {mm}\).

Calculate the force \(F\) at the circumference of the anchor.\begin {align*} F & =B\cdot I\cdot \ell \cdot N\\ & =0,8\,\frac {\mathrm {Vs}}{\mathrm {m}^2}\cdot 10\,\mathrm {A}\cdot 0,15\,\mathrm {m}\cdot 400\\ & =480\,\frac {\mathrm {kg}\cdot \mathrm {m}^2\cdot \mathrm {s}\cdot \mathrm {A}\cdot \mathrm {m}}{\mathrm {s}^3\cdot \mathrm {A}\cdot \mathrm {m}^2} = 480\,\mathrm {N} \end {align*}

2 Structure and housing design

The construction of the DC machine is illustrated using three figures. Figure 2 shows a diagonal sectional model of the DC machine, providing a general overview of the components of the stator and the rotor. For a more detailed illustration of the structure, Figure 3, focusing on the stator, and Figure 4, illustrating the rotor of a DC machine, are used.

The components of the stator, also called the stationary part, are clearly illustrated in the frontal cross-section of a DC machine (Figure 3). One of the fundamental components is the field windings , which, wound around a pole shoe, form a magnetic pole. The poles are responsible for generating a magnetic field, known as the excitation field.

Since a magnetic field always consists of a north and a south pole, the poles are installed in opposing pairs. The resulting characteristic quantity, the number of pole pairs, provides information about the operating characteristics of the DC machine. A higher number of pole pairs reduces the rotational speed but increases the torque. In very small machines, the field windings can be replaced by permanent magnets. In larger machines (approximately above 1 kW), additional interpole windings are present; however, these are neglected here.

In Figure 4, the components of the rotor are clearly visible. In general, the rotor is also referred to as the armature or the rotating part. The function of the rotor is to convert electromagnetic energy into mechanical energy by rotation about its own axis (and vice versa). For this purpose, the rotor is mounted on a motor shaft, which transmits the mechanical energy. The ball bearing at the end of the motor shaft reduces friction losses during energy transmission. To set the rotor in motion, the interaction between the commutator and the rotor winding is essential. The rotor winding, also called the armature winding, is responsible for generating a magnetic field, known as the armature field. Only through the interaction of the armature field with the excitation field is a torque exerted on the rotor, causing it to rotate. The laminated cores around which the coils are wound consist of insulated steel sheets in order to reduce eddy currents in the windings. The commutator, also called current reverser, has the function of supplying the rotor winding with current in a commutated manner. It consists of several mutually insulated segments (lamellae), each of which is connected to one branch of the rotor winding. The current is supplied to the commutator segments via carbon brushes mounted on the stator. Due to the rotation of the segments beneath the brushes, the commutator acts as a mechanical switch and ensures that the direction of current in the rotor windings located under the main poles remains constant.

3 Magnetic fields

The magnetic field in which the conductor moves is decisive for the Lorentz force. This field is generated by the stator with the excitation windings and is approximately parallel and homogeneous in the area of the rotor.

4 Calculation of torque

In Module 6 and Chapter 1, the force acting on a current-carrying conductor in a magnetic field has already been explained. To calculate the torque of the DC machine, the induced voltage is first determined (see Module 6). When the rotor of an excited DC machine rotates, a voltage is induced in each conductor loop of the armature. According to the law of induction (Equation ??), the magnitude of the induced voltage (source voltage) \(U_\mathrm {q}\) depends on the magnetic flux \(\varPhi \) and its time variation, in this case the rotational speed \(n\) or the associated angular frequency \(\omega = 2\pi \cdot n\). If the specific geometric properties of the rotor are additionally taken into account in the form of the armature constant \(K\), then the product of these characteristic quantities yields the induced voltage \(U_\mathrm {q}\) of the DC machine (see Equation 2).

\begin {equation} U_\mathrm {q} = K \cdot \varPhi \cdot \omega \label {GlInduzierteSpannungGM} \end {equation}

If both electrical and mechanical losses are neglected, the induced voltage can also be specified directly via the so-called internal power \(P_\mathrm {i}\). This then corresponds to both the electrical power \(U_\mathrm {q}\cdot I_\mathrm {A}\) and the mechanical power \(P_\mathrm {mech}\), which is calculated from the product of the internal torque \(M_\mathrm {i}\) and the angular velocity \(\omega \). \begin {equation} P_\mathrm {i} = U_\mathrm {q}\cdot I_\mathrm {A} = P_\mathrm {mech} = M_\mathrm {i}\cdot \omega \label {GlGMWirkungsgrad} \end {equation}

If this finding is now inserted into equation 2, the internal torque \(M_\mathrm {i}\) is calculated from the product of the armature constant \(K\), the magnetic flux \(\varPhi \) and the armature current \(I_\mathrm {A}\) \begin {equation} M_\mathrm {i} = K \cdot \varPhi \cdot I_\mathrm {A} \label {GlMomentGM} \end {equation} In motor operation, the torque at the machine shaft is the internal torque \(M_\mathrm {i}\) minus the losses \(M_\mathrm {V}\). The machine torque can also be expressed by the efficiency \(\eta _1\). However, this efficiency disregards the electrical losses due to the armature resistance and excitation. \begin {equation} M = M_\mathrm {i} - M_\mathrm {V}\qquad \qquad M = \eta _1\cdot M_\mathrm {i}\label {GLMomentWirkungsgradGM} \end {equation}

• Loss moment: \(M_\mathrm {V}\) [Nm]
• Efficiency: \(\eta \) [1]

5 Externally excited DC machine

The excitation circuit in the stator of the DC machine and the rotor circuit, which is supplied with current via the commutator, are in principle independent of each other. If both circuits are supplied by different voltage sources, the machine is referred to as separately excited. The equivalent circuit is shown in Figure 6.

The excitation circuit consists of the inductance of the excitation winding \(L_\mathrm {E}\) and the copper resistance \(R_\mathrm {E}\) of the coil. In the armature circuit, the winding is represented as a circuit with indicated slip rings, as it represents both an inductance and a voltage source. The armature also has an ohmic resistance \(R_\mathrm {A}\).

The mesh circulation in the rotor circle results in: \begin {equation} U_\mathrm {A} = U_\mathrm {q} + I_\mathrm {A}\cdot R_\mathrm {A} \end {equation}

Substituting equations 2 and 4 yields the speed/torque and armature current characteristic curve for the separately excited DC machine: \begin {equation} n = \frac {U_\mathrm {A}}{2\pi K\cdot \varPhi } - \frac {R_\mathrm {A}\cdot M_\mathrm {i}}{2\pi (K\cdot \varPhi )^2}\label {GlfremderregteGM1} \end {equation}

Externally excited direct current machine

A separately excited DC machine with the armature constant \(K=\frac {1}{2\pi }\) has a no-load speed of \(n=1200\,\frac {1}{\text {min}}\) at an armature voltage of \(U_\mathrm {A}=400\,\text {V}\). The armature resistance is \(R_\mathrm {A}=2.3\,\Omega \).

• How large is the pathogen flow? \(\varPhi \)?

  At idle speed, the internal torque \(M_\mathrm {i}\) is equal to zero. Equation 7 is therefore simplified to: \begin {align*} n&=\frac {U_\mathrm {A}}{2\pi K\cdot \varPhi }\\ \varPhi &=\frac {U_\mathrm {A}}{2\pi K\cdot n} = \frac {400\,\text {V}}{\frac {2\pi }{2\pi }\cdot 1200 \,\frac {1}{\text {min}}\cdot \frac {1}{60\,\frac {\text {s}}{\text {min}}}} = 20\,\text {Vs} \end {align*}

• How fast does the machine rotate at an internal torque of \(M_\mathrm {i}=10\,\text {Nm}\)? \begin {align*} n &= \frac {U_\mathrm {A}}{2\pi K\cdot \varPhi } - \frac {R_\mathrm {A}\cdot M_\mathrm {i}}{2\pi (K\cdot \varPhi )^2}\\ &= \frac {400\,\text {V}}{\frac {2\pi }{2\pi }\cdot 20\,\text {Vs}} - \frac {2,3\,\Omega \cdot 10\,\text {Nm}}{2\pi (\frac {1}{2\pi }\cdot 20\,\text {Vs})^2}\\ &= 20\,\frac {1}{\text {s}} - 0,362 \,\frac {1}{\text {s}} = 19,638\,\frac {1}{\text {s}} = 1178,3\,\frac {1}{\text {min}} \end {align*}
• How big is the anchor current? \begin {align*} I_\mathrm {A} &= \frac {M_\mathrm {i}}{K\cdot \varPhi } = \frac {10\,\text {Nm}}{\,\frac {1}{2\pi }\cdot 20\,\text {Vs}\,} = 3,61\,\text {A} \end {align*}

6 Series closure machine

In a series-wound motor, the field circuit and rotor circuit are connected in series. The field current is therefore equal to the armature current. This type of motor is often used in simple electrical appliances with alternating current and is therefore also called a universal motor. As a direct current motor, it was previously used primarily in traction drives, for example in trams. Nowadays, however, these have been replaced by three-phase drives with converters due to their higher efficiency.

• Can also be used for alternating voltage
• high tightening torque

Unlike externally excited DC machines, whose speed-torque characteristic curve is a straight line according to equation 7, series-wound machines behave non-linearly. Without load, the speed is theoretically infinite, meaning that the machine will accelerate until it destroys itself through centrifugal force. The machine „goes through“. However, in traction drive applications, idling never occurs; instead, a high starting torque is desired.