Direct-current motor is a device that transforms the electrical energy into mechanical energy. There are five major types of dc motors in general use: The separately excited and shunt dc motors The permanent-magnet dc motor The series dc motor The compounded dc motor DC motor drives some devices such as hoists, fans, pumps, calendars, punch- presses, and cars. The ability to control the speed with great accuracy is an attractive feature of the dc motor.

The voltage induced V a in the armature of a dc motor is expressed by: where V a = armature voltage (V) K = constant ω = speed of rotation of the motor (r/min) Φ = flux per pole (Wb) (2.1) Armature is the rotating part of a dc motor IaIa VsVs + + Fig.2-1: Simple circuit of a dc motor. R ω Φ VaVa N S

where Z = total number of conductors on rotor a = number of current paths P = number of poles on the machine The constant K can be calculated from: whereas total number of conductors can be expressed as: where C = number of coils on rotor a = number of turns per coil (2.2) (2.3)

In the case of the motor, the induced voltage is called counter-electromotive force (cemf) because its polarity always acts against the source voltage V s. In sense that the net voltage acting in the series circuit of Fig. 2-1 is (2.4) and not,

Referring to Fig. 2-1, the electrical power P e in Watt supplied to the armature is equal to the supply voltage V s multiplied by the armature current I a : so, The I a 2 R term represents heat dissipated in the armature and V a I a is the electrical power that is converted into mechanical power. (2.5) (2.7) According to the Khirchhoff’s voltage law (KVL), the source voltage is equal to the sum of V a plus the I a R drop in the armature: (2.6)

The mechanical power developed by a motor depends upon its rotational speed and torque it develops given by: where τ ind = induced torque developed by a dc motor (N.m) ω = speed of rotation (r/min) (2.9) Therefore, the mechanical power P m of the motor in Watt is equal to the product of the cemf multiplied by the armature current: (2.8)

and so (2.10) Combining Eq. 2.8 and 2.9, we obtain

With substituting V a from Eq. 2.1 into Eq. 2.6 and I a is determined from Eq. 2.10, we obtain Solving for the motor’s speed produces where R = armature resistance = internal resistance (Ω) (2.11)

Separately excited dc motor is a motor whose field circuit is supplied from separate constant-voltage power supply. Fig.2-2: Circuit of a separately excited dc motor. IfIf Field LfLf RfRf VfVf IlIl IaIa RaRa VaVa N S VsVs

In circuit of the separatly excited dc motor, the field current I f in Ampere is where R f = shunt-field resistance (Ω) (2.12) Fig. 2-2 shows that the current generated by voltage source I l is equal to the armature current I a : (2.13)

Shunt dc motor is a motor whose its armature and field circuit in parallel across terminals of a dc supply. VsVs VaVa RfRf RaRa Field Fig.2-3: Circuit of a shunt dc motor. IlIl IaIa IfIf LfLf The field current I f in Ampere is (2.12) N S Whereas the current generated by voltage source I l is (2.14)

There are three ways to control the speed of a shunt dc motor: 1.Adjusting the field resistance R f and thus the field flux Φ. 2.Adjusting the armature voltage V a. 3.Inserting a resistor in series with the armature circuit. Field resistance control is a method to control the speed of a dc motor by connecting a rheostat with a shunt motor. The speed of dc motor is controlled by varying the field flux Φ and keeping the armature voltage V a constant. Thus, if Φ is incresed ---- ω will drop, and vice versa. In order for the armature current limit not to be exceeded, the induced torque limit must decrease as the speed of the motor increses.

Fig.2-4: Schematic diagram of the field resistance control. This method is frequently used when the motor has to run above its rated speed, called base speed. VsVs IaIa IlIl IfIf shunt field RfRf + R field rheostat Φ VaVa If a motor is running at its rated terminal voltage, power, and field current, so it will be turning at base speed. In field resistance control, the lower the current flowing through the armature, the faster the armature turns and the higher the field current, the slower it turns. Because an increase in armature current causes a decrease in speed.

1.Increasing R f causes I f (=V s /R f ↑) to decrease. 2.Decreasing I f decreases Φ. 3.Decreasing Φ lowers V a (= K Φ↓ω). 4.Decreasing V a increases I a (= (V s – V a ↓)/R a ). 5.Increasing I a increases τ ind (= K Φ↓I a ↑↑ ), with the change in I a dominant over the change in flux. 6.Increasing τ ind makes τ ind > τ load, and speed ω increases). 7.Increasing ω to increase V a (= K Φω↑) again. 8.Increasing V a decreases I a. 9.Decreasing I a decreases τ ind until τ ind = τ load at a higher speed ω. Summary of the cause-and-effect behavior involved in this method of speed control:

Moto r τ ind τ load Load I Moto r τ ind τ load Load I ω1ω1 Moto r τ ind τ load Load I ω2ω2 Fig.2-5: A load coupled to a motor by means of a shaft. (a) Shaft is stationary τ ind = τ load. (b) Shaft turns clockwise τ ind = τ load. (c) Shaft turns counterclockwise τ ind = τ load.

Warning…..!! This method can only control the speeds of the motor above base speed but not for speeds below base speed. Because to achieve a speed slower than base speed, the armature requires excessive field current, possibly burning up the field windings. Since the torque limit decrease as the speed of the motor increases, and the power out of the motor is the product of the torque developed by dc motor and the rotation speed (see Eq.2-9), then the maximum power out of a dc motor under field resistance control is While the maximum torque varies as reciprocal of the motor’s speed. (2.15)

Fig.2-6: Armature voltage control of a shunt dc motor. VsVs VaVa RfRf RaRa Field IlIl IaIa IfIf LfLf Variable Voltage Controller VcVc

The lower the armature voltage on dc motor, the slower the armature turns and the higher the armature voltage, the faster it turns. Since an increase in armature current causes an increase in speed (see Eq. 2.1). The speed of dc motor is controlled by varying the armature voltage V a using a variable voltage controller and keeping the flux in the motor constant. If Φ = constant, so the maximum torque in the motor is Since the power out of the motor is the product of the torque developed by dc motor and the rotation speed (see Eq.2-8), then the maximum power of the motor under aramture voltage control is (2.16) (2.17)

Summary of the cause-and-effect behavior involved in this method of speed control: 1.An increase in V c increases I a (= (V c ↑ - V a )/R a ). 2.Increasing I a increases τ ind (= KΦI a ↑). 3.Increasing τ ind makes τ ind > τ load increasing ω. 4.Increasing ω increases V a (= KΦω ↑). 5.Increasing V a decreases I a (= (V c ↑- V a )/R a ). 6.Decreasing I a decreases τ ind until τ ind = τ load at a higher ω

 The motor speed is controlled by adjusting the magnitude of resistance R of a rheostat.  With varying R ---- the current flowing through the armature I a vary and thus, voltage across the armature.  However, the insertion of a resistor yields very large losses in the inserted resistor. Rheostat speed control is a way to control the speed of a dc motor by inserting a rheostat in series with the armature circuit. shunt field VsVs IfIf IaIa armature rheostat Fig.2-7: Armature speed control using a rheostat. + IlIl R + VaVa

Warning…..!! This method can only control the speeds above its rated speed or base speed but not for speeds below base speed. Because to achieve a speed faster than base speed, the armature requires excessive field current, possibly burning up the field windings.

A permanent-magnet dc (PMDC) motor is a dc motor whose poles are made of permanent magnets. Compared with shunt dc motors, PMDC motors offer a number benefits. Since these motors do not require an external field circuit and thus, they do not have the field circuit copper losses. Because no field windings are required, they can be smaller than corresponding shunt dc motors. However, PMDC motors also have disadvantages. Permanent magnets can not produce as high a flux density as an externally supplied shunt field, so PMDC motor will have a lower induced torque τ ind per ampere of armature current I a than a shunt motor of same size and construction. In addition, PMDC motors run the risk of demagnetization. A PMDC motor is basically the same machine as a shunt dc motor, except that the flux of a PMDC motor is fixed. Therefore, it is not possible to control the speed of a PMDC motor by varying the field current or flux.

A series dc motor is a dc motor whose field windings composed of a few turns connected in series with the armature circuit. Fig.2-8: a. Series motor connection diagram; b. Schematic diagram of a series motor. Φ o VsVs VaVa o+ - IlIl IlIl series field (a)(b) VaVa O O IlIl RaRa R L VsVs

In a series motor, the armature current, field current, and line current are all the same. The Kirchhoff’s voltage law equation for this motor is The induced torque in this motor is expressed as The flux in this motor is directly proportional to its armature current. Therefore, the flux in the motor can be written as where c is a constant of proportionality. Thus, the induced torque is (2.18) (2.19) (2.10) (2.20)

From Eq. 2.20, the armature current can be given by: Also, V a = KΦω. Substituting this expressions in Eq yields: Or, the resulting torque-speed relationship can be written as (2.22) (2.21)

Φ depends upon the armature current and, hence, upon load. Φ = constant at load, because the shunt field is connected to the line. Property samesimilar Shunt motor Construction Series motor Basic Principles and Equations Type of dc motor Similarities and differentiations between the shunt motor and the series motor According to Eq. (2.19) the speed of a series dc motor can be only controlled efficiently by changing the terminal voltage of the motor, unlike with dc motor.

A compounded dc motor is a motor that carries both a shunt and a series fields. o VsVs VaVa o + - I series field IxIx shunt field ► ► Fig.2-9: a. DC compound motor connection diagram;

VaVa O O IaIa RaRa R L VsVs RfRf IfIf LfLf IlIl Fig.2-9: b. Schematic diagram of dc compound motor.

Current flowing into a dot produces a positive magnetomotive force.  If current flows into the dots on both field coils the resulting magnetomotive forces add to produce a larger magnetomotive force. This situation is known as cumulative compounding.  If current flows into the dot on one field coil and out of the dot on the other field coil, the resulting magnetomotive forces subtract. The currents in the compounded motor are related by (2.23) (2.14) (2.12)