diploma queation and answers 2

Explain the electrical and mechanical characteristics of dc shunt motor

Electrical and Mechanical Characteristics of a DC Shunt Motor

In a DC shunt motor, the field winding is connected in parallel (shunt) with the armature winding across the constant supply voltage ($V$). Therefore, the shunt field current remains essentially constant:

$$I_{sh} = \frac{V}{R_{sh}} \approx \text{Constant}$$

Consequently, the magnetic flux per pole ($\Phi$) remains practically constant from no-load to full-load conditions (neglecting minor demagnetizing effects of armature reaction).

Characteristic Curves

1. Electrical Characteristics

The electrical behavior of a DC motor relates internal electrical quantities: armature current ($I_a$), torque ($T_a$), and speed ($N$).

A. Torque vs. Armature Current ($T_a$ vs. $I_a$)

The general torque equation of a DC motor is:
$$T_a \propto \Phi \cdot I_a$$
Since flux ($\Phi$) is constant in a shunt motor:
$$T_a \propto I_a$$
Curve Nature: The characteristic is a straight line passing through the origin. Torque increases linearly with armature current.
Effect of Heavy Load: At very high loads, the demagnetizing effect of armature reaction slightly weakens the main field flux, causing the actual torque curve to bend slightly downward from the theoretical straight line.

B. Speed vs. Armature Current ($N$ vs. $I_a$)

The speed equation of a DC motor is:
$$N \propto \frac{E_b}{\Phi} = \frac{V - I_a R_a}{\Phi}$$
Because $\Phi$ is constant:
$$N \propto (V - I_a R_a)$$
Curve Nature: As the load current ($I_a$) increases from no-load to full-load, the armature resistance drop ($I_a R_a$) increases slightly. Because $R_a$ is very small, this drop is marginal (only about 5% to 8% of rated speed from no-load to full-load).
Hence, the curve is a nearly horizontal line drooping very slightly downwards. For all practical purposes, the DC shunt motor is regarded as a constant-speed motor.

2. Mechanical Characteristic ($N$ vs. $T_a$)

The mechanical characteristic shows the relationship between mechanical output torque ($T_a$) and operating speed ($N$).

Since $T_a \propto I_a$, substituting $I_a \propto T_a$ into the speed equation gives:
$$N = \frac{V}{\Phi} - \left(\frac{R_a}{k \Phi^2}\right) T_a = N_0 - m T_a$$
where $N_0$ is the ideal no-load speed and $m$ is a constant representing the slope.
Curve Nature: The speed-torque characteristic is an almost straight, slightly drooping line. As the mechanical load (torque demand) increases, the speed drops only marginally.
Starting on No-Load: Unlike a DC series motor, a DC shunt motor can safely be started on no-load because its no-load speed is strictly finite and well-defined by $\frac{V - I_{a0} R_a}{k \Phi}$.

3. Summary Table

Characteristic	Mathematical Relation	Nature of Curve
Torque vs. Current ($T_a$ vs. $I_a$)	$T_a \propto I_a$	Straight line through origin (slight droop at severe overloads).
Speed vs. Current ($N$ vs. $I_a$)	$N \propto (V - I_a R_a)$	Nearly horizontal line with a slight downward droop (5–8%).
Speed vs. Torque ($N$ vs. $T_a$)	$N = N_0 - m T_a$	Slightly drooping straight line (mechanical characteristic).

Typical Applications: Lathe machines, centrifugal pumps, fans, conveyors, printing presses, and machine tools where approximately constant speed is required across variable loads.

-----------------------------------------------------------------------------------------------------------------------------Explain series parallel starting of dc traction motor

Series-Parallel Starting of DC Traction Motors

1. Introduction & Objective

In electric traction applications (such as electric trains, trams, and locomotives), two or more identical DC series motors are coupled to different driving axles.

Starting traction motors solely using external series resistors causes enormous $I^2 R$ power losses dissipated as heat. The Series-Parallel Starting Method significantly reduces these energy losses (saving up to 50% of rheostatic energy loss during starting) while providing smooth acceleration and two economical operating running speeds.

2. Circuit Connections & Operating Stages

3. Step-by-Step Working Principle

Step 1: Series Starting Period (0 to 50% Speed)

The two traction motors are connected in series with external starting resistance ($R_{\text{start}}$) across the overhead line voltage ($V$).
Because the motors are in series, the same current flows through both armatures. The supply voltage divides equally across the two machines:
$$V_{\text{motor}} = \frac{V - I_a R_{\text{start}}}{2}$$
As the train gains momentum, back EMF accumulates, and the controller cuts out starting resistance in steps.
Once all resistance is eliminated, each motor operates directly across $\frac{V}{2}$ without any external rheostatic loss. This corresponds to the first economical running speed ($\approx \frac{1}{2}$ rated base speed).

Step 2: Transition Period

To accelerate further, the circuit switches from series to parallel configuration. Three transition methods are used in traction systems:

Open Circuit Transition: Power to one or both motors is disconnected during switching. (Causes sudden tractive effort loss and mechanical jerks; rarely used now).
Shunt Transition: One motor remains powered while the second is momentarily short-circuited through a shunting resistor, disconnected, and reconnected in parallel. (Maintains continuous torque on one axle).
Bridge Transition (Most Preferred): Utilizes a bridge circuit of contactors and resistors. The tractive effort is never interrupted during transition, producing exceptionally smooth acceleration without current surges.

Step 3: Parallel Running Period (50% to 100% Speed)

Both motors are connected in parallel across the full line voltage ($V$), with individual resistor banks inserted into each branch.
The branch resistance is cut out in sequential controller notches until both motors run directly across the full line voltage ($V$).
At this stage, each motor develops rated back EMF and operates at full rated speed ($N$), forming the second economical running speed.

4. Energy Saving Derivation

Consider two identical motors accelerated to full base speed $N$ drawing a constant starting current $I$ during acceleration:

Parameter	Plain Rheostatic Starting	Series-Parallel Starting
Total Energy Drawn from Line	$$E_{\text{in}} = 2 V \cdot I \cdot t$$	$$E_{\text{in}} = \frac{3}{2} V \cdot I \cdot t$$
Useful Energy Converted	$$E_{\text{useful}} = V \cdot I \cdot t$$	$$E_{\text{useful}} = V \cdot I \cdot t$$
Starting Energy Wasted in Resistors	$$E_{\text{loss}} = V \cdot I \cdot t \quad (50\%)$$	$$E_{\text{loss}} = \frac{1}{2} V \cdot I \cdot t \quad (25\%)$$
Rheostatic Loss Reduction	Baseline (0% saved)	50% reduction in rheostatic loss

Summary of Benefits:

Cuts starting energy dissipation in half compared to plain rheostatic starting.
Offers two stable, zero-resistance running speeds ($\frac{N}{2}$ and $N$).
Reduces the physical size and thermal rating needed for starting resistance banks.

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Explain Speed Control of DC Shunt Motor by Field (Flux) Control Method

1. Working Principle

The speed ($N$) of a DC motor is governed by the fundamental speed equation:

$$N = \frac{E_b}{k\Phi} = \frac{V - I_a R_a}{k\Phi}$$

In a DC shunt motor operating on a fixed terminal voltage ($V$), the voltage drop across the armature resistance ($I_a R_a$) is relatively small compared to $V$. Thus, back EMF remains nearly constant ($E_b \approx V$), leading to the relation:

$$N \propto \frac{1}{\Phi}$$

This indicates that the speed of a DC motor is inversely proportional to the magnetic flux per pole ($\Phi$). By weakening the magnetic flux, the motor speed can be increased above its normal rated (base) speed.

2. Circuit Arrangement

A variable external resistor known as a Field Rheostat ($R_{\text{ext}}$) is connected in series with the shunt field winding across the DC supply mains.

3. Step-by-Step Operation

Normal Condition ($R_{\text{ext}} = 0$): When the external field rheostat resistance is zero, maximum rated field current flows through the field winding:
$$I_{sh} = \frac{V}{R_{sh}}$$
At this point, the magnetic flux ($\Phi$) is at its rated maximum, and the motor runs at its **normal rated speed (base speed, $N_b$)**.
Increasing Resistance ($R_{\text{ext}} > 0$): When resistance is added to the field circuit by adjusting the rheostat, the total circuit resistance increases to $(R_{sh} + R_{\text{ext}})$.
Drop in Field Current and Flux: The shunt field current decreases:
$$I_{sh} = \frac{V}{R_{sh} + R_{\text{ext}}} \quad \implies \quad \Phi \text{ decreases}$$
Speed Increase: Because back EMF cannot change instantaneously, the sudden drop in $\Phi$ causes the armature current to surge temporarily, generating excess accelerating torque. The motor accelerates to a higher equilibrium speed where the back EMF recovers to balance the applied voltage. As a result:
$$N > N_b$$

4. Constant Power Drive Characteristic

In this method of speed control:

The armature current ($I_a$) and terminal voltage ($V$) remain at their rated values. Thus, the power rating of the motor remains constant:
$$P = V \times I_a = \text{Constant}$$
Since torque is given by $T \propto \Phi I_a$, and flux $\Phi$ is reduced to gain speed, the developed mechanical **torque decreases inversely as speed increases** ($T \propto \frac{1}{N}$).
Therefore, the flux control method is classified as a Constant Power and Variable Torque Drive.

5. Advantages

High Efficiency: Shunt field current is small (only 2% to 5% of total line current). Hence, the $I_{sh}^2 R_{\text{ext}}$ power loss in the field rheostat is negligible.
Compact & Inexpensive Rheostat: Because it carries only a small current, the rheostat is physically small, light, and low-cost.
Smooth & Stepless Speed Regulation: Speed can be adjusted smoothly across the entire control range above base speed.

6. Limitations

Only Above-Base Speeds Possible: Flux cannot be increased beyond its rated value without saturating the magnetic iron core and overheating the field coils. Therefore, this method cannot achieve speeds below normal base speed.
Poor Commutation at Very High Speeds: At very high speeds (weakened main field), the demagnetizing armature reaction becomes dominant, shifting the magnetic neutral axis significantly and causing severe brush sparking. Interpoles are necessary to enable wider speed ranges (usually up to 2:1 or 3:1).
Mechanical Speed Limits: Centrifugal forces acting on the armature conductors and commutator bars limit the maximum allowable operating speed.

Summary: The flux control method is the most efficient and practical method for obtaining speeds above the base speed in DC shunt motors, operating as a constant power drive.

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