What are equation of motor?
To understand the torque equation, let us first understand the voltage equation of the DC motor.
Referring the above diagram, E is the supply voltage fed to the armature, Eb is the back emf developed across the armature. The back EMF always opposes the armature voltage and thus the it limits the armature current. Ra is the armature resistance. The IaRa drop takes place in the armature when the armature current Ia flows through the armature. The voltage equation of the DC motor is given below.
For calculating torque, first power needs to be calculated. If we multiply the back EMF(Eb) with armature current(Ia) we get power of the motor.
Multiplying both sides of equation(1) by armature current(Ia), We get
Ia2 Ra is the power loss occurs in the armature and wasted in the form of heat energy and thus the power developed in a DC motor is;
The torque is the rotational force and it depends on the developed power of the armature at particular speed. Thus the torque of motor depends on the speed of rotation.
Putting the value of Pm from equation(3) in equation(5),
The back EMF of DC motor is mathematically expressed as;
Putting the value of back emf (Eb) from equation(8) in equation(7),we get the torque equation of DC motor.
The mechanical torque developed by DC motor can be calculated by subtracting the mechanical loss from the gross torque.
Tm is also called shaft torque(Tsh) of the DC motor.
Ia = 100 AV = 460 VRa = 0.2 ΩP = 6A = P= 6 (Lap winding)Z = 864Φ = 0.05 WbTa = ?
Eb = ΦZN/60 x (P/A) ——–(1)Also, Eb = V – IaRa= 460 – 100 x 0.2= 460 – 20Eb = 440 Volts
Putting value of Eb in equation (1)Eb = ΦZN/60 x (P/A)440 = 0.05 x 864 x N /60 x (6/6)440 = 0.72 NN = 440 /0.72 = 611 r.p.m.
Motor Gross Torque
T = ΦIa/2π x Z (P/A)T = 0.159 ΦIa x Z (P/A)T = 0.159 x 0.05 x 100 x 864 x(6/6)T = 686.55 N-m
Read Next:
The motor equation is given bya)V = Eb – Ia Rab)V = Eb+ Ia Rac)E... Where V is the applied voltage, Eb is the back EMF (electromotive force), Ia is the armature current, and Ra is the armature resistance. Explanation of Option B: Option B is the correct answer, which states that the motor equation is V = Eb - Ia Ra.
E = V + IaRa + ωΦm
Where,
E = Back emf (voltage generated by the motor) V = Applied voltage (voltage supplied to the motor) Ia = Armature current (current flowing through the armature) Ra = Armature resistance (resistance of the armature) ω = Angular velocity (rotational speed of the motor) Φm = Flux per pole (magnetic flux produced per pole)
The voltage equation of DC motors explains how the back emf (E) generated by the motor is influenced by the applied voltage (V), current (Ia), armature resistance (Ra), and angular velocity (ω). In simple terms, the back emf opposes the applied voltage and reduces the current flowing through the armature, thereby increasing the motor’s efficiency.
Let’s take a closer look at the various components of the voltage equation of DC motors:
The back emf (E) is the voltage generated by the motor due to the rotation of the armature in the magnetic field. It is proportional to the angular velocity (ω) and the flux per pole (Φm). The back emf opposes the applied voltage and limits the armature current to maintain a steady-state operating condition.
The applied voltage (V) is the voltage supplied to the motor from an external source such as a battery or power supply. Its magnitude determines the speed and torque of the motor.
The armature current (Ia) flows through the armature winding of the motor. It is proportional to the torque produced by the motor. The armature current increases with an increase in the applied voltage and decreases with an increase in the back emf.
The armature resistance (Ra) is the resistance of the armature winding. It converts electrical energy into heat energy and affects the motor’s efficiency.
The angular velocity (ω) is the rotational speed of the motor. It is proportional to the back emf and the flux per pole.
The flux per pole (Φm) is the magnetic flux each motor pole produces. It is proportional to the applied voltage and the number of turns in the armature winding.
The voltage equation of DC motors has a significant impact on the performance of the motor. Let’s discuss some of the factors affected by the voltage equation:
The voltage equation determines the speed and torque of the motor. The applied voltage and the armature current determine the torque produced by the motor, while the back emf determines the speed. An increase in the applied voltage increases the torque and speed of the motor, while an increase in the back emf decreases the armature current, thereby reducing the torque.
The voltage equation affects the efficiency of the motor. The back emf reduces the armature current, thereby reducing the power loss due to armature resistance. A high back emf results in a more efficient motor.
The voltage equation determines the stability of the motor. The back emf opposes the applied voltage, thereby reducing the armature current and stabilizing the operation of the motor. If the applied voltage is too high, it can cause instability and damage to the motor.
The voltage equation is essential for the control of DC motors. By controlling the applied voltage, the speed and torque of the motor can be adjusted. The voltage equation is also used for speed control methods such as armature voltage control and field flux control.
1. What is the voltage drop equation of a DC motor?
The voltage drop equation of a DC motor is the relationship between the voltage applied to the motor and the voltage dropped across the armature resistance and the back emf. It is expressed as:
V = E + IaRa.
2. Why is the voltage equation of DC motors important?
The voltage equation of DC motors is essential for understanding the performance, efficiency, and control of DC motors. It helps in designing, analyzing, and troubleshooting DC motor systems.
3. How is the voltage equation used for speed control of DC motors?
The voltage equation is used for speed control methods such as armature voltage control and field flux control. By controlling the applied voltage, the speed and torque of the motor can be adjusted.
4. Can the voltage equation of DC motors be applied to AC motors?
No, the voltage equation of DC motors is specific to DC motors only. AC motors have different equations that describe their performance and behavior.
