**Principle of Electromechanical Energy Conversion**which will cover the topics such as

**Principle of Electromechanical Energy Conversion,Principle of induction,Principle of interaction,Principle of alignment,Energy stored in magnetic field,Forces and torques in magnetic field systems,Singly excited and Doubly excited magnetic field systems,Model of Electromechanical Systems.**

**Principle of Electromechanical Energy Conversion**

- Basically, the Principle of Electromechanical Energy Conversion involves the conversion of Energy from Electrical to Mechanical or vice-versa, For energy conversion between electrical and mechanical forms, electromechanical devices are developed. In general, electromechanical energy conversion devices can be divided into three categories:
- Transducers (for measurement and control) These devices transform the signals of different forms. Examples are microphones, pickups, and speakers.
- Force producing devices (linear motion devices) These type of devices produce forces mostly for linear motion drives, such as relays, solenoids (linear actuators), and electromagnets.
- Continuous energy conversion equipment These devices operate in rotating mode. A device would be known as a generator if it converts mechanical energy into electrical energy, or as a motor, if it does the other way around (from electrical to mechanical).

- Since the permeability of ferromagnetic materials is much larger than the permittivity of dielectric materials, it is more advantageous to use the electromagnetic field as the medium for electromechanical energy conversion.
- The magnetic subsystem or magnetic field fits between the electrical and mechanical subsystems and acting as a "ferry" in energy transform and conversion. The field quantities such as magnetic flux, flux density, and field strength, are governed by Maxwell's equations.
- When coupled with an electric circuit, the magnetic flux interacting with the current in the circuit would produce a force or torque on a mechanically movable part.
- On the other hand, the movement of the moving part will could variation of the magnetic flux linking the electric circuit and induce an electromotive force (emf) in the circuit.

- The product of the torque and speed (the mechanical power) equals the active component of the product of the emf and current.
**Therefore, the electrical energy and the mechanical energy are inter-converted via the magnetic field.**

**The Principle of Electromechanical Energy involves following phenomena’s**

- Principle of induction
- Principle of interaction
- Principle of alignment
- Energy stored in magnetic field
- Forces and torques in magnetic field systems
- Singly excited and multiply excited magnetic field systems
- Inductance
- Multiply excited magnetic field systems

**PRINCIPLE OF INDUCTION**

The induced emf is given by Faraday's Law of Induction

**PRINCIPLE OF INTERACTION**

**PRINCIPLE OF ALIGNMENT**

**ENERGY STORED IN MAGNETIC FIELD**

**Forces and Torques in Magnetic Field Systems**

**Induced emf in Electromechanical Systems**

When a conductor of length l placed in a uniform magnetic field of flux density B. When the conductor moves at a speed v, the induced emf in the conductor can be determined by

e= v x l *x *B

The direction of the emf can be determined by the "right-hand rule" or cross products.

In a coil of N turns, the induced emf can be calculated by

e = -dφ/dt

where φ is the flux linkage of the coil and the minus sign indicates that the induced current opposes the variation of the field. It makes no difference whether the variation of the flux linkage is a result of the field variation or coil movement.

In practice, it would convenient if we treat the emf as a voltage.

if the system is magnetically linear, i.e. the self-inductance is independent of the current. It should be noted that the self-inductance is a function of the displacement x since there is a moving part in the system.

**Force and Torque on a Current Carrying Conductor**

The force on a moving particle of electric charge q in a magnetic field is given by the Lorentz's force law:

F= q(vxB)

The force acting on a current carrying conductor can be directly derived from the equation as

F = I ʃ dl x B

For a homogeneous conductor of length l carrying current I in a uniform magnetic field, the above expression can be reduced to

F = I (B × L)

In a rotating system, the torque about an axis can be calculated by

T = r × F

where r is the radius vector from the axis towards the conductor.

**A Singly Excited Linear Actuator**

Consider a singly excited linear actuator as shown below. The winding resistance is R. At a certain time instant t, we record that the terminal voltage applied to the excitation winding is v, the excitation winding current i, the position of the movable plunger x, and the force acting on the plunger F with the reference direction chosen in the positive direction of the x-axis, as shown in the diagram.

After a time interval dt, we notice that the plunger has moved for a distance dx under the action of the force F.

dW_{m} = Fdx

The amount of electrical energy that has been transferred into the magnetic field and converted into the mechanical work during this time interval can be calculated by subtracting the power loss dissipated in the winding resistance from the total power fed into the excitation winding as

Since e = dφ/dt hence

We can also write

E – dλ/dt = v-Ri

The energy stored in a magnetic field can be expressed as

For a magnetically linear (with a constant permeability or a straight line magnetization curve such that the inductance of the coil is independent of the excitation current) system, the above expression becomes

In the diagram below it is shown that magnetic energy is the equivalent to the area above the magnetization curve, here If we define the area under the magnetization curve as the co-energy which does not exist physically

From the above diagram, **the co-energy** or the Area underneath the magnetization curve can be calculated by

For a magnetically linear system, the above expression becomes

& the force acting on the plunger is then

**Doubly Excited Rotating Actuator**

The general principle for force and torque calculation discussed above is equally applicable to multi-excited systems. Consider a doubly excited rotating actuator shown schematically in the diagram below as an example. The differential energy and co-energy functions can be derived as follows:

dW_{f}= dW_{e} – dW_{m}

where dw_{f} = e_{1}i_{1}dt + e_{2}i_{2}dt

e_{1}= dφ_{1}/dt ; e_{2}= dφ_{2}/dt

dw_{m} = Tdq

The Magnetic Energy & the Co-energy can then be expressed as

Respectively & it can be shown that they are equal.

**Model of Electromechanical Systems**

As discussed in the introduction, the mathematical model of an electromechanical system consists of circuit equations for the electrical subsystem and force or torque balance equations for the mechanical subsystem, whereas the interactions between the two subsystems via the magnetic field can be expressed in terms of the emf's and the electromagnetic force or torque. Thus, for the doubly excited rotating actuator, we can write

V_{1} = R_{1}i_{1} + dφ_{1}/dt = R_{1}i_{1} +{ d(φ_{11}+φ_{12})}/dt

V_{2} = R_{2}i_{2} + dφ_{2}/dt = R_{2}i_{2} +{ d(φ_{21}+φ_{22})}/dt

& **T-T _{load} = Jdω_{r}/dt**

Where **ω _{r} = dq/dt**

is the angular speed of the rotor, T load the load torque, and J the inertia of the rotor and the mechanical load which is coupled to the rotor shaft.

In the format of state equations, the above equations can be rewritten as

Together with the specified initial conditions (the state of the system at time zero in terms of the state variables):

The above state equations can be used to simulate the dynamic performance of the doubly excited rotating actuator.

If you are preparing for GATE and ESE, avail Online Classroom Program to get unlimited access to all the live structured courses and mock tests from the following link :

**ESE and GATE ECE Online Classroom Program (24+ Live classes and 150+ mock tests)**

**ESE and GATE EE Online Classroom Program (24+ Live classes and 193+ mock tests)**

**Thanks**

**Sahi Prep Hai to Life Set Hai!!!!!**

**Download BYJU'S Exam Prep, Best gate exam app**

**for Preparation**

## Comments

write a comment