Electromechanical Systems

Introduction

Electromechanical systems combine electrical and mechanical domains. They are essential in motors, generators, actuators, and energy conversion devices. By analyzing these systems, engineers can build mathematical models that describe how electrical inputs produce mechanical outputs and how mechanical motion generates electrical power in return.

law of motor

The interaction between electricity and magnetism forms the basis of electromechanical systems. When current flows through a conductor in a magnetic field, it produces a force:

(Here, F is force, B is magnetic flux density, l is the length of the conductor, and i is current.)

Induced electromotive force

When a conductor moves in a magnetic field, it induces a voltage:

(Here, e is induced EMF and v is velocity.)

back emf

Motors and generators rely on these principles. In a motor, a moving conductor generates a back EMF proportional to angular velocity:

At the same time, torque is generated as:

(Here, T is torque, Kₜ is the torque constant, and iₐ is the armature current.)

Motor Torque

The conversion of electrical energy into mechanical work is expressed as:

(Here, P is power and ω is angular velocity.)

Gear ratio

Gear trains transfer torque and angular displacement between connected shafts, expressed as:

Summary

These relationships highlight the dual nature of electromechanical systems:

• Electrical input produces mechanical motion (motors).
• Mechanical motion produces electrical output (generators).

By unifying these principles, electromechanical modeling enables precise control and efficient energy conversion across applications, from small actuators in robotics to large-scale industrial machinery. Understanding these interactions is fundamental for modern engineering, bridging the gap between two vital domains of energy.