Dynamics of Motor Load System

A motor generally drives a load (machines) through a transmission system. While the motor always rotates, the load may rotate or may undergo translational motion.

The load speed may be different from that of the motor. If the load has many parts, their speeds may also be different. Some parts rotate while others may move through translational motion.

An equivalent rotational system of motor and load is shown in Figure : Motor Load System

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Fundamental Equations of Torque

The dynamics of an electrical drive can be expressed using the following parameters.

Where,

J = Moment of inertia of motor load system referred to the motor shaft (kg·m²)

ωₘ = Instantaneous angular velocity of motor shaft (rad/sec)

T = Instantaneous value of developed motor torque (N·m)

Tₗ = Instantaneous value of load torque referred to the motor shaft (N·m)

Load torque includes friction and windage torque of the motor.

Fundamental Torque Equation

The motor load system shown in the figure can be described by the following fundamental torque equation.$$T – T_l = \frac{d}{dt}(J\omega_m)$$

Expanding the derivative,$$T – T_l = J\frac{d\omega_m}{dt} + \omega_m \frac{dJ}{dt}$$

…….Equation (1)

This equation is applicable to variable inertia drives such as: Winders, Reel drives, Industrial robots

Case: Drive with Constant Inertia

If inertia remains constant,$$\frac{dJ}{dt} = 0$$

Therefore the equation becomes$$T = T_l + J\frac{d\omega_m}{dt}$$

…….Equation (2)

Equation (2) shows that the motor torque must balance:

• Load torque $T_l$
• Dynamic torque $J\frac{d\omega_m}{dt}$

The term$$J\frac{d\omega_m}{dt}$$

is called dynamic torque because it appears only during transient conditions.

Note

The energy associated with dynamic torque is stored as kinetic energy, given by$$KE = \frac{J\omega_m^2}{2}$$