This document discusses equations governing the dynamics of a motor load system. It defines key terms like moment of inertia (J), angular velocity (ωm), motor torque (T), and load torque (Tl). It explains that during acceleration, the motor supplies the load torque plus an additional torque (Jdωm/dt) to overcome inertia. Load torques can include friction torque (TF), windage torque (Tw), and torque required for useful work (TL). Load torques are classified as either active if they can drive the motor, or passive if they always oppose motion. Different load types can have torque proportional to speed, speed squared, or inversely with speed.

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1
Dr. A. Ravi
Professor/EEE
FRANCIS XAVIER ENGINEERING COLLEGE
TIRUNELVELI - India
Equations governing motor
load dynamics

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Equations governing
motor load dynamics

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Dynamics of Motor load System
J – Moment of inertia of the 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 (Nm)
Tl - Instantaneous value of load torque referred to motor shaft
(Nm)
For constant inertia drive dJ/dt = 0

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Load
Torque
Dynamic
Torque
The acceleration or deacceleration of the drive
mainly depends on whether the load torque is greater or
less than the motor torque.
During acceleration, the motor supplies the load
torque along with an additional torque component
jdωmt/dt to overcome the drive inertia.
Dynamics of Motor load System

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Dynamics of Motor load System
Rotational Motion

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If the losses are neglected, then Kinetic energy
of equivalent inertia must be same as Moving
parts,
When many loads are connected , the above
equation expanded to,

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Again,
Power of the motor load systems are same,
Divided by wm

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Dynamics of Motor load System
Translational Motion

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If the losses are neglected, then Kinetic energy
of equivalent inertia must be same as Moving
parts,
When many loads are connected , the above
equation expanded to,

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Again, Power of the motor load systems are same,

11. Load Torques
Friction torque
TF
Windage
torque, Tw
Torque required
to do the useful
mechanical
work, TL
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Components of Load Torques
Friction will be present
at the motor shaft and
also in various parts of
the load. TF is
equivalent value of
various friction torques
referred to the motor
shaft.
When a motor
runs, wind
generates a
torque opposing
the motion. This
is known as
windage torque.
Nature of this
Components of Load
Torques depends on
particular application.

12. Active Load torques
Load torques which have the potential to drive the
motor under equilibrium conditions are called active load
torques. Load torques usually retain sign when the drive
rotation is changed.
Passive Load torques
 Load torques which always oppose the motion and
change their sign on the reversal of motion are called
passive load torques.
 Torque due to friction cutting – Passive torque.
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Classification of load torques

13.  Constant torque type load.
 Torque proportional to speed (generator type load)
 Torque proportional to square of the speed (fan
type load)
 Torque inversely proportional to speed (constant
power type load)
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Different speed torque characteristics.

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