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Understanding Mechanical

System Requirements

EES 472 Electric Drives

Assoc. Prof. Dr. Mutlu BOZTEPE Ege University, 2015

Motivation

How can the ASD accelerate and decelerate the load to

give desired speed profile

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Systems With Linear Motion

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Rotating Systems

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Rotating Systems

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Calculation of Moment of Inertia J of a Uniform Cylinder

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Accelaration, Speed and Position, Power and Energy

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Frictional Torque

Need for a high force (torque) in the beginning (from rest) to set an

object in motion. This friction is called stiction.

Once in motion, the friction may consist of a component called

coulomb friction which remains independent of speed magnitude

(always opposes rotation) or

another component called viscous

friction which increases

linearly with speed.

In general the friction torque has

all aforementioned components.

However it can be linearized

for an approximate analysis

as shown dotted line in which

characteristics is similar to that

of viscous friction.

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Torsional Resonances

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Mechanical - Electrical Analogy

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Electrical Analogy of Motor & Load

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Coupling Mechanisms

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Conversion between Linear and Rotary Systems

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Gears

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Gears (contd)

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Optimum gear ratio to minimize Tem

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Tem and load acceleration!

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Types of Loads

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Centrifugal loads

Tork ~ speed2

Power ~ speed3

Types of Loads

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Constant Torque loads

Tork =constantPower ~ speed

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Types of Loads

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Squared power loads

Tork ~ speedPower ~ speed2

Types of Loads

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Constant power loads

Tork beyond a certain speed rangevaries inversely with speedPower =constant

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Four-Quadrant Operation

In many high performance systems, drives are required to operate in

all quadrants of torque-speed plane.

In order to control the load speed rapidly, it may be necessary to

operate the system inn the regenerative breaking mode.

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Steady-state stability

The equilibrium point A is termed as stable if the operating point

restores itself after small disturbance in the motor or load.

Assume that disturbance casuses a reduction of m in speed.

At new speed motor torque is greater than load torque, consequently

motor will accelerate and operation will be restores to point A.

Therefore the drive is steady-state stable at point A.

For point B, a decrease in speed causes load torque is greater than

motor torque, drive decelerates and operating point moves away from

point B. Thus, point B is unstable point.

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Steady-state stability Alternative approach

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Let a small perturbation in speed, m results in T and Tl perturbations.

Removing average quantitites and rearranging the terms gives

For small perturbations, the speed-torque curves of motor and load can be assumed to be straight lines. Thus,

where dT/dw terms are the slopes. By substituting these Eq. into above Eq. gives

Solution of this 1st order differential equation.

For m 0

Dynamic Operation

How the operating point changes with time

Important for High Performance Drives

Speed change: rapid and without any oscillations

Requires good controller design

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Summary

What are the MKS units for force, torque, linear velocity, angular

velocity, speed, and power?

What is the relationship between force, torque, and power?

Show that torque is the fundamental variable in controllingspeed

and position.

What is the kinetic energy stored in a moving mass and arotating

inertia?

What is the mechanism for torsional resonances?

What are the various types of coupling mechanisms?

What is the optimum gear ratio to minimize the torque required from

the drive to accelerate a load?

What are the torque-speed and the power-speed profiles for various

types of loads?

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Problems

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Problems

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Problems

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Problems

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Problems

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