25Oct13 Modelling

8/13/2019 25Oct13 Modelling

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Role of Models in DesignRole of Models in Design

Course on

Systems Engineering

for

CASDE, Aero. Dept., IIT Bombay

ostgra uate tu ents o

25th October, 2013

Defence Institute of Advanced Technology, Pune


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Role of ModellingRole of Modelling

In system design, an important aspect of requirements

validationis the act of generating theexpected behaviour

of the system, sub-system oreven component.

Inconceptual design phase(i.e. phase involving concept

generation and selection) analyzing the performance or


.It is important to note that while solving the design

problems, it is necessary to take decisions and make

choices thatdepend on the behaviour.Therefore, it is necessary to setup problems whose

solution results inparametersthat characterize behaviour.


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Role of ModellingRole of Modelling

Modelling is that task, which helps thesystems engineer

to set up the specificproblem that needs to be solvedfor

arriving at thedesired behaviour patterns.

Models arethose descriptions of each design(or concept)

that are detailed just enough so that performance


.Modelling is the processthat helps the systems engineer

to arrive at such descriptions of the system/sub-system

under consideration.In general,modelling involves the representationof the

physical aspects of a systemthat govern its behaviour.


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System Behaviour Generation ProcessSystem Behaviour Generation Process

Given below is the overall task of generating the

behaviourof any system.


Laws of natureplay an important rolein this process.


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Generic Issues in Modelling


To Model


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Issues in Modelling

From Reality



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Modelling and Model Definitions

Model is;

an imitation of reality in terms of those

quantitative featuresthat describe theoperationof any given system.


o e ng s;an act of translating real world into a form that

can be studied in detail, for (1) gaining insight

into the real world as it exists, (2) making anassessmentof its behaviour or (3)controllingits

behaviour.


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Modelling ProcessModelling Process

Since models can include several different types ofinformation, it is important for adesigner to be awareof

the variety possible in themodelling process.

For example,a physical modelis the most common formthat most of us think whenever model is mentioned. It

can befrozen in timeor can bearticulatedthrough joints.


Models canalso be design sketches, assemblydrawingsetc. that help inresolving interferencesetc.

Models can also exist as mathematical equations that

describecharacteristics of productor system of interest.Models can also be a combination of geometric and

functionalrepresentation.


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Modelling Scenarios: Nuclear Reactor Burst



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Nuclear Reactor Burst Model



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Modelling Scenarios: Compressor Cutsection



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Compressor Pressure Model



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Modelling Scenarios: Coal Power PlantModelling Scenarios: Coal Power Plant



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Schematic Model of Coal Power PlantSchematic Model of Coal Power Plant



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Modelling Scenarios: Mathematical Model



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Modelling Scenarios: Response Based Model


1st

order system. Unit stepinput. Proposed model:

dc(t)/dt+(1/T)c(t)=u(t)

2nd order system. Unit step

input. Proposed model:

d2c(t)/dt2 + 2 dc(t)/dt + 2

c(t) = u(t)


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Model TypesModel Types

Models can be of various types, depending on the purposeof such models.

Models can either be descriptive (for communicating

ideas) orpredictive(for generating behaviour).

Models can also be (1)static/dynamic, (2)deterministic/


, .

In general,real world problemsare such that models are

usuallydynamic as well as probabilistic.

Iconic modelsare those that look like the real system butare only ascaledrepresentation.Analogmodels are based

on similitude.Symbolic modelsare the most general ones.


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Modelling Procedure


Validation Model Building


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Model Creation Guidelines

Identify the system, its boundary and environment

Identify sub-systemsand establish all interactions

Identify laws/processesgoverning the operations

Choose a model philosophy(Mathematical, Physical )


,

& Energy as basic quantities)

Set up continuity & compatibility Conditions

(Boundary conditions; Interfaces)

Create idealized elements & their constitutive

relations.


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Idealized Elements Mechanical

Spring/Stiffness Mass/Inertia Damping



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Idealized Elements Electrical

Sources Resistance/Inductance/Capacitance Magnetic

v iR

Resistance

Element

Ca acitance

v = i R

Voltage Source

Current


C

Element

InductanceElement

v = C i dt

v = L di/dt

i

Source

L

L1

L2

Magnetic

Element

i

vi= Lidii/dt

Mdij/dt


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Idealized Elements Thermal

Conduction Convection Radiation

Conduction

q1-q2=Mc dT/dt=C dT/dt

qs = -A dT/dl


= (

A /l) (T1-T2)Convection

qs = -hcA (Ts-Tf)

Radiationqs = Cr(T1

4-T24)

qs = Cr(T1-T2)


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Idealized Elements Fluidic/Pneumatic

Tank Pipe/Elbow Piston



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Given below is thestatement of an engineering designproblem,for which a modelneeds to be created.

Whatsize motor shouldbe selected to drive a conveyor

belt todeliver sand at a flow rate of 100 tons/hourusing

the design shown below?

A Modelling ExampleA Modelling Example



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Design Decision Space & BoundariesDesign Decision Space & Boundaries

In order to solve the problem we need to answer thefollowing questions.

What is the horsepower of the smallest electric motor

that can deliver 100 tons of sand per hour?

What is therelationship between the horsepowerand the


How does thewidth of the beltinfluence the design?

We limit themodelto the basic conveyor design.

Data extractedis as follows. h = 55 ft, H = 20o,= 100lb/ft3, A = 0.5 ft2.

Model is based onconservation of energy.


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Model ConstructionModel Construction

Followingassumptions are madefor model construction.

Friction in the rollers is neglected. Support structure

does not deform elastically.

The following are thesteps in the model construction.


We can refine the above model to include many other

physical effects and get amore accurate design solution.

2 22 2

2 2

2750 1.563 5 0.003 ( )

i p k f

i

E E E E Wh V V Wh Vg g g

E V VP Qh Q Q h V V HP

t g g

= + + = + + = +

= = + = + = + = +


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Given below is the plot ofpower vs. belt velocity.

Solution CharacteristicsSolution Characteristics


It can be shown thata 5 HP motorwill be able to give the

sand flow rateof 100 tons/hr or55.5. lb/s.


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In many engineering disciplines, models based onsimilitude, or scaling laws, are employed forgenerating

important design informationthrough experiments.

Similitude means that conditions for both the actualsystem and for the model operations, are similar. In

aeros ace s stems, wind tunnel models are commonl

Similitude and Scale ModelsSimilitude and Scale Models


employed for generating theaerodynamic characteristics.


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There are many situations where the developed

mathematical models cannot be solved directly and in

such cases, we take recourse to finite difference and

finite element modelsto help us generate the behaviour.

Finite Different ModelsFinite Different Models



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SummarySummary

Modelling is an important activity that needs to beperformed atall levels of system development.

The fidelity of the model depends on the level and in


general,system level models have lower fidelitywhile thecomponent and part level models are of significantly

higher fidelity.

25Oct13 Modelling

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