Post on 04-Jun-2018
8/13/2019 25Oct13 Modelling
1/30
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
8/13/2019 25Oct13 Modelling
2/30
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
CASDE, Aero. Dept., IIT Bombay
.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.
8/13/2019 25Oct13 Modelling
3/30
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
CASDE, Aero. Dept., IIT Bombay
.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.
8/13/2019 25Oct13 Modelling
4/30
System Behaviour Generation ProcessSystem Behaviour Generation Process
Given below is the overall task of generating the
behaviourof any system.
CASDE, Aero. Dept., IIT Bombay
Laws of natureplay an important rolein this process.
8/13/2019 25Oct13 Modelling
5/30
Generic Issues in Modelling
CASDE, Aero. Dept., IIT Bombay
To Model
8/13/2019 25Oct13 Modelling
6/30
Issues in Modelling
From Reality
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
7/30
Modelling and Model Definitions
Model is;
an imitation of reality in terms of those
quantitative featuresthat describe theoperationof any given system.
CASDE, Aero. Dept., IIT Bombay
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.
8/13/2019 25Oct13 Modelling
8/30
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.
CASDE, Aero. Dept., IIT Bombay
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.
8/13/2019 25Oct13 Modelling
9/30
Modelling Scenarios: Nuclear Reactor Burst
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
10/30
Nuclear Reactor Burst Model
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
11/30
Modelling Scenarios: Compressor Cutsection
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
12/30
Compressor Pressure Model
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
13/30
Modelling Scenarios: Coal Power PlantModelling Scenarios: Coal Power Plant
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
14/30
Schematic Model of Coal Power PlantSchematic Model of Coal Power Plant
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
15/30
Modelling Scenarios: Mathematical Model
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
16/30
Modelling Scenarios: Response Based Model
CASDE, Aero. Dept., IIT Bombay
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)
8/13/2019 25Oct13 Modelling
17/30
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/
CASDE, Aero. Dept., IIT Bombay
, .
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.
8/13/2019 25Oct13 Modelling
18/30
Modelling Procedure
CASDE, Aero. Dept., IIT Bombay
Validation Model Building
8/13/2019 25Oct13 Modelling
19/30
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 )
CASDE, Aero. Dept., IIT Bombay
,
& Energy as basic quantities)
Set up continuity & compatibility Conditions
(Boundary conditions; Interfaces)
Create idealized elements & their constitutive
relations.
8/13/2019 25Oct13 Modelling
20/30
Idealized Elements Mechanical
Spring/Stiffness Mass/Inertia Damping
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
21/30
Idealized Elements Electrical
Sources Resistance/Inductance/Capacitance Magnetic
v iR
Resistance
Element
Ca acitance
v = i R
Voltage Source
Current
CASDE, Aero. Dept., IIT Bombay
C
Element
InductanceElement
v = C i dt
v = L di/dt
i
Source
L
L1
L2
Magnetic
Element
i
vi= Lidii/dt
Mdij/dt
8/13/2019 25Oct13 Modelling
22/30
Idealized Elements Thermal
Conduction Convection Radiation
Conduction
q1-q2=Mc dT/dt=C dT/dt
qs = -A dT/dl
CASDE, Aero. Dept., IIT Bombay
= (
A /l) (T1-T2)Convection
qs = -hcA (Ts-Tf)
Radiationqs = Cr(T1
4-T24)
qs = Cr(T1-T2)
8/13/2019 25Oct13 Modelling
23/30
Idealized Elements Fluidic/Pneumatic
Tank Pipe/Elbow Piston
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
24/30
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
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
25/30
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
CASDE, Aero. Dept., IIT Bombay
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.
8/13/2019 25Oct13 Modelling
26/30
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.
CASDE, Aero. Dept., IIT Bombay
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
= + + = + + = +
= = + = + = + = +
8/13/2019 25Oct13 Modelling
27/30
Given below is the plot ofpower vs. belt velocity.
Solution CharacteristicsSolution Characteristics
CASDE, Aero. Dept., IIT Bombay
It can be shown thata 5 HP motorwill be able to give the
sand flow rateof 100 tons/hr or55.5. lb/s.
8/13/2019 25Oct13 Modelling
28/30
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
CASDE, Aero. Dept., IIT Bombay
employed for generating theaerodynamic characteristics.
8/13/2019 25Oct13 Modelling
29/30
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
CASDE, Aero. Dept., IIT Bombay
8/13/2019 25Oct13 Modelling
30/30
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
CASDE, Aero. Dept., IIT Bombay
general,system level models have lower fidelitywhile thecomponent and part level models are of significantly
higher fidelity.