ME14 ME1404 04
COMP COMPUT UTER ER AIDE AIDED D SIMUL SIMULA ATION TION AND AND ANA ANAL LYSIS YSIS LABO LABORA RAT TORY ORY
LIST OF EXPERIMENTS A.
Simulation
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Simula Simulatio tion n of Air condit condition ioning ing system system with with condens condenser er temper temperatu ature re and evapor evaporato ator r temperatures as input to get COP using C /MAT /MAT Lab Simulation of !ydraulic / Pneumatic cylinder using C / MAT MAT Lab Simulation of cam and follower mechanism using C / MAT MAT Lab Anal!"i" #Sim$l% T&%atm%nt onl!' (0 Stress analysis of a plate with a circular hole Stress analysis of rectangular L brac"et Stress analysis of an a#i$symmetric component Stress analysis of beams %Cantilever& Simply supported& 'i#ed ends( Mode fre)uency analysis analysis of a * + component Mode fre)uency analysis of beams %Cantilever& Simply supported& 'i#ed ends( !armonic analysis of a *+ component Thermal stress analysis of a *+ component Conductive heat transfer analysis of a *+ component Convective heat transfer analysis of a *+ component
LIST OF EXERCISES
Anal!"i" #Sim$l% T&%atm%nt onl!'
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Stre Stress ss ana analy lysi siss of bea beams ms %Ca %Cant ntil ilev ever er&& Simp Simply ly sup suppor porte ted d 0 'i#e 'i#ed d ends ends((
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Stre Stress ss anal analys ysis is of a pla plate te with with a cir circu cula larr hol hole e
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Stre Stress ss anal analys ysis is of rect rectan angu gula larr L brac brac"e "ett
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Stre Stress ss anal analys ysis is of an a#i$ a#i$sy symm mmet etri ricc com compo pone nent nt
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Mode Mode fre) fre)ue uenc ncy y ana anallysi ysis of of a * + comp compon onen entt
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Mode Mode fre)u fre)uen ency cy analy analysi siss of beams beams %Can %Canti tile leve verr& Sim Simpl ply y Supported& 'i#ed ends(
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!arm !armon oniic ana anallysis ysis of a *+ com compone ponent nt
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Ther Therma mall str stres esss anal analys ysis is of a *+ comp compon onen entt
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Cond Conduc ucti tive ve hea heatt tra trans nsfe ferr anal analys ysis is of a *+ *+ com compo pone nent nt
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Convective heat transfer analysis of a *+ component
Simulation
,# -o. Simulation of Air conditioning system with condenser temperature and evaporator temperatures as input to get COP using C /MAT /MAT Lab ,# -o. * Simulation of !ydraulic / Pneumatic cylinder using C / MAT Lab ,# -o. 1 Simulation of cam and follower mechanism using C / MAT Lab
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INTRODUCTION )*at i" Finit% El%m%nt Anal!"i"+
'inite ,lement Analysis& commonly called ',A& is a method of numerical analysis ',A is used for solving problems in many engineering disciplines such as machine design& acousti acoustics& cs& electr electromag omagnet netism ism&& soil soil mechan mechanics ics&& fluid fluid dynami dynamics& cs& and many many others others 9n mathema mathematic tical al terms& terms& ',A is a numeri numerical cal techni techni)ue )ue used used for solvin solving g field field proble problems ms described by a set of partial differential e)uations 9n mechanical engineering& ',A is widely used for solving structural& vibration& and thermal problems !owever& ',A is not the only available tool of numerical analysis Other numerical methods include the 'inite +ifference Method& the :oundary ,lement Method& and the 'inite ;olumes Method to mention
e any shape? ',A wor"s with different levels of geometry ideali>ati ideali>ation on and provides provides results results with the desired desired accuracy accuracy @hen implemented implemented into modern modern commer commercia ciall softwa software& re& both both ',A theory theory and numeri numerical cal proble problem m formul formulati ation on become completely transparent to users )*o "*oul, u"% Finit% El%m%nt Anal!"i"+
As a powerful tool for engineering analysis& ',A is used to solve problems ranging from very simple to very comple# +esign engineers use ',A during the product development process to analy>e the design$in$progress Time constraints and limited availability of product data call for many simplifications of the analysis models At the other end of scale& speciali>ed analyst analystss imple implemen mentt ',A to solve solve very very advance advanced d proble problems& ms& such such as vehicl vehiclee crash crash dynamics& hydro forming& or air bag deployment This boo" focuses on how design engineers use ',A as a design tool Therefore& we first need to e#plain what e#actly distinguishes ',A performed by design engineers from regular ',A @e will then highlight the most essential ',A characteristics for design engineers as opposed to those for analysts FEA -o& D%"in Enin%%&"/ anot*%& ,%"in tool
'or design design enginee engineers& rs& ',A is one of many many design design tools tools among among CA+& CA+& Protot Prototype ypes& s& spreadsheets& catalogs& data bases& hand calculations& ca lculations& te#t boo"s& etc that are all used in the design process FEA -o& D%"in Enin%%&"/ a"%, on CAD mo,%l" Modern design is conducted using CA+ tools& so a CA+ model is the starting point for analysis Since CA+ models are used for describing geometric information for ',A& it is
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essential to understand how to design in CA+ in order to produce reliable ',A results& and how a CA+ model is different from ',A model This will be discussed in later chapters
FEA -o& D%"in Enin%%&"/ onu&&%nt 2it* t*% ,%"in $&o%""
Since ',A is a design tool& it should be used concurrently with the design process 9t should "eep up with& or better yet& drive the design process Analysis iterations must be performed fast& and since these results are used to ma"e design decisions& the results must be reliable even when limited input is available Limitation" o- FEA -o& D%"in Enin%%&"
As you can see& ',A used in the design environment must meet high re)uirements An obvious )uestion arises. would it be better to have dedicated specialist perform ',A and let design engineers do what they do best $ design new productsB The answer depends on the si>e of the business& type of products& company organi>ation and culture& and many other tangible and intangible factors A general consensus is that design engineers should handle relatively simple types of analysis& but do it )uic"ly and of course reliably Analyses that are very comple# and time consuming cannot be e#ecuted concurrently with the design process& and are usually better handled either by a dedicated analyst or contracted out to speciali>ed consultants O3%ti%" o- FEA -o& D%"in Enin%%&"
The ultimate ob
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'igure $. Traditional Traditional and ',A$ driven product p roduct development Traditional product development needs prototypes to support design in progress. The process in FEA-driven product development uses numerical models, rather than physical prototypes to drive development. In an FEA driven product, the prototype is no longer a part of the iterative design loop.
What is Solid Works Simulation Solid @or"s Simulation is a commercial implementation of ',A& capable of solving problems commonly found in design engineering& such as the analysis of deformations& stresses& natural fre)uencies& heat flow& etc Solid @or"s Simulation addresses the needs of design engineers 9t belongs to the family of engineering analysis software products develop developed ed by the Struct Structura urall esear esearch ch 0 Analys Analysis is Corpor Corporati ation on %SAC( %SAC( SAC SAC was established in 76* and since its inception has contributed to innovations that have had a significant impact on the evolution of ',A 9n 773 SAC partnered with the Solid @or"s Corporation and created Solid @or"s Simulation& one of the first Solid @or"s Dold Dold Prod Produc ucts ts&& which which beca became me the the top$ top$se sell llin ing g anal analys ysis is solu soluti tion on for for Solid Solid @or"s or"s Corporation The commercial success of Solid @or"s Simulation integrated with Solid @or"s CA+ software resulted in the ac)uisition of SAC in *88 by +assault Systems& parent of Solid @or"s Corporation 9n *881& SA Corporations merged with Solid @or"s @or"s Corpor Corporati ation on Solid Solid @or"s or"s Simula Simulatio tion n is tight tightly ly integr integrate ated d with with Solid Solid @or"s or"s CA+ software and uses Solid @or"s for creating and editing model geometry Solid @or"s is a solid& solid& parametric parametric&& feature$dri feature$driven ven CA+ system As opposed to many other CA+ systems that were originally developed in a E-9F environment and only later ported to @indows& Solid @or"s CA+ was developed specifically for the @indows Operating System from the very beginning 9n summary& although the history of the family of Solid @or"s ',A
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products dates bac" to 76*& Solid @or"s Simulation has been specifically developed for @indows and ta"es full advantage this of deep integration between Solid @or"s and @indows& representing the state$of$the$art in the engineering analysis software
Fundamental steps in an FEA pro!ect pro!ect The starting point for any Solid @or"s @or"s Simulation proe the fact that they are not infinitesimally small& but only reasonably small in comparison to the overall model si>e Creating finite elements is commonly called meshing @hen wor"ing with finite elements& the Solid @or"s or"s Simu Simula lati tion on solv solver er appr appro# o#im imat ates es the the solu soluti tion on being being sough soughtt %for %for e#amp e#ample le&& deformations or stresses( by assembling the solutions for individual elements 'rom the perspective of ',A software& each application of ',A re)uires three steps. Preprocessing of the ',A model& which involves defining the model and then
splitting it into finite elements Solution for computing wanted results Post$processing for results analysis
@e will follow the above three steps every time we use Solid @or"s @or"s Simulation 'rom the perspective of ',A methodology& methodology& we can list the following ',A steps. :uilding the mathematical model :uilding the finite element model Solving the finite element model Analy>ing the results
The following subsections discuss these four steps :uilding the mathematical model The starting point to analysis with Solid @or"s Simulation is a Solid @or"s model Deometry of the model needs to be meshable into a correct and reasonably small element
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mesh mesh This This re)uir re)uireme ement nt of meshabi meshabilit lity y has very very import important ant impli implicati cations ons @e need to ensure that the CA+ geometry will indeed mesh and that the produced mesh will provide the correct solution of the data of interest& such as displacements& stresses& temperature distribution& etc This necessity often re)uires modifications to the CA+ geometry& which can ta"e the form of defeaturing& ideali>ation and/or clean$up& described below.
9t is important to mention that we do not always simplify the CA+ model with the sole ob
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'igure $*. :uilding the mathematical model The process of creating a mathematical model consists of the modification o #A$ geometry %here removing removing e&ternal fillets', definition definition of loads, restraint material material properties, and definition definition of the type of analysis %e.g., static' that "e "ish to perform. Buil,in t*% -init% %l%m%nt mo,%l
The mathematical model now needs to be split into finite elements through a process of discreti>ation& more commonly "nown as meshing %figure $1(Loads and restraints are also discreti>ed and once the model has been meshed the discreti>ed loads and restraints are applied to the nodes of the finite element mesh
'igure $1. :uilding the finite element model The mathematical model is discreti(ed into a finite element model. This completes the pre-processing pre-processing phase. The FEA model is then solved "ith one of the numerical solvers availa)le in Solid Works Works Simulation Solving the finite element model !aving created the finite element model& we now use a solver provided in Solid Works Simulation to Simulation to produce the desired data of interest %figure $1(
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Analy>ing the results Often the most difficult step of ',A is analy>ing the results Proper interpretation of results re)uires that we understand all simplifications %and errors they introduce( in the first three steps. defining the mathematical model& meshing its geometry ge ometry&& and solving
Errors Errors in FEA The process illustrated in figures $* and $1 introduces unavoidable errors 'ormulation of a mathematical model introduces modeling errors %also called ideali>ation errors(& discreti>ation of the mathematical model introduces discreti>ation errors& and solving introduces numerical errors Of these three types of errors& only discreti>ation errors are specific to ',A Modeling errors affecting the mathematical model are introduced before ',A is utili>ed utili>ed and can only be controlled by using correct modeling techni)ues Solution errors caused by the accumulation of round$off errors are difficult to control& but are usually very low low
A closer look look at finite elements elements Meshin Meshing g splits splits contin continuous uous mathem mathemati atical cal models models into into finite finite elemen elements ts The type type of elements created by this process depends on the type of geometry meshed& the type of analysis& and sometimes on our own preferences Solid Works Simulation offers Simulation offers two types of elements. tetrahedral solid elements %for meshing solid geometry( and shell elements %for %for meshin meshing g surfac surfacee geometr geometry( y(:ef :efore ore procee proceedin ding g we need to clarif clarify y an import important ant terminology issue 9n CA+ terminology solid denotes the type of geometry. solid geometry %as opposed to surface or wire frame geometry(& in ',A terminology it denotes the type of element
Solid elements The type of geometry that is most often used for analysis with Solid Works Simulation is Simulation is solid CA+ geometry Meshing of this geometry is accomplished with tetrahedral solid elements& commonly called tets in ',A
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'igure $2. +ifferences between first and second order tetrahedral elements First and the second order tetrahedral tetrahedral elements are sho"n )efore )efore and after deformation. *ote that the deformed faces of the second order element may assume curvilinear curvilinear shape "hile deformed faces of the first order element must remain fiat. 'irst order tetrahedral elements have four nodes& straight edges& and flat faces These edges and faces remain straight and flat after the element has e#perienced deformation under under the the appl applie ied d load load 'irs 'irstt orde orderr tetr tetrahe ahedr dral al elem elemen ents ts mode modell the the linea linearr fiel field d of displacement inside their volume& on faces& and along edges The linear %or first order( displacement field gives these elements their name. first order elements 9f you recall from the Mechanics of Materials& strain is the first derivative of displacement Therefore& strain and conse)uently stress& are both constant in first order tetrahedral elements This situation imposes a very severe limitation on the capability of a mesh constructed with first order elements to model stress distribution of any real comple#ity To ma"e matters worse& straight edges and flat faces cannot map properly to curvilinear geometry& as illustrated in figure $3
'igure $3. 'ailure of straight edges and flat faces to map to curvilinear geometry
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A detail of a mesh created "ith first order tetrahedral elements. *otice the imprecise imprecise element mapping to the hole+ flat faces appro&imate the face of the cylindrical hole.
Second order tetrahedral elements have ten nodes and model the second order %parabolic( displacement field and first order %linear( stress field in their volume& along laces& and edges edges The edges edges and faces faces of second second order tetrah tetrahedr edral al elemen elements ts before before and after after deformation can be curvilinear Therefore& these elements can map precisely to curved surfaces& as illustrated in figure $4 ,ven though these elements are more computationally demanding than first order order elemen elements& ts& second second order order tetrah tetrahedra edrall elemen elements ts are used used for the vast vast ma
'igure $4. Mapping curved surfaces A detail is sho"n of a mesh created created "ith second order tetrahedral elements. Second order order elements map "ell to curvilinear geometry.
Shell elements :esides :esides solid elements& elements& Solid @or"s @or"s Simulation Simulation also offers offers shell elements @hile solid solid elements elements are created created by meshing solid geometry& geometry& shell shell elements elements are created created by meshing surfaces Shell elements are primarily used for analy>ing thin$walled structures Since surface geometry does not carry information about thic"ness& the user must provide this information Similar to solid elements& shell elements also come in draft and high )uality with analogous conse)uences with respect to their ability to map to curvilinear geometry& as shown in figure $5 and figure $6 As demonstrated with solid elements& first order shell elements elements model the linear linear displacemen displacementt field field with constant strain and stress stress while second order shell elements model the second order %parabolic( displacement field and the first order strain and stress field
'igure $5. 'irst order shell element This shell element mesh "as created "ith first order elements. *otice the imprecise mapping of the mesh to curvilinear geometry.
'igure $6. Second order shell element Shell element mesh created "ith second order elements, "hich map correctly to curvilinear geometry g eometry.. Certain classes of shapes can be modeled using either solid or shell elements& such as the plate shown in figure $7 The type of elements used depends depe nds then on the ob
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'igure $7. Plate modeled with solid elements %left( and shell elements The plate sho"n can )e modeled "ith either solid elements %left' or shell elements %right %right'. '. The actual actual choice choice depends depends on the partic particula ularr reuir euirements ements of analysi analysiss and sometimes on personal preferences preferences
'igure $8& below& presents the basic library of elements in Solid @or"s @or"s Simulation ,lements li"e a he#ahedral solid& )uadrilateral shell or other shapes are not available in Solid @or"s Simulation
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'igure $8. Solid S olid @or"s @or"s Simulation element library Four element types are availa)le in the Solid @or"s Simulation element Simulation element li)rary. The vast ma!ority of analyses use the second order tetrahedral element. oth solid and shell first order elements should )e avoided. The degrees of freedom %+O'( of a node in a finite element mesh define the ability of the node to perform translation or rotation The number of degrees of freedom that a node possesses depends on the type of element that the node belongs to 9n Solid @or"s Simulation& nodes of solid elements have three degrees of freedom& while nodes of shell elem elemen ents ts have have si# si# degr degree eess of free freedo dom m This This mean meanss that that in orde orderr to desc descri ribe be transformation of a solid element from the components of nodal displacement& most often the #& y& > displacements 9n the case of shell elements& we need to "now not only the translational components of nodal displacements& but also the rotational displacement components
What is calculated in FEA ,ach degree of freedom freedom of every node in a finite element mesh constitutes constitutes an un"nown 9n structura structurall analysis& analysis& where we loo" at deformati deformations ons and stresses stresses&& nodal displacements displacements are the primary un"nowns 9f solid elements are used& there are three displacement components %or 1 degrees of freedom( per node that must be calculated @ith shell elements& si# displacement components %or4 degrees of freedom( must be calculated 2
,ver ,veryt ythi hing ng else else&& such such as stra strain inss and stre stress sses es&& are are calc calcul ulat ated ed base based d on the the nodal nodal displacements Conse)uently& rigid restraints applied to solid elements re)uire only three degrees of freedom to be constrained igid restraints applied to shell elements re)uire that that all si# degree degreess of freedo freedom m be constra constraine ined d 9n a therma thermall analysi analysis& s& which which finds finds temper temperatu atures res and heat heat flow flow&& the primar primary y un"now un"nowns ns are nodal nodal temper temperatu atures res Since Since temperature is a scalar value %unli"e the vector nature of displacements(& then regardless of what type of element is used& there is only one un"nown %temperature( to be found for each node All other results available in the thermal analysis are calculated based on temperature results The fact that there is only one un"nown to be found for each node? rather rather than than three three or si#& si#& ma"es ma"es therma thermall analys analysis is less less comput computati ational onally ly intens intensive ive than than structural analysis
o" to interpret interpret FEA results results esults of structural ',A are provided in the form of displacements and stresses :ut how do we decide if a design passes or fails and what does it ta"e for alarms to go offB @hat e#actly constitutes a failureB To answer these )uestions& we need to establish some criteria to interpret ',A results& which which may includ includee ma#imu ma#imum m accept acceptabl ablee deform deformati ation& on& ma#imu ma#imum m stress stress&& or lowest lowest acceptable natural fre)uency fre)uency @hile displacement and fre)uency criteria are )uite obvious and easy to establish& stress criteria are not LetGs assume that we need to conduct a stress analysis in order to ensure that that stre stress sses es are are with within in an acce accept ptab able le range range To
;on Mises stress& also "nown as !uber stress& is a stress measure that accounts for all si# stress components of a general 1$+ state of stress %figure $(
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'igure $. Deneral state of stress represented by three normal stresses. H#& Hy& H> and si# shear stresses I#y J Iy#& Iy> J I>y& >y& I># J I#> T"o components of shear stress and one component of normal stress stress act on each side of an elementary cu)e. $ue to euili)rium reuirements, the general /-$state of stress stress is characteri(ed )y si& stress components0
H#& Hy& H> and I#y J Iy#& Iy> J I>y& >y& I># J I#>
-ote that von Mises stress is a non$negative& scalar value ;on ;on Mises stress is commonly used to present results because structural safety for many engineering materials showing elasto$plastic properties %for e#ample& steel( can be evaluated using von Mises stress The magnitude of von Mises stress can be compared to material yield or to ultimate strength to calculate the yield strength or the ultimate strength safety factor factor P&ini$al "t&%""%"
:y properly ad
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'igure $*. Deneral state of stress represented by three principal stresses. H& H*& H1
1nits of measurements 9nternally& 9nternally& Solid @or"s simulation uses the 9nternational System of Enits %S9(!owever& for the userGs convenience& the unit manager allows data entry in three different systems of units. S9& Metric& and ,nglish esults can be displayed using any of the three unit systems 'igure $1 summari>es the available systems of units
'igure $1. Enit systems available in Solid @or"s simulation SI, 2etric, and English systems of units can )e interchanged "hen entering data or analy(i analy(ing ng result esultss in Solid @or"s @or"s simulation simulation ,#perience ,#perience indicates indicates that units of mass density are often confused with units of specific gravity The distinction between these two is )uite clear in S9 units. Mass density is e#pressed in 3kg4m/5, while specific gravity in in 3*4m/5.!owever& 3*4m/5.!owever& in the ,nglish system& both specific mass and specific gravity are e#pressed in 3l)4in./5, where 3l)5 denotes either pound mass or pound force As Solid @or"s simulation users& we are spared much confusion and trouble with systems of units
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!owever& we may be as"ed to prepare data or interpret the results of other ',A software where we do not have the convenience of the unit manager Therefore& we will ma"e some general comments about the use of different systems of units in the preparation of input data for ',A models @e can use any consistent system of units for ',A models& but in practice& the choice of the system of o f units is dictated by what units are used in the CA+ model The system of units in CA+ models is not always consistent? length can be e#press e#pressed ed in 3mm5, 3mm5, while mass density can be e#pressed in 3kg4m/5.Contrary 3kg4m/5.Contrary to CA+ mode models ls&& in ',A ',A all all unit unitss must be consistent 9nconsistencies are easy to overloo"& especially when defining mass and mass density den sity&& and they can lead to very serious errors SI, 2etric, and English systems of units can )e interchanged "hen entering data or analy(ing results in Solid @or"s simulation ,#perience indicates that units of mass density are often confused with units of specific gravity The distinction between these two is )uite clear in S9 units. Mass density is e#pressed in 3kg4m/5, while specific gravity in 3*4m/5.!owever& 3*4m/5.!owever& in the ,nglish system& both specific mass and specific gravity are e#pressed in 3l)4in./5, 3l)4in./5, wher wheree 3l)5 3l)5 denotes either pound mass or pound force As Solid @or"s simulation users& we are spared much confusion and trouble with systems of units !owever& we may be as"ed to prepare data or interpret the results of other ',A software where we do not have the convenience of the unit manager Therefore& we will ma"e some general comments about the use of different systems of units in the preparation of input data for ',A models @e can use any consistent system of units for ',A models& but in practice his choice of the system of units is dictated by what units are used in the CA+ model The system of units in CA+ models is not always consistent? length can be e#pressed in 3mm5, while mass density can be e#pressed in 3kg4m/5.Contrary 3kg4m/5.Contrary to CA+ models& in ',A all units must be must be consistent 9nconsistencies are easy to overloo"& especially when defining mass and mass density& and they can lead to very serious errors 9n the S9 system& which is based on meters 3m5 for length& "ilograms "ilograms 3kg5 for mass and seco second ndss 3s5 for for time time&& all all other other unit unitss are are easil easily y deri derive ved d from from thes thesee basi basicc unit units s 9n mechanical mechanical engineering& engineering& length length is commonly e#pressed in millimet millimeters ers 3mm5 3mm5,, force in -ewton 3*5, and time in seconds 3s5. All other units must then be derived from these basic units. 3mm5, 3*5, and 3s5.Conse)uently 3s5.Conse)uently&& the unit of mass is defined as a mass which& when sub
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'igure $2. Mass densities of aluminum in the three systems of units #omparison of numerical values of mass densities of aluminum defined in this system of units "ith the system of units derived from SI, and "ith the English %I6S' system of units.
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E6. No/ 1
St&%"" anal!"i" o- %am" %Simply supported& Cantilever 0 'i#ed ends(
AIM/
To perform perform displa displacem cement ent and stress stress analys analysis is for the given given beams beams %Simply supported& Cantilever0 'i#ed ends( using solid wor"s simulation and analytical e#pressions P&ol%m D%"&i$tion/
%i( %i( A dis distr trib ibut uted ed loa load d 0 Point Point loa load d will will be be appl applie ied d to a soli solid d stee steell beam beam with a rectangular cross section as shown in the figure %( below The cros cross$ s$se sect ctio ion n of the the beam beam is 1*m 1*mm m # *42m *42mm m whil whilee the the modu modulu luss of elasticity of the steel is *8DPa 'ind reaction& deflection and stresses in the beam
'ig
%ii( %ii( A dis distr trib ibut uted ed loa load d 0 Point Point loa load d will will be be appli applied ed to to a solid solid stee steell beam beam with a rectangular cross section as shown in the figure %*( below The cros cross$ s$se sect ctio ion n of the the beam beam is 38m 38mm m # 188m 188mm m whil whilee the the modu modulu luss of elasticity of the steel is *8DPa 'ind reaction& deflection and stresses in the beam
'ig*
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%iii( %iii( A dist distrib ribute uted d load load 0 Point Point load load will will be appl applied ied to to a solid solid steel steel beam beam with a rectangular cross section as shown in the figure %1( below The cross cross$se $sect ctio ion n of the the beam beam is 35*m 35*mm m # 22m 22mm m whil whilee the the modu modulu luss of elasticity of the steel is *8DPa 'ind reaction& deflection and stresses in the beam
'ig1
P&ol%m #I' Creation of solid model Soli, $a&t 1/
Sketch module0 Open a new part file Kselect the right plane Kselect normal viewK draw rectangular shape Kselect smart dimensions modify the dimensions as 1* F *42 mm
Feature Feature 2odule0 Select the s"etch K select e#truded boss K e#trude with a length 1888mm K o"
Soli, $a&t 7/
Sketch module0 Select the right end face Kselect normal viewK draw rectangular shape Kselect smart dimensions modify the dimensions as 1* F *42 mm
Feature Feature 2odule0 Select the s"etch* K select e#truded boss K e#trude with thic"ness 1888mm K unselect merge component K o"
*
The model must be a solid ob
S"etch K point K Select the top surface K select normal view K locate a point Kselect smart dimensions modify the location of the point as *888 mm from right end K o" Select reference point K select s"etch1 %point( 0 top surface K o"
Analysis the solid solid model
Step by step procedure for the analysis Simulation Module: Module:
;erify that simulation mode is selected in the Add$lns list To start Simulation& Once Solid @or"s @or"s Simulation has been added& Simulation shows in the main Solid @or"s @or"s tool menu Select the simulation Manager tab New Study:
To define define a new study& study& select select -ew Study either either from from the Simulation menu or the Simulation Command Manager @hen a study is defined& Solid @or"s Simulation creates a study window located below the Solid @or"s @or"s 'eature Manager window and places several folders in it 9t 9 t also adds a study tab that provides access to the window window
Static Study: Study:
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To select select static static study study in the study study tab tab Simulat Simulation ion automa automatic ticall ally y creates a study folder with the following sub folders. Static Study& Connections& 'i#tures& Loads& Mesh and eport folder
ight clic" on the Static study $ Treat the solid part 0 * as a beam separately
Apply Materials: Materials:
To apply apply materi material al to the Simulat Simulation ion model& model& right$ right$cli clic" c" the solid solid part folder in the simulation studyK select Apply/,dit Material from the the pop$ pop$up up menu menu K This This acti action on open openss the the Mate Materia riall K Sele Select ct 'rom 'rom library files in the the Select material source areaK Select Alloy Steel
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Calculate the Joints:
To calculate the
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Apply Fixtures: Fixtures:
To define define the 'i#ture%( 'i#ture%( at end AK ight$clic" ight$clic" the 'i#ture 'i#ture folder in Static study K select fi#ed geometry as 'i#ture type K Select the left end end
*3
To define the 'i#ture %*( at end : K ight$clic" the 'i#ture folder in Static Static study K select select fi#ed geometry geometry as 'i#tu 'i#ture re type type K Select Select the right end
Apply loads:
@e now define the load by selecting 'orce from the pop$up menu This action opens the 'orce window The 'orce window displays the portion where point load 0 uniformly distributed distributed load is applied E+L. igh ightt clic clic" " the the load load fold folder er K Sele Select ct forc forces es K select the solid part K select load / m K select the top surface as refer referen ence ce plan planee to repr repres esen entt the the dire direct ctio ion n of the the forc force e This This illust illustrat ration ion also also shows shows symbol symbolss of applie applied d restra restraint int and loadK loadK select the force direction which is normal to the selected reference button in order to load the beam with *8&888 -/m of uniformly distributed load over the selected face K o"
*4
Point Load. igh ightt clic clic" " the the load load fold folder er K Sele Select ct forc forces es K select the reference point K select the top surface as reference plane to represent the direction of the force K select the force direction which is normal to the selected reference button in order to load the beam with *8&888 - of point load on the selected point K o"
*5
Create the mesh:
@e are now now read ready y to mesh mesh the the mode modell K igh ight$c t$cli lic" c" the the Mesh Mesh folder K create mesh Run the analysis: analysis:
ight$clic"s the simulation mode K Select un to start the solution A successful or failed solution is reported and must be ac"nowledged before proceeding to analysis of results @hen the solution completes successfully& successfully& Simulat Simulation ion create createss a esult esultss folder folder with with result result plots plots which which are define defined d in Simulation +efault Options
Results:
@ith the solution completed simulation automatically creates esults folder with several new folders in the study Manager @indow li"e Stress& +isplacement& and Strain 0 +efor formation ,ach folder holds an automatically created plot with its respective type of results The solution can be e#ecuted with different properties Select one of the following analyses you want to see.
Stress distribution +isplacement distribution +eformed shape
*6
Ma"e sure that the above plots are defined in your configuration& if not& define them Once the solution completes& you can add more plots to the esults folder =ou can also create subfolders in the esults folder to group plots To disp displa lay y stre stress ss resu result lts& s& doub double le$c $cli lic" c" on the the Stre Stress ss icon icon in the the esults folder or right$clic" it and select Show from the pop$up menu P&ol%m #ii' 8 #iii'
'ollow the same procedure with re)uired changes
R%"ult/
The analysis of the beam was carried out using the solidwor"s simula simulatio tion n and the softwa software re result resultss were were compar compared ed with with theore theoretic tical al or analytical results
*7
E6. No/ 7
St&%"" anal!"i" o- a R%tanula& $lat% 2it* i&ula& *ol%"
Aim:
To perform displacement and stress analysis for the given rectangular plate with holes using using solid wor"s simulation and analytical e#pressions e#pressions Problem description: description:
A steel plate with 1 holes 1mm& 3mm 0 8 mm respectively is supported and loaded& as shown in figure @e assume that the support is rigid %this is also called built$in support or fi#ed support( and that the *8 tens tensil ilee load load is unifo uniforml rmly y dist distri ribu bute ted d on the the end end face face&& oppo opposi site te to the the supported face The cross section is 3 mm # *3 mm length is 88mm Material %Alloy steel(
T J 3mm +J1mm
+J8mm
+J3mm
! J *3mm
P J *8"Eniformly distributed
L J 88mm
Creation of the solid model usin solid wor!s S!etch module: S"etch%( Open a new part file Kselect the front plane Kselect normal viewK draw rectangular shape Kselect smart dimensions modify the dimensions as 3 F *3 mmK +raw three circles as 1mm& 3mm 0 8 mm with *3mm distance
18
Feature Module:
'eature %( Select the s"etch %N( K Select e#truded boss K e#trude with thic"ness 88mm S!etch module:
S"etch %*( K select the front surface Kselect normal view K +raw three circles as 1mm& 3mm 0 8 mm with *3mm distance Feature Module: 'eature %*( Select the s"etch %*( K select e#truded cut K e#trude with thic"ness 3mm K o"
Analysis of the the solid model Simulation Module: Module: ;erify that simulation mode is selected in the Add$lens list To start Simulation& Once Solid @or"s @or"s Simulation has been added& Simulation shows in the main Solid @or"s @or"s tool menu Select the simulation Manager tab New Study:
To define define a new study& study& select select -ew Study either either from from the Simulation menu or the Simulation Command Manager @hen a study is defined& Solid @or"s Simulation creates a study window located below the Solid @or"s @or"s 'eature Manager window and places several folders in it 9t 9 t also adds a study tab that provides access to the window window Static Study: Study:
To select static study in the study tab Simulation automatically creates a study folder with the following sub folders. Static Study& Connections& 'i#tures& Loads& Mesh and eport folder Apply Materials: Materials:
To apply material to the Simulation model& right$clic" r ight$clic" the part folder in simulation simulation study study and select Apply/,d Apply/,dit it Material Material from the pop$up menu K This action opens the Material K Select 'rom library files in the Select material source areaK Select Alloy Alloy Steel
1
Apply Fixtures: Fixtures:
To define the 'i#turesK ight$clic" the 'i#ture folder in Static study K select fi#ed geometry as 'i#ture type K select the left end face K o"
Apply loads:
@e now define the load by selecting 'orce from the pop$up menu The 'orce window window displays the selected selected face where tensile tensile force is applied applied KSelect use reference geometry K Select the right plane as reference plane to represent the direction of the force K Select the force direction which is normal to the selected reference plane button in order to load the Model with *8&888 - of tensile force uniformly distributed over the end face Create the mesh:
@e are now ready to mesh the model K ight$clic" ight$clic" the Mesh folder K create mesh Run the analysis: analysis:
ight$clic"ing the simulation mode K Select un to start the solution A successful or failed solution is reported and must be ac"nowledged before proceeding to analysis of results @hen the solution completes successfully& successfully& Simulat Simulation ion create createss a esult esultss folder folder with with result result plots plots which which are define defined d in Simulation +efault Options Results:
@ith the solution completed simulation automatically creates esults folder with with seve severa rall new new fold folder erss in the the stud study y Mana Manage gerr @indo indow w li"e li"e Stre Stress& ss& +isplacement& and Strain 0 +efor formation ,ach folder holds an automatically created plot with its respective type of results Stress showing in normal # direction +isplacement showing resultant displacements
To disp displa lay y stre stress ss resu result lts& s& doub double le$c $cli lic" c" on the the Stre Stress ss icon icon in the the esults folder or right$clic" it and select Show from the pop$up menu R%"ult/ The analysis of the rectangular plate was carried out using the solid wor"s simulation and software results were compared with theoretical or analytical values E6. No/ ( St&%"" anal!"i" o- a R%tanula& L B&a9%t 1*
Aim/
To perform displacement and stress analysis for the given rectangular L :rac"e :rac"ett %@ %@all all :rac"e :rac"et( t( using using solid solid wor"s wor"s simula simulatio tion n and analyt analytica icall e#pressions P&ol%m ,%"&i$tion/
An L$shaped brac"et is supported and loaded as shown in figure 1$ @e wish to find the +isplacements and stresses caused by a 3&888 - which is 48 inclined 9n particular& we are interested in stresses in the corner where the 3 mm round edge %fillet( is located Material Drey Cast 9ron 188mm Q 78mm Q 58mm
388838mm
48
Thic"ness 13mm 58mm
Creation of the solid solid model model S!etch module: Open a new part file Kselect the front plane Kselect normal viewK draw the re)uired shape Kselect smart dimensionsK modify the dimensions Kselect fillet mode Kenter radius 3mmKselect the specified edgesKo"
Feature Module: 11
Select the s"etch K select e#truded boss 7 select midplane option K e#trude with thic"ness 53mm S"etch Point. Select the front plane K normal view K draw a line %s"etch *( from the centre of the hole which is 48 inclined to the vertical Select the front plane K locate the intersection point of 48 inclined line 0 s"etch 1 Ko" eference point. Select Select reference reference point geometry geometry K select select s"etch s"etch 1 point point 0 inner surface of the hole K o"
Analysis of the the solid model Simulation Module: Module: ;erify that simulation mode is selected in the Add$lns list To start Simulation& Once Solid @or"s @or"s Simulation has been added& Simulation shows in the main Solid @or"s @or"s tool menu Select the simulation Manager tab New Study:
To define define a new study& study& select select -ew Study either either from from the Simulation menu or the Simulation Command Manager @hen a study is defined& Solid @or"s Simulation creates a study window located below the Solid @or"s @or"s 'eature Manager window and places several folders in it 9t 9 t also adds a study tab that provides access to the window window Static Study: Study:
To select static study in the study tab Simulation automatically creates a study folder with the following sub folders. Static Study& Connections& 'i#tures& Loads& Mesh and eport folder Apply Materials: Materials:
To apply material to the Simulation model& right$clic" r ight$clic" the part folder in simulation simulation study study and select Apply/,d Apply/,dit it Material Material from the pop$up menu K This action opens the Material K Select 'rom library files in the Select material source areaK Select Drey Cast 9ron Apply Fixtures: Fixtures:
12
To define the 'i#turesK ight$clic" the 'i#ture folder in Static study 9n 'i#turesK select fi#ed geometry as 'i#ture type K select the model face %left end face( where 'i#ture is to be appliedK o" Apply loads:
ight$clic" the 'orce folder K Select force K Select the reference point K select the reference plane to represent the direction of the force i n orde orderr to load load the the Mode Modell with with 3888 3888 - of whic which h is 48 48 incl inclin ined ed This This illustration also shows symbols of applied restraint and load Create the mesh:
@e are now ready to mesh the model K ight$clic" ight$clic" the Mesh folder K create mesh Run the analysis: analysis:
ight$clic"ing the simulation mode K Select un to start the solution @hen @hen the soluti solution on comple completes tes succes successfu sfully lly&& Simula Simulatio tion n create createss a esult esultss folder with result plots which are defined in Simulation +efault Options Results:
@ith the solution completed simulation automatically creates esults folder with several new folders in the study Manager @indow li"e Stress& +isplacement& and Strain 0 +efor formation ,ach folder holds an automatically created plot with its respective type of results The solution can be e#ecuted with different properties Stress showing von Misses stresses +isplacement showing resultant displacements
Once the solution completes& you can add more plots to the esults folder =ou can also create cr eate subfolders in the esults folder to group plots To disp displa lay y stre stress ss resu result lts& s& doub double le$c $cli lic" c" on the the Stre Stress ss icon icon in the the esults folder or right$clic" it and select Show from the pop$up menu
R%"ult/
The The anal analys ysis is of the the L $ :rac :rac"e "ett was was carr carrie ied d out out usin using g the the soli solidw dwor or"s "s simu simula lati tion on and and the the softw softwar aree resu result ltss were were comp compar ared ed with with analytical values E6.M E6.Mo. o.4 4 St& St&%"" %"" anal anal!" !"i" i" oo- an an a6i a6i:" :"!m !mm% m%t& t&i i om om$o $on% n%nt nt 13
Aim/
To perform stress analysis for the given a#i$symmetric component P&ol%m ,%"&i$tion/
Creation of the solid solid model model S!etch module: Open a new part file Kselect the top plane Kselect normal viewK draw draw the the rect rectan angu gula larr shap shapee Ksel Kselec ectt smar smartt dime dimens nsio ions nsK K modi modify fy the the dimensions 888mm # 3mm Ko" Select s"etch K draw centre a#is K o" Feature Module: Sele Select ct the the s"et s"etch ch K sele select ct revo revolv lvee 7 sele select ct the the cent centre re a#is a#isK K revolution angle 78 Surface Module: Module: Select surface K mid surface Kselect the two outer faces Ko" ight ight clic" the surface surface model K edit definit definition ion K enter thic"ness thic"ness 3mm K o"
Analysis of the the solid model Simulation Module: Module: New Study:
To define a new study K select -ew Study Kstatic Ko" Static Study: Study:
To select static study in the study tab Simulation automatically creates a study folder with the following sub folders. Static Study& Connections& 'i#tures& Loads& Mesh and eport folder Apply Materials: Materials:
To apply material to the Simulation Simulation model K right$clic" the part 14
folder in simulation study and select Apply/,dit Material Material K Alloy steel K o" Apply Fixtures: Fixtures:
To define the 'i#turesK ight$clic" the 'i#ture folder in Static study 9n 'i#turesK select Advance Advanced d geometry K select select symmetry K select select the end faces %left 0 right end face( where 'i#ture is to be applied K o" Apply loads:
ight$clic" the 'orce folder K Select Pressure K Select the inner surface of the sector K,nter pressure 3Mpa K o" Create the mesh: ight$clic ight$clic" " the Mesh folder folder K create create mesh K select select Automatic Automatic transition Ko" Run the analysis: analysis:
Select un to start the solution Results:
The solution can be e#ecuted with different properties stresses displacements strains
R%"ult/
The analysis of the a#i$symmetric component was carried out using the solidwor"s simulation and the software results were compared with analytical values
15
E6. No/ No/
Mo,% Mo,% -&% -&%;u% ;u%n! n! anal! anal!"i" "i" o- a 7 D om$ om$on% on%nt nt
E6. No/ No/ <
Mo,% Mo,% -&%;u -&%;u%n %n! ! anal!" anal!"i" i" o- %am %am"" #Canti #Cantil% l%%& %&== Sim$l! Sim$l! Su$$o&t%,= Fi6%, %n,"'
16
E6. E6. No/ No/ >
?a&m ?a&mon oni i anal anal!" !"i" i" o- a 7D 7D om om$o $on% n%nt nt
E6. No/ No/ @
T*%&m T*% &mal al "t&%"" "t&%"" anal!" anal!"i" i" o- a 7D 7D om om$on $on%nt %nt
E6. No/ No/
Con,u Con,uti ti%% *%at *%at t&an t&an"-% "-%&& anal anal!"i !"i"" o- a 7D om$ om$on% on%nt nt
AIM:
17
E6. No/ 10
Con%ti% *%at t&an"-%& anal!"i" o- a 7D om$on%nt
28
MATLA: O%&i%2 o- t*% MATLAB Eni&onm%nt
9-TO+ECT9O-.
The The MATL MATLA: A:R R high high$p $per erfo forma rmanc ncee lang langua uage ge for for tech techni nica call comp comput utin ing g integrates computation& visuali>ation& and programming in an easy$to$use envi enviro ronm nmen entt wher wheree prob proble lems ms and and solu soluti tion onss are are e#pr e#pres esse sed d in famil familia iar r mathematical notation Typical uses include Math and computation Algorithm development +ata ac)uisition Modeling& simulation& and prototyping +ata analysis& e#ploration& and visuali>ation Scientific and engineering graphics Application development& 9nclud 9ncluding ing graphi graphical cal user user interf interface ace buildi building ng MATLA MATLA: : is an intera interacti ctive ve syst system em whos whosee basi basicc data data elem elemen entt is an arra array y that that does does not not re)u re)uir iree dimensioning 9t allows you to solve many technical computing problems& especially those with matri# and vector formulations& in a fraction of the time it would ta"e to write a program in a scalar noninteractive language such as C or 'OTA- The name MATLA: stands for matri& la)oratory la)oratory MATLA: was originally writ writte ten n to prov provid idee easy easy acce access ss to matr matri# i# soft softwa ware re deve develo lope ped d by the the L9-PAC and ,9SPAC pro
2
SIMULIN INTRODUCTION/ Simuli Simulin" n" is a graphi graphical cal e#tens e#tension ion to MATLA MATLA: : for modeli modeling ng and simulation of systems 9n Simulin"& systems are drawn on screen as bloc" diagrams Many elements of bloc" diagrams are available& such as transfer functi functions ons&& summin summing g
The idea behind these tutorials is that you can view them in one window while while runnin running g Simulin Simulin" " in anothe anotherr window window System System model model files files can be downloaded from the tutorials and opened in Simulin" =ou =ou will modify and
2*
e#tend these system while learning to use Simulin" for system modeling& control& and simulation +o not confuse the windows& icons& and menus in the the tuto tutori rial alss for for your your actu actual al Simu Simuli lin" n" wind window ows s Most Most imag images es in thes thesee tutorials are not live $ they simply display what you should see in your own Simul Simulin in" " wind window ows s All All Simu Simuli lin" n" opera operati tion onss shou should ld be done done in your your Simulin" windows * 1 2 3
Starting Simulin" Model 'iles :asic ,lements unning Simulations :uilding Systems
Sta&tin Simulin9
Simulin" is started from the MATLA: command prompt by entering the following command. Simulin"
Alternatively& you can hit the Simulin" button at the top of the MATLA: window as shown below.
@hen it starts& Simulin" brings up the Simulin" Library browser browser 21
Open the modeling window with -ew then Model from the 'ile menu on the Simulin" Library :rowser as shown above This will bring up a new untitiled modeling window shown below below
22
Mo,%l Fil%"
9n Simulin"& a model is a collection of bloc"s which& in general& represents a syst system em 9n addi additi tion on to draw drawin ing g a mode modell into into a blan blan" " mode modell wind window ow&& previously saved model files can be loaded either from the 'ile menu or from the MATLA: command prompt =ou can open saved files in Simulin" by entering the following command in the MATLA: command window %Alternatively& you can load a file using the Open option in the 'ile menu in Simulin"& or by hitting CtrlO in Simulin"( filename
The following is an e#ample model window
23
A new model can be created by selecting -ew from the 'ile menu in any Simulin" window %or by hitting Ctrl-( Ba"i El%m%nt"
There are two ma
There are several general classes of bloc"s.
Continuous +iscontinuous +iscrete Loo"$Ep Tables Math Operations erific ation Model ;erification Model$@ide Etilities Model$@ide Ports 0 Subsystems Signal Attributes Signal outing Sin"s. Esed to output or display signals signals Sources. Esed to generate various signals Eser$+efined 'unctions Linear& discrete$time system elements %transfer functions& functions& state$ +iscrete. Linear& space models& etc( Linear Linear.. Linear Linear&& contin continuou uous$t s$time ime system system elemen elements ts and connec connectio tions ns %summing ero >ero to severa severall input input termin terminals als and >ero >ero to severa severall output output terminals Enused input terminals are indicated by a small open triangle Enused output terminals are indicated by a small triangular point The bloc" shown below has an unused input terminal on the left and an unused output terminal on the right
24
Lin%"
Lines transmit signals in the direction indicated by the arrow Lines must always transmit signals from the output terminal of one bloc" to the input terminal of another bloc" One e#ception to this is a line can tap off of another line& splitting the signal to each of two destination bloc"s& as shown below below
Lines Lines can never never in
25
The simple The simple model %from %from the the model files section( files section( consists of three bloc"s. Step& Transfer 'cn& and Scope The Step is a source bloc" from which a step input signal originates This signal is transferred through the line in the direction indicated by the arrow to the Transfer 'unction linear bloc" The Transfer 'unction modifies its input signal and outputs a new signal on a line to the Scope The Scope is a sin" bloc" used to display a signal much li"e an oscilloscope There are many more types of bloc"s available in Simulin"& some of which will be discussed later ight now& we will e#amine
A bloc" can be modified by double$clic"ing on it 'or e#ample& if you double$clic" on the Transfer 'cn bloc" in the simple model& simple model& you will see the following dialog bo#
26
This dialog bo# contains fields for the numerator and the denominator of the bloc"Gs transfer function :y entering a vector containing the coefficients of the desire desired d numera numerator tor or denomi denominat nator or polyno polynomia mial& l& the desire desired d transf transfer er funct functio ion n can can be ente entered red 'or 'or e#am e#ampl ple& e& to chan change ge the the deno denomi mina nato torr to s**s& enter the following into the denominator field. U * V
and hit the close button& the model window will change to the following.
which reflects the change in the denominator of the transfer function The step bloc" can also be double$clic"ed& bringing up the following dialog bo# 27
The default parameters in this dialog bo# generate a step function occurring at timeJ sec& from an initial level of >ero to a level of %in other words& a unit step at tJ( ,ach of these parameters can be changed Close this dialog before continuing The most complicated of these three bloc"s is the Scope bloc" +ouble clic"ing on this brings up a blan" oscilloscope screen
38
@hen a simulatio simulation n is performed& performed& the signal which feeds into the scope will be displayed in this window window +etailed operation of the scope will not be covered in this tutorial The only function we will use is the autoscale button& which appears as a pair of binoculars in the upper portion of the window Runnin Simulation"
To run a simulation& we will wor" with the following model file. simple*mdl +ownload and open this file in Simulin" following the previous instructions for this file =ou should see the following model window
:efore running a simulation of this system& first open the scope window by double$clic"ing on the scope bloc" Then& to start the simulation& either select Start from the Simulation menu %as shown below( or hit Ctrl$T in the model window
3
The simulation should run very )uic"ly and the scope window will appear as shown below below 9f it doesnGt&
-ote that the simulation output %shown in yellow( is at a very low level relat relativ ivee to the the a#es a#es of the the scop scope e To fi# fi# this this&& hit hit the the auto autosc scal alee butt button on %binoculars(& which will rescale the a#es as shown below below
-ote that the step response does not begin until tJ This can be changed by double$clic"ing on the step bloc" -ow& we will change the parameters of the system and simulate the system again +ouble$clic" on the Transfer 'cn bloc" in the model window and change the denominator to 3*
U *8 288V
e$run the simulation %hit Ctrl$T( and you should see what appears as a flat line in the scope window !it the autoscale button& and you should see the following in the scope window
-otice that the autoscale autoscale button only changes the vertical a#is a#is Since the new transfer transfer function has a very fast response& it compressed into a very narrow part of the scope window window This is not really a problem with the scope& but with the simulation itself Simulin" simulated the system for a full ten seconds even though the system had reached steady state shortly after one second To correct this& you need to change the parameters of the simulation itself 9n the model window& select Parameters from the Simulation menu =ou will see the following dialog bo#
31
There are many simulation parameter options? we will only be concerned with the start and stop times& which tell Simulin" over what time period to perform the simulation Change Start time from 88 to 86 %since the step doesnGt occur until tJ8 Change Stop time from 88 to *8& which should be only shortly after the system settles Close the dialog bo# and rerun the simula simulatio tion n After After hittin hitting g the autosc autoscale ale button button&& the scope scope window window should should provide a much better display display of the step response as shown shown below below
32
Buil,in S!"t%m"
9n this section& you will learn how to build systems in Simulin" using the building bloc"s in Simulin"Gs :loc" Libraries =ou =ou will build the following system
'irst you will gather all the necessary bloc"s from the bloc" libraries Then you will modify the bloc"s so they correspond to the bloc"s in the desired model 'inally& you will connect the bloc"s with lines to form the complete system After this& you will simulate the complete system to verify that it wor"s at*%&in Blo9"
'ollow the steps below to collect the necessary bloc"s.
Create a new model %-ew from the 'ile menu or Ctrl$-( =ou will get a blan" model window window
33
Clic" Clic" on the the Library Library :rowser :rowser button button to open the Simulin" Library :rowser Clic" on the Sources option under the e#panded Simulin" title to reveal possible sources for the model
34
+rag the Step Step bloc" from the the sources window window into into the left side of your your model window
35
'rom the Simulin" Library Library :rowser& drag drag the Sum and Dain Dain from Math Operations option found under the Simulin" title
Switch to the Continuous option and drag two instances of the Transfer 'cn %drag it two times( into your model window arranged appro#imately as shown below The e#act alignment is not important since it can be changed
36
later Wust try to get the correct relative positions -otice that the second Transfer 'unction bloc" has a after its name Since no two bloc"s may have the same name& Simulin" automatically appends numbers following the names of bloc"s to differentiate between them
Clic" on the Sin"s option then drag over the Scope icon
37
Mo,i-! Blo9"
'ollow these steps to properly modify the bloc"s in your model
+ouble$clic" your Sum bloc" Since you will want the second input to be subtracted& enter $ into the the list of signs field Close Close the dialog bo# +ouble$clic" your Dain bloc" Change the gain to *3 and close the dialog bo# +oub +ouble le$c $cli lic" c" the the left leftmo most st Trans ransfe ferr 'unc 'uncti tion on bloc bloc" " Chan Change ge the the numerator to U *V and the denominator to U 8V Close the dialog bo# +oub +ouble le$cl $clic ic" " the the right rightmo most st Trans ransfe ferr 'unc 'uncti tion on bloc bloc" " Leav Leavee the the numerator UV& but change the denominator to U * 2V Close the dialog bo# =our model should appear as.
48
Change the name of of the first Transfer Transfer 'unction bloc" by clic"ing on the words Transfer 'cn A bo# and an editing cursor will appear on the bloc"Gs name as shown below Ese the "eyboard %the mouse is also useful( to delete the the e#is e#isti ting ng name name and and type type in the the new new name name&& P9 P9 Cont Contro roll ller er Clic Clic" " anywhere outside the name bo# to finish editing
4
Similarly& Similarly& change the name of the second second Transfer Transfer 'unction bloc" from Transfer 'cn to Plant -ow& all the bloc"s are entered properly =our model should appear as.
Conn%tin Blo9" 2it* Lin%"
-ow that the bloc"s are properly laid out& you will now connect them together together 'ollow these steps
+rag the mouse from the output terminal of the Step bloc" to the upper %positive( input of the Sum bloc" Let go of the mouse button only when the mouse is right on the input terminal +o not worry about the path you follow while dragging& the line will route itself =ou =ou should see the following
4*
The resulting line should have a filled arrowhead 9f the arrowhead is open& as shown below& it means it is not connected to anything
=ou can can cont contin inue ue the the part partia iall line line you you
41
you want to redraw the line& or if the line connected to the wrong terminal& you should delete the line and redraw it To delete a line %or any other ob
+raw a line connecting the Sum bloc" output to the Dain input Also draw a line from the Dain to the P9 Controller& a line from the P9 Controller to the Plant& and a line from the Plant to the Scope =ou =ou should now have the following
The line remaining to be drawn is the feedbac" signal connecting the output of the Plant to the negative input of the Sum bloc" This line is different in two ways 'irst& since this line loops around and does not simply follow the shortest %right$angled( route so it needs to be drawn in several stages Second& there is no output terminal to start from& so the line has to tap off of an e#isting line To tap off the output line& hold the Ctrl "ey while dragging the mouse from the point on the e#isting line where you want to tap off 9n this case& start
42
-ow& -ow& the open arrowhead of this partial line can be treated as an output terminal +raw a line from it to the negative terminal of the Sum bloc" in the usual manner
43
-ow& -ow& you will align the bloc"s with each other other for a neater appearance Once connected& the actual positions of the bloc"s does not matter& but it is easier to read if they are aligned To move each bloc"& drag it with the mouse The lines will stay connected and re$route themselves The middles and corners of lines can also be dragged to different locations Starting at the left& drag each bloc" so that the lines connecting them are purely hori>ontal Also& ad
'inally& you will place labels in your model to identify the signals To place a label anywhere in your model& double clic" at the point you want the label to be Start by double clic"ing above the line leading from the Step bloc" =ou will get a blan" blan" te#t bo# with an editing cursor as shown shown below
44
Type an r in this bo#& labeling the reference r eference signal and clic" outside it to end editing
Label the error %e( signal& signal& the control %u( signal& signal& and the output output %y( signal in the same manner =our final model should appear as.
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To save your model& model& select Save Save As in the 'ile 'ile menu and type in any desired model name Simulation
-ow that the model is complete& you can simulate the model Select Start from the Simulation menu to run the simulation +ouble$clic" on the Scope bloc" to view its output !it the autoscale button %binoculars( and you should see the following
Ta9in 5a&ial%" -&om MATLAB
9n some cases& parameters& such as gain& may be calculated in MATLA: to be used in a Simulin" model 9f this is the case& it is not necessary to enter the result of the MATLA: calculation directly into Simulin" 'or e#ample& suppose we calculated the gain in MATLA: in the variable ,mulate this by entering the following following command at the MATLA: MATLA: command prompt J*3
This variable can now be used in the Simulin" Dain bloc" 9n your Simulin" model& double$clic" on the Dain bloc" and enter the following in the Dain field
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Close this dialog bo# -otice now that the Dain bloc" in the Simulin" model shows the variable rather than a number number
-ow& -ow& you can re$run the simulation and view the output on the Scope The result should be the same as before
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-ow& -ow& if any calculations are done in MATLA: MATLA: to change any of the variables used in the Simulin" model& the simulation will use the new values the ne#t time it is run To try this& in MATLA:& change the gain& & by entering the following at the command prompt J3 Start the Simulin" simulation again& bring up the Scope window& and hit the autoscale button =ou will see the following output which reflects the new& higher gain
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:esi :eside dess varia variabl bles es&& sign signal alss and and even even enti entire re syst system emss can can be e#ch e#chan ange ged d between MATLA: MATLA: and Simulin"
Simulation u"in MAT LAB/ E6No E6No / 1 Simula Simulatio tion n oo- S$&i S$&in n Ma"" Ma"" S!"t%m S!"t%m )&itin Matla Funtion"/ Dam$%, "$&in "!"t%m
9n this e#ample& we will create a Simulin" model for a mass attached to a spring with a linear damping force
A mass on a spring with a velocity$dependant damping force and a time$ depend dependant ant force force acting acting upon upon it will will behave behave accord according ing to the follow following ing e)uation.
The model will be formed around this e)uation 9n this e)uation& GmG is the e)uivalent mass of the system? GcG is the damping constant? and G"G is the constant for the stiffness of the spring 'irst we want to rearrange the above e)uation so that it is in terms of acceleration? then we will integrate to get the e#press e#pression ionss for veloci velocity ty and positi position on earran earrangin ging g the e)uati e)uation on to accomplish this& we get. 5
To build the model& we start with a GstepG bloc" and a GgainG bloc" The gain bloc" represents the mass& which we will be e)ual to 3 @e also "now that we will need to integrate twice& that we will need to add these e)uations together& and that there are two more constants to consider The damping constant GcG will act on the velocity& that is& after the first integration& and the constant G"G will act on the position& or after the second integration Let c J 813 and let " J 83 Laying all these bloc" out to get an idea of how to put them together& we get.
:y loo"ing at the e)uation in terms of acceleration& it is clear that the damping term and spring term are summed negatively& while the mass term is still positive To add places and change signs of terms being summed& double$clic" on the sum function bloc" and edit the list of signs.
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Once we have added places and corrected the signs for the sum bloc"& we need only connect the lines to their appropriate places To be able to see what is happening with this spring system& we add a GscopeG bloc" and add it as follows.
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The values of GmG& GcG and G"G can be altered to test cases of under$damping& critical$damping and over$damping To accurately use the scope& right$clic" the graph and select Autoscale The mdl$file can now be saved The following is a sample output when the model is run for 18 iterations
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E6NO/1< Simulation o- Ai&:on,itionin o- a *ou"%
Air Conditioning of a !ouse. Simulation of oom oom !eater This illustrates how we can use Simulin" to create the Air Condit Condition ioning ing of a house house $ oom oom !eat !eater er This This syste system m depend dependss on the outdoor environment& the thermal characteristics characteristics of the house& and the house house heatin heating g system system The airXcond airXconditi ition onm m file file initia initiali> li>es es data data in the model model wor"space To ma"e changes& we can edit the model wor"space directly or edit the m$file and re$load the model wor"space Opening the Model 9n the MATLA: MATLA: window& window& load the model by e#ecuting the following code %select the code and press '7 to evaluate selection( mdlJYairXcondition8Y? openXsystem%mdl(? The !ouse !eating Model Mo,%l InitialiGation InitialiGation @hen the model is opened& opened& it loads loads the informatio information n about the house house from the airXconditionm airXconditionm file The M$file does the following. following. +efines the house geometry %si>e& number of windows( Specifies the thermal properties of house materials Calculates the thermal resistance of the house Provides the heater characteristics %temperature of the hot air& flow$ rate( +efines the cost of electricity %s288/"@hr( Specifies the initial room temperature %8 deg Celsius J 38 deg 'ahrenheit( -ote. Time is given in units of hours Certain )uantities& li"e air flow$rate& are e#pressed per hour %not per second( Mo,%l Com$on%nt" S%t Point 54
Set Point is a constant bloc" 9t specifies the temperature that must be maintained indoors 9t is set at 64 degrees 'ahrenheit which is e)ual to 18 degrees Centigrade :y default default Temperatures emperatures are given given in 'ahrenheit& 'ahrenheit& but then are converted to Celsius to perform the calculations T*%&mo"tat Thermo Thermosta stat t is a subsys subsystem tem that that contai contains ns a elay elay bloc" bloc" The thermostat allows fluctuations of 3 degrees 'ahrenheit above or below the desi desired red room room temp tempera eratu ture re 9f air air temp temper erat atur uree drop dropss belo below w 6 degr degree eess 'ahrenheit& the thermostat turns on the heater @e can see the Thermostat subsystem by the following command in MATLA: MATLA: Command window openXsystem%Umdl&G/ThermostatGV(? ?%at%& !eater !eater is a subsystem subsystem that has a constant constant air flow rate& Mdot& Mdot& which is specified in the airXconditionm M$file The thermostat signal turns the heater on or off @hen the heater is on& it blows hot air at temperature T!eater %38 degrees degrees Celsius Celsius J ** degrees degrees 'ahrenheit 'ahrenheit by default( default( at a constant flow rate of Mdot %"g/sec J 1488"g/hr by default( The heat flow into the room is e#pressed by the ,)uation ,)uation . %dZ/dt( J %T heater [ Troom(\Mdot\c where c is the heat capacity capacity of air at constant pressure pressure @e can see the !eater !eater subsystem subsystem by the following following command command in MATLA: MATLA: Command window openXsystem%Umdl&G/!eaterGV(? Co"t Calulato& Cost Calculator is a Dain bloc" Cost Calculator integrates the heat flow over time and multiplies it by the energy cost The cost of heating is plotted in the Plotesults scope ?ou"% !ouse is a subsystem that calculates room temperature variations 9t ta"es into consideration consideration the heat flow flow from the heater and heat losses to to the environment !eat losses and the temperature time derivative are e#pressed by ,)uation * ,)uation * %dZ/dt(loss J%Troom [ Tout( / e) wher wheree e) is the e)uiv e)uival alen entt ther therma mall lossees resistance of the house 55
@e can see the !ouse !ouse subsys subsystem tem by the follow following ing comman command d in MATLA: Command window openXsystem%Umdl&G/!ouseGV(? Mo,%lin t*% Eni&onm%nt @e model the environment as a heat sin" with infinite heat capacity and time varyin varying g temper temperatu ature re Tout Tout The constant constant bloc" Avg Avg Outdoo Outdoor r Temp specifies the average air temperature outdoors The +aily Temp ;ariation ariation Sine @ave bloc" generates generates daily temperatur temperaturee fluctuatio fluctuations ns of outdoor temperature @e can vary these parameters and see how they affect the heating costs Runnin t*% Simulation an, 5i"ualiGin t*% R%"ult" @e can run the simulation and visuali>e the results Open the Plotesults scope to visuali>e the results The heat cost and indo indoor or vers versus us outd outdoo oorr temp temper erat atur ures es are are plot plotte ted d on the the scop scope e The The temperature outdoor varies sinusoidally& whereas the indoors temperature is maintained within 3 degrees 'ahrenheit of Set Point Time a#is is labeled in hours evalc%Gsim%mdl(G(? openXsystem%Umdl G/PlotesultsGV(& emar"s This particular model is designed to calculate the heating costs only only 9f the temperature of the outside air is higher than the room temperature& the room temperature will e#ceed the desired Set Point] P oint]
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E6NO/ 1> CAM an, FOLLO)ER SYSTEM A cam and follower system is system/mechanism that uses a cam and follower to create a specific specific motion The cam is in most cases merely merely a flat piece of metal that has had an unusual shape or profile machined onto it it This cam is attached to a shaft which enables it to be turned turned by applying applying a turnin turning g action action to the shaft shaft As the cam rotates rotates it is the profile or shape of the cam that causes the follower to move in a particular way The movement of the follower is then transmitted to another mechanism or another part of the mechanism
,#amining the diagram shown above we can see that as some e#ternal turning force is applied applied to the shaft %for e#ample. by motor or by hand( hand( the cam rotates with it The follower is free to move in the = plane but is unable to move in the other two so as the lobe of the cam passes the edge of the follower it causes the follower to move up up Then some e#ternal downward downward force %usually a spring and gravity( pushes the follower down ma"ing it "eep contact contact with the cam This e#ternal e#ternal force is needed needed to "eep the follower follower in contact with the cam profile +isplacement +iagrams. +isplacement diagrams are merely a plot of two different displacements %distances( These two dispalcements are.
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the distanc distancee travelled travelled up or or down by by the followe followerr and * the angula angularr displaceme displacement nt %distance( %distance( rotated rotated by by the cam cam
9n the diagram shown opposite we can see the two different displacements represented by the two different arrows The green arrow representing the disp displa lace ceme ment nt of the the foll follow ower er ie ie the the dist distan ance ce trav travel elle led d up or down down by the the follow follower er The mustard mustard arrow arrow %curve %curved d arrow( arrow( shows shows the angula angularr displa displacem cement ent travelled by the cam
-ote. Angular displacement displacement is the angle through which the cam has rotated rotated 9f we e#am e#amin inee the the diag diagra ram m show shown n belo below w we can see see the the rela relati tion onsh ship ip betw between een a disp displa lace ceme ment nt diagr diagram am and and the the actua actuall prof profil ilee of the the cam cam -ote -ote only only half half of the the displacement diagram is drawn because the second half of the diagram is the same as the first The diagram is correct from a theoretical theoretical point of view but would have to changed slightly if the cam was to be actually made and used @e will consider this a little more in the the following section $ Eniform ;elocity ;elocity
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Eniform ;elocity. Eniform ;elocity means travelling at a constant speed in a fi#ed direction and as long as the speed or direction donGt change then its uniform velocity 9n relati relation on to cam and follower follower systems& systems& unifor uniform m veloci velocity ty refers refers to the motion of the follower -ow letGs consider a typical displacement diagram which is merely a plot of two different displacements %distances( %distances( These two displacements displacements are. the distanc distancee travelled travelled up or or down by by the followe followerr and * the angula angularr displacem displacement ent %distanc %distance( e( of the the cam Let us consider the case of a cam imparting a uniform velocity on a follower over a displacement of 18mm for the first half of its cycle @e shal shalll ta"e ta"e the the cycl cyclee in step steps s 'irs 'irstl tly y if the the cam cam has has to impa impart rt a displacement of 18mm on follower over half its cycle then it must impart a displacement of 18mm^68 for every turned by the cam ie it must move the followe followerr 845mm 845mm per degree degree turn This distance distance is to much much to sma small to draw raw on a disp isplac lacemen ementt dia diagram gram so we will will cons onside ider the the displacement of the follower at the start& at the end of the half cycle& the end of the full cycle and at certain other intervals %these intervals or the length of these intervals will be decided on later( Anl% t*% am &otat%, t*&ou* Sta&t o- t*% C!l%
8
8mm
En, o- -i&"t ?al- o- t*% 68 C!l% En, o- t*% Full C!l%
*a" Di"tan Di"tan% % mo%, mo%, ! t*% t*% -ollo2%&
18mm
148
8mm
@e shall consider this in terms of a displacement diagram. 'irst we will plot the graph :efore doing this we must first consider the incr increm emen ents ts that that we will will use use @e will will use use mill millim imet eter erss for for the the follo followe wer r displacement increments and because is too small we will use increments of 18 for the angular displacement
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Once this is done then we can draw the displacement diagram as shown below below -ote a straight line from the displacement of the follower at the start of the motion to the displacement of the follower at the end of the motion represents uniform velocity velocity Di"$la%m%nt Dia&am -o& Uni-o&m 5%loit!
Simple !armonic Motion. 'or this type of motion the follower displacement does not change at a constant rate 9n other words the follower doesnGt travel travel at constant speed The best way to understand this non$uniform motion is to imagine a simple pendulum swinging
Eniform Acceleration and etardation. This motion is used where the follower is re)uired to rise or fall with uniform acceleration& that is its velocity is changing at a constant rate To conclude this. A cam can impart three types of motion on its follower. Eniform velocity
Simple harmonic motion
Eniform acceleration and retardation
,ach of these motions can be represented by a displacement diagram
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Simply supported beam.
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