Getting Started Using Universal Mechanism
Contents
1. F FO c xD d y sin arta FO Jo Figure 2 4 Elastic and damping joint forces Universal Mechanism 4 0 38 Getting Started 2 3 6 Visualization of spring and damper After all we have completely described object from the mechanical point of view We described all elements we need rigid bodies Joints and force elements However our model now looks not so good spring and damper introduced as Joint forces that cannot be visualized see the Fig 2 5 left In order to visualize spring and damper we will create two bipolar forces in the model Their values we set to zero That 1s why these bipolar forces will not influence on the dynamics of the model but give us a possibility to show the spring and the damper see the Fig 2 5 right ane ERT a E EM REN WW Figure 2 5 Visualization of forces Note There are several possible ways to describe elastic and damping forces in our model We used the way to describe them as joint forces but it 1s not the only right way We could introduce them as bipolar as well And in this latter case we would visualize them and introduce forces at once without intricate describing additional fake bipolar forces But such a way leads to a following problem Our ideal case that we consider here allows to model the situation when the length of the spring and damper equal to zero Imagine that the brick has so large amplitude that the attachment points of the spring and damper will be2. Universal Mechanism 4 0 17 Getting Started 1 3 7 Preparation for simulation Program package Universal Mechanism UM consists of two programs UM Input program UMInput exe and UM Simulation program UMSimul exe The UM Input is used for creating objects generating their equations and compiling them with the help of an external compiler As a result you have got a dynamic linked library UmTask dll containing equations of motion of your object The DLL is always located in the object directory When DLL of the object exists a model 1s ready for simulation Now we should generate and compile equations of motion and start UM Simulation for dynamical analysis of the system Paths to external compilers Universal Mechanism supports using Borland Delphi Borland C Builder Microsoft Visual C as external compilers 1 Select Tools Options menu item Your further actions depend on what external compiler you are going to use Delphi 2 Select Paths Delphi tab 3 Click Search Delphi button Borland C Builder Microsoft Visual C 2 Select Paths C tab 3 Click one of the following buttons Search Visual C or Search Borland C Builder depending on which C compiler is installed on your PC If UM successfully detects external compiler all paths are set automatically Universal Mechanism 4 0 18 Getting Started Generating and compiling equations of motion 1 Select Object Generate equations If your description of the
3. It assumes that you go through the manual step by step sequen tially simulation of such mechanical systems as cars and railway vehicles has cer tainly its own features but basic concepts using UM still the same These concepts are shown in this manual Contact information Universal Mechanism demo version you can download using the following link http www umlab ru um40demo exe The latest UM version as well as up to date UM user s manual available at http www umlab ru download htm Please send you bug report questions and suggestions to um umlab ru Address Russia 241035 Bryansk bulv 50 let Oktyabrya 7 Bryansk State Technical University Laboratory of Computational Mechanics Prof Dmitry Pogorelov Phone fax 7 4832 568637 Universal Mechanism 4 0 d Getting Started 1 Model of a pendulum 1 1 What we will learn This lesson shows you how to create new model add rigid bodies and joints generate and compile equations of motion simulate dynamics of a model and ob tain plots of various performances of the model This lesson 1s devoted to general overview of the UM possibilities and workflow At the end of the lesson we will have the model of the pendulum you can find the final model in the fum root Xutorial eng pendulum directory which will include one rigid body pendulum itself one rotational joint and graphical object of the environment support After describing the model we will go through
4. a set of graphical objects GO of the elements of the model 1 3 3 1 Scene image Creating new graphical object scene Scene is a graphical object corresponding to fixed elements of the object De scribing the scene 1s optional To create a scene you should make a usual graphical object and assign it to the scene image As for our example it is an image of the fixed joint where the pendulum is attached to support In order to create the cor responding image you should do the following steps 1 Point to Images element of Tree of elements 2 Click 2 button in the top of the Inspector to create new graphical object see Figure 3 Biel Es x Add new graphical object Figure 3 Adding a new element Note You can add new element of any type in the same way Universal Mechanism 4 0 8 Getting Started Renaming the graphical object As you create objects UM automatically assigns names to them Each name consists of a string containing the element type and a unique integer ID for that type UM named the recently created graphical element GO1 1 Point to the field with the name of the element and replace GO1 with Sup port see Figure 4 Support Support Name of graphical object Delete graphical object Copy graphical object Add graphical element Figure 4 Renaming the graphical object Universal Mechanism 4 0 9 Getting Started Creating graphical elements Every graphical ob
5. model is correct the corresponding dialog box ap pears If your model description 1s not correct then tab Summary which contains all detected errors appears 2 Select Compile equations 3 Click Generate button If generating and compiling equations of motions end successfully you ll see the message box Compiling successful Object is ready for simulation The model is ready to be loaded in the UM Simulation program Run UM Simulation program 1 Select Object Simulation menu item UM Simulation program starts and opens the current model Universal Mechanism 4 0 19 Getting Started 1 4 Simulation of the motion Now we are in the simulation program We will open new animation window deflect the pendulum from vertical position to 1 radian and run simulation of dy namics of pendulum Creating new animation window 1 From the Tools menu select Animation window New animation window appears Familiarize yourself a bit with animation window Rotating Point the mouse cursor to the animation window so that cursor looks like the picture in the figure to the right Press left mouse button and rotate the de model in the animation window shifting Point the mouse cursor to the animation window so that it has Rotating shape press Ctrl key and mouse cursor changes to Shifting mode Press left e mouse button and shift model in the animation window Zoom in zoom out Point the mouse cursor to the animation window and press S
6. on the same level In such a case we have degeneration of bipolar forces that act along the line between the attachment points When we have zero length we could not find the direction of the bipolar forces Joint forces have no such a degeneration because they direction always coincide with the axis of the Joint That is why we used very joint forces here Universal Mechanism 4 0 Getting Started 1 So select the Bipolar force in the tree of elements 2 Add two bipolar force elements Set their parameters as it is shown in the Fig 2 6 FictitiousSpring FictitinusD amper Mame FictitieusSpring OX e Comments Top E rick E pression pring Autodetection Attachment point Length U4 Description of fore PFascal L expression F F x47 t Example EstifP xU ediss v ampl sin om t F n FictitiousLD amper FictitiousS pring Mame FictitieusD amper X e Comment Top Brick Expression Damper Autodetection Attachment point Length U 4 Description of fore Fascal L expression F F x t E sample Estif P is 40 ediss v eampl sin am t Flo E Figure 2 6 Fictitious bipolar forces Universal Mechanism 4 0 40 Getting Started 2 3 7 Additional parameters Using UM you can express one parameter via others Here we will add two new parameters in the model accurate analytical values of the natural frequency and t
7. E position Material Box Box 44 S D 1 GE position Material Parameters Color 4 0 2 r B Jaz C C a2 Discretization t Universal Mechanism 4 0 30 Getting Started Boe x Spring Now we will create the graphical object for the spring Create new graphical object set its name to Spring Add new graphical element Spring Set Spring parameters as it 15 shown below Description Gd position Spring GE position Material Parameters Color Radius 0 07 C Height 1 d bar 0 02 C Humber of coils b Coil discretization 0 Bar discretization 10 Universal Mechanism 4 0 31 Getting Started Aa U N e Damper Now we come to the last graphical object in this model damper Create new graphical object Set its name to Damper Add new graphical element for the Damper Cone Set parameters as follows R2 0 02 R1 0 02 h 1 Select the Color tab and choose blue for diffuse and specular colors 6 Add one more Cone with the following parameters R2 0 04 R1 0 04 h 0 5 In the GE Position tab set Translation Z to 0 25 Select red diffuse and specular colors Universal Mechanism 4 0 32 Getting Started peu I 2 3 3 Creating rigid bodies Top Create new rigid body Top Add new rigid body Set its name to Top In the Image list select Top Leave Mass and Inertia tensor empty F Top Mame Top a
8. Elipsoid Cone Box Parameters Color GE position I aterial Figure 6 Graphical element position Universal Mechanism 4 0 12 Getting Started Assigning Support as scene image 1 Point to Object item of Tree of elements 2 Select Support in the field Scene image General Hall vehicle Support Universal Mechanism 4 0 13 Getting Started 1 3 3 2 Image of pendulum 1 Return to the Images item in the Inspector 2 Create new graphical object 3 Rename new graphical object to Pendulum Note Do not forget to press Enter after any modification of the text data in order to reflect this The pendulum image consists of two graphical elements an ellipsoid and a cone 4 Add new graphical element Ellipsoid and set its parameters a 0 05 b 0 2 c 0 2 Set diffuse color to blue 5 Add new graphical element Cone and set its parameters R2 0 03 R1 0 03 h 1 Set diffuse color to blue Now image of the pendulum is ready Universal Mechanism 4 0 14 Getting Started 1 3 4 Creating rigid bodies The pendulum as a mechanical system consists of the only body eS de 9 Point to the Bodies item in the Inspector Create new body Rename body to Pendulum Select Pendulum from the drop down list Image set Mass 1 kg Pendulum Mame Pendulum Oriented points Parameters To element Image Pendulum Compute automatic Inertia parameter Mass In
9. Universal Mechanism 4 0 1 Getting Started GETTING STARTED USING UNIVERSAL MECHANISM 2 t MODEL OF Ay PENDUEUDJ 12 028 0 09 0901590522016 92169 0 Aaaa Inc biu Er FF Erian SEn arsi 3 LL VV AE We Wall GEI p nr RR ODE R a ISIN SPON VIP ce oU eS 3 IEEE EDI C C C C UU T M 4 Pe ME P iii adunume 5 1 3 1 Running UM Input and creating new model eeeeeeeeeeeeeseseeeeeee 5 1 3 2 Familiarizing yourself with Universal Mechanism esses 5 1 5 5 Crea nb SrapBicab ODICCIS E AE NI MP A E S 7 1 3 3 1 DCEDC Id SE Loose deitatem nee eee ee ee ecd n 7 1 3 3 2 Poso or pen ceo Sieht ret eee nae ni M IINE MEME UM MEM MUI 13 1 3 4 CHI CE DOGS S oot tas asec nee nes pn nes one ees cat peas ores amas mae De D eres oe 14 1 3 5 cu AM oi arse cca cnet T UU 15 1 3 6 VT AO SN ERROR ERROR ET 16 E35 Proar On FOr Sinha Olt a corse eese boe ESU YHP nance santsiepeeasenaeansesieyen par ERUDS IRURE SEU EEE 17 LA iunulati n OF TNE HOO ues race eso EY Yi 20D Eu E ovo daa e p P YE Ye ease ER EH EE aae e Soy as i 19 iP EE LE s iusti rc n 25 2 FREE AND FORCED OSCILLATIONS 1 ee eere eere nennen nnn 26 LEER LUE SUE ymP 26 Date Modil Se MeO reri eio oboe 00001900 E E E E 26 2 5 amp re
10. ariable appears in the container of variables Drag the vari able to the graphical window Close the Wizard of variables 5 From menu Analysis select Simulation The Object simulation inspector ap pears 6 Arrange windows on the desktop as you prefer for example as it is shown in the Fig 2 7 a UM Simulation d um40 tutorial oscillator el ES imati indo ct i bi Ef i e t e Se e E Ss KVA E Information Tools Identifiers Initial conditions Simulation process parameters Solver options Solve Type of solvin e P je Null Space Method C Pak C Gear Range Space Method Simulation time 10 000 Step size for animation and data storage 02 Frrartalerance n nm Fl 0 0 2 0 4 0 6 0 8 1 Ranges are not used Figure 2 7 Desktop of the simulation program Universal Mechanism 4 0 44 Getting Started 7 Select the Object simulation inspector and click the Identifiers tab 8 Set a to 0 and press Enter So we set zero amplitude of the oscillations of the Top body in other words we fix the Top in order to analyze free oscillations Object simulation inspector Object variables MB Information Tools Solver Identifiers Initial conditions e rH Whole ist Mame Expression Value Comment 10 I 10 250 U4 10 sqi cm z Natural frequency mu star 2 sqrtim c 100 Critical damping coefficient Integration Figure 2 8 Parameters of the model Universal Mechan
11. auno the MOO CE oa oc cose ccdecececeecsscesasasesscetseasswasesccsaciesssesssasessecsotnsncesecccsaciessssssiasessecseises 27 2 91 Running UM Input and creating new model essssseeeeeeeeeennenne 2 2 3 2 Crane Ch AP IC Al DIS CIS sses opti oec iUnd TeEdpPIS o cube oes oie UosIS ES 28 2 9 5 Crede dro IO DOE a escena eed eu p caris td ss acceceosaceee det ss pias isse ad odes ceoueca Iud css n eo eau dE 32 2 3 4 CEC ATI OMA NENNEN NT 34 2 90 Creating force elements 00 0 cccccccccsssesssseseeeeeeccceceeeeeeeeeeeaaaeeeeseseeeeeeeeeeeeeeeeeeeeaaaaas 37 2 3 6 Visualization of spring and damper esos ne rta riri ora den onare Era ie 38 2 957 PCI TA At AUC SIS oper oN toS E RR NS 2G ONE rtr St Eti oru upPaR RN E 40 2 949 Preparation for simulation esssssssseeeseeeeeseeeene nnne eene enne nnne ness nnns 42 Zee Simu lafion ofthe MONON E 43 2 4 1 Dice ose ouescacetem to E Mines UMEN eU Ue 43 2 4 2 WIE BIS BTers E VISA e ETT T TETUR 49 2 4 3 IE ATA YI PE s 50 2 4 4 For er ose aO eere E E E E EE eo E 32 3 SUBSEQUENT STUDYING UNIVERSAL MECHANISM 54 Universal Mechanism 4 0 2 Getting Started Getting Started Using Universal Mechanism This manual leads you through the basic possibilities of Universal Mechanism software and shows you how to create and simulate models of several simple me chanical systems
12. c one again use the Copy as static variable item from the context menu 2 Select the Pause inspector and click the Interrupt button Object simulation inspector appears 3 Select the Identifiers tab and set mu 100 4 Click Integration Now you can see that the motion of the brick 1s non periodic see the Fig 2 11 lx TULIT rz Brick Coo Mi rz Brick Coo 10 rz Brick Coo ee HEBEL UR UR RR ERR REI il QUEDA Ex 1 Ey 1 Ranges are not used Figure 2 11 Graphical window after three numerical experiments 5 Make numerical experiments for other values of the damping coefficient Do not forget to copy variables as static ones 6 If you changed the value of the damping coefficient set it again to mu 100 Ns m Universal Mechanism 4 0 49 Getting Started 2 4 2 Statistical analysis Now we will come through some additional tools for analysis of results of the simulation 1 From the Tools menu select Statistics New Statistics window appears 2 Drag the variable which corresponds to free oscillations from the graphical window to the Statistics window 3 Select the Statistics window and point to Power spectral density The characteristic shape of the power spectral density shows the process has the only frequency which corresponds to natural frequency We have the accurate ana lytical solution 5 rad s Not let us obtain this frequency numerically from the plot of the power sp
13. dulum3 4 Select Joints and copy the joint two times too 5 Change the connecting bodies Pendulum and Pendulum for the second joint Pendulum2 and Pendulum for the third one Note Use the amp button in the top of the animation window to switch the mode of window Full object Single element Generate and compile equations of motion Run UM Simulation Create a new animation window P SS Select the Analysis Simulation menu item 10 Seta proper initial position of the chain with the help of the Initial condi tions tab 11 Click Integration to run the simulation Universal Mechanism 4 0 26 Getting Started 2 Free and forced oscillations 2 1 What we will learn In this lesson we will learn how to add forces preset movement of a body as a time function and use parameterization of a model We will use Linear analysis for obtaining the equilibrium position of a system natural frequencies and forms As well as we will analyze the spectrum of output data using the Statistics tool 2 2 Model scheme The example of simulation of free and forced damped oscillations 1s considered In this lesson we will create the model shown in the Fig 2 1 Model consists of two rigid bodies Top and Brick two translational joints a linear spring and a damper We will set vertical coordinate of the upper body as a sinusoid function You can find the final model in the tum root tutorial oscillator directory or download it using the fol
14. ectral density see the Fig 2 12 It 1s approximately 0 78 Hz see abscissa in the left bottom corner 0 78 Hz gives us 0 78 2a 4 9 rad s You can see that numerically obtained values are quite close to analytical one Note To pick the frequency more precisely use changing scale of the window as it 15 shown in the Fig 2 12 Ee Statistics spectral estimations Warables Histagram Integral law Correlation functor a r2 Brick Co Power spectral density Spectrum module Spectrum phase Statistics 0 7805 0 03411 E Figure 2 12 Power spectral density of the free oscillations Universal Mechanism 4 0 50 Getting Started 2 4 3 Linear analysis Let us consider an example of using the Linear analysis With the help of this tool we will find the equilibrium position of the system its natural frequencies and forms define how much the actual damping ration relative to the critical one Well at first you need to close Pause and Object simulation inspector win dows 1 Select the Pause windows and click Interrupt 2 Select the Object simulation inspector and click Close Open Linear analysis window 3 From the Analysis menu select Linear analysis The Linear analysis window appears Equilibrium position 4 In the Linear analysis window select the Equilibrium tab Click the Compute button You can see the message Equilibrium position is successfully com puted The brick in the animati
15. ersal Mechanism constructor window see Figure 2 Tree of elements of a model in the left top corner of the constructor window 1s used for getting access to elements of the model Animation window in the center shows the model or its elements A frame is shown in the center of animation window There is the following identification for axes Red X Green Y Blue Z RGB Point of view zoom and other settings can be changed via toolbar buttons Using the context menu you can set perspec tive parameters supporting grid etc Inspector at the right hand side of the constructor is the main tool for the de scription of elements It shows parameters of an active element It contains full in formation about current element of the model MBS means multibody system Universal Mechanism 4 0 6 Getting Started UM Object data input Um bj Fie bject Tools Edit Help LI Component Car wwhesls A os xii BXe AA X UmObjo Pile E x l T d Een em 8 Ef e E e e x Object Options Animations eT E Path D SLM AOST utoral UmObj0 Comment Type of objec UMS f General um eS Rail vehicle OO PSSOSOS OS oec Jo Sq widow PSS ae os im in Figure 2 Constructor window Universal Mechanism 4 0 y Getting Started 1 3 3 Creating graphical objects We recommend to start describing any mechanical system with creating
16. ertia tensor Added mass matrix T Coordinates of center of mas Universal Mechanism 4 0 15 Getting Started 1 3 5 Creating joints The rotational joint connects the Pendulum and the Base0 To create new joint do the following actions 1 Point to Bodies Pendulum 2 Click the button Adjust joint and select Rotational joint in the context menu After that the rotational joint is created and named as jPendulum automatically Joint points and joint vectors describe the position of the rotation axis relative to each of the bodies Their coordinates must be given in the corresponding body fixed systems of coordinates 3 In the fields Joint points Pendulum set Z position to 1 So the pendulum will swing around its upper point iFendulurn Mame iPendulum Based Pendulum Rotational GO none w eight O A NDOF 2 1 In tree Geometry Description Joint fa Y Y component Joint points Basel h re RT a A vectors Basel aris 1 0 0 n p T o Pendulum axis X 1 0 1 no p qp Universal Mechanism 4 0 16 Getting Started 1 3 6 Saving the model Now your model is described completely And it 1s high time to save it Let the object name be Pendulum 1 Select menu item File Save as 2 Set Path to UM Path Pend in the way how it is shown in the figure be low Save as Path including object name D UM404M tModels Pend E l E L ancel
17. graphical window Point to the r z Brick variable in the list of vari ables Open context menu Select the Copy as static variable menu command The second variable appears 2 Select the Pause inspector and click the Interrupt button Object simulation inspector appears Note The r z Brick variable which we dragged from the Wizard of vari ables will be recalculated for every numerical experiment It 1s so called dynamic variable In order to compare plots for different ex periments we need to copy dynamic variables as static ones Static vari ables are not changed from one experiment to another 3 Select the Object simulation inspector and point to the Identifiers tab 4 Set mu 0 and press Enter So we have just turned off damping Universal Mechanism 4 0 47 Getting Started 5 Click the Integration button It will take you some seconds to finish the simulation In the Fig 2 10 you can see the graphical window after two numerical experiments l Plots zialx VARI LAU Vil rz Brick Coo Vil rz Brick Coo ill T Ex 1 Ey 1 Ranges are nat used Figure 2 10 Graphical windows after the first experiment Universal Mechanism 4 0 48 Getting Started Free oscillation critical damping As we showed above critical damping coefficient is mu 100 Ns m Let us analyze the motion of the Brick in such a case 1 Point to the graphical windows Select the first variable r z Brick and copy it a stati
18. he critical damping coefficient Our model is very simple that is why we can ob tain analytical solutions easily Natural frequency can be obtained according to the following formula k where k natural frequency rad s c stiffness coefficient N m m mass of the body kg Critical damping coefficient can be found as u 22 cm where Uu critical damping coefficient Ns m 1 Well add new identifiers parameters to our model Click the E button in the list parameters or select the New identifier menu command from the context menu Edd from subsystems Insert identifier Shift Ins Edit identifier Delete identifier Del Copy value to clipboard Ctrl C Mew sheet Rename tab Page identitier list Delete tab Pelete sheet Universal Mechanism 4 0 41 Getting Started 2 Fill out the Add identifier form as it 1s shown in the figure below Add identifier x MH ame lk Expression sattic m Comment Natural frequency Cancel 3 Add one more identifier mu star 2 sqrt c m It is a critical damping coef ficient Universal Mechanism 4 0 42 Getting Started 2 3 8 Preparation for simulation 1 Save the model as Oscillator use menu command File Save as 2 From the Object menu select the Generate equations item New dialog box appears Turn on the Compile equations check box 3 Click the Generate button Deriving and compiling of equations Pa
19. hift key and q with the help of left mouse button zoom in out the model After some practice you can get something like shown in the figure below zs Animation window OF x i amp E 9 986 9 ss p AC Au p Q MH Fe O D E J ER nT nrc me p un o Universal Mechanism 4 0 20 Getting Started Start simulation l From the Analysis menu select Simulation Window of the Object simulation inspector appears Object simulation inspector Object variables PM Information Solver Initial conditions Solver options Type of salvin Null Space Method C Gear Range Space Methad Simulation time 10 000 Step size for animation and data storage 0 02 Error tolerance 0 001 Integration Universal Mechanism 4 0 21 Getting Started Initial conditions You should deflect the pendulum a bit in order to obtain its motion There ex ists a special tool for this purpose a wizard of the initial conditions 1 Select the Initial conditions tab You can see a complete list of the object coordinates In our case there 1s only one coordinate in jPendulum joint 2 Set Coordinate to 1 Press Enter key Your pendulum has deflected Note Universal Mechanism uses System International SI Angular values have dimensions of radian p an erat iolx di t C PU Object variables AMA Information Solver Initial condi
20. in the resonance case the amplitude of the os cillations increases in the long run see the Fig 2 14 I Plots ES x ra rz Brick Coo Ex 1 Ey 1 Ranges are not used Figure 2 14 Forced oscillations resonance case Universal Mechanism 4 0 54 Getting Started 3 Subsequent studying Universal Mechanism You have come through two examples of dynamical systems pendulum and sprung body and have seen the basic tools and features of the UM Base version The Getting Started series includes other manuals that devoted to the rest mod ules of the Universal Mechanism Here they are e Getting Started simulation of road vehicles e Getting Started railway vehicle dynamics e Getting Started Matlab Simulink interface e Getting Started optimization module e Getting Started elastic bodies with UM FEM Library of simple models how to The Part 7 of the UM User s Manual is devoted to consideration of simple models that show you how to create model various graphical elements joints and force elements Studying these examples helps you familiarize yourself with basics of Universal Mechanism and approaches for simulation of objects of different kind The library of models is in the tum root Mibrary directory The part7 pdf you can find in the fum root manual directory or download using the following link http www umlab ru download docs eng part7 pdf
21. inate in this Joint as a time function 1 Select the Top body in the tree of elements 2 Click the amp button Select Create joint and in the drop down list select Trans lational see the Fig 2 2 left The new joint of this type is created Now you can see parameters of the joint 3 Select the Geometry tab and set joint parameters as it is shown in the Fig 2 2 right x g Brick e MH ame Top 4h Ex Hame iTop mT Comments B i o x op 1 Translational fan none Oriented points Vectors Geometry Description Joint force Parameters Points Ta element Rotational Create joint P Translational General Quaternian Coordinates of center af mass Figure 2 2 Creating translational joint Universal Mechanism 4 0 aD Getting Started 4 Point to Description tab 5 Turn on the Prescribed function of time check box 6 Set the Type of description to Expression and then input a sin omega t see the Fig 2 3 and press Enter Top Mame iTop my Basel Top Translational fan none Geometry Description Configuratio Rotation 0 000000000000 KA Translation 0 QO0000000000 t Joint coordinat If Prescribed function of time Type af descriptio Expression C Time table C Function File s sin omegat Figure 2 3 Prescribed function of time 7 In the Initializati
22. ism 4 0 45 Getting Started 9 Select the Initial conditions tab In the Coordinate 1 1 input 0 1 We need to shift the brick a bit because its position at zero coordinate is quite near to its equilibrium position that gives us small amplitude of oscillations if we do not shift the body Object simulation inspector Object variables PM Informatian Tools Solver Identifiers Initial conditions L Eee qum Mo Message d 0 1 y da 0 1 y Number of d o f 1 Integration 10 Select the Solver tab Set Simulation time to 25 seconds 11 Run simulation clicking the Integration button Process of the numerical simulation starts for 25 seconds period You can see oscillations of the Brick in the animation window and time history of the vertical position of the brick Universal Mechanism 4 0 46 Getting Started 12 Click the 100 button in the drop down tool panel in the top or click the Show all menu command in the context menu see the Fig 2 9 Plot now fits the win dow vi rz Brick Cao Show all D UE D T Show according the ruler pointers Copy bo clipboard B 55 Fo n226 Ex 1 Ey 3 Rar Print Fix tool panel Show ruler Figure 2 9 Graphical windows after the first experiment Free oscillations without damping Now we will turn off damping and compare plots for damped and free oscilla tions Using zero damping coefficient gives us free oscillations 1 Select the
23. ject GO can include any number of various graphical ele ments GE So you are able to create quite complicated 1mages Let s create three elements sphere cone and box which form the image of the support altogether Creating new graphical element sphere 1 Click Add new graphical element button see Figure 4 New tab GEI appears see Figure 5 Support Support Type of graphical element Parametric 3D profile Figure 5 Type of the graphical element 2 Choose type for the new graphical element Ellipsoid 3 Point to the Parameters tab and set a b c 0 05 4 Point to the Color tab and set diffuse color to red Universal Mechanism 4 0 10 Getting Started Creating new graphical element cone l Create new graphical element and set its type to Cone Note Do not add new graphical object instead new graphical element within graphical object In this example we create the only graph ob ject Support which contains three graphical elements sphere cone and box 2 Point to Parameters tab and set R2 0 1 R1 0 h 0 15 3 Set diffuse color to red Universal Mechanism 4 0 11 Getting Started Creating new graphical element box 1 Create new graphical element and set its type to Box 2 Point to Parameters tab and set A 0 5 B 0 5 C 0 05 3 Point to GE Position tab Set Translation Z to 0 15 see Figure 6 Support Support ar Hs Dem Description Go position
24. lowing link http www umlab ru download 40 oscillator zip Asin ot Brick Figure 2 1 Model scheme Universal Mechanism 4 0 27 Getting Started 2 3 Creating the model 2 3 1 Running UM Input and creating new model Running UM Input program 1 Click Start Programs Universal Mechanism 4 0 UM Input Creating a new model 1 From the File menu point to New object The window of the constructor ap pears Universal Mechanism 4 0 28 Getting Started aS sc de d 2 3 2 Creating graphical objects Top We will create a thin rectangular plate as a graphical object for the Top body Create new graphical object Set its name to Top Add new graphical element Box Set parameters and GE position for the Box as it 1s shown below select the Color tab and choose blue for diffuse and specular colors GE position Material Parameters Color Parameters Color GE position Material afoz E B j2 EH moon G Discretization ho H Universal Mechanism 4 0 29 po e im i 1 Getting Started Brick Let us describe the brick as a cube of 0 2 m side length Create new graphical object Set its name to Brick Add new graphical element Box into this graphical object Set its parameters and GE position select the Color tab and set red for diffuse and specular colors x g Description Go position Description GO position Bos D Parameters Color G
25. n of mode Natural frequencies Hz Amplitude Eigenvalues il 5 00009 0 Animate Save ko File Copy to clipboard Frequency damping ratio Note Damping ration shows us if all forms are damped properly and thus change damping coefficients or geometry of attachment point of damp ers if necessary 9 You can change the value of the mu identifier in the Identifiers tab and see what will happen with damping ratio 10 Close the Linear analysis window Universal Mechanism 4 0 52 Getting Started 2 4 4 Forces oscillations Let us consider simulation of forced oscillations without damping 1 Delete all variables from the graphical window except the first dynamic one 2 From the Analysis menu select Simulation 3 Select the Identifiers tab Set the following values a 0 05 omega 8 mu 0 4 Run integration Now you can see that the body Top also moves The time his tory of the vertical position of the Brick is given in the Fig 2 13 I Plots E x 1 rz Brick Cao 24 96 0 08579999 Ex 1 Ey 1 Ranges are nat used Figure 2 13 Forced oscillation omega 8 rad s Universal Mechanism 4 0 53 Getting Started Resonance In conclusion we consider the resonance case when the excitation frequency 1s equal to the natural frequency of the system l In the Pause window click the Interrupt button 2 In the Object simulation inspector set omega 5 3 Run integration As we expected
26. on of values window set a 0 05 m and omega 10 rad s Initialization of values Add ta the sheet Whale lis Universal Mechanism 4 0 36 Getting Started Pa ud Joint for the brick Select the Brick bod y in the tree of elements Click the K amp l button In the drop down list select Prismatic again Select the Top as the first body instead Base0 see the figure below Set the rest parameters of the joint as it is shown below Top Brick Name iBrick Gur amu Top Brick Translational jan none Geometry Description Joint force axis z 0 0 1 Dun ee es Brick axis z 0 0 1 DELE a Universal Mechanism 4 0 or Getting Started 2 3 5 Creating force elements Now we will describe elastic and damping force elements between the top and the brick Let us use c parameter for the stiffness coefficient of the spring and mu parameters for the damping coefficient of the damper Length of the unloaded spring let us denote as 10 1 Select the jBrick joint 2 Select the Joint force tab 3 In the Joint force list select the Linear 4 In the c field input c stiffness coefficient in the x0 field input 10 and set d to mu see Fig 2 4 Press Enter Set values of parameters as follows c 250 10 0 4 mu 5 Top Brick Mame Brick a4 i nnm Top Brick Translational jan none Geometry Description Joint Force Joint force Linear Y
27. on window is now in its equilibrium position Note Obtained coordinates which correspond to equilibrium position you can save to a file To do it use the H button in the Initial conditions tab This file with initial conditions you can loaded using Object simulation inspector in order to start simulation form the equilibrium position if necessary Natural frequencies and forms 5 Select the Frequencies tab In the left list you can see the natural frequencies of the system As you can see our system has only one frequency and this fre quency is 0 795775 Hz what corresponds to 5 0000 rad s 6 Click the Show button to start animation of the natural forms Adjust appropri ate Amplitude and Rate Click the Stop button to finish animation Universal Mechanism 4 0 51 Getting Started Stability Let us find the roots of the linearized system It gives us the information about stability of the model 7 Set the Compute to Eigenvalues You can see that the real parts of roots are negative therefore system is stable Damping ratio 8 Let us describe the damping ratio of the system Click the right mouse button on the list of eigenvalues and from the context menu select the Fre quency damping ratio menu command We have Beta 100 95 that corre sponds to critical damping Linear analysis X Equilibrium Frequencies Root locus Initial conditions Identifiers Options Compute gAnmatia
28. ontainer with the help of the button v New variable r y Pendulum appears in the container of variables Universal Mechanism 4 0 23d Getting Started 6 Select the variable in the Wizard of variables and drag it to the graphical window 7 Select the Object simulation inspector and click the Integration button You can see the plot of your variable in the graphical window l Plots in x ToU FPendulum 3 Ex 1 Ranges are nok used Animation of vectors and trajectories During the simulation you can animate various vector variables in an animation window Let us animate the vector of the mass center velocity Firstly we need to create such variable in the Wizard of variables l Select the Wizard of variables and there select the Linear var tab 2 Select v velocity in the Type group 3 Select V vector in the Component group 4 Add this variable to the container clicking the v button 5 Drag new variable to the animation window Universal Mechanism 4 0 24 Getting Started A list of animated vectors is hidden by default You can make it visible and change its position with the help of the Position of list of vectors command of the pop up menu of the animation window 6 Select animation window click right mouse button and select Position of the list of vectors Left To draw a trajectory of the pendulum create a new variable with the help of the master 7 Repeat all steps we made f
29. or the velocity but the Type of the variable set to r radius vector Drag this variable to the animation window 8 Double click on the velocity item in the List of vectors and select red color for the vector of velocity and than double click trajectory item and select blue color for it 9 Click the Integration button in the Object simulation inspector Now you can see the vector of the velocity and trajectory of the center of the mass of the pendulum You should use the Scale of vectors command of a pop up menu to specify its scale Double click on an element of the list of vectors or on a vector trajectory image to change the color of the vector and trajectory in addition for the trajectory to change the number of points on the curve gs Animation window Mel x B Se 963 MI yur Mi rv P D 1 68 1 36 m22 16 Vector wii Pendulum velocity of point D 0 0 of bor Universal Mechanism 4 0 25 Getting Started 1 5 Multibody pendulum It is very easy to convert the object to a multibody system which contains sev eral bodies a chain of pendulums l Close the UM Simulation program and come back to the UM Input program 2 Select Bodies and copy the pendulum two times Fh Pendulum Delete body AX E mie Mame Pendulum Comments Copy body Oriented points Vectors Parameters Points Add new body To element Image Pendulum 3 Rename new bodies to Pendulum2 and Pen
30. rameters Protocol Farmalizm for equation generatio Language for output file Autodetectian Pascal f Direct da Composite body method C Articulated body method L NN Recommended method Direct Iv Compile equations Run simulation module i Generate all Close In the case of successful generation and compiling equations of motion you will see the following message Compiling successful Object is ready for simula tion It is true The model is really ready Let us start its simulation 4 Click the Close button Now we will come to the simulation program 5 From the Object menu select Simulation or simply press F9 key The simulation programs starts and opens the current model Universal Mechanism 4 0 43 Getting Started 2 4 Simulation of the motion Let us consider some particular cases of oscillations free damped oscillations and forced oscillations without damping 2 4 1 Free oscillations Free damped oscillations 1 Open new animation window Tools Animation window Open new graphical window where we will plot time history of the vertical po sition of the brick 2 Open new graphical window Tools Graphical window Open Wizard of variables Tools Wizard of variables 4 Select the Linear var linear variables tab select Brick in the list of bodies U2 set Type to r coordinate set Component to Z Click the y button to create new variable The v
31. rmar i Oriented points Vectors Parameters Points To element ES Image none Coordinates of center of mas Universal Mechanism 4 0 aJ Getting Started Brick Now we will create one more rigid body Brick Its mass we will express via parameter identifier m Such a parameterization gives us a possibility to change its mass easily and quickly obtain results for various values of the mass of the brick without regeneration equations of motion Otherwise we would have to gen erate equations every time we want to change its mass Add new rigid body Rename it to Brick In the Image list select Brick set Mass to m and press Enter New Initialization of values window appears set Value to 10 Press Enter This new parameter appears in the parameter list in the bottom left corner of the cR 24 E ou constructor window see the figure below x Top Brick Initialization of values Name Brick ave aT ER Oriented points Vechors Parameters Points Add to the sheet To element ES Image Brick mt ge ET a d Le E Compute autamatic ea Inertia parameter Inertia tenzor Coordinates of center of mass Universal Mechanism 4 0 34 Getting Started 2 3 4 Creating joints Joint for the top The Top body moves along the vertical direction according A sin co t function Now we will describe the translational joint between the base and the top and set the coord
32. the all stages of the working with the model synthesis and compiling of equations of motion and then will come to the simulation of motion of the pendulum support Pendulum Figure 1 Complete model Pendulum model is also available at http www umlab ru download 40 eng pendulum zip Universal Mechanism 4 0 4 Getting Started 1 2 Model scheme Before modeling the pendulum with the help of UM we recommend to draw its sketch like you can see at the left As you can see we drew a simple pendulum and cho se two systems of coordinates SC the base frame OXo YoZo SCO and the body fixed frame SC1 The SCO origin is placed in the center of the joint the second one SC1 at the mass center of the pendulum The axes of SC1 are directed along the pendulum principle axes of inertia The base frame exists in every object and as a rule 1s connected with the Earth There is only rotational joint connecting the pendulum and the base frame the wall which the pendulum 1s attached to Universal Mechanism 4 0 5 Getting Started 1 3 Creating the model 1 3 1 Running UM Input and creating new model Running UM Input program 1 Click Start Programs Universal Mechanism 4 0 UM Input Creating a new model 1 From the File menu point to New object MBS The window of the constructor appears see fig 2 1 3 2 Familiarizing yourself with Universal Mechanism Take a few minutes to familiarizing yourself with the Univ
33. tions B B g _ m ri 0 Message 1H zi da 01 zd integration Universal Mechanism 4 0 22 Getting Started Simulation Now your model is ready for simulation Simply start simulation process for the 10 seconds 1 Click Integration button in the Object simulation inspector At the end of the simulation the Pause window appears You can increase the simulation time change the numerical method etc 2 Press the Interrupt button Object simulation inspector appears Drawing plots During the simulation you can see plots of various variables Such as velocities accelerations forces and so on We will open new graphical window create new variable to plot Y coordinate of the center of mass of the pendulum and draw its plot Well let us create new graphical window 1 From the Tools menu select Graphical window Open Wizard of variables 2 From the Tools menu select Wizard of variables The Wizard of variables is a special tool for creating variables which can be drawn in graphical windows or animated in animation windows in cases of vec tors or trajectories Let us draw a plot of Y coordinate of the mass center of the pendulum 3 Select Linear var tab linear variables coordinates velocities accelera tions etc 4 Select Y in the Component group 5 Then move the variable to the c
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