SIMULATION MODELING ON THE COORDINATION MECHANISM OF ETHYLENE MONOMER ON VARIOUS PREREDUCED CrⅡ

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Lakd 0 ⎥ 0 Lakq ⎦ 0 0
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(21)
3
Note that (19) through (21) express three separate sets of apparently independent flux/current relationships. These may be re-cast into the following form:
1
Introduction
In this document we develop models useful for calculating the dynamic behavior of synchronous machines. We start with a commonly accepted picture of the synchronous machine, assuming that the rotor can be fairly represented by three equivalent windings: one being the field and the other two, the d- and q- axis “damper” windings, representing the effects of rotor body, wedge chain, amortisseur and other current carrying paths. While a synchronous machine is assumed here, the results are fairly directly applicable to induction machines. Also, extension to situations in which the rotor representation must have more than one extra equivalent winding per axis should be straightforward.

Abstract
Two new modeLs for "slp-stick ion are presented. One, called the "bristle model," is an apprxiation designed to apture the psical phenomenon of sticking. This model is relatively inefficent numericaly. The other model,called the "resetintegratormodel," does not Capture the details of the sticing phenomenon, but is numerically efficient and exhibits behavior similar to the model propoed by Karnopp in 1985. All threeof these modelsare preferable to thecassical model which poorly represents the friction force at zero velcdty. Simulation experiments show that the new models and the Karnopp model give simflar results in two examples In a dosed-loop example, the classical model predkts a mimit cycle which is not observed in the laboratory. The new modeis and the Karnopp model, on the other hand, agree with the experimental obserntio.

Modeling Illumination Variation with Spherical Harmonics
Ravi Ramamoorthi Columbia Universi
Introduction
Illumination can have a significant impact on the appearance of surfaces, as the patterns of shading, specularities and shadows change. For instance, some images of a face under different lighting conditions are shown in figure 1. Differences in lighting can often play a much greater role in image variability of human faces than differences between individual people. Lighting designers in movies can often set the mood of a scene with carefully chosen lighting. To achieve a sinister effect, for instance, one can use illumination from below the subject—a sharp contrast to most natural indoor or outdoor scenes where the dominant light sources are above the person. Characterizing the variability in appearance with lighting is a fundamental problem in many areas of computer vision, face modeling, and computer graphics. One of the great challenges of computer vision is to produce systems that can work in uncontrolled environments. To be robust, recognition systems must be able to work oudoors in a lighting-insensitive manner. In computer graphics, the challenge is to be able to efficiently create the visual appearance of a scene under realistic, possibly changing, illumination. At first glance, modeling the variation with lighting may seem intractable. For instance, a video projector can illuminate an object like a face with essentially any pattern. In this chapter, we will stay away from such extreme examples, making a set of assumptions that are approximately true in many common situations. One assumption we make is that illumination is distant. By this, we mean that the direction to, and intensity of, the light sources is approximately the same throughout the region of interest. This explicitly rules out cases like slide projectors. This is a reasonably good approximation in outdoor scenes, where the sky can be assumed to be far away. It is also fairly accurate in many indoor environments, where the light sources can be considered much further away relative to the size of the object. Even under the assumption of distant lighting, the variations may seem intractable. The illumination can come from any incident direction, and can be composed of multiple illuminants including localized light sources like sunlight and broad area distributions like skylight. In the general case, we would need to model the intensity from each of infinitely many incident lighting directions. Thus, the space we are dealing with appears to be infinite-dimensional. By contrast, a number of other causes of appearance variation are low-dimensional. For instance, appearance varies with viewing direction as well. However, unlike lighting, there can only be a single view direction. In general, variation because of pose and translation can be described using only six degrees of freedom. Given the daunting nature of this problem, it is not surprising that most previous analytic models have been restricted to the case of a single directional (distant) light source, usually without considering shadows. In computer graphics, this model is sufficient (but not necessarily efficient) for numerical Monte Carlo simulation of appearance, since one can simply treat multiple light sources separately and add up the results. In computer vision, such models can be reasonable approximations under some circumstances, such as controlled laboratory conditions. However, they do not suffice for modeling illumination variation in uncontrolled conditions like the outdoors. Fortunately, there is an obvious empirical method of analyzing illumination variation. One can simply record a number of images of an object under light sources from all different directions. In practice, this usually corresponds to moving a light source in a sphere around the object or person, while keeping camera and pose fixed. Because of the linearity of light transport—the image under multiple lights is the sum of that under the individual sources—an image under arbitrary distant illumination can be written as a linear combination of these source images. This observation in itself provides an attractive direct approach for relighting in computer graphics. Furthermore, instead of using the source images, we can try to find linear combinations or basis images that best explain the

LMS/CAE MST DivisionLMS Virtual Lab MotionAircraft Application TrainingAgendaIntroductionLanding Gear Modeling in VLM Catia Kinematics ImportAnalysis coupled with DesignParameterizationAssembly Constraints andExternal ReferencesDesign TablesConfigurationsSolver DiscussionPost-processingScripting and Automation Tire ModelingOleo ModelingExpressionsHydraulicsImagine CouplingFlexible bodiesStrut compliance refinementNVM ExportContactFlexible contactPart 1Part 2 Aircraft configurationSubmechanismsDynamic LandingDynamic TaxiLanding Gear ShimmyGround Handling ConfigurationsPart 3LMS, 25 years of engineering innovationA future built on strong fundamentalsDriven by a compelling visionThe industry largest R&D commitment to EngineeringInnovationTalented people, over 800 professionals committed tocustomers’successOver $125M in annual revenueMore than 3000 manufacturing companies actively use LMSproducts and servicesStrong financial track record of double digit profitable growthLMS bLMS bLMS SCADASMobile -LabLMS and IMAGINE,a unique portfolio of engineering innovation solutionsEnterprise-wideEngineering Collaboration &Simulation Integration in PLMLMS Tec.ManagerLMS Engineering and Deployment ServicesTechnology Transfer Process Transformation& Best Practices System SupportLMS bAircraft Development ProcessFeasibilityDefinitionInServiceConceptDevelopmentM a rk et St u dyCo n c ep t S el ec t e dA g r ee m e n t W i t h P r i m a r y P a r t n e r sA u th o r i ty T o O f f e rP ro g r a m L a u n c h M a j o r A s se m b l i e sE n t r y I n t o S e r v i c eCe r t if i ca t i o nF i r s t F li g h tM a j o r B o d y S e c t i o n sCo mp o n e n t D e s i g nP hy s ic al P e rf o r ma n c e C e r t i f i c a t i o nDesign / Loads CyclesComponent Verification/CertificationAssembly Verification/CertificationVehicle Level Verification/CertificationV ir tu a lP e r fo r ma n c eCe rt i f i c a t i o nVehicle Level AnalysisAssembly AnalysisComponent AnalysisC o n c e p t V a l i d a t i o n T ar g e t C a s c a d i n gAircraft mechanisms Mechanisms are Everywhere!Aircraft Development Development of mechanismsFeasibility Definition In ServiceConcept DevelopmentDefinition VirtualPrototype Dressing Component optimizationPhysical Proto Testing Virtual Proto Validation &CertificationConcept & Configuration Design System OptimizationEMBRAER ERJ-145 & ERJ-170 seriesLMS References in Process Deployment supportDeployment of LMS Tools & Technology in supportof ERJ-145 & ERJ-170 series:LMS Supports Embraer development team with:Design analysis methods & tools Simulation & Customisation forprocess implementation & improvementModeling know-how & best practicestransferredforA/C Ground LoadsLanding Gear developmentHigh-Lift Device developmentCessna (multiple programs & recently Citation Columbus)LMS References in Process Deployment supportDeployment of LMS Tools & Technology in supportof Citation series:LMS Supports Cessna development team with:Simulation & Customisation forprocess implementation & improvementModeling know-how& best practicestransferredforA/C Ground LoadsLanding Gear developmentStructural Dynamic Testing, Correlation &UpdatingAirbus A350 & A30XLMS References in Process Deployment supportAirbus Ground Loads team selects LMS b Motion for Ground Loads analysis for A350XWB, A3OX...LMS Supports Airbus Ground Loads team(transnational team in France, UK, Spain, Germany)Ground Loads Workshops to discuss on Best Modeling PracticesCustomisation projects to adapt to Airbus processIntegration of tools in A/C vehcile level optimisation frameworkMistubishi Aircraft Corporation on MRJLMS References in Process Deployment supportDeployment of LMS Tools & Technology in support of MJET:LMS Supports Mitsubishi Aircraft Corporation and SumitomoPrecision Products (MRJ LG supplier) development teamwith:Simulation process implementation & improvementConcept & Structural OptimisationModeling know-how& best practices transferredforFlap System developmentA/C Ground LoadsLanding Gear development with Sumitomo PrecisionProductsmore to come...Boeing on 777, 787, ...LMS References in Process Deployment supportDeployment of LMS Tools & Technology in support of 777,787, etc.:LMS Supports Boeing development team with:Simulation process improvement CustomisationModeling know-how & best practicesforA/C MechanismsHigh lift device development Landing Gear development ...Review of Modeling in VLM MenusWorkbenchesView controlCompassSpecification treePartSketcherProductAnalysisSave ManagementMechanismsElement definitionSolvingAnimatingPost-processingWorkshop 1: Construct MLG from CAD Geometry Goal: generate a drop test mechanism model of thelanding gear system using standard MechanismtechniquesGuidelinesStart with Product:Models\Models\WS_01_CAD_Import_MLG\Starting\MLG_Product.CATProductUse Bodies from ProductGroup agreement on joint topologyUse existing axis systems for joints/forcesLinear spring/damper for oleo (k=4.5e5N/m,c=3.6e4kg/s )Linear tension only spring for oleo stop(k=1e8N/m , c=2.5e5kg/s )Lock retraction actuator DOFFull tire, linear vertical stiffness and damping(k=7.5e6N/m , c=2.0e3kg/s, μ=1.0 )Apply conditions for drop test with 50 m/s fwdvelocity, 3 m/s descent rate, 10000kg aircraftweightEvaluate: Tire slip, Aircraft position and acceleration,Main bearings loads, Oleo forceCATIA Kinematics ImportQ: Is it necessary to redefine all the kinematic joints if they already exit in the CATIA model?A: No, VLM can fully import the CATIA Kinematic’s modelOpen the Product containing the Mechanism in a second windowStart Mechanism DesignInsert -> Import-> Kinematics MechanismSelect the Kinematic Mechanism from the Product StructureWorkshop 2: Catia Kinematics Import Convert the Kinematics model inModels\Catia_Kinema\Maingear_F15Review the element conversions:Joints -> JointsCommands->DriversChange the RET driver function toretract the gearAnalysis driving Design?Design driving Analysis?Virtual Lab is an open tool. How you choose to work it is flexible…Design approach: Import or create CAD, create elements, solve…•Benefits: quick, uses existing geometry•Drawbacks:Doesn’t allow for geometry based design studiesDoesn’t allow re-use of the modelTime consuming to update the model for new CADAnalysis approach: sketch reference elements (points and axes),apply elements, solve…•Benefits:Allows for geometry based design studiesModel can be reused easilyCreate a library of sub-mechanism models•Drawbacks:Additional modeling effortUp front planning to make sure design and analysis intent is capturedVirtual Lab is a visual tool…Take advantage of geometry capabilitiesEven if the geometry is there for cosmetic appearanceTop Down DesignLayout analysis/design model to be “parameterize”Parameterize and inter-relate componentsDrive analysis from the Top down: Mechanism is the Top levelProduct Structure SuggestionsKey points when laying out a Product Structure for use as a Mechanism…Group all the sub-Products and Parts together that will be a single Mechanism BodyChanging the node referenced by the Mech Body will invalidate the body and all connections into that bodyChanging nodes below the referenced node will not cause problems, unless elements reference geometry features in that sub-nodeOrganize the structure to meet current and future needsMake use of External references and Assembly constraintsSuggested structure for an openProduct structure to couple with a Mechanism Analysis:Product_Root_Mechanism_Name•Product Document for Body 1–Product Document for CAD Geometry•CAD Hierarchy–Part Document for Hardpoints–Product Node for Cosmetic geometryParameterization Overview Defining user parametersUsing formulasDriving parameters from the Top down Design TablesLayout sketchesDefining ParametersIn VL Basic you learned where to enabled Parameters…Motion ProductPartFormulasMost input fields can accept Measures and ForumlasThe entire model is already parameterizedYou can create your own parameters to make a more concise, meaningful set for your model.Use the Formula editor to:Browse the parameters and formulas of the modelCreate new parameters at the current document levelDelete parametersCreate formulasDelete formulasImportFilterDriving Parameters from the Top -> DownIf a Parameter is to be driven from a Parent, it is critical the Parent own the parameter. This is tied to the Update mechanism of VL.If a Parameter belongs to a child, when it goes out of date, the parent will not knowThis will cause non-updating mechanismsIt is Ok to define Parameters in the children, but make sure to tie them to Parameters in parent.This applies to any Parameter and Design table.Layout SketchesA technique of letting top level sketches drive the entire model.Puts all your geometric parameters in one placeProvides a visual referenceAllows you to create an easily variable model with or without ties to CAD Sketcher good for visualizing basic kinematicsWorkshop 3: Generate Layout Sketch for MLGGoal: Create a layout sketch of apost-type MLG model.Guidelines:Sketch layout for the Post,Piston/Axle, Torque Links,Lateral Brace, and WheelsDrive the dimensions:•Diameters•Strut position•Bearing Locations•Lateral BraceAssembly ConstraintsThe standard method of letting Mechanism Joints and Constraints automatically create Assembly constraints has limitations…Forces and JointsMechanism Joints by default create Assembly constraintsForce elements do not create assembly constraintsMechanism Joints define a limited set of Assembly constraintsDirect use of Assembly constraints provides much greater modeling and parameterization capabilityDisable creation of Assembly Constraints in the Mechanism Design workbench using Tools->Options->Mechanism Design -> Assembly ConstraintsExternal ReferencesExternal references are “links”between part parameters. They can behave as constraintsWhich can cause a joint to not be created if itconflicts with an assembly constraintParts with external references are noted by their Part Icon having a “chain link”To enable the automatic creation of external references: Tools -> Options -> Infrastructure -> PartInfrastructure -> GeneralTo enable the automatic creation of external references:Tools -> Options -> Infrastructure -> Part Infrastructure -> GeneralWorkshop 4: Adding bodies to the Parameterized MLG Define bodies with simple geometry for the MLGmodelGuidelines:Use the following Product structure for eachBody:•Body_Product(Product)Body_Hardpoints(Part)Use assembly constraints to position the bodiesin relation to the LayoutUse external references to tie key partdimensions to the LayoutCreate points and axis systems for referenceand Joint/Force element creationUse good naming convention for Point andAxesModel to include: Post, Piston, 2 Wheels,Aircraft_Attachment, and Test_Stand to positionand orient the MLG in preparation for drop testWorkshop 4 continuedQ: Drop test configuration, how do we change the A/C attitude? A: Parameterize the orientation of the Test StandWorkshop 5: Defining Joints and Forces for MLGBaseline MLG model will include basic constraints and simple force elements. Refinements will be made in later workshopsGuidelines:Use same spring, mass, and IC values as in first workshopInclude bearing constraints (as in 1st workshop) and include bushings to modelcompliance.Parameterize stiffness, damping, mass (aircraft attachment), and speed valuesUse a Boolean parameter to toggle between constraints and bushings for the main bearings.Study the differences between the responses with constraints vs.bushings •Spring-back: Plot wheel fore/aft positionWorkshop 5: continuedDesign TablesA Design Table can serve two purposes:Collection of parameter values from within the b Motion interface that arethen written to an external document.Provides a direct link within b Motion to model parameter values stored in an external document. If this external document is updated, the parameter valueswithin b Motion synchronize with the change.An Excel worksheet or a tabulated text file can be associated to a Design Table.For a large number of parameters, Text files should be used (ie: spline curves)Automatic parameter association is available. This requires that the parameter titles in the Design Table contain the complete description of the parameter in the required format. For example:`Analysis Model\GlobalFixedToGroundBody\FIXED.TO.GROUND`This example parameter is of type Boolean with allowable values being TRUE or FALSEClick the Design Table buttonfound by default on the Knowledge Toolbar found at the bottom of the b Motion Interface.This will start up the Creation of aDesign Table dialog. Using a pre-existing file is the default selection. There are two orientation options for the Design Table, Vertical and Horizontal.Vertical Parameter RecordsHorizontal Parameter RecordsThe Design Table will search for parameter values in the first worksheet of an Excel document. As many calculations and assignments, including visual basic code, can be linked to the following sheets provided the values are returned to the first worksheet.ConfigurationsA Configuration consists of a set of Parameters. These Parameter settings are passed to b through a Design Table. Each Configuration represents a different Analysis Case.Depending on the orientation of the Design Table, a single column or row of the table represents the parameter values assigned to a single configuration.Creating ConfigurationsTo utilize a Configuration in an Analysis Case, a Configuration element must be created. The Analysis Case Operations toolbar of the Mechanism Design Workbench contains the button to create a Configuration element.First the appropriate Design Table must be selected from the References branch of the Specification Tree. The Configuration Number Field Entry corresponds to the row or column in a Design Table that specifies the set of parameter values to be used during the Analysis.Workshop 6: Add Design Tables and ConfigurationsCreate 3 Design Tables for the MLG modelAircraft Attachment mass.•Define 3 values: 7000kg, 10000kg, and 12000kgSpeed:•Descent: 3, 5, and 7 m/s•Fwd: 50, 60, and 70 m/sBearing model: Constraint and BushingCreate Configurations in the 2 analysis cases in the Workshop 5 modelRerun the 2 solution sets with the most severe case configurationsSolver DiscussionQ:Solver to use for dynamic casesSolver to use for rigid part onlySolver to use for flexible part onlySolver to use for static casesA (Dynamics):Dynamic systems, rigid and flexible, BDF is typically the best choice for Integration MethodExtremelydiscontinuoussystemsExplicit, Singlestep DOPRI5Runge-Kutta RK Smooth, stiff,SystemsImplicit, Multistep DASSL Backwards Difference Formulation BDF Discontinuous Systems and Non-stiff systemsExplicit, Multistep Shampine-Gordon’s DE Predict -Evaluate-Correct-EvaluateAdams-Bashforth-Moulton Method PECE Strengths Type Code based on Name AcronymSingle Step versus MultistepMultistep –Means next predicted step is dependent on past stepsSingle Step –Only current information is used to define next stepIn general multistep methods are more efficient, but single step methods can handle discontinuities very well.•Since single step methods do not store past data then they are not as affectedby an abrupt change in a coordinateExplicit versus ImplicitExplicit methods are non-iterative. Predict step based on past data and do a single small correctionImplicit methods iterate on current value to find solutionsIn general implicit methods can take large steps, but step is more expensiveImplicit methods require Jacobian; abrupt discontinuity causes ill-conditionedJacobian.Stiff SystemsNumerically “stiff”systems –Quickly decaying transient, i.e. large negative eigenvalue.Causes small steps in explicit methods (RK and PECE)BDF because it is iterative can handle stiff systems•During initial part of transient BDF will take step size similar toPECE•BDF can increase step size as transient dies outSystems with large negative eigenvalueHydraulics, shock absorbers, hydrobearing, HLAWhich Integrator to UseCertain Elements do not support BDFTRACKBushLinkBDFHydraulic models –definitely AMESIMFlexible ModelsAnything with High damping and is smooth will run better in BDFPECESystems with little or no dampingTrack SuperelementMany sharp discontinuitiesRKHelical Spring : Fine-to-coarse runIn general try BDF first, revert to PECE if model contains unsupported elementsPlot CPU usage. BDF will typically have high CPU usage ramp-up, then solve much faster. PECE step-size will depend on highest natural frequency in the system.Other Solution ParametersMost Solution Set Parameters are left at their default values. Some should be considered carefully for each model…System (Advanced)Integer and Double Array sizes. If the solver fails and the INFO file indicates it is due to an overflow of the Main arrays, increase these values (by a factor of 2 or 3).Output file: Binary is typical, may desire RestartMatrix Scaling: This is a new option introduced in R5A, so it defaults to the old value of Standard.However, for most models this increases stability and decreases solution time. Should be set toIterative.Solver Units: most elements have units, but controls and expressions will always solve and report back in these units.DynamicMax Int Step: keep small for contact models or other abrubt event modelingSolution and Integration tolerances: keep in mind your Solver Units and the relative scale of your model. These values relate to the amount of error you are allowing.Solver Acceleration: Use Banded for most systems, Iterative for flexible body models with a large number of modes.Initial ConditionsQ: To apply an initial speed to the full A/C, is it necessary to apply the initial condition on each body? A: No, only to the independent coordinates and only if you don’t want them to be auto-calculated.Automatically calculated initial velocities are fine, unless you couple initial velocities with stiffness coupled DOF. Then you should always specify a consistent set of initial conditions, or let the system settle through its transient phase.Consider the simple system below. The initial velocity on Body 1 will not cause an initial condition on Body2, resulting in an abrupt and large initial force.Body 1 Body 2Initial Velocity Force ElementStatic AnalysisIn static solver find positions that result in all net forces are zero.F = m*a, in statics “a”the acceleration is zeroF = 0 In our solver this is Reaction forces must balance Applied forces while satisfying the constraints Requirement of static’s solver is a nonsingular stiffness matrix.Every independent degree of freedom must contain a stiffnessTie-rods are an example of a model with no stiffness on a degree of freedom•One-body connected to two other bodies by spherical jointsΦ(q)0Q λΦa Tq ==−Body1Body2Spherical Joints Tie-rod bodyIf there is no stiffness resisting this degree of freedom static solver will fail.Static Mode Animation Tool (SMAT)Created in response to an internal need to understand how to improve ourstatic’s algorithms several years agoStatic Mode Animation computes the stiffness, force, and predicteddisplacement at a certain model configuration to help you understand theseaspects.Knowing this information can help you improve the convergence and speed of static analysis for your model.Static Solution OptionsTo alleviate problems, you have the following options:1.Add stiffness or constraints to the model.e the percent mass or damping option. This option may be difficult touse and is not guaranteed to succeed. It can slow convergence on well-defined models. Therefore it's off by default.3.In rare cases, internally computed derivatives used by static’s (computedanalytically) may be inaccurate, so switching to finite difference Jacobianmay solve the problem.4.If static’s is slow, disable the debug flag. It generates IO that can reallyslow things down.Workshop 7: Static AnalysisPerform static analysis on the MLG modelGuidelines:Rename the 2 Analysis cases: 1 for statics, 1 for dynamicsUse the same configurations (config1 for each design table) Compare tire reaction forces and aircraft Z positionLinearizationVL forms a nonlinear set of equationsLinearization reduces this set of equations to a linear system Linear systems are needed for control theory design Can write out matrices in forms for Matlab and EASY5 U is the input vector these are usually control forces/torques activated by turning on linear flag in control input element Y are the system outputs activated by turning on linear flag in control output element (New with VL)D δC δδy B δA δxδ+=+=&。