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UT ME 244L - Experimental Determination of Rigid Body Parameter

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1ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinExperimental Determination ofRigid Body ParametersProf. Raul G. LongoriaOctober 20, 2000Version 1.0ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinOverview• This lecture reviews the design of experimentsfor measuring inertia properties of rigid bodies,mainly for rotational dynamics.• A knowledge of basic pendulum dynamics isrequired.2ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinFunctional Types of Engineering Experiments• Determination of material properties and object dimensions• Determination of component parameters, variables, andperformance indices• Determination of system parameters, variables and performanceindices• Evaluation and improvement of theoretical models• Product/process improvement by testing• Exploratory experimentation• Acceptance testing• Use of physical models and analogues• Teaching/learning through experimentationME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinSpecific Tasks• Modeling of a rotational pendulum with eithertwo or three suspension files.• Design of experiments using “bifilar”or“trifilar” configuration.• Perform experiments with simple rigid bodiesto confirm model.3ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinNeed for Inertia PropertiesSuspensionPuma 560ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinMoment of Inertia• The moment of inertia, J, of a rigid body aboutan axis is defined by,• You can interpret J as a measure of a body’srefusal to be angularly accelerated.• Parallel axes theorem2Jrdm=∫2oCG cJJ ml=+4ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinMoments of InertiaFrom Ogata, “System Dynamics”.ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinCompound Pendulum• Equation of motion for rotation of a rigid bodyabout a fixed axis.• Only gravity is external force (neglect anydamping due to air, pivot, etc.)• Apply Newton’s law,sincJmglθθ=−!!5ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinRadius of gyration• The radius of gyration, k, is the distance fromthe point of suspension of the pendulum atwhich we must concentrate the total mass, m, inorder to obtain the moment of inertia, J,oftheactual mass distribution.• Equivalent simple pendulum has• k is the geometric mean,2Jmk=eqcJlml=2eqckll=⋅ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinExperiment Design - Bifilar6ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinExperiment Design - Bifilar22sin 22sin sinsin 2 0202nnmgJT RLRLRmg RJRLmgRJLmgRTJLθφφθφθθθθθπω==− ××=⋅=⋅+⋅ ××=+===∑!!!!!!222nTmgRJLπ=Moment of inertiaME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at Austin“Adjustable” Bifilar102Txxdd∂= ⇒ =∂Predict aminimum period:The torques on each file will be different here atthe point of attachment, so the period depends on x.2()/JTmgx d x lπ=−7ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinTrifilar - More practical in the lab?ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinTypical Drivetrain ValuesRef. SAE Universal Joint and Driveshaft Manual, 1979.8ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinOther Methods (1)22128dndGJfLπ=Basic torsional pendulumwire diameterG=shear modulus of wiremeasured natural frequency ofmotion inndfθ==ME 244LDynamic Systems and Controls LaboratoryDepartment of Mechanical EngineeringThe University of Texas at AustinOther Methods (2)t = time to fall height, HH = height weight fallsW=weight2222tWRJHg=−⋅What is the model that governs this experiment


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