Design, Multi Rigid Body Dynamic And Modal
Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 7 Issue 11, November-2018Design, Multi Rigid Body Dynamic and ModalAnalysis of a Centrifugal Governor by usingANSYSVanga Padmasri1Student (M.Tech)Dept. of Mechanical engineeringWarangal institute of technology and scienceWarangal (TS), IndiaElumagandla Surendar3Associate professor & HODDept of mechanical engineeringWarangal institute of technology and scinceWarangal (TS), IndiaAbstract: The function of a governor is to regulate the meanspeed of an engine, when there are variations in the load e.g. whenthe load on an engine increases, its speed decreases, therefore itbecomes necessary to increase the supply of working fluid. On theother hand, when the load on the engine decreases, its speedincreases and thus less working fluid is required. The governorautomatically controls the supply of working fluid to the enginewith the varying load conditions and keeps the mean speed withincertain limits. And keeps the mean speed within certain limits. byan equal and opposite radial force, known as the controllingforce. It consists of two balls of equal mass; these balls are knownas governor balls or fly balls. The balls revolve with a spindle, whichis driven by the engine through bevel gears. The upper ends of thearms are pivoted to the spindle, so that the balls may rise up orfall down as they revolve about the vertical axis. The arms areconnected by the links to a sleeve, which is keyed to the spindle.This sleeve revolves with the spindle; but can slide up and downthe balls and the sleeve rises when the spindle speed increases,and falls when the speed decreases.In this project we model of centrifugal governor individual partsand assembly of individual parts of Centrifugal governor usingCatia V5 and Import into ANSYS WORKBENCH 14.5 for MultiRigid body dynamic Analysis and Modal Analysis, in this Multibody dynamic analysis how the deformation, spring probe andvelocity takes in to the structure and in modal analysis how themode shapes at different natural frequencies.Nalla Suresh2Assitant professorDept. of Mechanical engineeringWarangal institute of technology and scienceWarangal (TS), IndiaM Vidyasagar4Student (M.Tech)Dept. of Mechanical engineeringWarangal institute of technology and scienceWarangal (TS), IndiaTerms Used in Governors:The following terms used in governors are important from thesubject point of view1. Height of a governor. It is the vertical distance fromthe centre of the ball to a point where the axes of the arms(or arms produced) intersect on the spindle axis. It isusually denoted by h.2. Equilibrium speed. It is the speed at which thegovernor balls, arms etc., are in complete equilibrium andthe sleeve does not tend to move upwards or downwards.3. Mean equilibrium speed. It is the speed at the meanposition of the balls or the sleeve.4. Maximum and minimum equilibrium speeds. Thespeeds at the maximum and minimum radius of rotationof the balls, without tending to move either way areknown as maximum and mini- mum equilibrium speedsrespectively.5. Sleeve lift. It is the vertical distance which the sleevetravels due to change in equilibrium speed.Key Words: CATIA, Spindle, Weight of the Arms, Centrifugal,Governor Etc.I.INTRODUCTIONA flyweight mechanism driven by the engine is linked to thethrottle and works against a spring in a fashion similar to thatof the pneumatic governor, resulting in essentially identicaloperation. A centrifugal governor is more complex to designand produce than a pneumatic governor. However, thecentrifugal design is more sensitive to speed changes andhence is better suited to engines that experience largefluctuations in loading.IJERTV7IS110049Fig1.1: Centrifugal governorwww.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)73
Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 7 Issue 11, November-2018Types of governors:Fig1.2: Types of Centrifugal governorsII. LITERATURE SURVEY1. Sumit Kumar1, Rajeev Kumar2, Harish Kumar3There are many types of governors. Watt governor is thesimplest form of governors. It is known that the wattgovernor has low speed range because in watt governorcontrolling force is less. To improve the range variousgovernor was invented some of them are Porter governor,Proell governor & Hartnell governor in the mentioned thecontrolling force is increased by dead weight on thesleeve in Porter & Proell governor and by spring inHartnell governor. In the current investigation wattgovernor is modified such that it increases the controllingforce .in modification the fly-ball is fixed on the lowerarm at the small distance below from the point ofintersection of arms. The analysis is carried out bymounting the fly ball at the various positions on the lowerarm.2. Jorge Sotomayor, Luis Fernando Mello andDenis de Carvalho Braga In this paper we study theLyapunov stability and Hop bifurcation in a systemcoupling a Watt-centrifugal-governor with a steamengine. Sufficient conditions for the stability of theequilibrium state in terms of the physical parameters andof the bifurcating periodic orbit at most criticalparameters on the bifurcation surface are given3. Surarapu Giribabu1, Uotkuri Nagamani2 AndMekala Rajitha3 The function of the governor is tomaintain the mean speed of the engine with in specifiedlimits whenever there is a variation of the load. Theobjective of our investigation is modifying the WattGovernor (pendulum type) to increase minimum speedlimit. Generally we seen that watt governor is bestsuitable for 60-80r.p.m minimum speeds only, in ourstudy we extend lower arm and fly ball position of thewatt governor to the downside from the intersection oflink and arm, and then we derive the equation forgovernor speed. This analysis carried out by extension oflower links of the governor and position of fly balls. Andalso identify the stress concentration areas, areas whichare most susceptible to failure when governor is rotatingabout its axis, also the value of these stresses is measured.This analysis is carried out with the help of PRO E andANSYS. Effect of the “WEIGHT OF THE ARMS” is themajor area of concern for our study and all thecalculations are done considering the weight of the arms.Weight of the arms acts on the centroid of the arms andIJERTV7IS110049when the governor assembly rotates, centrifugal forcestarts acting on the centroid of the arms and tends todeflect the arms, this deflection or bending is to beobserved. In our work, we have done the Stress analysison a particular configuration of governor assembly andthen various materials are suggested on a theoreticalbasis.1. GiriBabu Surarapu1, Shashidar PeddiReddy2,Nagamani Uotkuri3:-The function of the governor is tomaintain the mean speed of the engine with in specifiedlimits whenever there is a variation of the load. Theobjective of our investigation is modifying the WattGovernor (pendulum type) to increase minimum speedlimit. Generally we seen that watt governor is bestsuitable for 60-80r.p.m minimum speeds only, in ourstudy we extend lower arm and fly ball position of thewatt governor to the downside from the intersection oflink and arm, and then we derive the equation forgovernor speed. We fabricated the model of governor andobserved effect of the extension of lower link and fly ballweight on minimum speed of the governor. This analysiscarried out by extension of lower links of the governorand position of fly balls.III. DESIGING AND RIGIDBODY DYNAMICANALYSISWe have been supplied with the .igs file of the CentrifugalGovernor; I have designed the Centrifugal Governoraccording to the dimensions supplied to me in CATIAV5.Multi body simulation deals with deals with study andanalysis of dynamic behavior of system of flexible and/orrigid interconnected bodies. These bodies are subjected toconstrain with respect to one another through a kinematicconstraints modeled as joints. These systems canrepresent a space structure with antenna deploymentcapabilities, an automobile, a robot with manipulatorarms, an aircraft as an assemblage of rigid and flexibleparts, and so on. The components may be subjected tolarge displacement, large rotation, and also effects offinite strain.Multi body systems have conventionally been modeled asrigid body systems with superimposed elastic effects ofone or more components. A major limitation of thesemethods is that non-linear large-deformation, finite straineffects or non-linear material cannot be incorporatedcompletely into model.The FE method used in ANSYS offers an attractiveapproach to modeling a multi body s y s t e m . TheANSYS multi body analysis method may require morecomputational resources and modeling time compared tostandard analysis; it has the following advantages: The finite element mesh automatically represents thegeometry while the large deformation/rotation effects arebuilt into the finite element formulation.www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)74
Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 7 Issue 11, November-2018 Inertial effects are greatly simplified by theconsistent mass formulation or even point massrepresentations. Interconnection of parts via joints is greatlysimplified by considering the finite motions at the twonodes forming the joint element. Define connectionsApply mesh control and preview meshEstablish the analysis settingDefine the initial conditionsDescription of solve toolA general steps for FEM for non-linear analysis is asfollows:Connections include contact regions, joints, springs, orbeams. Explicit analysis connections include bodyinteractions.(i) Build the model: A flexible mechanism usuallycomprises of flexible and/or rigid body parts connectedvia joint elements. The modeling the flexible parts withany of the 3-D solid, shell, or beam elements. Theflexible and/or rigid parts are connected using jointelements. In one scenario, two parts may be simplyconnected to ensure that the displacements at the jointsare identical. In other scenario, the two connected partsmay involve joint such as the universal joint or a planarjoint. While modeling these joints, a suitable kinematicconstraint is implemented on the relative motion(displacement and rotation) between the two nodes thatform the joint.Contact conditions arise where bodies meet. On importingan assembly from a CATIA system, contact betweenvarious parts is automatically detected. In addition to thiscontact regions can also be set up manually. It ispossible to transfer heat flow across the contactboundaries and structural loads and connects thevarious bodies. The analysis can be linear or nonlinear,depending on the type of contact.A joint is an idealized kinematic linkage that controls therelative movement between two bodies. Joint types arecharacterized by their translational and rotational DOFas being fixed.(ii)Define element types: Simulation of a flexible multibody involving flexible and rigid components joinedtogether subjected to some form of kinematicconstraints, using appropriate joint and contact elementtypes.(iii)Define materials: Defining the linear and non-linearmaterial properties for each components of multi bodysystem.(iv )Mesh the model: Mesh the all flexible components ofmulti body system. Two nodes define joint elements andno special meshing is required to define them.Fig3.1: Fixed joint (body to ground)(v) Solve the model: Multi body analyses generallyinvolve large rotations in static or transient dynamicsanalysis, so non-linear geometric effects must beaccounted for.(vi) Review the results of model: Results from a flexiblemulti body analysis consist mainly of displacements,velocities, accelerations, stresses, strains, and reactionforces in structural components. Constraint forces,current relative positions, relative velocities, and relativeaccelerations in joint elements are also available.Rigid body dynamic Analysis of Centrifugal governor inANSYSThe procedure for rigid and dynamic analysis ofmechanism in ANSYS Workbench software is asfollows: Selection of types of analysis Define engineering data Attach geometry Define the part behaviorIJERTV7IS110049Fig 3.2: Revolute joint (body to body)Fig 3.3: Revolute joint (body to body)www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)75
Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 7 Issue 11, November-2018Fig3.4: Cylindrical joint (body to body)Fig 3.8: Applying remote displacement to modalIV. RESULTS AND DISCUSSIONSTotal deformation: of centrifugal governor when it ismulti rigid body dynamic Analysis:Fig3.5: Spring probe (body to body)Fig 4.1: Total deformationFig3.6: Mesh modelGraph 4.1: Total deformation graph (time (sec) vs. deformation (mm))Total Velocity:Fig3.7: Step for setting the analysis stepsFig 4.2: Total velocityIJERTV7IS110049www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)76
Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 7 Issue 11, November-2018Graph4.2: graph between Times (s) Vs total velocity (mm/s)Directional velocity:Graph 4.4: graph between time(sec) Vs total acceleration(mm/s2)Directional Acceleration:Fig 4.3: total directional velocityFig 4.5: Directional AccelerationGraph 4.3: total directional velocity graph (Time (sec) Vs Directionalvelocity (mm/s)) Red line indicates directional velocity in X-directionGreen line indicates directional velocity in ZdirectionTotal Acceleration:Graph 4.5: graph between time (sec) Vs directional acceleration (mm/s2)Spring Probe:Table 4.1: spring probe force, elongation and velocityFig 4.4: Total AccelerationCntdIJERTV7IS110049www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)77
Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 7 Issue 11, November-2018CntdV.MODAL ANALYSIS OF CENTRIFUGALGOVERNORFig 5.1: First order mode shape latitude deformationFig 5.2: Second order mode shape longitudinal deformationGraph 4.5: Graph between time(s) Vs spring probe force (N), springelongation (mm) and spring probe velocity (mm/s)Table: 4.2 Detail of cases simulated in present studyFig 5.3: Third order mode shape twist deformationS.no1234Cases considered forsimulationPosition analysisVelocity analysisAcceleration analysisDetermination of springprobe forceANSYSNoYesYesYesImportance ofstudyNecessaryfor dynamicanalysisFig 5.4: Fourth order mode shape bending and torsion deformationIJERTV7IS110049www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)78
Published by :http://www.ijert.orgInternational Journal of Engineering Research & Technology (IJERT)ISSN: 2278-0181Vol. 7 Issue 11, November-2018Future Scope: For accurate modeling of Centrifugal Governor usingCatia V5, the model was meshed and added constraints,to obtain the first 6 order natural frequency and vibrationmode, and the vibration modes are described. The resultsof this analysis for the following dynamic analysis andstructure optimization design provides an importantbasis, also laid the foundation for more in-depth studyon the vibration and noise problems, to provide areference and basis for the practical experiment. Vibration analysis will give better results inaccuracy. Study on various factors (i.e. stability, sensitivity,and hunting) of the governors.Fig 5.5: Fifth order mode shape bending deformationVII. REFERENCESR.S. Khurmi, The Technical Writer’s Handbook, Theory ofmachines Surarapu Giribabu, “dynamic analysis of watt andmodified watt governor to increase minimum speed,” ISSN: 23499745, IJMTER.[2] Ravindra Singh Rana, “Design and stress analysis of watt and portergovernor”, IJSRP, Volume 2, Issue 6, June 2012 1 ISSN 2250-3153[3] Amitabha Ghosh, The Technical Writer’s Handbook, Department ofMechanical Engineering Indian Institute of Technology, Kanpur[4] Surarapu Giribabu, “dynamic analysis of watt and modified wattgovernor to increase minimum speed,” ISSN: 2349-9745, IJMTER.[5] IJSRP, Volume 2, Issue 6, June 2012 ISSN 2250-3153[6] IJSRP, Volume 5, Issue 2, February 2015 ISSN 2250-3153[7] THEORY OF MACHINES, Third Edition by S S RATTAN, withTata McGraw Hill Education (p) L.t.d.[8] WWW.ANSWERS.COM/TOPIC/GOVER-DE[9] HTTSP//EN.WIKIPEDIA.ORG/WIKI/GOVER-DE.[10] http://en.wikipedia.org/wiki/Governo(device)[1]Fig 5.6: sixth order mode shape bending and twist deformationVI. CONCLUSION AND FUTURE SCOPEConclusion:The analysis type determines the results available foruser to examine after solution.After the solution has been obtained, it is possible toreview and interpret the output as explained below: Vector Plots - Displays some results in the form ofvectors (arrows). Probes - Displays a result at a single time point, oras a variation over time, using a table as well as agraph. It is also possible to set up various probes toreview results. Charts – Shows various results over period oftime, or displays one result versus another, forexample, Time versus displacement, Time versusvelocity, time versus spring probe.Animation - Animates the change of results overgeometry along with deformation of structure.IJERTV7IS110049www.ijert.org(This work is licensed under a Creative Commons Attribution 4.0 International License.)79
Catia V5 and Import into ANSYS WORKBENCH 14.5 for Multi Rigid body traveldynamic Analysis and Modal Analysis, in this Multi body dynamic analysis how the deformation, spring probe and velocity takes in to the structure and in modal analysis how the mode shapes at different natural frequencies.
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Introduction to Quantum Field Theory for Mathematicians Lecture notes for Math 273, Stanford, Fall 2018 Sourav Chatterjee (Based on a forthcoming textbook by Michel Talagrand) Contents Lecture 1. Introduction 1 Lecture 2. The postulates of quantum mechanics 5 Lecture 3. Position and momentum operators 9 Lecture 4. Time evolution 13 Lecture 5. Many particle states 19 Lecture 6. Bosonic Fock .
