Engine Dynamics And Torsion Vibration Reduction

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Engine Dynamics and Torsion VibrationReductionInvestigation of various flywheel modelsMaster’s thesis in Applied MechanicsANOOP SURYANARAYANADepartment of Applied MechanicsDivision of DynamicsCHALMERS UNIVERSITY OF TECHNOLOGYGothenburg, Sweden 2015Master’s thesis 2015:20

MASTER’S THESIS IN APPLIED MECHANICSEngine Dynamics and Torsion Vibration ReductionInvestigation of various flywheel modelsANOOP SURYANARAYANADepartment of Applied MechanicsDivision of DynamicsCHALMERS UNIVERSITY OF TECHNOLOGYGöteborg, Sweden 2015

Engine Dynamics and Torsion Vibration ReductionInvestigation of various flywheel modelsANOOP SURYANARAYANA ANOOP SURYANARAYANA, 2015Master’s Thesis 2015:20ISSN 1652-8557Department of Applied MechanicsDivision of DynamicsChalmers University of TechnologySE-412 96 GöteborgSwedenTelephone: 46 (0)31-772 1000Cover:Centrifugal pendulum absorber model in AVL Excite Timing drive, for moreinformation see Chapter 3.3.Chalmers ReproserviceGöteborg, Sweden 2015

Engine Dynamics and Torsion Vibration ReductionInvestigation of various flywheel modelsMaster’s thesis in Automotive EngineeringANOOP SURYANARAYANADepartment of Applied MechanicsDivision of DynamicsChalmers University of TechnologyABSTRACTDemand for fuel efficient engines and stringent rules on emissions have madeautomotive industries to down speed or downsize the engines. Down speeding anddownsizing will lower the CO2 emissions but increases vibrations due to instability,which might lead to deleterious consequences like wearing of parts and power losses.This has a huge impact on truck industries making them less durable and lesssustainable. Therefore, this thesis focuses on reducing one of these vibrations calledtorsional vibrations. Reducing torsional vibration will help to achieve higher torquesout of multi-cylinder engines at lower speed. Usually internal dampers are used toabsorb these torsional vibrations but due to energy dissipations, one has to look foradvance flywheels which stores rotational inertia during engine operation that can beused to isolate vibrations with less energy dissipation and transfer power totransmission with less fluctuations. Various concepts to reduce torsional vibrationswhich are either in research stage or implemented in automotive industry have beeninvestigated in this thesis through modelling and simulation. The work starts withDual Mass flywheel which is currently being implemented in Volvo Trucks. Alternateconcepts includes Powersplit flywheel, Centrifugal Pendulum Vibration Absorberflywheel, and Triple Mass flywheel.Key words: NVH, Torsional Vibration, Flywheel

ContentsABSTRACT . IContents . IIIAcknowledgement . V123Introduction . 11.1Torsional Vibration . 11.2Background . 21.3Goal . 21.4Limitations and Assumptions . 3Theory & Modelling Approach . 52.1Vibration in Internal Combustion engines . 52.2Systems for absorbing Torsional vibrations . 52.2.1Conventional dual mass Flywheel . 52.2.2Centrifugal Pendulum Vibration absorber . 72.2.3Hydrodynamic Torque Converter . 72.2.4Planetary gear Dual Mass Flywheel . 82.2.5Power Split . 92.2.6Triple Mass Flywheel . 102.2.7General design steps . 102.3Formulation of equations of motion for dynamics of the flywheel. 112.4Method of approach . 15Modelling and Simulation of different concepts . 173.1Dual mass flywheel . 173.1.1Modelling of DMF complete model . 173.1.2Modelling of DMF in AVL Excite timing drive . 183.2Power split. . 193.2.1Modelling in Adams . 193.2.2Alternate model of power split . 203.3Centrifugal pendulum vibration absorber . 213.3.1Model in Adams . 213.3.2Dual mass flywheel with CVPA . 223.3.3CPVA flywheel Model in AVL Excite . 233.3.4DMF with CPVA flywheel in AVL Excite. 243.4Triple Mass flywheel . 253.4.1Model in Adams . 25

3.4.24Model in AVL Excite. 26Results . 274.1Dual mass flywheel . 274.2Power split model . 304.3Centrifugal pendulum vibration absorber . 324.4DMF with CPVA . 334.5Triple Mass flywheel . 354.6Comparision with single mass Solid flywheel . 365Conclusion and Future work . 376References . 397Appendix . 417.1CPVA model in AVL Excite . 41

AcknowledgementIn the journey of obtaining a Master's degree in Applied Mechanics, this thesis has animportant role and it would be incomplete without acknowledging the support fromvarious people for its successful completion. The thesis project has been carried out atthe Advanced Technology & Research division of Volvo Group Trucks Technologyunder the supervision of Arne Andersson. I would like to thank him for giving me theopportunity to explore my ideas and supervising me with his technical guidance. Iwould also like to extend my gratitude to Per Salomonsson, Tommy Simonsson, andeveryone in the department at Volvo GTT/ATR for their unparalleled support with theproject.I would also like to express my deep gratitude to my supervisor and examinerProfessor Viktor Berbyuk for suggesting me to Volvo GTT for this thesis and also toHåkan Johansson for his supervision from Department of Applied Mechanics, atChalmers University of technology. During the project, monthly meeting and regularsupervision had been provided by Viktor and Håkan, without their help, advice,expertise and encouragement this thesis would not have happened.I would also like to thank Rahul Kilpadi and Nandeep Mysore for their continuoussupport with discussions about my project and their opinions to make my modelsmore realistic. I would like to thank Fredrik Sjöqvist for helping me with flywheeldata for simulation models. I would also like to thank Martin Svensson, HansBondeson, Christer Örtlund and their colleagues at Simulation & NVH division inPowertrain Engineering at Volvo GTT for all their support during the project. I wouldalso thank Laurent Margerie and Sasa Bukovnik from AVL for their support withAVL Excite software. I would also thank MSC Adams support centre for clarifyingsome doubts with the software.Finally I would like to thank my family and friends for their moral support during thisjourney of pursuing my Master’s. I would like to thank my father, mother, sister andmy dearest love Suchetha for supporting me morally and emotionally during thisendeavour. Through their love, support, encouragement and camaraderie I havegrown and developed into a better person.Göteborg, June 2015ANOOP SURYANARAYANA

1IntroductionMedium to long term developments in Heavy Duty trucks and bus technology willfocus on improvements in engine and vehicle efficiency, while meeting increasinglystringent exhaust emissions standards. Ways to increase the fuel conversion efficiencyand reduce CO2 emissions include increased peak cylinder pressure or new enginearchitectures. This will call for engines with fewer cylinders (downsizing) andrunning at lower speed (down-speeding). [1]With the target of high powered and highly efficient engines in future, engines withless number of cylinders compared to current engines will definitely reduce themanufacturing costs. This makes downsizing a challenging task to achieve betterdriving performance and durability of the vehicle when compared to current vehicles.1.1Torsional VibrationDown speeding and downsizing will inevitably increase the excitation of torsionalvibrations from the combustion engines. High dynamic fluctuations with high meantorque will create problems associated with Noise, vibration and harshness (NVH)and durability of engine and drivetrain components. This creates a need for improvedtechnology for reduction of torsional vibrations. More efficient engines also create atemperature problem for the after treatment system. One way to address too lowexhaust temperature is partial cylinder cut off which also generates torsionalvibrations. Figure 1-1 shows the concept of downspeeding by pushing the limits ofpeak torque to lower speed and downsizing by reducing the number of cylinders in theengine. Figure 1-2 shows the need for vibration reduction with downsizing.Figure 1-1: Engine development trends effect on engine excitation [1]CHALMERS, Applied Mechanics, Master’s Thesis 2015:201

Figure 1-2: Effect on excitation from rotor with downsizing [1]1.2BackgroundIn trucks, heavy engines with high torque capacities are used. IC engines less than 8cylinders and engines with odd firing orders have worse torsional pulsing than 8cylinder engines. When the engine is downsized, balancing of these torsionalfluctuations becomes major issue. Usually, these torsional vibrations are dampedeither using torsional dampers which are attached to crankshaft or by using advancedflywheels. Torsional dampers tend to dissipate energy in the form of heat thus,cooling of these dampers is necessary in order to avoid overheating which might leadto failure.A flywheel on the other hand, serves the major purpose of storing rotational energyand provides continuous supply of energy during non-operation condition of internalcombustion engine. Heavier flywheels have higher rotational inertia, which makesthem ideal for reducing torsional fluctuations. But due to increased weight andpackaging issues, a heavier flywheel is not practical to use in automobiles such astrucks. Also, large intertias usually require more effort to speed up. This led toinvention of advanced flywheels which serves the purpose of storing energy and alsoto isolate torsional vibrations. Various concepts regarding this development arediscussed in further chapters.1.3GoalEvaluation different technologies for torsional vibration reduction by creatingsimulation models. Furthermore, propose a suitable solution that can be adopted forthe engine specified by Volvo GTT. The goal formulation can be clarified in thefollowing points: 2To build and validate the model of current vibration absorber investigated byVolvo GTT.Evaluation of the model is done by analysing input and output torque andangular velocity fluctuation in the vibration absorber.Perform a parametric study on number of cylinders (example 3, 4 and 5cylinder engines), shape, size and mass of flywheel to create an advancedmodel.Different technologies which are already implemented or a novel methoddeveloped during the project.CHALMERS, Applied Mechanics, Master’s Thesis 2015:20

1.4Limitations and AssumptionsTo complete the project within the given time frame, a clear project must be definedwith boundaries that are listed: Only torsional vibrations will be considered. The overall vibration analysis of engine and powertrain will not be performed. The simulation data and material properties required for the project is providedby Volvo GTT. The project will consider using software available at Volvo GTT such as MSCAdams, AVL Excite, GT power and Matlab. Balancing of the engine will not be analyzed in this project. Confidentiality of data provided by Volvo GTT will be maintained. The project will be done mainly on numerical simulations henceexperimentation will not be included in this project.CHALMERS, Applied Mechanics, Master’s Thesis 2015:203

4CHALMERS, Applied Mechanics, Master’s Thesis 2015:20

2Theory & Modelling ApproachA thorough investigation of the project is done by going through the basic conceptsinvolved, history of research and current advances. This chapter will give a theoreticalfoundation of the problem to be solved and a brief review of advanced concepts offlywheels which can be used to reduce torsional vibration.2.1Vibration in Internal Combustion enginesMost modern Internal Combustion (IC) engines in automobiles implements a 4-strokecycle. These engines vary from 4-cylinders, 6-cylinders and 8-cylinders depending onpower output specification and requirement on the truck. During the operation of a 4stroke IC engine, torque pulses are generated in power stroke. Thus, power isgenerated periodically in every second rotation of crankshaft for each cylinder. Thiscreates dynamic forces on the crankshaft which need despite balancing createsvibrations. Twisting forces acting on the crankshaft leads to torsional vibrations whicheventually lead to crankshaft failure. If these torsional vibrations are not minimised,they will also damage transmission components. Hence, torsional vibrations areviewed as a critical parameter that needs to be isolated.2.2Systems for absorbing Torsional vibrationsSeveral devices featuring absorber, isolation and damping effects are implemented inautomotive powertrains that reduce torsional vibrations. Meingaßner et al. [2] havegiven a short overview of the functional principles of common torsional vibrationreduction systems. The following subsection explains various concepts of vibrationabsorption that are being published. This includes dual mass flywheel (DMF),Centrifugal pendulum vibration absorber (CPVA), DMF with CPVA, hydrodynamictorque converter, planetary gear DMF, power split flywheel and triple mass flywheel(TMF) that are explained as follows.2.2.1Conventional dual mass FlywheelThis is the most conventional system to reduce torsional vibrations which consists oftwo flywheels, Primary flywheel and secondary flywheel, which are connected bytorsional arc springs. A German company, LuK [4] is the major manufacturer andsupplier of Dual Mass flywheel to various automobile companies. Figure 2-1 shows aschematic diagram of dual mass flywheel. The arc spring has two stages stiffness,stage one called soft spring and stage two called hard spring. Figure 2-2 shows thespring stiffness variation with winding angle. The performance of DMF is limited totorsional spring stiffness characteristics. Hence, tuning of the flywheel towards lowfrequency in order to have a low-pass filtering of dynamics torques with highamplitudes is achieved.CHALMERS, Applied Mechanics, Master’s Thesis 2015:205

Figure 2-1: Schematic diagram of Dual Mass Flywheel1Normalized Arc Spring Stiffness 0.4-0.200.20.4Normalized Windup angle [deg]0.60.81Figure 2-2: Normalized Spring Stiffness vs. Windup angleUlf Schaper et al. [3] has worked on modelling and torque estimation of a DMF inMATLAB/SIMULINK and compared the results with test data. The paper presents aconclusion that, DMF is an oscillation dampening device at low engine speeds. Thespring model shows a hysteresis effect due to speed-dependent friction. But at higherspeeds the DMF becomes unobservable and both flywheels rotate as one unit.6CHALMERS, Applied Mechanics, Master’s Thesis 2015:20

Figure 2-3: Standard-Dual Mass flywheel [4]2.2.2Centrifugal Pendulum Vibration absorberThis is a type of tuned mass damper where a number of small masses are attached tothe main flywheel using roller pins. During high torque fluctuations, the pendulumoscillates to-and-fro applying centrifugal force that leads to increase in inertia of theflywheel. This concept was first patented in 1937 by R. Sazrin and different versionwas also patented by Chilton in 1938. Anders Wedin [19] made a study on differenttypes of CPVA and created simulation models for Volvo Cars Corporation.Figure 2-4: DMF with CPVA [5]The car industry has also adopted an advanced version of flywheel called DMF withCVPA. Schaeffler is the main manufacturer of DMF with CVPA flywheel [5]. Thistype of flywheel has a primary flywheel attached with CVPA on secondary side usingarc spring. The main constraint with this type of flywheel is that manufacturing errorscan reduce the efficiency of the pendulum to a large extent. Also, problems related toNVH may increase due to improper tuning of pendulum.2.2.3Hydrodynamic Torque ConverterThese are generally fluid couplings used in Automatic transmissions and Continuousvariable transmissions. The fluid coupling plays the main role to transfer torque fromCHALMERS, Applied Mechanics, Master’s Thesis 2015:207

drive side to driven side. Due to fluid coupling, it has a dampening effect whichcauses energy dissipation. This makes the operation at higher speeds difficult. Figure2-5 shows the implementation of Hydrodynamic torque converter in an automobile.Figure 2-5: Hydrodynamic Torque converter in a car engine [6]2.2.4Planetary gear Dual Mass FlywheelJust like conventional dual mass flywheel, the primary mass is connected tosecondary mass with the help of arc spring and further extended by a set of planetarygears between the two flywheels. This type of flywheel also includes torsional damper[7] which helps to reduce torsional vibration and planetary gear set helps to createanti-resonance in the transfer system behaviour. For vibrational excitations withfrequencies close to the anti-resonance frequency a very good vibration reduction canbe achieved. For excited vibrations with other frequencies the influence of the DMFtransfer behaviour dominates. Drawbacks of this system are not well explained. Themain manufacturer and supplier of this type of flywheel is SACHS which is a Germanbrand from ZF.Figure 2-6: Planetary gear DMF [7]This concept was further developed by ZF which is called as power split explained inthe next section.8CHALMERS, Applied Mechanics, Master’s Thesis 2015:20

2.2.5Power SplitThis concept is developed by ZF [8]. The main idea of this concept is that the torqueis split into one alternating and one steady part, the upper part travels through arcspring to the ring gear of the primary side. While the lower part through planetarygears. When the torque travels through upper part, the phase changes, and when theyare superimposed again with the lower part, the alternating torque cancels andconstant torque is obtained. Figure 2-7 shows the concept of power split model andFigure 2-8 explains the rotary configuration of the flywheel.Figure 2-7: Power split concept [8]Figure 2-8: Rotary configuration of Power split model [8]D. Lorenz et al. [8] have published a paper which gives an account that power splitflywheel is a better option than compared to next flywheel which is CVPA.CHALMERS, Applied Mechanics, Master’s Thesis 2015:209

2.2.6Triple Mass FlywheelIn this concept, three flywheels are connected to each other with the help of torsionalsprings. Primary mass is connected to engine crankshaft; secondary is connected totransmission input shaft. A third mass called intermediate mass is placed in-betweenprimary and secondary flywheel with the help of torsional arc spring. This conceptwas developed during this thesis, hence it concept has not been published in anyresearch papers. Though this concept was developed during the thesis, later it wasfound that this had been patented in Korea by Lee Hee Rak and Hur Man Dae in 2008[9]. A research paper is also published by Shi Wen-ku et al. [10] in 2011, where it isstated in abstract that TMF is better than conventional DMF. However it hasn’t beenimplemented in any automobile. Both patent and the research paper are inaccessible.2.2.7General design stepsMeingaßner et al. [2] has presented an abstract overview for basic design of torsionalvibration reduction system. Figure 2-9 shows the schematic diagram of the flywheel.Figure 2-9: Schematic diagram of a flywheelFollowing are the basic design steps:10 First step to develop a mechanical concept of the vibration reduction system. Depending on the mechanical concept major parameters like masses, massmoments of inertia, spring stiffness and damping parameters are pre-set. Integration and functional parameters such as mass, dimensions and flangegeometry for the integration in Vehicle/ test rig has to keep in mind whiledesigning. Installation and manufacturing aspects is considered in design process itself. Iterative process with design parameters and simulation.CHALMERS, Applied Mechanics, Master’s Thesis 2015:20

2.3Formulation of equations of motion for dynamics of theflywheelThe dynamics of the system is explained in the following subsection by deriving thesimple equations of motion (EOM) of the system. However, these equations are notimplemented as Adams and AVL excite have in-built algorithms to solve the givenengineering model.Dual Mass flywheelFigure 2-10: Free body diagram of DMFFigure 2-10 shows free body diagram of a DMF. The equations of motion are givenbelow.J pθ p Tin k1 (θ p θ s ) c1 (θ p θ s )2.1J sθ s Tbreak k1 (θ p θ s ) c1 (θ p θ s )2.2θ p ω pθ ω2.3ssThese equations can be used to obtain the Torque Tbreak by calculating using theangular velocities of primary and secondary flywheels.CHALMERS, Applied Mechanics, Master’s Thesis 2015:2011

Power Split flywheelFree body diagram of power split model is given in Figure 2-11Ring Gear 2Planet GearPlanet CarrierRing Gear 1Figure 2-11: Free body diagram of Power split flywheelSince the torque is split in two path,Tin TRG1 TPC2.4𝑇𝑇𝑅𝑅𝑅𝑅1 is the power transmitted through Ring Gear1 and 𝑇𝑇𝑃𝑃𝑃𝑃 is the power transmittedthrough Planet Carrier.Path 1: Power through Ring Gear 1J pθ p Tin k (θ p θ RG1 ) c(θ p θ RG1 )2.5J RG1θ RG1 TRG1 k (θ p θ RG1 ) c(θ p θ RG1 )2.6These two equations are solved to obtain 𝑇𝑇𝑅𝑅𝑅𝑅1 and angular velocity of Ring Gear 1.Path 2: Power through Planet CarrierAs the planet carrier is directly coupled to primary flywheel, the angular velocity ofPrimary flywheel will be equal to Planet carrier. From the gear relations, angularvelocity of planet gear is calculated asω P g RP .ω RG1 ( g RP 1)ωc2.7The torque transfer is calculated asTP TRG1 Tlossg RP2.8With 𝑇𝑇𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 0 in ideal caseThe power is then transferred to Ring Gear 2 depending on the gear ratio 𝑔𝑔𝑅𝑅𝑅𝑅2TRG 2 g RP 2TP12CHALMERS, Applied Mechanics, Master’s Thesis 2015:202.9

Centrifugal Pendulum Vibration Absorber flywheelIn this concept, the total inertia of the flywheel is a function of time and velocity i.e,as angular velocity varies; the centrifugal force of oscillating pendulum counterbalances the fluctuating torque. The concept was first patented by Sarazin in 1937which includes a compact design pendulum with rollers. The concept was furtherdeveloped and patented by Kutzbach, Carter and Salomon. In this section, EOM(given in [33]) of Sarazin model will be analysed which consists of pendulum massthat acts as absorber mass connected to bifilar rotor using rollers as shown in Figure2-12.Figure 2-12: Centrifugal Pendulum Vibration absorber design by SarazinThe rollers are free to roll in the grooved shape relative to rotor and pendulum. Thelinearized absorber frequency 𝑓𝑓𝑎𝑎𝑎𝑎𝑎𝑎 is calculated as a function of rotor speed Ω𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟 as𝑟𝑟𝑓𝑓𝑎𝑎𝑎𝑎𝑎𝑎 2.10Where 𝑛𝑛 𝜌𝜌 is a tuning order calculated from geometrical parameters as shown in𝑜𝑜Figure 2-12. The tuning order relates to centrifugal field which happens by thestiffness of the system.Moment 𝑀𝑀(𝑡𝑡) drives the rotor includes 𝑀𝑀𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 (constant torque) and Δ𝑀𝑀(𝑡𝑡)(fluctuating torque of certain order) is obtained from GT power in our case.Denman [32] has derieved EOM for a CPVA with epicycloidal pendulum path byneglecting roller masses and damping with only one pendulum, using Lagrangeequation of second kind that results inΘ𝑇𝑇 Θ𝑃𝑃 𝑚𝑚𝑝𝑝 (𝑐𝑐 2 𝑛𝑛2 𝑠𝑠 2 )𝑚𝑚𝑝𝑝 χ𝑚𝑚𝑝𝑝 χ φ̈ 𝑚𝑚𝑝𝑝 𝑠𝑠̈𝑠𝑠2𝜑𝜑̇ 𝑠𝑠̇ 𝑚𝑚𝑝𝑝 𝑛𝑛2 𝑠𝑠 𝑠𝑠̇ 2 𝑚𝑚𝑝𝑝 𝑛𝑛2 (1 𝑛𝑛2 ) 𝜒𝜒 𝑀𝑀(𝑡𝑡) 0𝜑𝜑̇ 2 𝑚𝑚𝑝𝑝 𝑛𝑛2 𝑠𝑠 With 𝜒𝜒 𝑐𝑐 2 𝑛𝑛2 (1 𝑛𝑛2 )𝑠𝑠 2and 𝑐𝑐 𝜌𝜌𝑜𝑜 𝑟𝑟CHALMERS, Applied Mechanics, Master’s Thesis 2015:202.112.1213

Triple Mass FlywheelThis method of approach has the following freebody diagram shown in Figure 2-13Figure 2-13: Free body diagram of TMFUsing Newton method, the Equation of motion are as follows𝐽𝐽1 𝜃𝜃̈1 𝑇𝑇𝑖𝑖𝑖𝑖 𝑘𝑘1 (𝜃𝜃1 𝜃𝜃2 ) 𝑐𝑐1 (𝜃𝜃̇1 𝜃𝜃̇2 )𝐽𝐽2 𝜃𝜃̈2 𝑘𝑘1 (𝜃𝜃1 𝜃𝜃2 ) 𝑐𝑐1 𝜃𝜃̇1 𝜃𝜃̇2 𝑘𝑘2 (𝜃𝜃2 𝜃𝜃3 ) 𝑐𝑐2 𝜃𝜃̇2 𝜃𝜃̇3 𝐽𝐽3 𝜃𝜃̈3 𝑇𝑇𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑘𝑘2 (𝜃𝜃2 𝜃𝜃3 ) 𝑐𝑐2 (𝜃𝜃̇2 𝜃𝜃̇3 )2.132.142.15Using these equation, 𝑇𝑇𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 , angular velocity of imtermediate and angular velocityof secondary mass can be calculated.14CHALMERS, Applied Mechanics, Master’s Thesis 2015:20

2.4Method of approachThe simulation model of DMF is made using the general purpose multibody dynamicssimulation software MSC ADAMS [11]. A simple rigid body model of DMF withmass and inertias of the real flywheel used in Volvo Trucks. The arc spring stiffness isalso obtained from the existing flywheel. The torque curves are taken from GT power[13] model of Volvo MD13 euro DST engine. This is a 4-stroke, 6 cylinder enginewith 1572 [Nm] torque at 800 [rpm]. The reason for choosing this rpm is to extractmaximum torque with minimum rpm from the given engine. At low rpm and hightorque torsional vibration is a major issue. Figure 2-14 shows the Torque vs Crankangle obtained from GT power model.1Normalized Engine Torque [Nm]0.80.60.40.20-0.20100200300400Crank Angle [deg]500600700Figure 2-14: Normalized Torque vs Crank angleAs Adams performs calculations in time domain, the torque has to be plotted againsttime which is calculated by Equation 2.16.𝑡𝑡 𝜃𝜃720𝑟𝑟𝑟𝑟𝑟𝑟 1 2 60 [s]2.16Therefore, if the speed is 800 [rpm], total time for one cycle is 0.15[s] in a 4-strokeengine. The torque plotted against time is shown in Figure 2-15CHALMERS, Applied Mechanics, Master’s Thesis 2015:2015

1Normalized engine torque [Nm]0.80.60.40.20-0.200.10.050.15time [s]Figure 2-15: Normalized Torque vs TimeAs the torque is a harmonic function, Fourier series is used to form an equation forTorque with respect to time which is given below. Matlab command cftool is used toformulate this equation.𝑇𝑇(𝑡𝑡) 𝑇𝑇𝑜𝑜 ���𝑛) [Nm]2.17Where 𝑇𝑇𝑜𝑜 is a constant torque, 𝑛𝑛 is excitation order, 𝜔𝜔 ia angular velocity in [rad/s]and 𝑡𝑡 is time in seconds. This is the torque load applied from the engine side and anexcitation load will be applied from the transmission side to hold the flywheel at 800[rpm] assuming the gear ratio is 1.This simulation will be used to evaluate the performance of the flywheel bycomparing the Torque, Angular Velocity and Angular Acceleration at points ofobservation before and after the flywheel.In the later part of the simulation, complete upstream model and downstream modelhas been added to simulate torsional vibrations reduction model.The CPVA flywheel has also been modelled and simulated in AVL Excite which willbe useful to Simulation and NVH group at Volvo GTT for further analysis. AVLExcite is a powertrain oriented rigid and flexible multi-body dynamic analysissoftware that provides advanced techniques to calculate the dynamics, strengths,vibration and acoustics of combustion engines, transmissions and conventional orelectrified powertrains and drivelines [12]. It has various tools for different purposes,and in this project AVL Excite Timing Drive is used

Dual Mass flywheel which is currently being implemented in Volvo Trucks. Alternate concepts includes Powersplit flywheel, Centrifugal Pendulum Vibration Absorber flywheel, and Triple Mass flywheel. Key words: NVH,

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