ABSTRACT: One of the major limitations of the UAV currently, is its limited flighttime due to the low power density of batteries. This can be tackled by using ahybrid power source such as an engine. Our work proposes a structural mountwhich supports the engine and dampens the vibrations generated by DLE-35RA, atwo stroke engine to be used on a co-axial octacopter (UAV). The modelling andassembly of the components is done using CATIA and finite element analysis iscarried out on analysis software ANSYS. The analysis involves the study ofmodal frequencies and the dynamic response of the system.

Subsequently, statespace model for the governing equations of motion are generated for the mount,based on which the vibration performances of the proposed mount are evaluatedand verified using response curves. Keywords: vibration, modal analysis, design, UAV, enginemount  INTRODUCTIONEnduranceof an unmanned aerial vehicle is one of the most important performance metrics.Due to limitations in battery power density and management, it is seen that theUAVs are not able to maintain its flight for a long duration of time.Introduction of hybrid energy concepts such as an engine can be a feasiblesolution to increase the endurance.

But using this power source hasdisadvantages of its own. Engines as we know are the major cause of strayvibrations in machines and for a system as delicate as an UAV this strayvibrations can cause serious effects which can hamper the mission. There are manyapplications which require high stability of flight and especially very lowvibrations levels. Mechanical vibrations have a negative effect on IMU sensorswhich influences the operation of the whole vehicle. It also causes generationof destabilised signals, unwanted sensor data and sensor drift which mayinterfere with the results the user wants to obtain from the UAV and givesinaccurate data. One way to solve this is to sample the data with rate at leasttwice the maximum frequency of the signal.

However, there is a limit to theupper range of sampling frequency and thus the relative high frequencyvibrations caused by the engines would still interfere with the useful signals.The other way is to eliminate or minimisethe mechanical vibrations altogether with the help of anti-vibration mounts orisolators. This paper discusses in details the design and development ofanti-vibration mounts which dampens the stray vibrations generated by DLE-35RA,a two stroke engine to be used on a co-axial octocopter. The rubber damper andstructural mount has been discussed in details with a brief theoreticalresearch on selection of proper materials for manufacturing of the mount.Structural, Modal and dynamic analysis done on the dampers would be elaboratedand an insight to the step response of the same is provided, based on whichvibration performance of the mount is verified.

 Basic Theoretical BackgroundVibration Damping:Dampersare materials used to dissipate mechanical energy from disturbing vibration outof the system by absorbing the energy and converting to other forms of energysuch as heat. Normally, anti-vibration devices available in the market are bothisolators and dampers, where isolators are used to lower the natural frequencyof the system to below the excitation frequency to prevent resonance.Transmissibility and Hysteresis curves:For effective isolationof undesired vibration in a system, the ratio of disturbing frequency overnatural frequency needs to be more than ?2.

To explain this, transmissibilitycurves are exploited, which is a representation of the ratio of forcetransmitted through the suspension apparatus to force applied by vibration i.e.            (1)where A0and Ai are the amplitudes for output and input respectively, a0and ai are the accelerations for output and input respectively, F0and Fi are the forces for output and input (applied and transmitted)respectively.

Similarly,damping of vibration can be estimated by analysis of hysteresis curves whichgives the energy dissipated during the cycle which is the heart of dampingconcept(in case of a viscoelastic material). The area of the displacement-forcehysteresis loop will give the damping capacity of the material 99.Vibrationscannot be removed completely, but it can be reduced to a large extent by properanalysis of these curves.Damper SelectionCriteria:Based onstudies, the following criteria for the selection of materials and designingthe mount were used: Durable and Flexible; Natural frequency outside UAV structural resonance zone; Low compression set and Low creep; Good resistance to external forces experience by vehicle. ModelDesignCATIA V5is used to design the model and Figure-1 shows the existing model of the mountwith rubber dampers. The mount is carefully modelled with emphasis on thedamping property of the rubber and isolation property of the structural design.To ensure the vibrations are damped appropriately, the dampers are placed onthis structure which is then attached to the UAV with nylon mounts.   Thestructure comprises of two major components viz.

the base plate and two supportplates, and secondary components to keep them in place, i.e. the side platesand ‘L’ shaped contacts which links up with the engine and rubber dampers.

Althoughwe have a wide range of materials which can be considered for the design, welimit our spectrum as the vehicle needs to be airborne, and thus weight is anoverriding factor. The same can be said for the aerodynamic loads and inertiaduring take-off and in-flight manoeuvring which further limits our choices. Inthe existing model, we use carbon fibre as the main structure i.e. all theplates, structural steel as the ‘L’ shaped contact surfaces, nylon material asthe mounting points and rubber as the damping units.

Fig. 1 CATIA Model of the MountMaterials Used Carbo fibre SheetsIt is used in most of the structural members of the mount, differentkinds of plates based on the type and number of layers it is made up of. It hashigh strength to weight ratio, rigidity, tensile strength etc.

It is alsocorrosion resistant and most of all fatigue resistant. Structural Steel’L’ shaped clamps made of structural steels are used as a support forthe mount structure and contact surfaces for the dampers. It has a goodformability, relatively low tensile strength and cheap. Nylon Mounts’C’ shaped mounts are made from nylon blocks which are used to fastenthe structure to the UAV. It is made sure that the nylon mounts would be able toisolate as much vibration as possible away from the UAV. Due to its morecompact molecular structure, softer “hand”, excellent abrasion resistance thismaterial was chosen.

 Rubber DampersRubber used in standard engine anti-vibrationmounts is used to make the damping system. This is ensured by analysing itsproperties. It has a high abrasion resistance, tear resistance, resilience andtensile strength. Analysis of theModel                                             The analysis involves static structural analysisfollowed by modal analysis. The analysis was done in a sequential flow. Theresults from static structural are used for modal as well as harmonic analysis.

 To understand the dynamic response, alumped mass model is made in MATLAB. This provides us with the outputcharacteristics of the system. StructuralAnalysisThe structural analysis was carried out in ANSYS.For structural analysis, the boundary involved the weight of the engine and themaximum force produced due to the oscillatory motion of the piston.Weight of the engine= 1.2kg=11.76NSince the mount has 6 clamping units, every unitexperiences 1.

96N of force. This was used as the initial static structuralcondition.   This data was sequentially used to perform modalanalysis of the structure.  Modal AnalysisModal analysis was used to determine the modeshapes and the frequencies of vibration. It is important to determine whetherthe operating frequency and the natural frequency of the structure are in thesame range or not. For the modal analysis, the natural frequencies arecalculated by providing the necessary boundary conditions. It does not requireany other load conditions.                                       Mode Frequency(Hz) 1 187.

79 2 197.29 3 249.43 4 250.45 5 315.81 6 316.29  The maximum operable speed of the engine is9000rpm, which equals to a frequency of 150Hz. As can be seen from the table__the operable speed and the natural frequency do not interfere. Hence thestructure is will not experience resonance.

 Dynamic AnalysisStroke length, s= 30mmWeight of the engine, m= 947gMaximum operating rpm, N=8000rpmAssume that 50% of engine weight is rotating mass. The dynamic load acting on the mount will be,Where  r = s/2Based onthese formulas,Fd=4984.8N.

Having afactor of 2, Fd~10000N, which distributed over 6 mounts. So the force acting onthe mount will be, Fd’~1700N Transient dynamic analysis is used to calculatedynamic response of vibration isolation pad, based on the time depends on thedynamic load condition.  Manufacture ofthe Model PlatesThe plates are made up of custom made carbon fiber sheets. Each type ofplates varies on its properties depending on the number of layers of carbonfiber sheet used to make them. The base plate is made up of 16 layers of sheetsand is approximately 3 mm thick.

This is to make sure that it can withstandextreme loads as these plates face eccentric loading conditions. The otherplates are made up of 8 – 10 layers of sheets. ClampsAn ‘L’ cross section beam is cut in equal thickness to make clamps.  MountsThe mounts are made from nylon blocks after modelling them in CATIA V5and cutting them out using CNC using a standard numerical path generation toolsuch as Vectric Aspire. DampersEPDM rubber is used to make the damping materialwhich is then sandwiched between the clamps and the structure so that most ofthe vibrations from the engine dissipates.  Dummy UAV FrameA dummy model of the octacopter is built usingaluminium frames to test the mount.Fig.2 Manufactured Model       Experiment andValidationThe structure is mounted on the dummy frame and the engine is placed inthe structure.

Throttle is increased slowly and accelerometer readings arerecorded for both cases i.e. when the rubber dampers are present and when it isnot. VibrationPerformance Analysis Mathematical Model of the MountTo verify the performance of the mount a lumped model dynamics of thedamper is generated which describes the relationship between the input andoutput of the system.

In the mount model, the mass is free to heave roll, pitchand yaw. Also all the translational motion is considered unconstrained. Thefinal system we get is a 6DOF model whose state space is represented as:     (2)where X(t) is a matrix ofgeneralised coordinates and the velocity vectors defined as:              (3)where = ()T isthe orientation of the engine i.e. roll around x-axis, pitch around y-axis andyaw around z-axis respectively,  = (x,y,z)T is the position vectorof the centre of mass with respect to fixed inertial frame,  =  is the angular velocity vector  and  =  is the translational velocity vector of thebody. The axis system is given in the figure below:Fig.3 Axis system for the modelInfigure 3 the centre of mass is given by ‘X’, and distances d1, d2, d3 and d4are the distances of the dampers from the centre of mass of the engine. MatrixA11 =  , A12 =  are zero vector andidentity matrix respectively.

A21 is the coefficient matrix for thestiffness ‘k’, and A22 is the coefficient matrix for dampingcoefficients ‘c’ of the system both of which is elaborated in appendix A. ” constitutesthe displacements by vibrational forces and moments caused by the vehicleitself which can be considered negligible in case of engines. The parameters ofthe mathematical model is summarised in the table below: m = 1.

27kg Izz = 0.4572kg/m4 Ixx = 0.1143kg/m4 k = 1.22E5N/m Iyy = 0.4572kg/m4 c = 0.

6E3N-s/m d1 = 0.027m d2 = 0.041m d3 = 0.0035m d4 = 0.08m Table1 Parameters derived from the model SimulationResultsSimulations are done with a unit step input givento the system. The step response is summarised in figure 4, where the outputs are   and thevelocity vectors corresponding to these coordinate vectors in the same order.The points highlighted in the response curves are the settling time for theimpulse given and the steady state values. From the plot it is clear that thesettling time is very less, stating that the performance of the damper modelledis quite appreciable.

By analysis of the plots we can get the damping factorsof the structural mount.Fig.4 StepResponse for the modelResults and DiscussionsText Here CONCLUSIONSThe following conclusionsare deduced from this study:·       Conclusion xxx.·       Conclusion yyy.·       Conclusion zzz.

 ACKNOWLEDGEMENTSAcknowledgements, if any,are mentioned here. REFERENCESReferences should be given in alphabeticalorder. (font to be used: Verdana 8)1 Grace, N F et al (2004), Flexural Response of CFRP Prestressed Highway Bridge Box-Beams, PCI JOURNAL, Vol. 49,No.

1, pp. 92-104. 2 HughesBrothers Inc (1999), Hughes Brothers ReinforcementsProduct Guide Specification, Website:http://www.hughesbros.

com.3 Singh S B,  and Madappa V R (2008), Flexural Capacity of SteelReinforced ECC beams,Proc. 7th RILEM Symposium on FiberReinforced Concrete (BEFIB-2008), Chennai, India, September 17-19, pp.495-500.

4 Terzaghi,K and Peck, R B, (1987), Soil Mechanics in Engineering Practice, 2nded., McGraw Hill, New York, pp.85-100.5 Triantafillou, T C et al. (2006), Concrete Confinement with Textile-ReinforcedMortar Jackets, ACI Structural Journal, Vol.103,No.1, pp 28-37.  99-https://books.

google.co.in/books?id=AKjnOnhGDXYC=PA410=PA410=hysteresis+curves+for+vibration+dampening=bl=S8APfRKaXO=NyHeE-1M3_wx0Akfn27qxU5IHOY=en=X=0ahUKEwjzgdv3l4DYAhXMtY8KHeKIBBgQ6AEITTAI    EquationsEquations have to be clearly typed using MS officeequation editor and presented wherever required. Eq.1 is given in the following section. Numbering of equation can also be followed the manner givenbelow.              (1) References inside the textThe references have to be referred by mentioningauthor’s name and year, i.

e. Shetty A. et al. (2011), Yamada and Sato (2010). At the references section, the referencesshould be listed in alphabetical order.

 Appendix A

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