Dynamic Analysis And Design Modification Of A Ladder .

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Amity Journal of Computational Sciences (AJCS)ISSN: 2456-6616(Online)Volume 1 Issue 2Dynamic Analysis and Design Modification of aLadder Chassis Frame Using Finite Element MethodShrinidhiRaoDr. Ajay BhattuPG Student, Mechanical Engg. Dept.,College of Engineering, Pune, Maharashtra, Indiamail2shrinidhi@gmail.comAssociate Professor, Mechanical Engg. Dept.,College of Engineering, Pune, Maharashtra, Indiabhattuajay@gmail.com, apb.mech@coep.ac.inAbstract—In this paper, dynamic analysis of a ladder chassisframe has been done using Ansys. Firstly, modal analysis of thechassis was done using three different materials namelystructural steel, aluminium alloy and carbon/epoxy composite.The first six non-zero natural frequencies and theircorresponding mode shapes were extracted and the results werecompared. It was observed that the maximum relativedeformation per mode for structural steel chassis was less whencompared to the other two materials. The structural steel chassiswas thus selected for further analysis. It was observed that the 2 ndnatural frequency of the chassis was close to the engine excitationfrequency at idling condition and the 5 th natural frequency wasclose to the engine excitation frequency at high speed cruisingcondition. Thus, in the next part, some modifications were madein the chassis design so as to study their effect on the naturalfrequencies and push the frequencies away from the criticalrange, so as to avoid resonance. Finally, harmonic responseanalysis was done on the original and modified chassis to checkthe response under a harmonic force.Keywords—Vibration; Resonance; Chassis; Dynamic Analysis;FEMI.INTRODUCTIONVibration problem occurs where there are rotating or movingparts in machinery. The effects of vibration are excessivestresses, undesirable noise, looseness of parts and partial orcomplete failure of parts [1]. The structures designed tosupport heavy machines are also subjected to vibrations. Thestructure or machine component subjected to vibration can failbecause of material fatigue resulting from cyclic variation ofthe induced stress.Chassis frame is the basic frame work of the automobile. Allthe automobile systems like transmission, steering,suspension, braking system etc. are attached to and supportedby the chassis frame. The frames provide strength as well asflexibility to the automobile. When the vehicle travels alongthe road, the chassis is subjected to excitations from the engineand transmission system as well as due to the road profile. Dueto these excitations, the chassis begins to vibrate [2]. If thewww.amity.edu/ajcsnatural frequency of vibration coincides with the frequency ofexternal excitation, resonance occurs, which leads to excessivedeflections and failure [3].In the current paper, dynamic analysis of a ladder chassisframe has been done using Ansys software. Modal analysis ofthe chassis was done using three materials and theirperformance was compared. The structural steel chassis waschosen for further consideration and modifications were triedout to push the natural frequencies beyond the critical range.Harmonic analysis was done on original and modified chassisto check the response to harmonic force.Ladder chassis frame:The ladder chassis frame consists of twosymmetrical long members and a number of connecting crossmembers. This type of chassis is commonly found in busses,trucks, SUV’s and pick-up vans.Modal Analysis:Modal analysis is used to determine the modeshapes and natural frequencies of a machine or a structure. It isthe most basic form of dynamic analysis .The output of modalanalysis can further be used to carry out a more detaileddynamic analysis like harmonic response analysis, transientanalysis etc.Harmonic response analysis:From the natural frequenciesobtained by modal analysis, the harmonic analysis determineswhich vibration modes contribute more significantly to thedynamic response of the structure through frequency responsecurves [4].II.DYNAMIC ANALYSIS OF LADDER CHASSISFRAMEA.ModalAnalysis of Chassis Frame Using Three DifferentMaterials and their ComparisonA ladder chassis frame has been chosen for analysis. Thechassis frame consists of long members and cross members as16

Amity Journal of Computational Sciences (AJCS)ISSN: 2456-6616(Online)Volume 1 Issue 2shown in Fig. 1. The FE model of chassis is shown in Fig. 2.Modal analysis of chassis frame has been carried out in Ansysin the free-free condition. Analysis is done using threedifferent materials namely structural steel, aluminium alloyand carbon/epoxy composite. Since free-free condition hasbeen used, the first six natural frequencies are either zero orvery close to zero. They correspond to rigid body motion andhave been neglected. The first six non-zero natural frequenciesand their corresponding mode shapes have been extracted andthe results have been compared.Mode 1ModeFig. 1.3D model of chassis frame.2Mode 3Fig. 2.FE model of chassis frame.Material: Structural Steel. Material properties: Density 7850kg/m³, Young’s Modulus 200 GPa, Poisson’s Ratio 0.3.Table 1.Natural frequencies and deformations for structural steel.ModeFrequency (Hz)Max. deformation 4.3112548.594.7416662.4996.561Mode 4The first six mode shapes for the structural steel chassis areshown in the figure below.Mode 5www.amity.edu/ajcs17

Amity Journal of Computational Sciences (AJCS)ISSN: 2456-6616(Online)Volume 1 Issue 2For composite material chassis, the first mode is the firsttwisting mode, the second mode is the vertical bending mode,while the fourth and fifth modes are again twisting modes.Mode 6Fig. 3.Mode shapes for structural steel chassis.Comparison of results:The natural frequencies, maximumrelative deformation per mode and weight of chassis havebeen compared for the three materials used in the followingfigures.It can be seen from Fig. 3 that the first mode shape is the firsttwisting mode of the chassis and occurs at a frequency of14.211 Hz. The fourth mode is the vertical bending mode andoccurs at 37.933 Hz frequency. The fifth mode occurs at afrequency of 48.59 Hz and is the second twisting mode of thechassis.Material: Aluminium Alloy. Material properties: Density 2770kg/m³, Young’s Modulus 71 GPa, Poisson’s Ratio 0.33.Table 2.Natural frequencies and deformationsfor aluminium alloy.ModeFrequency (Hz)Max. deformation 7.252548.7247.978662.90111.042Fig. 4.Natural frequency Vs. mode number.The mode shapes for aluminium alloy chassis are same as thatfor the structural steel chassis. The only difference is in thevalues of relative deformations.Material: Carbon/epoxy. Material properties: ρ 1490 kg/m³,Ex 121 GPa, Ey 8600 MPa, Ez 8600 MPa, νxy 0.27, νyz 0.4,νxz 0.27, Gxy 4700 MPa, Gyz 3100 MPa, Gxz 4700 MPa.Where, ρ Density, E Young’s modulus, ν Poisson’s ratio,G Shear modulus.Fig. 5.Max. deformation Vs. mode number.Table 3.Natural frequencies and deformationsfor carbon-epoxy.ModeFrequency (Hz)Max. deformation .52528.8328.936645.00814.301www.amity.edu/ajcs18

Amity Journal of Computational Sciences (AJCS)ISSN: 2456-6616(Online)Volume 1 Issue 2member has been added. Material of chassis is structural steel.The modified chassis 1 is shown in Fig. 7 below.Fig. 6.Comparison of weights.From the above comparisons, we can say that the frequencyvalues for Structural steel and aluminium alloy chassis arenearly the same, while those for carbon-epoxy compositematerial chassis are on the lower side. However, the maximumrelative deformation per mode is the lowest for structural steelchassis. As compared to the steel chassis, the weight of thecomposite material chassis is 80% less.The structural steel chassis was selected for further analysis.B.Chassis Modifications to Avoid ResonanceAs can be seen from the previous discussion, the first sixnatural frequencies for the structural steel chassis lie in therange from 14-63 Hz. In practise, the road excitation hastypical values varying from 0-100 Hz. At high speed cruising,the excitation is about 3000 rpm or 50 Hz [2, 5, 6]. Dieselengine is known to have operating speed varying from 8-33rps [7]. In low speed idling condition, the speed range is about8-10 rps. This translates into excitation frequencies varyingfrom 24-30 Hz [2]. From modal analysis results of structuralsteel chassis, we can see that the second natural frequency liesin the 24-30 Hz range, while the fifth frequency is close to 50Hz. Thus the chassis may experience structural resonance atidling and high speed cruising condition. We will try tomodify the chassis and try to push the natural frequenciesaway from the critical range. The modifications will lead toeither change in mass or change in stiffness or both. Anincrease in mass will reduce the natural frequency, while anincrease in the stiffness will increase the natural frequency.Fig. 7.Modified chassis 1.The natural frequencies obtained are compared with theoriginal case as follows:Table 4.Comparison of natural frequencies for original chassisand modified chassis 1.Mode123456Frequency(original) odification 1) (Hz)13.68121.88832.03134.89146.6352.998It can be seen from the above comparison that due to themodification, all the six natural frequencies have reduced andthe second and fifth frequencies have moved away from thecritical zone. Also, this modification decreases the weight ofchassis to 223.36 kg. Thus, the effect of this modification is toreduce the natural frequencies.Modification 2.In this iteration also, two changes have beenmade to the original chassis. Firstly, the overall length hasbeen reduced from 3825 mm to 3675 mm. Also, two extracross members made of steel have been added. Material ofchassis is structural steel. The modified chassis 2 is shown inFig. 8.The original chassis is as shown in Fig. 1 and consists of sixcross members. The long members are of hollow rectangularbox-section with 5 mm thickness. The weight of originalchassis considering structural steel material is 240.1 kg. Theoverall length is 3825 mm.Modification 1:In this iteration, two changes have been madeto the original chassis. The thickness of the long members hasbeen reduced from 5 mm to 4 mm and an additional steel crosswww.amity.edu/ajcs19

Amity Journal of Computational Sciences (AJCS)ISSN: 2456-6616(Online)Fig. 8.Modified chassis 2.The results as compared to the original chassis are givenbelow:Table 5.Comparison of natural frequencies for original chassisand modified chassis 2.ModeFrequency(original) ency(modification 2)(Hz)14.95530.71437.68738.36650.31665.116The above table shows that due to this modification, thenatural frequency of chassis for all six modes has increased.The second natural frequency has moved beyond 30 Hz andthe fifth natural frequency has moved beyond 50 Hz. Theweight of chassis after this modification is 247.68 kg, which isslightly more than that of the original chassis. Thus, the effectof this modification is to increase the natural frequencies.Volume 1 Issue 2From the above table, we can say that this modification alsoresults in an increase in the natural frequency values for allmodes. The second and fifth mode frequencies have movedbeyond the critical range. Also, the weight of chassis hasreduced from 240.1 kg to 237.93 kg due to this modification.Thus, the effect of this modification is to increase the naturalfrequencies.C.HarmonicResponse Analysis of Original and ModifiedChassisIn this part, a harmonic force having magnitude equal toengine weight (1000 N) is applied to one of the cross memberand the average response of the entire chassis to this harmonicforce at different frequencies is recorded. The output is thefrequency response curve, where the peaks correspond to thenatural frequencies corresponding to the vertical bendingmodes of the chassis.Modification 3.In this iteration, the length of chassis has beenreduced from 3825 mm to 3675 mm and two extra crossmembers made of carbon-epoxy composite material have beenadded. The remaining body of chassis is made of structuralsteel. The modified chassis 3 is shown in Fig. 9 below.Fig. 10.Harmonic force applied to chassis.The frequency response curves for the original chassis and thethree modified chassis are shown in the figures below.Fig. 9.Modified chassis 3.The comparison of frequencies is given in the table below:Table 6.Comparison of natural frequencies for original chassisand modified chassis 3.Mode123456www.amity.edu/ajcsFrequency(original) odification 3) (Hz)14.52530.35238.34339.30650.77565.09Fig. 11.Frequency response curve- original chassis.20

Amity Journal of Computational Sciences (AJCS)ISSN: 2456-6616(Online)Volume 1 Issue 2three modifications, the amplitude of vibration is minimum formodification 3.III.CONCLUSIONIn this paper, dynamic analysis of a ladder chassis frame wascarried out and based on the results, some modifications weremade to the chassis to study their effect on the naturalfrequencies of the chassis. The modifications includedreduction in overall length of chassis, reduction in thickness oflong members, addition of extra cross members and use ofalternate materials for cross members. These modificationshelped in pushing the frequencies away from the critical range.The following conclusions can be drawn from this work:Fig. 12.Frequency response curve- modified chassis-1. Fig. 13.Frequency response curve-modified chassis 2. The frequency values for Structural steel andaluminium alloy chassis are nearly the same and liein the range 14-63 Hz, while those for carbon-epoxycomposite material chassis are on the lower side (945 Hz). However, the maximum relative deformationper mode is the lowest for structural steel chassis. Byusing composite material for the chassis, there is areduction in weight by 80 % over steel chassis.These frequencies lie in the range of excitationfrequencies due to engine vibrations and road profileexcitations.Reducing the length of chassis increases its stiffnessand hence increases its natural frequencies.Extra cross members added to chassis mainly affectits second natural frequency and increase itsignificantly.Using these methods, we can alter the naturalfrequencies of the chassis and place them in thenatural range and hence prevent resonance andunusual chassis vibrations.Out of the three modifications made, harmonicanalysis showed that for the given inputs, theamplitude of vibration is minimum for modification3. It also reduced the weight of chassis by 3 kg.REFERENCESFig. 14.Frequency response curve-modified chassis 3.From the above four frequency response curves, we can seethat the maximum amplitude of vibration is 6.5799 mm at 93Hz for the original chassis, 31.227 mm at 71 Hz formodification 1, 15.97 mm at 78.5 Hz for modification 2 and7.8215 mm at 81.5 Hz for modification 3. Thus, out of thewww.amity.edu/ajcs[1] Grover G.K., “Mechanical Vibrations,” NemChand & Bros, EighthEdition, 2009.[2] Fui. T. H. and Rahman R. A., “Static and Dynamic Structural Analysis ofa 4.5 Ton TruckChassis,” JurnalMekanikal, December 2007, No.24,56-67.[3]Rao S.S., “Mechanical Vibrations,” Wesley, Third Edition, 1995.[4] Rodrigues, A., Gertz, L., Cervieri, A., Poncio, A.,Oliveira, A., Pereira,M., "Static and Dynamic Analysis of a Chassis of a Prototype Car," SAETechnical Paper 2015-36-0353, 2015, doi: 10.4271/2015-36-0353.[5] Mekonnen, K., “Static and dynamic analysis of a commercial vehiclewith van body,” Thesis Submitted to the School of Graduate Studiesof Addis Ababa University in partial fulfilment of the requirements forM.Sc. Degree in Mechanical Engineering, 2008.[6] Hadipour, M., Alambeigi, F., Hosseini, R., Masoudinejad, R., “A Studyon the Vibrational Effects of Adding an Auxiliary Chassis to a 6-21

Amity Journal of Computational Sciences (AJCS)ISSN: 2456-6616(Online)Volume 1 Issue 2Ton Truck,” Journal of American Science. 7, 6(2011), pp. 1219-1226,ISSN: 1545-1003.[7] Johansson, I., Edlund, S., “Optimizationof Vehicle Dynamics in Trucksby Use of Full Vehicle FE-Models,” Göteborg, Sweden, Department ofVehicleDynamics & Chassis Technology, Volvo Truck Corporation.[8] Mahmoodi-k, M et al., “Stress and dynamic analysis of optimized trailerchassis,” Technical Gazette 21, 3(2014), 599-608.[9] Renuke. P. A., “Dynamic Analysis of a Car Chassis,” InternationalJournal of Engineering Research and Applications (IJERA), ISSN: 22489622, Vol.2, Issue 6, December 2012, pp.955-959.www.amity.edu/ajcs22

Modal analysis of chassis frame has been carried out in Ansys in the free-free condition. Analysis is done using three different materials namely structural steel, aluminium alloy and carbon/epoxy composite. Since free-free condition has been used, the first six natural frequencies are either zero or very close to zero.

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