Dynamic Structure and Vibration Characte

7/24/2019 Dynamic Structure and Vibration Characte

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Dynamic Structure and Vibration Character istics

Analysis of Single Piece Drive shaft Using FEM

*Ashwani KumarDepartment of Mechanical Engineering

Graphic Era University, Dehradun

India-248002

*[email protected]

Rajat Jain, Himanshu Jaiswal,#

Pravin P PatilDepartment of Mechanical Engineering

Graphic Era University, Dehradun

India-248002#[email protected]

Abstract The main objective of this research work isdynamic structure and vibration characteristics analysis of single

piece drive shaft of a heavy vehicle truck transmission system.

The research work focused on replacement of conventional two

piece stainless steel drive shaft with single piece kevlar epoxy

composite material drive shaft for heavy vehicle. A single piece

drive shaft was designed using Pro-E. Structural analysis was

performed to check the design suitability and modal analysis was

performed to find the natural frequency and mode shape. Now a

days composite material are used very frequently in automobile

industry due to strength, weight and long life span advantage.

Kevlar epoxy composite material has been used for driving shaft

to reduce the weight and cost. The main function of driving shaft

is to transmit torque from vehicle transmission system to rear

wheel differential system. During this process of torque

transmission it is subjected to shear stress, deflection, bending

and torsional vibration. The weight of drive shaft was reduced by

using new design which solved the deflection and bending

problem. FEM based Ansys 14.5 has been used as an analysis

tool. The FEM simulation result determines the strain, stress,

deflection, principal stress, strain energy, natural frequencies and

mode shapes under real time boundary conditions. The resultconcluded that kevlar epoxy composite material suited more for

single piece drive shaft.

Keywords Transmission drive shaft, Kevlar CompositeMaterial, Natural frequency, Weight, Single piece.

I. INTRODUCTION

Drive shaft is manufactured in two pieces using steelmaterial. An attempt has been made to replace two piece drive

shaft in composite material single piece drive shaft. In rear

wheel drive system, drive shaft transmits torque and connects

vehicle transmission or engine system to rear end of vehicle.

This type of transmission drive shaft is known as propeller

shaft. Two-piece drive shaft is fitted with three universal

joints, with jaw coupling. Universal joints and coupling

increases the total weight of drive shaft. Higher weight of

drive shaft causes bending and torsional vibrational problem.

Kevlar epoxy composite material drive shaft have two

universal joints and jaw coupling. The simple design of single

piece drive shaft reduces the weight. The reduced weight and

use of composite material increases the mechanical strength

and prevents failure condition.

Sevkat et al. [1] authors have studied the problem of residual

torsional properties of composite shafts. Shafts are subjectedto impact loading condition. Impact and without impact

properties of shaft was compared for torsion. The research

work concludes that the impact loading reduce the maximum

torque, twisting angle and this reduction increases as increase

in impact energy. Baryrakceken [2] research work concernedwith the failure analysis of pinion shaft mounted at theentrance. The pinion gear and shaft are manufactured in single

part. The fatigue and fracture condition was monitored. The

mechanical property of material was obtained and then

chemical and microstructure properties were determined.

Zhang et al. [3] authors have studied the self-excited vibration

of a propeller shaft. The excitation is caused due to friction

induced instability. The shaft is supported on rubber bearing

lubricated by water. The system was modeled in consideration

with torsional vibration of continuous shaft and tangential

vibration of rubber bearing. Authors have determined the

stability and vibrational characteristics using complexeigenvalues analysis method. Solanki et al. [4] have studied

the failure reason of AISI 304 stainless steel drive shaft. The

main vibration reason for failure is low natural bending

frequency. The failure of drive shaft hampers the function of

vehicles. Mutasher [5] research work present study of

advanced composite, aluminum/ composite for hybrid shaft

having high torque transmission, high natural bending

frequency with less noise and vibration. Ansys and FEM have

been used for numerical simulation. The linear and nonlinear

properties of materials were considered. The maximum torque

transmitted through hybrid shaft is 295Nm. The numericalresult was verified with experimental results.

Aleyaasin et al. [6] have investigated the problem offlexural vibration for cantilevered marine propeller shaft. Thefrequency response method with inverse Fourier transformtechnique was used for identification of resonance andgyroscopic effects. Kim et al. [7] authors have investigated the

problem of thermal residual stresses setup during bondingprocess of composite layer and aluminum tube for hybridshaft. Thermal residual stresses are resultant of difference incoefficient of thermal expansion (CTE) for two materials. Toeliminate the residual stresses a smart cure cycle of cooling

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 10, Number 11 (2015) Research India Publications ::: http://www.ripublication.comb

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and reheating was applied and this method effectively solvedthe stress problem. Cho et al. [8] authors have studied thecomposite material single-piece drive shaft. The shaft wasmanufacture using fiber epoxy composite and aluminum tubefor obtaining high natural bending frequency and torquetransmission capability. The results shows that the shaftsustain for 10

7cycles with dynamic load of + 500 Nm. Cho et

al. [9] authors have studied the method to reduce the residual

thermal stresses using co-curing operation. Aluminumcomposite shaft was prepared using aluminum tube andcomposite material. During bonding process residual stresseswas generated. Kevlar epoxy composite materials have higherspecific stiffness to provide the required strength against lessweight of single piece drive shaft. Higher stiffness of kevlarepoxy composite material solves the problem of high strengthrequirement for drive shaft and less weight solves the problemof inertia. So kevlar epoxy composite material can be used asa one-piece drive shaft material without resonance.

II. CADMODELOF SINGLE PIECE DRIVE SHAFT

Single-piece drive shaft was designed using the Solid Edgeand Pro-E [10-11] software. FEA based analysis was done

using Ansys 14.5 [12]. Structural analysis finds the stresses

and strain value in drive shaft. Modal analysis of composite

single-piece drive shaft was performed to evaluate the modal

frequency and mode shape to prevent the resonance condition.

For structure rigidity the natural bending frequency of drive

shaft should be high. The design model of automobile truck

drive shaft consists of a single-piece shaft with universal joints

at ends portion. Figure 1 shows the single-piece drive shaft

with universal joint. FEM based Ansys 14.5 works on meshingconcept of nodes and elements (nodes- 87718, elements-

453477). Figure 2 shows the meshed finite element model of

transmission drive shaft. Ansys 14.5 have high qualitymeshing facility.

Figure 1. 3 D solid model of single piece drive shaft

Figure 2. Meshed model of single piece drive shaft.

III. MATERIAL PROPERTIES AND BOUNDARY CONDITIONS

The main objective of this research work is to replace

conventional stainless steel material two piece three universal

joints drive shaft with kevlar composite material single-piece

drive shaft. Stainless Steel as conventional material and

Kevlar Epoxy was selected as composite material. In 1985single-piece drive shaft was used for the Ford econoline van

models. Mainly drive shafts are used in automobiles,

aerospace, cooling towers etc. This research work highlights

the use of composite material single-piece drive shaft for

heavy vehicle truck application. In this numerical simulation

of drive shaft it was assumed that the shaft is balanced, has

circular cross section and rotates at constant speed. Table 1

shows the material mechanical properties of stainless steel andkevlar epoxy composite material. Kevlar epoxy composite

material best suited for single-piece drive shaft having less

weight, high specific stiffness and torsional stiffness. The

geometric properties of the drive shaft are length of shaft 1250

mm, Outer Diameter-90 mm, inner diameter-83.36mm. Tosimulate the same working conditions real time boundary

conditions frictionless support, fixed support, rotational

velocity and moment were applied. Rotational velocity of

1500rpm (157.08 rad/sec, figure 3) was applied for structural

and vibration analysis. The rotational motion of drive shaft

generates a torsional moment in whole body of drive shaft.

This moment is applied on all 43 faces (figure 4) in oppositedirection of rotational velocity.

Figure 3. Rotational velocity applied (157.08 rad/sec).


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Table 1 Material property of stainless steel and Kevlar composite material.

Figure 4. Moment components applied (245, 0, 0 Nm)

IV. FEASIMULATIONRESULTSANDDISCUSSION

FEA based numerical simulations evaluate the results of

structural and modal analysis for stainless steel and kevlar

epoxy composite material. In analysis inertia and damping

effects was not considered. Rotational and moments values are

applied in form of loading. The automobile drive shaft is

subjected to torque transmission, no direct load value act on it.The result of this analysis evaluates the static failure condition

of drive shaft.

A. Structural Analysis of Stainless Steel Single Piece Drive

Shaft

Stainless Steel is used as conventional two-piece driving shaft

material. The structural analysis simulation results are shown

in figure (5, 6, 7, 8). Table 2 shows the structural analysis

results comparison for stainless steel and kevlar epoxy

composite material.

Figure 5. Shear Stress distrubutation (XY plane).

Figure 6. Total Deformation.

Figure.7. Equivalent elastic strain.

Figure 8. Strain Energy distribution.

PropertiesNonlinear

Effects

Density

(kg m^-3) Young's Modulus (Pa) Poisson's Ratio Shear Modulus (Pa)

Stainless Steel Considered 7750 1.93e+011 0.31 7.366e+010

Kevlar Epoxy Composite

Material Considered 1402 9.571e+010 0.34 2.508e+010


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Figure 5 shows the shear stress distribution. The analysis

result shows that the shear stress variation is in safe limit

(5.6524e6 Pa). The green hues variation shows that thestainless steel has high rigidity and strength to bear the

torsional vibration and shear stresses. Figure 6 shows the total

deformation in single piece drive shaft under loading

conditions. The deformation is high (0.05 mm) at the

differential side of drive shaft. The yellow and red hues

variation in shaft shows the high deformation zone. Figure 7shows elastic strain variation in drive shaft. The variation is

shown by blue hues, which signify the minimum level of

strain. Figure 8 shows the strain energy distribution in drive

shaft. The transmission end of drive shaft shows small

variation of strain energy near constraining point of universal

joint. Strain energy value is 0.0000345 J for steel drive shaft.

B. Structural Analysis of Kevlar Epoxy Composite Material

Drive Shaft

Figure 9. Shear Stress variation.

Figure 10. Total Deformation

Figure 11. Equivalent Elastic Strain

Figure 12. Strain Energy Distribution.

Figure 9 explain the shear stress simulation result in single-

piece kevlar epoxy composite drive shaft. The maximum value

of shear stress for composite material is 1.4484e6 Pa which is

very less in comparison to max. shear stress (5.624e6 Pa) for

stainless steel material. The result shows that kevlar materialhas less shear stress generation due to loading, so single piece

drive shaft design is safe. Figure 10 shows the total

deformation under dynamic loading conditions. The

deformation is high at the transmission end side of drive shaft.

The maximum deformation value is 0.03mm for kevlar epoxy

drive shaft. For the same loading conditions the deformationof steel shaft is 0.05 mm. The deformation results signify that

kevlar epoxy material is suitable for single piece drive shaft.

Figure 12 shows the strain energy variation in drive shaft. The

strain energy distribution is found at the constraining point of

universal joint. Strain energy value is 0.0000089 J. Table 2shows comparison of structural analysis result for stainless

steel and kevlar composite material. The numerical results

conclude that kevlar epoxy composite material is best suited

for single-piece drive shaft.


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Table 2 Structural Analysis results comparison.

C.Modal Analysis of Stainless Steel Material Single Piece

Drive Shaft

f=76.163 Hz

f=216.19 Hz

f=400.52 Hz

f=400.57 Hz

Figure 13. Modal frequency and mode shapes of stainless steel singlepiece drive shaft.

Figure 13 shows the vibration mode shapes and corresponding

natural frequency for stainless steel. The FEA analysis shows

the first valid frequency is 76.163 Hz (mode 7) and the criticalspeed is equal to 4569 rpm which is nearer to whirling speed.

Mode 7 shows the deformation at the transmission end side.Mode 8 shows lateral vibration with bending effect. The

bending frequency is 216.19 Hz and critical speed is 12971

rpm. Table 3 shows the frequency variation for stainless steel

and kevlar epoxy composite materials.

D.Modal Analysis of Kevlar Epoxy Composite Material

Single Piece Drive Shaft

f=120.75 Hz

Material Type Total Deformation Equivalent Elastic StrainMaximum Principal Elastic

StrainShear Stress Strain Energy

StainlessSteel

Minimum 0. m 0. m/m -3.9815e-7 m/m -5.2485e6 Pa 0. J

Maximum 5.5335 e-5 m 10.434e-5 m/m 10.703e-5 m/m 5.6524e6 Pa 3.4586e-5 J

Kevlar

EpoxyComposite

Minimum 0. m 0. m/m -1.4613e-6 m/m -1.1419e6 Pa 0. J

Maximum 3.0365e-5 m 7.9354e-5 m/m 7.6985e-5 m/m 1.4484e6 Pa 8.9916e-6 J


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f=342.79 Hz

f=660.6 Hz

f=660.68 Hz

Figure 14. Modal frequency and mode shapes of kevlar epoxy

composite material drive shaft

Figure 14 shows the vibration mode shapes and naturalfrequency for kevlar epoxy composite material. The first valid

frequency is 120.75 Hz and critical speed 7245 rpm which is

much higher than 2400 rpm resonance critical speed

preventing the resonance condition. The external excitation

causes resonance. Mode 8 has deformation at centre portion

due to axial bending vibration. Mode 10 shows torsionalvibration at 660.68 Hz. The single-piece drive shaft deformed

at end points. The relation between critical speed and natural

frequency is given as (Ncr = 60 fnt).

Table 3 Modal frequency variation for stainless steel and Kevlar epoxy

Composite Materials.

Figure 15. Natural frequency variation

Figure 15 shows the variation of natural frequencies forstainless steel and kevlar epoxy composite materials. Kevlarepoxy composite material shows the excellent material

properties for the design of single-piece composite drive shaft.

In modal analysis all valid bending frequency are higher than

3000 rpm in order to avoid the whirling or resonance

condition. For trucks and vans bending frequency should be

higher than (2400-4000) rpm. These technical requirements

are fulfilled by the Kevlar epoxy composite material. The

bending natural frequency is 7245 rpm much higher than 2400

rpm, so it reduces the chances of whirling or resonance. The

torque transmission capability of single-piece drive shaft was

considered as 245 Nm.

V. CONCLUSION

Fem based numerical simulation of single piece drive shaft has

theoretical significance in design stage for weight

optimization. The two-piece drive shaft design was replaced

using single-piece kevlar epoxy composite material drive

shaft. The structural and vibration response of driving shaft

shows that Kevlar epoxy composite is suited for single-piece

drive shaft. The research work concludes the following points-

ModeModal Frequency

Stainless Steel

Modal Frequency Kevlar

Epoxy Composite Material

7.

76.163 120.75

8.216.19 342.79

9.400.52 660.6

10.400.57 660.68


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1. Conventional two-piece drive shaft can be replaced

with kevlar epoxy composite single-piece drive shaft

for heavy vehicles. The aim of design and analysis

was achieved.

2. The study has investigated the use of composite

materials for single-piece light weight drive shaft.

Kevlar epoxy composite material suited on design

and vibration criteria.

3. The structural analysis evaluates the shear stresses,

maximum principal stress, total deformation, strain

energy, max. principal elastic strain and equivalent

elastic strain for stainless steel and kevlar epoxy

composite material.

4. All the structural analysis values are in permissible

limit for Kevlar epoxy composite, which ensures the

strength of single-piece drive shaft. Vibration mode

shapes (axial bending vibration, torsional vibration)

were identified for steel and composites material

single-piece drive shaft.5. Composite material kevlar epoxy provides the

structural strength against shearing, torsional

vibration and axial bending vibration.

In conclusion kevlar epoxy composite material can be used for

single piece drive shaft based on strength and modal frequency

output parameters. Modal analysis based vibration study find

that, modal frequency of kevlar epoxy composite materials are

in higher order range which prevents resonance condition.

FEA based analysis tool Ansys14.5 has been used for

structural and modal analysis. Solidedge and Pro-E software

has excellent features for complex design. The FEA resultshows that on design and vibration index kevlar epoxy

composite can be used as single-piece drive shaft material.

FEA results are in good agreement offering satisfactory

results.

ACKNOWLEDGEMENT

This research work is carried out at advanced Modelling and

Simulation lab funded by Department of Science and

Technology (DST) and research cell of Graphic Era

University, Dehradun. Authors are thankful to DST, New

Delhi and Management of Graphic Era University, Dehradun

for the necessary funding.

REFERENCES

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1428, 2006.

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Dynamic Structure and Vibration Characte