# Finite Element Analysis Of Composite Drive Shaft Engineering Essay

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Abstract- In this work, the behavior of one-piece carbon/epoxy composite drive shaft is studied. This work comprises of the static, modal and buckling analysis using finite element modeling software ANSYS for composite drive shaft. Substituting laminated composite materials for conventional materials has many advantages because of their higher specific stiffness and strength. It is carried out to find the effect of fiber orientation and stacking sequence on natural frequency and buckling torque of composite drive shaft. Finite element analysis is carried out for four different stacking sequences and fiber orientation. The result of the configuration which gives high natural frequency and torque carrying capacity is further selected for manufacturing and testing.

Keywords-Composite Drive shaft; Finite Element Analysis; Modal ;Buckling; Stacking Sequence

Introduction

A driveshaft is the connection between the transmission and the rear axle of an automobile. Power generated by the engine is transferred to the transmission via a clutch assembly. The transmission is linked to the driveshaft by a yoke and universal joint, or u-joint, assembly.

The two piece steel drive shafts has a complex and heavy structure simultaneously have lower specific stiffness, lower critical speed and high weight, so the performance of steel shaft is limited. The two main functional requirements of automotive drive shafts are the transmission of static and dynamic torsional loads and it should have high fundamental bending natural frequency to avoid whirling of shaft at high speed. The steel shaft cannot easily satisfy these two functional requirements.

An efficient design of composite drive shaft could be achieved by selecting the proper variables, which are specified to minimize the chance of failure and to meet the performance requirements. As the length and outer radius of drive shafts in automotive applications are limited due to spacing, the design variables include the inside radius, layers thickness, number of layers, fiber orientation angle and layer stacking sequence. FEM analysis is carried out on one piece composite shaft to analyze the maximum torsion capacity and fundamental natural frequency; furthermore a one-piece propeller shaft for rear wheel drive automobile is manufactured with carbon fiber and epoxy resin as a composite material. The composite drive shaft has many benefits such as reduced weight, less noise and vibration and these materials have relatively high damping characteristics. The use of one piece drive shaft reduced assembly time, inventory cost, maintenance, and part complexity.

A.R. Abu Talib et.al, [1] have carried out Finite Element Analysis of composite drive shaft using carbon and glass fibers within an epoxy matrix. Chih-Yung Chang et.al, [2] studied the vibration behaviors of the rotating composite shafts containing randomly oriented reinforcements. Dai Gil Lee et.al [3] developed a new manufacturing method of automotive hybrid aluminum/composite drive shaft, in which a carbon fiber epoxy composite layer was co-cured on the inner surface of an aluminum tube rather than wrapping on the outer surface to prevent the composite layer from being damaged by external impact and absorption of moisture. Durk Hyun Cho et.al, [4] developed a hybrid one-piece drive shaft composed of carbon fiber epoxy composite and aluminum tube and manufactured by co-curing the carbon fiber on the aluminum tube. H.B.H. Gubran et.al [5] studied the dynamic performance and cross-section deformation of shafts made of metals (steel and aluminum), composites and hybrids of metals and composites. Hak Sung Kim et.al, [6] studied optimal stacking sequence of the composite material and optimal thickness of aluminum tube for the drive shaft for low velocity impact. Mahmood M. Shokrieh et.al, [7] studied the effect of boundary conditions, fiber orientation and stacking sequence on the mechanical behavior of composite drive shafts and also on torsional stability of composite drive shaft. S.A.Mutasher et.al, [8] have performed the numerical analysis for the hybrid shaft using finite element software ANSYS. Here the maximum torsion capacity of the hybrid aluminum/composite shaft for different winding angle, number of layers and stacking sequences was studied.

## Theoretical Analysis

The main aim is to study the dynamic behavior of the hollow rotating composite shaft on rigid bearings. In this model the transverse shear deformation, rotary inertia and gyroscopic effects, as well as the coupling effect due to the lamination of composite layers have been incorporated. The critical speeds were determined using equivalent modulus beam theory (EMBT), assuming the shaft to be a thin-walled circular tube simply supported at the ends. The shaft rotates at a constant speed about its longitudinal axis. It has uniform circular cross section, it is perfectly balanced, i.e. at every cross section; the mass center coincides with the geometric center, All damping and nonlinear effects are excluded, since lamina is thin and applied load is not out of plane, it is considered under the plain stress.

## Stresses In K Th Layer Of Composite Drive Shaft

The lamina is thin and if no out-of-plane loads are applied, it is considered as the plain stress problem. Hence, it is possible to reduce the 3-D problem into 2-D problem. For unidirectional 2-D lamina, the stress-strain relationship in terms of physical material direction is given by [1]

(1)

The matrix Q is referred as the reduced stiffness matrix for the layer and its terms are given by

(2)

## ;

; (3)

## Buckling Torque

Since the drive shaft is long, thin and hollow, there is a possibility for it to buckle. The expression of the critical buckling torque for thin-walled orthotropic tube is given by

(4)

Where r, is the mean radius and t is the total thickness. It is obvious that the stiffness modulus at hoop direction (Eh) plays the big role in increasing the buckling resistance. The factor of safety is the ratio of the buckling torque to the ultimate torque.

## Lateral And Bending Natural Frequency

The drive shaft is idealized as simply supported at it's or pinned -pinned beam. The lowest natural frequency is given by

(5)

Where g is the acceleration, W is the weight per unit length, L is the length and I is the moment of inertia, which is, in the thin walled tube equal to

(6)

Where r is the mean radius and t is the wall thickness. To increase the natural frequency, carbon fibers are required to be oriented in axial direction.

## Static ,Modal And Buckling Analysis Of Composite Drive Shaft (Fea)

A static analysis is used to determine the displacements, stresses, strains and forces in structures or components caused by loads that do not include significant inertia and damping effect

## Modeling

The model is created in ANSYS and meshed by using SHELL 181 element. The finite element model of the composite drive shaft geometry was built using 3360 elements and 3600 nodes. The finite element model is shown below figure.1.Material properties of the composite shaft considered for the finite element analysis are listed in table 1.Thickness of shaft is 5 mm and eight layers of different ply orientations are considered for analysis.

## Meshing

Meshing the geometry is nothing but creation of finite element model, which consists of nodes and elements. The element or mesh density is set in ANSYS using ESHAPE, ESIZE, KESIZE and LESIZE command. Meshing can be done by using AMESH, VMESH commands. Composite drive shaft is meshed using AMESH (free) command

Figure 1: Finite Element Meshed Model

## Boundary Condition And Loading for Static Analysis

One end if fixed, all the nodes at one end of the shaft are constrained in all directions i.e all degrees of freedom are fixed at these nodes. All the nodes at other end of the shaft are subjected to the torque load (1100 N-m) around Z-axis which is shown in fig.2.

## Boundary Condition And Loading For Modal Analysis

In free - free analysis, no boundary conditions are applied to the shaft, i.e. no constraints are applied to the finite element model. No nodes are constrained in any degree of freedom. Also, there should not be any external force acting on the shaft. The study reveals the different types of bending and torsion behavior of the composite shaft during the different modal frequencies i.e. mode shapes. For different stacking sequence modal analysis is carried out.

## Boundary Condition And Loading For Buckling Analysis

The composite drive shaft is subjected to pure torsion. One end is fixed with all degrees of freedom arrested. The other end is subjected to a torque is applied as distributed forces in tangential direction to the outside nodes at this end of the shaft. A force of 40 N is applied on total 40 nodes on the periphery of the shaft.

Figure 2: Loading and Boundary conditions

## Stacking Sequence

While making the finite element model and meshing the model, different Stacking Sequences/ Layer Orientations are considered for the composite shaft. They are as shown in Table 2

Table 2 Different stacking sequences

## Configuration

## Stacking Sequence/ Layer Orientation (degree)

1

[0,+45,-45,90,90,-45,+45,0]

2

[30,-30,-30,30,30,-30,-30,30]

3

[45,-45,45,-45,-45,45,-45,45]

4

[90,0,90,90,0,90,0,90]

Sample stacking sequence for Configuration-1 is shown in figure 3.

Figure 3: Sample stacking sequence

## Results And Discussion

## Stress Analysis Result

Figure 4: Angular deformation of the shaft

Displacement of the shaft for four different stacking sequence are plotted in the table 3, it is clear that the displacement of the shaft is changing as the stacking sequence changes. For the third configuration the displacement is 13 mm which is minimum as compare to other configurations. Also angle of twist of the shaft is minimum for third stacking sequence.fig.4 shows the angular displacement of the shaft for configuration 4.

Table 4 shows the stresses in the composite drive shaft for different stacking sequence and ply orientation. The configuration 3 is quiet good for the design.

## Modal Analysis Result

Figure 5 : Mode shape1(Configuration 3)

From the modal analysis results it is found that by using the different stacking sequence one can obtain the high fundamental natural frequency .Also there is strong effect of fiber orientation on natural frequency. For Fourth stacking sequence the fundamental frequency is high but using that stacking sequence the drive shaft fails in torsion because shear stress in static analysis is beyond the allowable stress. For configuration one and two the fundamental natural frequency is very low because of fiber orientation angle. The natural frequency for third configuration is 99Hz,which is shown in fig.5. So for obtaining the best stacking sequence buckling analysis is necessary. The results of modal analysis are shown in table 5.

## Buckling Analysis Result

The results obtained from the analysis are higher than the static applied torque. So using finite element analysis, the strength of a composite drive shaft can be simulated. The effect of the stacking sequence of the composite layers on the strength of the drive shaft is studied. The stacking sequence of the layers for a composite drive shaft strongly affects the buckling torque which is shown in the table 6. Design of composite drive shaft is safe for buckling as the buckling torque is higher than the applied torque. Fig.6 shows the overall buckling displacement plot for configuration 3

Figure 6 :Overall buckling displacement plot for (configuration 3)

## Effect Of Stacking Sequence On Natural Frequency

Figure 7 Graph of Mode No.V/s frequency

Fig. 7 shows that there are higher modes of frequency for configuration 3, while modes of other configurations are at lower side. The functional requirement of composite shaft is that it should have high natural frequency to avoid whirling of shaft at high speed and that is fulfill by using configuration 3.

## Effect Of Stacking Sequence On Buckling Torque

Fig. 8 shows that there is large effect of stacking sequence on buckling torque. Configuration consists only one fiber orientation angle cannot gives high buckling torque, as the fibers are strong along the longitudinal direction while they are weak along transverse direction. Configuration 1 consists 00, 450, and 900 so it is having high buckling torque. Configuration 3 gives buckling torque of 3562 N-m which is higher than the applied torque so it is safe for buckling.

Figure 8 Effect of stacking sequence on buckling torque

## Conclusion

From the static, modal and buckling analysis configuration three is selected as it is having safe in shear torsion also it is having natural frequency 99 Hz which is higher than configuration one & two and buckling torque is higher than the applied torque for configuration three.

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