Design, Static and Modal Analysis of A Propeller Shaft …€¦ · shaft are steel, carbon Epoxy...

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 10, October 2013)

98

Design, Static and Modal Analysis of A Propeller Shaft for

Reducing Vibrations Using Composite Damping Srimanthula Srikanth

1, Jithendra Bodapalli

2, Avinash Gudimetla

3

1Student of M.Tech (CAD/CAM) in Dept. Of ME, NCET College, Vegavaram.

2Assoc. Professor and HOD, Dept. Of ME, NCET College, Vegavaram

3Assoc. Professor, Dept. of ME, Pragati Engineering college, surampalem

Abstract-- With the growing demand for the energy

efficient and smart materials, the necessity for reducing the

vibrations in the highly sophisticated parts of the machinery is

playing a major role. High-technology structures often have

stringent requirements for structural dynamics. Suppressing

vibrations is crucial to their performance. Passive damping is

used to suppress vibrations by reducing peak resonant

response. Viscoelastic damping materials add passive

damping to structures by dissipating vibration strain energy

in the form of heat energy. The incorporation of damping

materials in advanced composite materials offers the

possibility of highly damped, light-weight structural

components that are vibration-resistant.

The main theme of the project is to analyze a shaft with

and without damping material and also for various isotropic

and orthotropic materials. Along with alloys of various

materials, composite materials are also considered to analyze

the case to increase its robustness. The materials used for

shaft are steel, carbon Epoxy and E – Glass Epoxy. The model

of a particular shaft is taken and analyzed using ANSYS. The

structural analysis is done to verify the strength of the shaft

and to compare the results for the three materials. Modal

analysis is also done on the shaft to determine mode shapes

and to find their frequencies.

Keywords— Viscoelastic damping, frequency, Propulsion

Shaft, Damping Material, Carbon Epoxy, steel, Carbon

Epoxy, E-Glass Epoxy

I. INTRODUCTION

All engineering structures experience vibratory motion

whether in reference to the world’s tallest building or a

printed circuit board in a flight control computer. The

effect of operating environments and inherent dynamic

behavior cause the transmission of periodic waves

throughout a structure. In turn, the structure undergoes

mechanical vibrations. These unwanted vibrations result in

fatigue and catastrophic failure of structures. Hence, the

control of vibrations is a serious concern for engineering

design.

A structure subjected to oscillatory deformation consists

of a combination of kinetic and potential energy. In the

case of real structures consists of energy dissipative

elements as some of the energy is lost in each cycle. The

amount of energy dissipated is a measure of the structure’s

inherent damping. Damping can be viewed as the

conversion of mechanical energy of a vibrating structure

into thermal energy, which ultimately is lost to the

structure’s environment.

Vibration control can be accomplished through active

and/or passive damping treatments. Active damping

control involves the use of a feedback control system that

senses structural vibrations and then calculates the

necessary control input for actuators. On the other hand,

passive damping control refers to a structure’s ability to

damp its own oscillations as a result of its structural design,

material properties, or by the incorporation of devices like

coatings and elastomers that dissipate energy.

II. LITERATURE SURVEY

Viscoelastic damping materials add passive damping to

structures by dissipating vibration strain energy and

generate heat energy. The incorporation of damping

materials in advanced composite materials offers the

possibility of highly damped, light weight structural

components that are vibration resistant. Concurring

viscoelastic damping materials in composites has shown to

be successful in greatly increasing the damping of

composite structures. The damping performance, however,

is often not as high in co cured composites as in

secondarily bonded composites, where the damping

material does not undergo the cure process. Substituting

composite structures for conventional metallic structures

has many advantages because of higher specific stiffness

and specific strength of composite materials. The fiber

enhanced Viscoelastic damping polymer is intended to be

applied to lightweight flexible structures as a surface

treatment for passive vibration control.



99

A desirable packing geometry for the composite material

is proposed, which is expected to produce maximum shear

strain in the Viscoelastic damping matrix. A general

method for modeling material damping in dynamical

systems is presented and it is primarily concerned with a

dissipation model based on Viscoelastic assumptions.

Different numerical approaches for modeling and analyzing

the behavior of structures having constrained layer

damping. Two numerical studies are presented that reveal

the accuracy limits of the different finite element modeling

approaches for additive and integrally damped plate type

structures. Now through the use of improved computational

– based approaches (i.e. finite element method) along with

the availability of reliable damping materials with accurate

thermal and dynamic property characterizations, it is

possible to incorporate damping treatments as part of the

initial structural design process, thereby virtually

eliminating sharp resonant peaks. Cylindrical shells with a

constrained damping layer treatment are studied using three

theories. Constrained layer damping in structures is a very

popular method to control resonant amplitudes of vibration.

Shells of revolution (e.g., cylindrical and conical) find wide

application in the aerospace industry. An efficient method

is described for finite element modeling of three-layer

laminates containing a viscoelastic layer. Modal damping

ratios are estimated from undamped normal mode results

by means of the Modal Strain Energy (MSE) method. The

solution for a radially simply supported shell has been

obtained and the procedure for determining the damping

effectiveness in terms of the system loss factor for all

families of the modes of vibration in a multilayered shell

with elastic and viscoelastic layers is reported.

Approximately 85% of the passive damping treatments in

actual applications are based on viscoelastic materials. The

solution for the vibration and damping analysis of a general

multilayered cylindrical shell consisting of an arbitrary

number of orthotropic material elastic and viscoelastic

layers with simply supported end conditions has been

reported. Damping mechanics for predicting the damped

dynamic characteristics in special composite structures

with compliant inter laminar damping layers are presented.

Designed –in passive damping for structures is usually

based on one of four technologies: Viscoelastic materials,

viscous fluids, magnetic, or passive piezoelectrics. The

technology of using viscoelastic materials for passive

damping is discussed in more detail than the other methods

since it is presently the most widely used type of damping

technology. The effectiveness of damping treatments in

structures is related to the amount of vibration energy

converted into other forms of energy.

Two viscoelastic models, namely ADF and GHM, which

account for frequency dependence and allow frequency and

time domain analysis of hybrid active-passive damping

treatments, is compared which is made of viscoelastic

layers constrained with piezoelectric actuators. The ever

increasing need to improve the efficiency of structural

system places a growing importance on dynamic analysis

in the design or development cycle. Damping analysis is

performed by the complex stiffness (modulus and loss

factor) approach (variation of material properties and

damping factors with frequency is taken into account), and

by consideration of the dissipation of vibratory energy

through friction. It is well known that considerable

reduction in resonant vibration can be realized by the use of

highly damped viscoelastic materials as cores in sandwich

structures. Such reductions are of practical interest in

design applications where resonant excitation cannot be

avoided. Embedding viscoelastic materials to dissipate

energy within the structures provides a robust means of

incorporating damping without encountering several of the

common disadvantages associated with external damping

treatments. A systematic analytical study of the

improvement of damping in polymer composites at the

micromechanical level under transverse normal loading by

the use of special fiber coatings is described. The

formulation of a theory for the prediction of damping and

natural frequencies laminated composite beams with

multiple viscoelastic damping layers are described.

III. OBJECTIVE

This project work expresses the difference between the

structures with and without damping material. The effect

of damping on the performance of isotropic (steel) and

orthotropic (Carbon Epoxy & E-Glass Epoxy) structures is

to be analyzed by using Finite Element Analysis. The

values of the static deflection for Steel Shaft, Carbon

Epoxy Shaft and E-Glass Epoxy Shaft are to be compared

with and without visco elastic polymer (Rubber).

IV. NEED FOR DAMPING

When a structure suffers from excessive vibration or

noise, it is being subjected to undesirable excitations. These

excitations can be reduced by varying the parameters

damping, modal stiffness and mass. Consider a structure

excited at its boundary and vibrating in its fundamental

mode of vibration. Such a structure can be represented by a

single degree of freedom system shown below.



100

Fig1: Boundary Excitation

The equation of motion of such a system can be written

in the form:

0)ww)(i1(kwm 0

..

Where k, m and are the modal stiffness, mass and

damping values, respectively. The ratio of the response of

the mass to the input vibration, w/ wo is illustrated in

forthcoming figures.

A. Effect of Mass Changes For The Boundary Excitation

Case

Fig2: Temperature Vs Frequency for two masses

In the Fig.2 by keeping the stiffness and damping

constant the effect of the structure can be seen by varying

the mass. Here the same amount of response is occurred but

at different frequency.

B. Effect of Stiffness Changes for the Boundary

Excitation Case

Fig3: Temperature Vs Frequency for two different stiffness values

In Fig.3, by keeping the mass and damping constant the

effect of the structure can be seen by varying the stiffness.

The response is same as that in the case of change of effect

in mass.

C .Effect of Damping Changes for the Boundary

Fig 4: Temperature Vs Frequency for two different damping values

In this case by keeping the mass and stiffness constant

the effect of the structure can be seen by varying the

damping. In this case it reduces the maximum amplitude by

increasing the damping. .

There are three different zones in the above figures.

One below the natural frequency

One above the natural frequency

One at the natural frequency

It is evident from the above figures that the stiffness and

mass modifications affect the frequency range above

resonance, whereas damping affects the response near

resonance, and no important changes occur below the

resonant frequency from changes in damping, mass or

stiffness.

The primary effect of increased damping in a structure is

a reduction of vibration amplitudes at resonance's, with

corresponding decreases in stresses, displacements, fatigue,

and sound radiations.

V. PROBLEM FORMULATION

A. Introduction to Propulsion Shaft:

The torque transmission capability of the propeller shaft

for ship should be larger than 3,500 Nm and fundamental

natural bending frequency of the propeller shaft should be

higher than 6,500 rpm to avoid whirling vibration. The

outer diameter of the propeller shaft should not exceed 100

mm due to space limitations. The propeller shaft of

transmission system is shown in figure 4, for following

specified design requirements as shown in Table 1. The

description of shaft is given in fig. Due to space

limitations the outer diameter of the shaft is restricted to

90.24 mm.



101

Fig5: Pictorial representation of shaft transmission system.

B. Problem Description:

The one-piece hollow composite drive shaft should

satisfy three design specifications, such as static torque

transmission capability, torsional buckling capacity and the

fundamental natural bending frequency. For given

specification, the damping factor for Steel, carbon Epoxy

and E-Glass Epoxy are to be calculated and compared with

and without damping material (Rubber).

Table 1

Problem Specification

Table 2

Material Properties

VI. BRIEF OVER VIEW OF STRUCTURAL STATIC ANALYSIS

Static analysis is one in which the loads/boundary

conditions are not the functions of time and the assumption

here is that the load is applied gradually. The most common

application of FEA is the solution of stress related design

problems.

Typically in a static analysis the kind of matrix solved is

[K] * [X] = [F]

Where K is called the stiffness matrix, X is the

displacement vector and F is the load matrix. This is a force

balance equation. Some times, the K matrix is the function

X. Such systems are called non-linear systems.

Nodal Displacements ui, uj

Nodal Forces fi, fj

Spring constant k

Spring force displacement relationship

F = k with = uj – ui

Where K = F/ (>0) is the force needed to produce a unit

stretch.

Consider the equilibrium forces for the spring.

At node i, we have

fi = -F = -k(uj – ui) = kui – kuj

And at node j,

fj = F = k(uj – ui) = - kui + kuj

Ductile material

Under combined static loading, the machine parts made

of ductile material will fail by yielding. The working or

allowable stress is therefore, passed on the yield point

stress. The maximum shear stress theory will be used for

the design because it is conservative and easy to apply.

Brittle materials

Failure in brittle materials, takes place by fracture.

Brittle materials do not have a distinct yield point and so,

the ultimate strength is used as the basis for determining

the allowable or design stress. Separate design equations

should be used in tension and compression, since for

materials like cast iron; the ultimate compressive strength

is considerably greater than the ultimate tensile strength.

The maximum principal stress theory will be used for the

design. Due consideration will be given to the sign of

principal stresses. If both the principal stresses (2-D case)

are of the same sign, the effect of the smaller stress is

neglected. If the two principal stresses are of opposite sign,

then the maximum principal stress theory does not give

conservative results. In that case another equation should

be used.

A. Static Analysis Comparison of Theoretical and Ansys

Analysis

In this part static deflection of the steel shaft is

calculated and compared with ANSYS results. The

specification for the shaft is given in the Table 3. For

calculating the deflection, the boundary condition is taken

by considering its self weight.

S. No Parameter Notation Units Value

1. Torque T N-m 3500

2. Max

Speed

N RPM 6500

3. Length L m 1.250



102

Table 3

Specification for Steel Shaft

VII. STEEL SHAFT

A. Steel Shaft without damping material

Material for Shell 99

In this case shell element is taken to calculate the

deflection value for steel shaft. Here Shell element is taken

due to specify the number of layers to include the damping

polymer. Here steel shaft without damping material is

considered and specifications are tabulated in table 3.

Fig 6: Steel Solid model

Fig7: Meshed Model

Using ANSYS the deflection value is calculated. The

value is 0.252e-4

m. The deformed shape of the shaft is

shown in the Fig 7.

B. Steel Shaft with Damping Material

In this type a damping material (i.e.) Rubber is inserted

between the two layers of shaft and the deflection value is

calculated using ANSYS. The specification of the shaft

with damping material is shown in the Table 4.

Table4

Specifications for Steel Shaft with Rubber

Sl. No. Parameters Values

1 Outer Diameter 0.09024 m

2 Thickness of each

layer 1.05 e

-3 m

3 Number of layers 3

4 Damping Material Rubber

5 Element Shell 99



2 Thickness 2.1 e -3



103

Fig8: Stacking Sequence for Steel Shaft with Rubber

In the above Fig 8. Stacking sequence of the steel shaft

with damping material is shown.

Fig 9: Deflection of Steel Shaft with Rubber

Using ANSYS the deflection value is calculated. The

value is 0.41 e -4

m. The deformed shape of the shaft is

shown in the Fig 9.

C. Carbon Epoxy Shaft without Damping Material

In this case Carbon Epoxy shaft is modeled with 13

layers by considering the shell element. The specifications

are shown in the table5.

Table 5

Specification for Carbon Epoxy Shaft



2 Thickness of each

layer 1.5 e

-4 m


4 Element Shell 99

Fig 10: Stacking Sequence for Carbon Epoxy Shaft

In the above Fig 10. The stacking sequence of the

Carbon Epoxy shaft without damping material is shown.

Fig 11: Static Deflection for Carbon Epoxy Shaft

The value is 0.376 e -4

m. The deformed shape of the

shaft is shown in Fig 11.

D. Carbon Epoxy Shaft with Damping Material

In this case Carbon Epoxy shaft is modeled with

damping material (Rubber) and it is incorporated in

between the layers. The specification of the shaft is shown

in the Table 6.



104

Table 6

Specification for Carbon Epoxy Shaft with Rubber



2 Thickness of each layer 1.5 e -4

m



5 Element Shell 99

The stacking sequence of the Carbon Epoxy shaft with

damping material (Rubber) is shown in the fig 12. Here the

8th

layer is the rubber.

Fig 12: Stacking Sequence for Carbon Epoxy Shaft

Fig 13: Static Deflection for Carbon Epoxy Shaft with Rubber.



shaft is shown in the Fig 13.

E. E-Glass Epoxy Shaft without Damping Material

In this case E-Glass Epoxy shaft is modeled with 23

layers by using the shell 99 element. The specifications are

shown in the table 7.

Fig14: Stacking Sequence Layers from 1 to 12

Fig 15: Stacking Sequence Layers from 13to23

The stacking sequence of the Carbon Epoxy shaft

without damping material is shown in above figures.

Fig16: Static Deflection for E-Glass Epoxy Shaft

The value is 0.00116 m. The deformed shape of the shaft

is shown in the Fig 16.



105

F. E-Glass Epoxy Shaft with Damping Material

In this case E-Glass epoxy shaft is modeled with

damping material (Rubber) and it is incorporated in

between the layers. The specification of the shaft is shown

in the table 8.

Table 7

Specification for E- Glass Epoxy Shaft

Sl.

No. Parameters Values

1 Outer Diameter .09024 m

2 Thickness of each

layer 1.5 e

-4 m



5 Element Shell 99

Fig17: Stacking Sequence Layers from 1 to 13

Fig18: Stacking Sequence Layers from 14to24

The stacking sequence of the E-Glass Epoxy shaft with

damping material (Rubber). Here the 12th

layer is the

rubber.

Table 8

Specification for E- Glass Epoxy Shaft with Rubber

Fig 19: Static Deflection for E-Glass Epoxy Shaft with Rubber



shaft is shown in the Fig 19.

VIII. MODAL ANALYSIS

Any physical system can vibrate. The frequencies at

which vibration naturally occurs, and the modal shapes

which the vibrating system assumes are properties of the

system, and can be determined analytically using Modal

Analysis.

Modal analysis is the procedure of determining a

structure's dynamic characteristics; namely, resonant

frequencies, damping values, and the associated pattern of

structural deformation called mode shapes. It also can be a

starting point for another, more detailed, dynamic analysis,

such as a transient dynamic analysis, a harmonic response

analysis, or a spectrum analysis.

Modal analysis in the ANSYS family of products is a

linear analysis. Any nonlinearities, such as plasticity and

contact (gap) elements, are ignored even if they are

defined. Modal analysis can be done through several mode

extraction methods: subspace, Block Lanczos, Power

Dynamics, Reduced, Unsymmetric and Damped. The

damped method allows you to include damping in the

structure.



2 Thickness of each layer 1.5 e -4 m


4 Element Shell 99



106

A. Uses of Modal Analysis

Modal analysis is used to determine the natural

frequencies and mode shapes of a structure. The natural

frequencies and mode shapes are important parameters in

the design of a structure for dynamic loading conditions.

They are also required to do a spectrum analysis or a

mode superposition harmonic or transient analysis. Another

useful feature is modal cyclic symmetry, which allows

reviewing the mode shapes of a cyclically symmetric

structure by modeling just a sector of it.

B. Modal Analysis of Steel Shaft without Damping

Material by Shell Element

In this part Modal analysis of the shaft is calculated

using the same specifications given in the static analysis.

Modal analysis is needed because the output of this

analysis is used in the transient analysis to calculate the

time step.

C. Modal Analysis of Steel Shaft Using Shell Element

Without and With Rubber

In this case Steel shaft is modeled using Shell 99. The

specifications used are same as in the Static Analysis

Fig20: Modal Analysis for Steel Shaft using Shell 99

In this case Rubber is embedded in between the steel

layers. The stacking Sequence and the specifications are

same as in the Static Analysis.

Fig 21: Modal Analysis for Steel Shaft with Rubber

E. Modal Analysis of Carbon Epoxy Shaft without And

With Rubber

Fig22: Modal Analysis for Carbon Epoxy Shaft

Fig23: Modal Analysis for Carbon Epoxy Shaft with Rubber

F. Modal Analysis of E-Glass Epoxy Shaft without and

With Rubber

Fig 24: Modal Analysis for E-Glass Epoxy Shaft



107

Fig25: Modal Analysis for E-Glass Epoxy Shaft with Rubber

IX. RESULTS

In this case all the results of Static and Modal Analysis

of Steel Shaft, Carbon Epoxy Shaft and E-Glass Epoxy

shaft with and without damping polymer are tabulated and

compared.

Fig 26: Modal Analysis for Steel Shaft with Rubber

A. Comparison of Steel Shaft with and Without Damping

Material

Table 9

Comparison of Results for Steel Shaft

Type of

the

Shaft

Results

Steel without

Viscoelastic

Material

Steel with

Viscoelastic

Material

Static Deflection

(in m) 0.41 e

-4 0.252e-4

B. Comparison of Carbon Epoxy Shaft with and Without

Damping Material

C. Comparison of E-Glass Epoxy Shaft with and Without

Damping Material

Table 10

Comparison of Results for Carbon Epoxy Shaft

Type of the

Shaft

Results

Glass Epoxy

without

Damping

Material

Glass Epoxy with

Damping Material

Static

Deflection

(in m)

0.102 e -3

0.00116

Table 11

Comparison of Results for E- Glass Epoxy Shaft

X. CONCLUSIONS

As the aim of the project is to reduce the damping

effects of the driven shaft, the major sources used for this

purpose are composite materials. By using three different

kind of composite materials steel, carbon epoxy, E-glass

epoxy the project has been carried out. For controlling the

damping effects by using passive damping the materials

which reduces these damping like rubber are employed in

the center of the shaft. Shaft is analyzed using layer

stacking method in ANSYS software which utilizes finite

element method technologies. These layer stacking

techniques are employed for shafts with and without

damping material. Static analysis is done for observing the

steady loading conditions. The results have shown that the

shaft with damping material made of any composite

material has less damping effects when compared with

shaft without damping material. The results have clearly

proved that the static deflection of the shaft made with

three composite materials with damping material when

compared with without damping material. For the purpose

of dynamic loading conditions and for determining natural

frequencies, mode shapes modal analysis is also done.

Type of the

Shaft

Results

Carbon Epoxy

without

Damping

Material

Carbon Epoxy

with

Damping

Material

Static Deflection

(in m)

0.42 e -4

0.376 e -4



108

The final result of the project is the shaft made with

composite material and damping material has less damping

effects compared with composite material shaft.

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1997.

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Newyork.

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Elements", Prentince Hall PTR, New Jeresy, 1995.

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Composite Structures, Vol. 43, 1998, pp. 115-125.

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[6] Jin Kook Kim, Dai Gil Lee, and Durk Hyun Cho, 2001,

―Investigation of Adhesively Bonded Joints for Composite Propeller shafts‖, Journal of Composite Materials, Vol.35, No.11, pp. 999-

1021.

[7] T. E. Alberts and Houchun Xia, ―Design and Analysis of Fiber Enhanced Viscoelastic Damping Polymers‖, Journal of Vibration

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Design, Static and Modal Analysis of A Propeller Shaft …€¦ · shaft are steel, carbon Epoxy...

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