Design Optimization & Analysis of Drive Shaft - vsrd international ...

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VSRD-MAP, Vol. 2 (6), 2012, 210-215
Design Optimization & Analysis of Drive Shaft
ABSTRACT
1 Anup A. Bijagare*, 2 P.G. Mehar and 3 V.N. Mujbaile
This work deals with the replacement of conventional two-piece steel drive shaft with a single-piece high
strength carbon/ epoxy composite drive shaft for an automotive application. The design parameters were
optimized with the help of Genetic Algorithm (GA) with the objective of minimizing the weight of composite
drive shaft. The design optimization also showed significant potential improvement in the performance of drive
shaft. The results of GA are used for modelling of carbon/ epoxy composite drive shaft& steel drive shaft using
Pro-E software, to perform static, buckling & modal analysis of both the drive shafts using ANSYS software.
Finally compare both the analysis result.
Keywords : Driveshaft; GA; Optimization; Composites; Weight Minimization; Pro-E Software; ANSYS
Software.
1. INTRODUCTION
The Overall objective of this work is to design composite drive shaft for power transmission application for
automobiles. This work deals with the replacement of conventional steel drive shaft with high strength
carbon/epoxy composite drive shaft. Also in this work Genetic Algorithm is successfully applied to minimize
the weight of shaft which is subjected to the constraints such as torque transmission & fundamental natural
frequency. The design variables are number of plies & thickness of the ply. With the help of results of Genetic
Algorithm model of carbon/epoxy composite drive shaft and model of steel drive shaft are created with the help
of Pro-e software, to perform static analysis, buckling analysis& modal analysis of both the drive shafts using
ANSYS software. The analysis result of carbon/epoxy composite drive shaft & steel drive shaft are compared to
shows beneficial shaft among those two shafts.
1 Research Scholar, 2,3 Assistant Professor, 1,2,3 Department of Mechanical Engineering, K.D.K. College of Engineering,
Nagpur, Maharashtra, INDIA. *Correspondence : bijagare_anup@yahoo.com

Anup A. Bijagare et al / VSRD International Journal of Mechanical, Auto. & Prod. Engg. Vol. 2 (6), 2012
1.1. The Genetic Algorithm
GA is non-traditional method of optimization in which solving the problem of minimise or maximise the
objective function. On traditional algorithm are very difficult to solve manually. Solution for the non-traditional
method can be obtained computerising algorithm using c-language. GA is the direct search algorithm based on
the mechanics of biological evolution.GA is developed by John Holland university of Michigan (1970’s) .To
understand the adaptive process of the natural systems. To provide efficient, effective techniques for
optimization & machine learning applications.
1.2. Introduction of Drive Shaft
Fig. 1: Two Piece Drive Shaft Arrangement for Rear Wheel Vehicle Driving System
The drive shaft is one of the important parts in the automobiles which correspond to design with rear wheel
drive and front engine installation. The weight reduction of the drive shaft can have a certain role in the general
weight reduction of the vehicle and it is a highly desirable goal. If it can be achieved without increased in cost
and decreased in quality and reliability. It is possible to achieve design of composite drive shaft with less weight
to increase the natural frequency of the shaft and to decreases the bending stress. By doing this the torque
transmission and torsion buckling capabilities are maximized.
2. COMPOSITE MATERIAL
Composite consist of two or more material phase that are combine to produce a material that has superior
properties to these of its individual constituent. Technologically the most important composite are those in
which the dispersed phase is in the form of fibre. The design of fibre-reinforced composite is based on the high
strength and stiffness on a weight basis, the principal basis. The principle fibres in commercial use are various
types of glass, carbon, graphite and Kevlar. Here carbon fibres are selected as potential material for the design
of shaft.
Table 2.1 : Properties of High Strength Carbon/Epoxy Composite Material
Property Symbol Unit HS Carbon /E-poxy Steel
Young's Modulus E Gpa 210 207
Poisson Ratio V 0.3 0.3
Density Kg/m 3 1600 7600
Shear strength Ss Mpa 420 370
Shear Modulus G Gpa 70 80
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Anup A. Bijagare et al / VSRD International Journal of Mechanical, Auto. & Prod. Engg. Vol. 2 (6), 2012
3. SPECIFICATION OF THE PROBLEM
The torque transmission capability of the drive shaft for passenger cars, small trucks, and vans should be larger
than 3500 Nm (Tmax) and fundamental natural bending frequency of the drive shaft should be higher than 6500
rpm (Nmax) to avoid whirling vibration. The drive shaft outer diameter do should not exceed 100 mm due to
space limitations. Here outer diameter of the shaft is taken as 90 mm. The drive shaft of transmission system
was designed optimally to the specified design requirements
4. DESIGN OF STEEEL DRIVE SHAFT
Mass of the steel drive shaft
Table 4.1 : Design Parameter of Steel Drive Shaft
Parameter of Shaft Symbol Value Unit
Outer Diameter do 90 mm
Inner Diameter di 83.36 mm
Length Of the Shaft L 1250 mm
Thickness Of shaft T 3.32 mm
m= AL= × ×( do 2 - di 2 ) ×L … (1)
m = 8.58
Torque transmission capacity of steel drive shaft
T= Ss× ×[( do 4 - di 4 ) × do ] … (2)
T = 55.93 ×
4.1. Fundamental Natural Frequency
Lateral or Bending Vibration : The shaft is considered as simply supported beam undergoing transverse
vibration .Natural frequency can be found using the Timoshenko Beam Theory - Ncrt.
Timoshenko Beam Theory - Ncrt : It considers both transverse shear deformation as well as rotary inertia
effects. Natural frequency based on the Timoshenko beam theory is given by
a
= natural frequency base on Timoshenko beam theory, HZ
= Shear coefficient of lateral natural frequency
… (3)
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Anup A. Bijagare et al / VSRD International Journal of Mechanical, Auto. & Prod. Engg. Vol. 2 (6), 2012
p = 1, first natural frequency
r = mean radius of shaft
Shape factor, 2 for hollow circular cross section
= 0.982
5. DESIGN OF COMPOSITE DRIVE SHAFT
… (4)
For designing a composite drive shaft, Genetic Algorithm (GA) is successfully applied to minimization of the
weight of the shaft which is subjected to the constraints such as torque transmission, torsional buckling
capacities and fundamental natural frequency. The design variables are number of plies and thickness of the ply.
5.1. Formulation of Work for Genetic Algorithm
Objective Function : To minimize the weight of the shaft.
(Mass) m = AL= × ×( do 2 - di 2 ) ×L … (5)
Design Variable : No. of ply thickness of ply
3200.1< >0.5
6. RESULT OF GENETIC ALGORITHM
Table 6.1 : Result of Genetic Algorithm
7. FINITE ELEMENT ANALYSIS USING ANSYS
7.1. Analysis Procedure
… (6)
In this research, finite element analysis is performed using ANSYS 11.0 software. The model of both the
composite shaft & steel shaft created in Pro-e software, are imported in the ANSYS software. The shaft is
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Anup A. Bijagare et al / VSRD International Journal of Mechanical, Auto. & Prod. Engg. Vol. 2 (6), 2012
subjected to torsion. The shaft is fixed at one end in axial, radial and tangential directions and is subjected to
torsion at the other end. After performing a static analysis of the shaft, the output of static analysis is used to
calculate the buckling load. The output of the buckling analysis is a load coefficient which is the ratio of the
buckling load to the static load. This software also calculates the modes of buckling of the composite shaft. The
modal analysis is performed to find the natural frequencies in lateral directions.
7.2. Results of Finite Element Analysis
Table 7.1 : Results of Finite Element Analysis
Analysis Type Composite Shaft Steel Shaft
Static Analysis
Total Deformation 0.27026 10 -2 mm 1.1981 10 -2 mm
Maximum Principal Elastic Strain 6.117e -6 mm/mm 40.905 10 -6 mm/mm
Maximum Principal Stress 1.4616 Mpa 8.3599 Mpa
Maximum Shear Elastic Strain 8.7279 e -6 mm/mm 54.993 e -6 mm/mm
Maximum Shear Stress 0.70495 Mpa 4.3783 Mpa
Equivalent Stress 1.3606 Mpa 8.5473 Mpa
Buckling Analysis
Total Deformation 0.15151 10 -3 mm 0.69922 10 -3 mm
Fig. 7.1 : Analysis Results in ANSYS Software
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8. CONCLUSION
Anup A. Bijagare et al / VSRD International Journal of Mechanical, Auto. & Prod. Engg. Vol. 2 (6), 2012
The high strength carbon/epoxy composite drive shaft has been design to replace conventional steel drive shaft
of an automobile.
A one piece composite drive shaft for rear wheel drive automobiles has been design optimally by using Genetic
Algorithm (GA) for high strength carbon/epoxy composites with the objective of minimization of weight of
shaft, & analyzed using ANSYS for better torque transmission capacity and bending vibration characteristics.
When the value of tk= 0.31 and n = 8 then the weight of composite drive shaft is 1.36 kg i.e. the weight saving
by the composite drive shaft as compared to steel drive shaft is about 83.47 %.
These results are encouraging and suggest that GA can be used effectively and efficiently in other complex and
realistic designs often encountered in engineering applications.
9. REFERENCES
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