International Journal of Scientific & Engineering Research, Volume 6, Issue 2, February-2015 628

ISSN 2229-5518

Reliability of Automobile Car Wheel Subjected to

Fatigue Radial Loading by Weibull Analysis

A. Chennakesava Reddy

Abstract— W hile the car is running, the radial load becomes a cyclic load with the rotation of the wheel. This has become essential to test the wheel under radial fatigue load for the structural integrity. The survival of the wheel was analyzed through Weibull analysis. It was found that 50 percent of the wheels have survived at 4542041 cycles under radial fatigue loading.

Index Terms— car wheel, radial fatigue loading, ANSYS, Weibull analysis.

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1 INTRODUCTION

Ajected to high loads. The durability of the wheel is im-


lnln(   

UTOMOTIVE wheels are part of a vehicle and are sub-

1 ) = β lnx

portant for the safe operation of the vehicle. Therefore it

1 − F (x)

 

α

is essential to examine the wheel for both strength and fatigue

lnln( 1 = x

(2)

resistance. Stearns et al. [1] summarized the application of fi- nite element technique for analyzing stress and displacement

)

1 − F (x)

β ln

β lnα

distributions in the vehicle wheels subject to conjoint influence of inflation pressure and radial load. They used aluminum alloy A356-T6 for the wheel. They observed that the rim tend to ovalize about the point contact under radial load with a maximum displacement occurring at the location of the bead seat. Wright [2] presented various methods of testing the au- tomotive wheels. The different tests were cornering fatigue test, radial fatigue test and impact test.


Comparing this equation with the simple equation for a line, we see that the left side of the equation corresponds to Y, lnx corresponds to X, β corresponds to m, and -β ln corre- sponds to c. Thus, when we perform the linear regression, the estimate for the Weibull β parameter comes directly from the slope of the line. The estimate for the parameter must be calculated as follows:

c

The automotive wheel has to pass three types of tests be- fore going to use, they are cornering fatigue test, radial fatigue

α = e β

(3)

test and impact test. The objective this paper was to perform radial fatigue analysis find the number cycles at which the wheel would fail. The fatigue analysis was carried our using ANSYS software.

2 ESTIMATION OF WEIBULL PARAMETERS

Weibull analysis is a method for modeling data sets containing values greater than zero, such as failure data. Weibull analysis can make predictions about a joint's life. The Weibull cumula- tive distribution function can be transformed so that it appears in the form of a straight line (Y=mX+c).To compute Weibull cumulative distribution the following formulae were used:

x β

α

3 METHODOLOGY

The material of wheel was aluminum A356-T6. The specifica- tions of the wheel (figure 1) are given below:
Rim diameter = 375 mm Rim width = 150 mm Profile of the rim = J
Offset = 40 mm Pitch circle diameter = 100 mm Hub diameter = 60 mm The yield strength = 155 MPa Tensile strength = 260 MPa Modulus of Elasticity = 71 GPa
Density = 2.685 g/cc
Poisson’s ratio = 0.33

F (x) = 1 − e

1

 

x β

(1)

The gross weight of the vehicle on the wheel is equal to kreb weight of vehicle + number of passengers x weight of

ln(

) =  

1 − F (x)

 α 

each person +overages added (619 + 5x70 +50 = 1500 Kg). The
load on each wheel is equal to 254.85 Kg (=1019/4) which is
equivalent to 2500 N. the torque of the wheel is 500 N-m.

————————————————

Professor, Department of Mechanical Engineering, JNTUH College of

Engineering, Kukatpally, Hyderabad – 500 085, Telangana, India

acreddy@jntuh.ac.in, 09440568776

The 2D of the wheel was created in MDT (Mechanical De- sign Technologies), the drafting package [3] and the same was exported to ANSYS, the finite element package using IGES (Initial Graphics Exchange Specification) translator. The 3D

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ISSN 2229-5518


model (figure 2) of the wheel was created in the ANSYS. The wheel was meshed with SOLID 45 elements. This ele- ment as shown in figure 3 is defined by eight nodes having three degrees of freedom at each node: translations in the nod- al x, y, and z directions [4]. The number of elements was found to be 9988 and the number of nodes was 19903 as shown in figure 4a. For boundary conditions a pressure of 0.207 N/mm2 was applied on the outer surface of the rim. The pitch circle holes were constrained in all degrees of freedom as shown in figure 4b. A load of 2500 N was applied on the inner surface of hub diameter by taking one middle node. The pitch circle holes were constrained in all degrees of freedom. The analysis was carried using fatigue module of ANSYS to find the life of the wheel. The material properties of interest in a fatigue evaluation was S-N curve, a curve of alternating stress intensi- ty ((σmax - σmin)/2) versus allowable number of cycles.


Fig. 1. Specification of the wheel.
Fig. 2. Solid model of aluminum alloy wheel.

Fig. 3. Solid 45 element. Fig. 4. Finite modeling of wheel (a) meshed model (b)
boundary conditions on wheel.

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4 RESULTS AND DISCUSSION

The total weight of the car is to be balanced with vertical reac- tion force from the road through the tire. This load constantly compresses the wheel radially. While the car is running, the radial load becomes a cyclic load with the rotation of the wheel. Hence the evaluation of the wheel fatigue strength un- der radial load is an important performance characteristic for the structural integrity. The maximum deformation was 0.0515 mm at rim of the wheel as shown in figure 5a. The defor- mation on engine side was also 0.0515 mm as shown in figure
5b. The von-Mises stress and equivalent alternating stress were 9.205 MPa and 12.27 MPa respectively as shown in figure
6. After running the fatigue cycles it was found that the life of the wheel was 1.0x108 cycles (figure 7).

burn-in will subsequently exhibit a constant failure rate. A β >1.0 indicates an increasing failure rate. This is typical of products that are wearing out. The car wheel has β value higher than 1.0 as seen in figure 8. The joints fail due to fa- tigue, i.e., they wear out.

Fig. 6. Stress distribution (a) von-Mises stress (b)
equivalent alternating stress.

Fig. 5. Deformation of wheel (a) under radial load (b)
on engine side
The Weibull shape parameter, β, indicates whether the fail- ure rate is increasing, constant or decreasing. A β <1.0 indi- cates that the product has a decreasing failure rate. This sce- nario is typical of "infant mortality" and indicates that the joint is failing during its "burn-in" period. A β=1.0 indicates a con- stant failure rate. Frequently, components that have survived
Fig. 7. S-N curve.

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5 CONCLUSIONS

The automobile car wheel was tested for radial fatigue loading using ANSYS. The maximum deformation was 0.0515 mm at rim of the wheel. At 4542041cycles, about 50 percent of wheels have survived.

Fig. 8. Weibull criterion for wheel.

REFERENCES

[1] J.Stearns, P.C.Lam, and T.S. Srinivasan, “An analysis of stress and displacement in a rotating rim subjected to pres- sure and radial loads”, The Goodyear Tire and rubber com- pany, Akron, Ohio, USA, 2000.

[2] D.H.Wright, (1983) ‘Test method for automotive wheels’, Proceedings of Institute of Mechanical Engineering, No. c278/83, 1983.

[3] Chennakesava R Alavala, CAD/CAM: Cocepts and Applica-

tions, PHI Learning Private Limited, New Delhi, 2008.

[4] Chennakesava R Alavala, ‘Finite element methods: Basic concepts and applications’, PHI Learning Private Limited, New Delhi, 2009.

Fig. 9. Relaibility of wheel.

The straight line equation for the wheel was obtained as:

Y = 0.238x − 4.027

(4)

The Weibull characteristic life is a measure of the scale in the distribution of data. It so happens that equals the number of cycles at which 63.2 percent of the joint has failed. In other words, for a Weibull distribution R( =0.368), regardless of the value of β. For the vee-joint design about 37 percent of the joints survive at least 3189 cycles. For the plain-joint design about 37 percent of the joints survive at least 2497 cycles. About 37 per- cent of the wheels survive at least 21073184 cycles. Figure 9 allows a comprehensive comparison of the wheel survival rates. At 4542041cycles, about 50 percent of wheels have survived.

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