Free Vibration Analysis of Radial Pneumatic Tire Using FEM

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Free Vibration Analysis of Radial Pneumatic Tire Using

FEM

Abhijeet Chatterjee1 Vinayak Ranjan2

1,2

Department of Mechanical & Mining Machinery Engineering Indian School of Mines, Dhanbad-826004, India

Abstract— A finite element modeling of tire using Ansys is used to analyze the free vibration of radial pneumatic tires. The natural frequencies and mode shapes of pneumatic tires are investigated. The effects of some parameters such inflation pressure, tread pattern, ply-angles and thickness of belts on the natural frequency of tires are investigated.

Keywords— natural frequency, inflation pressure, treads pattern, ply-angles and thickness of belt.

I. INTRODUCTION

One of the main reason of the noise of the vehicle is considered due to the tire vibration. Different researcher and scholar use different methods for study of vibration of tires. Niclas and Fredrik [2001] used the event sampling method as the signal processing problem to separate the signal component from noise in both amplitude and time domains. Muggleton et.al. [2003] used the tread and sidewalls of tire modeled as thin, flat orthotropic plates with in-plane tension joined together by a translational stiffness and rigid rim. Sahin and Ibrahim [2003] used neural network analysis to predict the amplitude of acceleration for different road conditions such as concrete waved stone block paved and country roads. Ines Lopez Arteaga [2011] used Green’s functions of a loaded rotating tire in the vehicle-fixed Eulerian reference frame for tire/road noise predictions showing Green’s functions of a rotating tire in the Eulerian reference system as a function of the eigen frequencies and eigen modes of the statically loaded tire. Molisani et. al. [2003] considered the tire modeled as an annular cylindrical shell in which the outside shell is flexible, the tire sidewalls and wheel are assumed rigid and considering the analytical solution of the eigen problems, both the tire structure and cavity acoustic responses are expanded in terms of their eigen functions. Byoung et. al. [2007] used spring-mass system model,

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Julien et. al. [2009] used measurements of contact forces and close proximity noise levels for a slick tire rolling on six different road surfaces between 30 and 50km/h. Andersons and Kropp [2009] measured Adhesion forces in the tire/road contact interface. Kindt et. al. [2009] did experimental analysis of the structure-borne tire/road noise due to road discontinuities. Valentin et. al. [2010] measured identifying parameters, characterizing the interaction of a tire with different ground surfaces. Yang et.al. [2009] used self-excited vibration with vehicle velocity considering polygonal wear of tire based on the non-linear character of friction coefficient combining the concept of static and kinetic friction to a tread pavement model. Che and Lijun [2009] utilized Adaptive Immune Genetic Algorithm in measuring noise from tire thread. Campanac et. al.[2000] determined rolling tire vibrations using perturbation method, numerical computation of vibration using Flonquet theory and Bloch theory. Perisse [2002] Measured acceleration responses inside the tire belt during rotation and investigated the radial vibrations of a smooth tire rolling on different road surfaces. Byoung et. al. [2007] measured the natural frequency and damping ratio of tire-wheel system and shown the influence of boundary condition on natural frequency and damping ratio using Hamilton’s principle. Maik et. al. [2008] represented the tire by plate or shell structures and used numerical method with Arbitrary Lagrangian Eulerian (ALE) approach. Zhou et. al. [2010] studied the effect of radius ratio, subtended angle, and initial slope angle on frequency to provide a complete vibration spectrum of structures using Ritz method.

In this paper, a radial tire is modeled by finite element method. The tool used is Ansys. The effects of some parameters such as the tread pattern, ply-angles and thickness of ply on the natural frequency of tires are investigated.

II FINITE ELEMENT MODELING OF TIRES

A radial tire as shown in Fig. 1(a) and1 (b) is investigated. The geometry of the tire considered is that of P215/70R16. The pneumatic tire is assumed to be fixed on the hub and no vertical load is applied. The effects of damping and temperature on the free vibration are not considered in this investigation.

The tire consists of one layer of carcass, two layers of steel belts, two layers of nylon belts and the outer rubber as shown in Fig. 1. Carcass, steel belts and nylon belts are modeled as orthotropic materials while the rubber is approximated as an elastic material. Material properties of each layer are assumed as shown in Tables 1 and 2.

Table 1

Material properties of the rubber

E, Young’s modulus of elasticity (MPa)

Poisson’s ratio

Density (kg/m3)

Rubber 18 0.49 1.15E03

Table 2

Material properties of cord layers

Nylon belt

Steel belt Carcass

E1 (MPa) 809.367 27317.708 1196.15

E2=E3 (MPa) 14.75 12.478 13.3

Poisson’s ratio 0.44 0.45 0.46

G12(MPa) 4.924 4.16 4.4375

G23=G31(MPa) 4.924 4.16 4.4375

Density (kg/m3) 1.15E03 2.50E03 1.15E03

Angle (degree) 90 70 0

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Fig. 1(a) and (b) Configuration of the P215/70R16 tire

.

TABLE 3:

The specification of radial tire P215/70R16

Sl.No Specification millimeter

1. Sectional width 215

2. Rim diameter 400

3. Rim width range 158

4. Outer diameter 700

5. Height 150

6. Circumference 2200

7. Speed 100(km/h)

Solid185 Structural Solid element is used to model the tire. The element is defined by eight nodes I, J, K, L, M, N, O, P as shown in Fig.2. This element is having three degree of freedom i.e. UX, UY and UZ. For the radial tire P216/70R16, the total number of nodes taken is 7532 whereas the total number of elements comes out to be 34945.The Fig.3 represents the meshed tire

FIG .2 SOLID ELEMENT 185

Fig .3 The meshed tire.

III

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Fig.4. Mode shapes of radial vibrations of the tire P215/70R16 (a) Mode shape at natural frequency 74.6 Hz; (b) Mode shape at natural frequency 94.4 Hz; (c) Mode shape at natural frequency 117.9 (d) Mode shape at natural frequency 147.8 Hz (e) Mode shape at natural frequency 187.1Hz.

A. Effect of Inflation Pressure:

Table 5 and Fig. 6 depict the effect of different inflation pressure on the natural frequencies of the tire. The inflation pressure directly influences the stiffness of the tire. As inflation pressure increases, the stiffness of the tire also increases and therefore the natural frequencies increase. However it has also been observed from the Fig. 6. that when inflation pressure increases above 240 KPa the increase of natural frequencies at mode 1 and 5 are not very significant. This suggests that for modes 1 and 5, the stiffness of the tire reaches some optimum values and further increase of inflation pressure does not increases the natural frequencies.

Table. 5.

Variation of natural frequencies of radial vibrations of the tire under different inflation pressure

Modes Natural Frequencies (Hz) P=80

KPa

P=160 KPa

P=240 KPa

P=320 KPa

1 57.2 63.2 74.6 75.5

2 66.1 81.3 94.4 105.4

3 85.2 101.6 117.9 128.3

4 110.2 127.4 147.8 156.2

5 146.9 168.2 187.1 190.5

B. Effect of Tread Pattern

Tread patterns generally increases the friction between the tire and the road and improve the driving, rolling

Fig 6 Variation of inflation pressure and natural Frequency

resistance, braking, and cornering characteristic. The effect of tread patterns on the natural frequency is investigated here. The tread is created by four shallow circumferential notches, grooved on the tread as shown in Fig.7. Under the inflation pressure of 240 KPa, the natural frequencies of tires with and without patterns are studied. From table 6, it is observed that with tread patterns, the natural frequencies increases. From Fig.7 it is clear that natural frequency of mode 1 does not vary significantly with or without pattern. But for higher modes, the variations in the natural frequencies are more pronounced and with pattern, the frequencies increase.

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Table.6.

Variation of natural frequency with thread pattern and without thread pattern

Sl. No. Natural frequency

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Without

pattern

74.6 94.4 117.9 147.8 187.1

With pattern

77.6 112.3 136.8 182.4 213.5

C. Effect Of The Ply Angles Of The Steel Belts

Steel belts absorb the force and pressure of the radial tire. Two layers of steel belts are laminated in different directions. Ply angle is defined as the angle between the orientation of the belt and meridian direction. Generally the ply-angles of steel belts are between 60-70 degree on both the direction. The influence of the ply-angles on the natural frequencies is investigated here under 240 KPa inflation pressures. From the Table 7, it is observed that as the ply-angles increase, the natural frequencies also increase, but this increase is not very significant.

Table 7

The influence of different angle of steel belt with natural frequency

Sl No. Steel belts

1 2 3 4 5 6

Ply angle in degree

60 62 64 66 68 70

Natural frequency

in Hz

70.6 72.1 72.4 72.7 73.8 74.6

Fig .7 variation of natural frequency with pattern and without pattern

D. Effect Of Thickness Of Belts

The effect of thickness of belts on the natural frequencies of the tire is shown in the Tables 8. The following cases are studied:

Case1: caracas, steel, nylon, rubber belts, each have thickness = 0.5 cm

Case2: caracas thickness = 1cm and steel, nylon, rubber belts, each have thickness = 0.5 cm

Case3: steel belt thickness = 1cm and caracas, nylon, rubber belts, each have thickness = 0.5 cm

Case4: nylon belt thickness =1cm and caracas, steel, rubber belts, each have thickness = 0.5 cm

Case5: rubber belt thickness = 1cm and caracas, steel, nylon belts, each have thickness = 0.5 cm

We notice that the variation of thicknesses of different belts does not have a significant effect on the natural frequencies of the tire.

Table 8

Natural frequency of tire having the same thickness of Caracas and all belts

Sl.No Natural frequencies (Hz)

Modes 1 2 3 4 5

Case 1 74.6 94.4 117.9 147.8 187.1 Case 2 79.1 98.2 123.5 156.1 197.1 Case 3 75.4 92.3 118.1 149.1 191.9 Case 4 80.5 95.1 123.6 156.3 197.9 Case 5 73.2 89.7 119.9 146.7 192.3

IV. CONCLUSIONS

1. The inflation pressure directly influences the stiffness of the tire. As inflation pressure increases, the stiffness of the tire also increases and therefore the natural frequencies increase. However, this suggests that for modes 1 and 5, the stiffness of the tire reaches some optimum values and further increase of inflation pressure does not increases the natural frequencies. 2. The natural frequency of mode 1 does not vary

significantly with or without thread pattern. But for higher modes, the variation in the natural frequencies is more pronounced and the frequencies with pattern increase more than that of without pattern.

3. As the ply-angles increase, the natural frequencies also increase, but this increase is not very significant. 4. With variation of different belt thickness, the natural

International Journal of Emerging Technology and Advanced Engineering

324 REFERENCES

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