Finite Element Analysis of Deep Groove Ball Bearing to obtain stress and

contact pressure

Ritininių guolių analizė baigtinių elementų metodu siekiant nustatyti

įtempius ir maksimalų kontaktinį slėgį

Author: Shankar Bhandari

Co- author: prof. Egle Jotautiene, Amith Ganta,, Antanas

Juostas

Vytauto Didžiojo Universitetas

Žemės ūkio inžinerijos fakultetas

Žemės ūkio inžinerijos ir saugos institutas

Studentų 15A, LT-53361 Akademija

Kauno raj.

Kaunas, 2020

Contents

1. Introduction

2. Problems

3. Methods

4. Hertzian Stress Theory

5. Static Analysis Using ANSYS

6. Results

7. Conclusion

8. References

1. Introduction

➢ In today’s context, agriculture machineries are

vital for agricultural operation.

➢Hence these machineries should be maintained

effectively to ensure long period performance

without breakdown.

➢ Hertzian and non-Hertzian contact studies of

bearing can be performed to obtain stress, strain,

deformation, contact pressure and penetration by

using the numerical Approach developed using

ANSYS in order to assure the safety for

manufacture.

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2. Problem

➢ Due to complex structure of combine harvester

threshing’s bearing location it is challenging to

conduct reliability testing very often.

➢ The statistical analysis of bearing with the

identified loading condition on the bearing using

simulation software will help to analyze and

optimize the manufacturing and performance

parameters of bearings.

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3. Methods

➢ The comparative analysis of analytical Hertzian maximum contact pressure and

numerical analysis in ANSYS software is performed of the deep groove ball bearing

model 6208-2RS SKF of discharge beater of a threshing unit of Dominator 38 CLAAS

combine harvester . Furthermore, The Von Mises stress analysis is conducted in inner

race and rollers to identity the impact on these parts under applied bearing radial load.

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4. Hertzian stress theory

➢ The Hertzian stress theory is extensively used for a numerical approach to calculate the generated stress and pressure in

contacting elastic bodies. For deep groove ball bearing line and point contact is considered between spherical balls and the

races to determine contact pressure and deformation respectively.

The deep groove ball bearing maximum contact stress is given by

𝑃𝑚=

1

𝜋𝑒𝑎𝑒𝑏

∗3

(σ𝜌)

2∗

5𝐹𝑟

𝑍 𝑐𝑜𝑠𝑎

(1)

Where ea, eb are Hertzian contact coefficient;

σ𝜌)

is sum of main curvature.

Fr is radial load;

Z is number of rollers;

𝑎 is contact angle under loads.

a) Maximum radial load (Frmax)

𝐹𝑟=

4.37∗𝐹

𝑍

(2)

Where Frmax is the maximum radial load of the rolling element, N,

F is the size of the external radial load, N, Z is the number of rolling elements ,

Striebeck coefficient for Spherical Roller bearings is 4.37. 6

Contd..

The maximum normal load Fn

𝐹𝑛 =𝐹𝑟𝑚𝑎𝑥

𝑐𝑜𝑠𝛼

(3)

where=450 is contact angle.

The maximum normal load of rolling element, MPa:

𝑄𝑚𝑎𝑥 = 𝐹𝑛 (4)

The maximum contact pressure according to the Hertz theory in MPa:

𝜎𝑚𝑎𝑥 = 4.37 ∗ 𝜀𝜎∗2 𝑄𝑚𝑎𝑥

𝑑𝑒2(5)

Where, de is the diameter of rolling element, mm.

𝜀𝜎=40.4686 is the empirical coefficient of contact pressure

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5. Static analysis using Ansys

➢ The dimension of the bearing is shown on the table 1.

Z (No. of balls) 9

d (Inner Diameter) 40mm

D (Outer Diameter) 80mm

B (Width) 18mm

d1 (Inner Raceway groove) 52.6mm

D2 (Outer Raceway groove) 69.8mm

dr. (Roller Diameter) 12.30mm

Z (No. of balls) 9

Table 1: Bearing Dimension

➢ Three-dimensional modal is designed in solid

works and exported as STEP file to Ansys for

simulation and the static analysis is performed

in deep groove ball bearing. The material is

assigned as a steel structure with details as

shown in table 2.

No. Properties Value

1 Density 7850 kg/m3

2 Young’s modulus 2E+11 Pa

3 Poisson’s ratio 0.3

4 Tensile Yield

Strength

2.5E+08 Pa

5 Compressive

Yield Strength

2.5E+08 Pa

6 Bulk Modulus 1.6667E+11 Pa

7 Shear Modulus 7.6923E+11 Pa

Table 2: material properties 8

Contd..

➢ Frictional contact is applied with a coefficient of friction of 0.05 and a Normal stiffness factor of 0.1 between the rollers and

races. Hexa Dominant mesh is applied for Inner race and Outer race with element size 5 and automatic mesh is described for

rollers with element size 3.No. Properties Value

1 Elements 21900

2 Nodes 41542

Table 3: Mesh Statistics

➢ The displacement boundary condition is applied and a bearing

load of 40 kN is applied on the inner race in the negative y-

axis. In the global Cartesian coordinate system, both the races'

displacement is removed on the z-axis and allowed in y and x-

axes. Outer race displacement was taken in the y-direction and

allowed in the x-axis and z-axis directions in the cylindrical

global coordinate system. Roller's displacements are taken in

the x-direction and allowed in the y and z-direction (Fig. 1).

➢ Simulation for 1 sec is applied for impact load. Equivalent

Von-Misses Stress and elastic deformation are obtained at the

inner race. Maximum contact pressure between rolling

elements and raceways is obtained.

Figure 1: Static Structural loading condition

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6. Hertzian stress theory ( Analytical Analysis) : Results

From the analytical analysis Maximum radial load is calculated to be 19.42 kN (equation 2) and maximum normal load is

found to be 9.71 kN (equation 3). Maximum Hertzian contact pressure analytically is found to be 1416 MPa (equation 5). The

analytical maximum contact pressure for different loads is shown in Table3.

No. Loads, kN Analytical Maximum Pressure,

MPa

1 10 708

2 20 1001

3 30 1227

4 40 1416

5 50 1584

Table 3: Results of Analytical Analysis

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6. Static analysis using

Ansys : Results

• Maximum contact pressureobtained from ANSYS as 1207MPa (Fig. 2) having 14%deviation from the HertzianAnalytical data of 1416 MPa.

Figure 2: Maximum Contact Pressure

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Contd..

➢ Furthermore, The Von Mises stress analysis is conducted in inner race (Fig 4) and (Fig 3) rollers to identity the impact on

these parts under applied bearing radial load.

➢ Maximum Von Mises stress is maximum in rollers as 1475 MPa compared to inner race as 804 MPa under the same

loading condition (Fig. 3&4) that implies that maximum stress is exerted more on rollers than inner races.

Figure 4: Von Mises Stress in Inner RaceFigure 3: Von Mises Stress in rollers

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3. Conclusion

Contact mechanism based on Hertzian contact theory is briefly studied and numerical analysis

is conducted to calculate the maximum contact pressure in 6208 2RS deep groove ball bearing

is found to be 1416 MPa on 40 kN bearing load.

Finite element analysis is performed in the ANSYS platform with nodal analysis to study the

stress, strain, displacement, and contact details. The maximum contact pressure is found to be

1207 MPa.

The variation in analytical and FEM Analysis is found to be 14 percentage deviation.

So, it is concluded that the FEM analysis can be used to calculate the maximum contact

pressure in a deep groove ball bearing with radial loading condition of combine harvester for

ensuring the safety of the bearing in different loading conditions.

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3. List of Literatures1. L. Špokas, V. Adamčuk, V. Bulgakov, and L. Nozdrovicḱ, “The experimental research of combine harvesters,” Res. Agric. Eng., vol. 62, no. 3, pp. 106–112, 2016, doi:

10.17221/16/2015-RAE.

2. Z. Zhao, Y. Li, J. Chen, and J. Xu, “Grain separation loss monitoring system in combine harvester,” Comput. Electron. Agric., vol. 76, no. 2, pp. 183–188, 2011, doi:

10.1016/j.compag.2011.01.016.

3. Brian Hollaz; Porta Alegra (BR), “( 12 ) United States Patent,” US 8,118,652 B2, 2012.

4. A. O. Köhn and F. A. Silva, “A study of the stress field generated by the contact between a sphere and a flat plate for a simplified model of deep-groove ball bearing,” Ing. e Investig.,

vol. 40, no. 2, pp. 37–42, 2020, doi: 10.15446/ing.investig.v40n2.79469.

5. J. L. Gomez, A. Bourdon, H. André, and D. Rémond, “Modelling deep groove ball bearing localized defects inducing instantaneous angular speed variations,” Tribol. Int., vol. 98, pp.

270–281, 2016, doi: 10.1016/j.triboint.2016.02.032.

6. C. Ra. Daniel Rezmires, Daniel Nelias, “Hertzian and Non Hertzian Contact Analisys in Ball Bearings,” Ann. Univ. “Dunarea Jos” Glati Fascicle VIII ISSN 1221-4590, pp. 105–108,

2004.

7. Z. Tang and J. Sun, “The contact analysis for deep groove ball bearing based on ANSYS,” Procedia Eng., vol. 23, pp. 423–428, 2011, doi: 10.1016/j.proeng.2011.11.2524.

8. X. Li, L. Liang, and S. Wu, “A numerical and effective method for the contact stress calculation of elliptical partial slip,” J. Mech. Sci. Technol., vol. 29, no. 2, pp. 517–525, 2015,

doi: 10.1007/s12206-015-0112-3.

9. J. L. Gomez, A. Bourdon, H. André, and D. Rémond, “Modelling deep groove ball bearing localized defects inducing instantaneous angular speed variations,” Tribol. Int., vol. 98, pp.

270–281, 2016, doi: 10.1016/j.triboint.2016.02.032.

10. Z. Tang and J. Sun, “The contact analysis for deep groove ball bearing based on ANSYS,” Procedia Eng., vol. 23, pp. 423–428, 2011, doi: 10.1016/j.proeng.2011.11.2524.

11. W. W. Thet, S. O. E. Kyaw, and M. M. Sein, “Design and Stress Analysis of Threshing Cylinder Drum for A Combine Paddy Harvester ( 25HP ),” vol. 3, no. 4, pp. 185–190, 2019.

12. M. N. K. Harris, Tedric A., “Essential Concept of bearing technology,” Taylor Fr. Gr., vol. Fifth edit, pp. 123–133, 2007.

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Thank You

Presenter: Shankar BhandariDoctoral StudentAgricultural Mechanical EngineeringVytautas Magnus UniversityKaunas, Lithuania.Shankar.bhandari@vdu.lt+37063554571