Archard and Kirk’s Lubricant Film Thickness for Deep Groove Ball Bearings 6008, 6208, and 6308 using Engine Lubricants

Archard and Kirk’s Lubricant Film Thickness for Deep Groove Ball Bearings 6008, 6208, and 6308 using Engine Lubricants

Sheetal Gajjalwar1

1Research Scholar, Department of Mechanical Engineering,

National Institute of Technology, Raipur (C.G.), India 492001

Surendra Pal Singh Matharu2

2Professor,

Department of Mechanical Engineering, National Institute of Technology, Raipur (C.G.), India 492001

Abstract The service life of a machine can be seriously affected, decreasing its overall performance, if there is any defect, during operation, in the bearings of that machine. And if the machine is of rotating type, then Rolling Element Bearings becomes its most essential parts. One of the major defects arises due to the insufficient lubricant between the rolling elements of a bearing, which leads to the early failure of the bearings. In the present paper, the lubricant film thickness for the deep groove ball bearings of 6008, 6208, and 6308 series, is calculated for different engine lubricants, based on the theory proposed by Archard and Kirk. An on-line condition monitoring of the rolling element bearing can be carried out by using the developed formula (proposed by Archard and Kirk) along with inexpensive measuring instruments.

Keywords On-line condition monitoring, deep groove ball bearings, minimum lubricant film thickness, friction, rolling elements bearings, expected service life.

1. INTRODUCTION

   In order to avoid metal to metal contact between the rolling elements of a bearing, a lubricant film, which separates the rolling elements of a bearing should be there, to prevent the damage of the bearing as well as the total failure of the associated large system. Appropriate lubrication of the rolling element bearings is necessary for the proper functioning of the machine. Hence in order to ensure smooth functioning of the machine, a sufficient amount of the lubrication is a must for the rolling element bearings. Thus, the estimation of the minimum lubricant film thickness is essential for optimum performance of the rolling element bearings. Therefore, the present work deals with the determination of the minimum lubricant film thickness for the deep groove ball bearings of series 6008, 6208, and 6308, with the engine lubricants designated as A, & B, based on the formula developed by Archard and Kirk.

2. METHODOLOGY

   Archard and Kirk [1] proposed the non-dimensional minimum lubricant film thickness for ball bearing,

   as,

   Where,

   H0 = Non-dimensional lubricant film thickness = h0/R, h0 = minimum lubricant film thickness (mm) = H0xR ,

   , U, Q are the dimensionless parameters, which are given as

   below,

   = E; E = E/(1-2) ; U = 0 U/ 2ER ; U = U1 + U2 ; U1 = diN/60 ; U2 = 0 ; Q = Q/ER2 ;

   = 0.1122 (0/104)0.163 ;

   Where,

   = Pressure coefficient of viscosity, mm2/N,

   For steel, Poissons ratio, = 0.3, and E = 206900 N/mm2, 0 = Oil viscosity at atmospheric pressure, N-s/mm2,

   U = Entrainment velocity, mm/s,

   U1 = Entrainment velocity of Inner race, mm/s; U2 = Entrainment velocity of Outer race, mm/s,

   Q = Force/ load acting on the balls, N

   E = E/(1-2) = Equivalent modulus of Elasticity = 227363 N/mm2,

   Thus, after the determination of the above said parameters, and the bearing dimensions, and for the known lubricant, the dimensionless lubricant film thickness can be obtained from equation no.(1). In the present work, the determination of the minimum lubricant film thickness is done for different engine lubricants, which are designated as A, & B.

   The Viscosities of these lubricants [3] & [4], for the calculations of the lubricant film thickness is given in Table 1.

   Table 1: Viscosities of the Lubricants A, & B.

   Viscosity	Lubricant A	Lubricant B
   0 (in cP)	69.96	111.2298
   0 (in N-s/mm2)	69.96 x 10-9	111.2298 x 10-9
   o (cSt)	79.5	125.4

   The Bearing parameters/dimensions used in the analysis, for the deep groove ball bearings 6008, 6208, & 6308 is given in Table 2.

   Deep Groove Ball bearing	Ri ( in mm)	Ro ( in mm)	di ( in mm)
   6008 series	3.75	5.25	45
   6208 series	5.091	7.908	47
   6308 series	6.0307	9.9692	49

   Table 2: Bearing Dimensions for different series of deep groove ball bearings.

   H 0

   0.84(U ' )0.741

   ,

   (Q ' )0.074

   (1)

   or, h0

   0.84(U ' )0.741

   (Q ' )0.074

   xRi

   Where,

   Ri = Equivalent contact Radius of Inner Race, Ro = Equivalent Contact Radius of Outer Race,

   di = Contact diameter of Inner Race.

   Hence, the total lubricant film thickness, will be,

   h0,T ( A) h0,i( A) h0,0( A)

   d 0.741xN 0.741

3. ESTIMATION AND ANALYSIS FOR LUBRICANT h

   2.2452203×10 7 (R0.407 R0.407 ) i (mm)

   0,T ( A)

   i 0 Q0.074

   FILM THICKNESS

   Estimation for the minimum lubricant film thickness for the deep groove ball bearing 6008, with the lubricant A is shown below. And in the similar way the calculations for the

   Thus, after substituting the values of bearing dimensions for the ball bearing 6008 series,

   we get,

   lubricant B, is performed by taking the bearing dimensions of 6008, 6208, & 6308 series deep groove ball bearings, which

   h0,T ( A) 1.385812×10

   0.741

   • N5

   (mm)

   Q0.074

   (2)

   are not shown in this paper. Finally, the minimum lubricant

   film thickness for the lubricants A, & B, with the bearing

   dimensions of the ball bearing 6008,6208, and 6308, is tabulated in Table 3.

   For Lubricant A,

   This is the relationship for the total lubricant film thickness

   while taking the lubricant A, and the deep groove ball bearing 6008. And a similar derivation is carried out for the lubricant

   B, with the ball bearing 6008, and subsequently for the ball bearing series 6208 and 6308.

   0,( A)

   0.795cm2 / s ,

   0.163

4. RESULT

   0.795

   0.214664mm2 / N ,

   On observing the equation no. (2), it is concluded that the

   ( A)

   0.1122

   104

   lubricant film thickness is directly proportional to the bearing

   ( A) 0.214664×227363 48806.72119 ,

   9 i

   d N

   (69.96×10 )

   U ' 60 8.055613×1015 di N

   speed, but inversely proportional to the load acting on the bearing. The total lubricant film thickness is calculated for the engine lubricants A, & B, with the deep groove ball bearings 6008, 6208, 6308, and is shown in Table-3

   ( A)

   (2x227363xR)

   ,

   R

   Table 3: Total lubricant film thickness for lubricants A, & B.

   ( .U ' )

   48806.72119×8.055613×1015 di N 3.93168×1010 di N

   ( A)

   R

   Deep Groove Ball Bearing	Lubricants	0 (in cp)	o (cSt)	h0,T (in mm)
   008	A	69.96	79.5	N 0.741 h 1.385812×105 0,T ( A) Q0.074
   6208	A	69.96	79.5	5 N 0.741 h0,T ( A) 1.658235×10 Q0.074
   6308	A	69.96	79.5	5 N 0.741 h0,T ( A) 1.857908×10 0.074 Q
   6008	B	111.2298	125.4	N 0.741 h 4.081907×106 0,T ( B) Q0.074
   6208	B	111.2298	125.4	6 N 0.741 h0,T ( B) 4.884329×10 Q0.074
   6308	B	111.2298	125.4	6 N 0.741 h0,T ( B) 5.472466×10 Q0.074

   R

   Q

   '

   ( A)

   Q

   (227363xR 2 )

   4.398253×106 ( Q ) ,

   R 2

   On substituting these values in equation no. (1), the minimum lubricant film thickness for the contact of ball elements with the Inner race is given as,

   0.84(U ' )0.741

   h0,i( A) (Q' )0.074 xRi

   d 0.741xN 0.741xR 0.407

   h 2.2452203×107 i i (mm)

   0,i( A)

   Q0.074

   Similarly, the minimum lubricant film thickness for the contact of ball elements with the Outer race is,

   d 0.741xN 0.741xR 0.407

   h0,0( A)

   2.2452203×10 7 i

   0

   Q0.074

   (mm)

5. CONCLUSIONS

From the above analysis it may be concluded that the lubricant film thickness is a function of bearing speed and load acting on the bearing [5]. The lubricant film thickness increases with the bearing speed and decreases with the load acting on the bearing. And this is in-line with the classical theory of lubrication [2]. It can be seen that with the increase in lubricant viscosity the total lubricant film thickness for the bearings 6008, 6208, and 6308 also increases. It may be further noted that the lubricant film thickness for the bearing 6308 is more than that of the bearings 6008 and 6208 for the same lubricant. As larger the size of the bearings, the larger will be the balls size (rolling elements) with more elastohydrodynamic contact area. The larger balls will have more lubricant entrapped than that with smaller balls to take- up more loads. This validates the values obtained for the bearings with different engine lubricants.

Hence, the above method can be linked directly with the inexpensive instruments [6] for the on-line condition monitoring of the rolling elements bearing, since the speed and load can be readily measured during the operation.

REFERENCES

1. T.A. Harris, 2001, Rolling Bearing Analysis, Fourth Edition, John Wiley & Sons, Inc.

2. A. Cameron, 1981, Basic Lubrication Theory, Third Edition,Wiley Eastern Ltd.

3. K. Lingaiah, 2001, Machine Design Data Book, Second Edition, Tata McGraw Hill Education Private Ltd.

4. PSG Design Data, 2004, Data Book of Engineers, Revised Edition 1978, Reprinted July, 2004, Kalaikathir Achchagam Coimbatore 641037.

5. R.K. Dewangan, and S.P.S. Matharu, 2012, Evaluation of Archard and Kirks Lubricant Film Thickness for 6007 Ball bearing, International Journal of Advances in Engineering Research, Vol. No. 03, Issue No. IV, April 2012, pp. 43-46.

6. S.P.S. Matharu, S. Sanyal, and D.S. Bal, March 2010, Development of a Multipurpose, efficient, and inexpensive bearing test rig, Journal of Engineering and Technology Research, Volume 2(3), pp. 044-049.