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Abrasive wear of rolling bearings
Abrasive wear of rolling bearings G.Ya. Yampolski, I.V. Kragelskii and I.V. Yushakov*
Various mechanisms of microslip are discussed; abrasive wear is considered the most important. An equation to predict the wear rate of rolling bearings is presented, based on previous work, and illustrated by an example
Rolling bearings of road-building,mining, transport, agricultural and other types of equipment undergo intensive abrasive wear which is difficult to prevent despite the constant improvement of bearing assembly protection 2'3's. One of the main factors affecting the wear of rolling elements is the microslip in the contact. The following types of microslip are known: kinematic, connected with the deflection of nominal sizes of rolling elements and also differential slip according to the Heathcote scheme; Reynolds' slip caused by different elastic moduli and Poisson's moduli of the elements; and dynamic slip connected with elastic interaction in the presence of periodic perturbations 1,2 . These types of microslip together with elastic hysteresis and adhesive interaction give very low wear rates for rolling bearings operating with pure oil but they are not the cause of abrasive wear. The friction surface analysis of rolling bearings shows that more important sources of microslip, leading to quite long 'traces' caused by abrasive particles and a high degree of wear, must exist. This specific type of microslip which is due to trapping of abrasive particles in the contact zone may be estimated from the fact that the projection V~ and V21 for the same linear speeds V of these abrasive particles of radius R are different due to different values of radius of curvature Pl and P2 (Fig 1). The difference of these projections is the value of microslip (v,' - v~' ). Pl +P2 2VR - - -(1) P~P2 where plus and minus are related respectively to the contact of rolling elements with the same (roller-outer race) and different (roller-inner race) curvature. VlI - V21 =
The equations 3'6 obtained before estimate the influence of the abrasive action A, physical and mechanical properties of materials M and the kinematic and geometric parameters of conjugation K on the wear rate W. For a pair of contact elements in rolling friction A KI(2), WI(2) = 4x 10 2 - - - MI(2) where
(2)
A = J / 3 R ° ' S 0 2.s
(3)
MI(2) = 8 1(2) t Hl(2) i.s H2(I) KI(2 ) =p,Vz I
VI l - V2 1 ]
V
(4) nl(2)
(5)
*Laboratory of Friction and Friction Materials, hlstitute of Mechanical Engineering, Moscow. USSR
0301-679X/81/030137-02 $02.00 © 1981 IPC Business Press
\\
Fig 1 Microslip o f abrasive particles in the contact zone o f rolling elements moving with the equal speed, V
In these equations the group of factors A (Eq (3)) shows the influence of abrasive values on the wear. The number of abrasive particles is defined by their volumetric concentration e, %, in lubricant or air. Wear is caused by those abrasive particles which are larger than the oil layer thickness and height of the microroughness. Since these particles constitute the majority, the full concentration e, including the full range of particle sizes, must be taken into account. The abrasive value in Eq (3) is calculated using the mean radius of the particles R. The kind of abrasive particle is determined by its mechanical strength o, defined as the conventional compression stress or ultimate tensile stress of particles equal to the ratio of the load affecting the particle's fatigue to its diametric section 7r R 2 4 According to the group of factors M in Eq (4), wear depends on the physico-mechanical properties of contact materials. In this case, the hardness of friction and contact elements HI and//2 (Brinel hardness) plays an important role. Wear also depends to a certain extent on the elasticity ~ (the percentage elongation at rupture corresponding to the maximum deformation force). The 8 characteristic may be determined by data obtained during tensile tests, as well as with the indentor method 4. Eq (4) also includes the coefficient of contact frictit~n fatigue t which varies between 0.3 and 0.5 for rolling bearing materials.
TRIBOLOGY international June 1981 137
Yampolski,
Kragelskii and Yushakov - Abrasive wear of rolling
The third group of factors K, in Eq (5) shows the influence of geometric and kinematic parameters on wear: p*, the PlPZ
where p1 and pz are radius of curvature equal to -~ PI +Pz’ the radii of curvature of rolling bodies 1 and 2 (plus and minus refer to the contact of rolling bodies with the same or different curvature); Vr ’ and V,’ are projections of linear speeds of rolling bodies 1 and 2; I/ is the absolute value of linear speed of the rolling bodies; nlc2) is the number of loadings on the rolling bodies 1 and 2 per minute (revolutions per minute). By substituting Eqs (1) (3), (4) and (5) in Eq (2) using known formulae for definition of the number n, />, , we may evaluate the abrasive wear of rolling eleme;t?in axial loadings EZ/3 RI.5 g2.5 W 1_2,3= 8x lo* K 1,2,3 nl (6) 6 1A3 H:‘:> , 3 H2 >12 9 In this equation, the subscripts 1, 2, 3 relate to the inner race, roller and outer race, respectively.
=
(Pl$
(Pl_P2
(7)
p,p,‘:XfiJP.
Pl +P2
PlP2
P2P3
P3-P2
~pZ(Pl+PZ)
(8)
30x 10 % 30-10 GGlO’
(--30x
10x50 % 5ot10
lo’+(GX? 30 tFO)
1
x 8 = 1.83
(iG&
50x 30
10(30+10)=
2.27
x 8 = 2.54
Then, according to Eq (6) we obtain the values of wear rate of the elements for the inner race x 1.83x 200 = 0.89Hm/h,
Pl
)p,
(9) p2p3
Pl
According to Eq (6) the wear of rolling bearings depends mostly on the hardness of contact surfaces. Besides elasticity and coefficient of contact friction, fatigue plays a very important role. The influence of these different factors on the abrasive wear of rolling bearings may be used in solving a number of engineering problems eg the prediction of bearing assembly life and optimization of geometric and kinematic bearing parameters.
international June 1981
12’3x 0 05”s x 302.5 ’ x2.27x 200=1.11 pm/h 4°.5 x 6OOr.’ x 600’ -
and for the outer race
+P2
From Eq (6) we know that the abrasive wear of rolling bearings depends mostly on the concentrations, size and hardness of abrasive elements rather than on the loading conditions. Contact stress is defined only by the mechanical stability of abrasive particles under loads which intensively crush them. Bearing wear is determined by the total number of revolutions and not by the frequency of rotation.
x 600
for the roller
‘~’
where p1 , p2 and p3 are the radii of the inner race, roller and outer race respectively and P is the number of rollers.
TRIBOLOGY
30x10 % 30-10 50 36x1o)(3o+1o) 30+10) (
Kr =(
W2=8x102
P2P3 )I/i,s+P2)(
K3= (---
138
p1 =
at an abrasive content of the lubricant E = l%, with an average particle size of R = 0.05 mm with mechanical strength u = 30 kg/mm2. The bearing element materials have the following physico-mechanical properties HI = Hz = H3 = 600 kg/mm2 (Brinel); 6 = 4%; fatigue coefficient f = 0.5 and speed of inner race IZ~ = 200 rev/min. From Eqs (7)-(9) we may determine kinematic indices for the inner race K1, roller K2 and outer race K3.
qa5 x 600”’
and for the outer race
P3-P2
rolling bearing with characteristics
12’3x 0.05”5 x 302*5
P3Pl
+Pz
A heavy-loaded
30 mm, p2 = 10 mm, p3 = 50 mm, P = 8 is subject to wear
W1 =8x102
for the roller
LPl
Example
10x 50 % 50+10 K3 =(---loxso) 50-10) (
For the inner race K1
bearings
W3=8xlO*
12’3x 0 051.5 x 302.5 x 2.54x 200=1.27 urn/h. _ ’ 4’.’ x 6001.’ x 600
References 1. Moore D.F. Principles
and Applications
of Tribology.
Dublin,
19 75, 488 2. Pinegin C.V. Contact Machinery,
Strength
and Rolling
Resistance.
1972, 172
3. Yampolsky
G.Ya. and Kragelskii 1.V. Investigation of Abrasive Wear in a Pair of Elements of Rolling I:riction. Wear, 1972, 21, 231-262
4. Kragelskii
I.V., Bobyuchin of Calculations for Friction
M.N. and Kombalov VS. Basic Data and Wear. Machinery, 1977, 526
P. Paper of American Society of Mechanical Engineers. NWA/lu h. -2 7, 196 7
5. Eschmann
6. Yampolsky
G.Ya. and Kragelskii Wear in a Pair of Rolling Friction 64
I.V. Investigation of Abrasive Elements. Science, 1973.
Various mechanisms of microslip are discussed; abrasive wear is considered the most important. An equation to predict the wear rate of rolling bearings is presented, based on previous work, and illustrated by an example
Rolling bearings of road-building,mining, transport, agricultural and other types of equipment undergo intensive abrasive wear which is difficult to prevent despite the constant improvement of bearing assembly protection 2'3's. One of the main factors affecting the wear of rolling elements is the microslip in the contact. The following types of microslip are known: kinematic, connected with the deflection of nominal sizes of rolling elements and also differential slip according to the Heathcote scheme; Reynolds' slip caused by different elastic moduli and Poisson's moduli of the elements; and dynamic slip connected with elastic interaction in the presence of periodic perturbations 1,2 . These types of microslip together with elastic hysteresis and adhesive interaction give very low wear rates for rolling bearings operating with pure oil but they are not the cause of abrasive wear. The friction surface analysis of rolling bearings shows that more important sources of microslip, leading to quite long 'traces' caused by abrasive particles and a high degree of wear, must exist. This specific type of microslip which is due to trapping of abrasive particles in the contact zone may be estimated from the fact that the projection V~ and V21 for the same linear speeds V of these abrasive particles of radius R are different due to different values of radius of curvature Pl and P2 (Fig 1). The difference of these projections is the value of microslip (v,' - v~' ). Pl +P2 2VR - - -(1) P~P2 where plus and minus are related respectively to the contact of rolling elements with the same (roller-outer race) and different (roller-inner race) curvature. VlI - V21 =
The equations 3'6 obtained before estimate the influence of the abrasive action A, physical and mechanical properties of materials M and the kinematic and geometric parameters of conjugation K on the wear rate W. For a pair of contact elements in rolling friction A KI(2), WI(2) = 4x 10 2 - - - MI(2) where
(2)
A = J / 3 R ° ' S 0 2.s
(3)
MI(2) = 8 1(2) t Hl(2) i.s H2(I) KI(2 ) =p,Vz I
VI l - V2 1 ]
V
(4) nl(2)
(5)
*Laboratory of Friction and Friction Materials, hlstitute of Mechanical Engineering, Moscow. USSR
0301-679X/81/030137-02 $02.00 © 1981 IPC Business Press
\\
Fig 1 Microslip o f abrasive particles in the contact zone o f rolling elements moving with the equal speed, V
In these equations the group of factors A (Eq (3)) shows the influence of abrasive values on the wear. The number of abrasive particles is defined by their volumetric concentration e, %, in lubricant or air. Wear is caused by those abrasive particles which are larger than the oil layer thickness and height of the microroughness. Since these particles constitute the majority, the full concentration e, including the full range of particle sizes, must be taken into account. The abrasive value in Eq (3) is calculated using the mean radius of the particles R. The kind of abrasive particle is determined by its mechanical strength o, defined as the conventional compression stress or ultimate tensile stress of particles equal to the ratio of the load affecting the particle's fatigue to its diametric section 7r R 2 4 According to the group of factors M in Eq (4), wear depends on the physico-mechanical properties of contact materials. In this case, the hardness of friction and contact elements HI and//2 (Brinel hardness) plays an important role. Wear also depends to a certain extent on the elasticity ~ (the percentage elongation at rupture corresponding to the maximum deformation force). The 8 characteristic may be determined by data obtained during tensile tests, as well as with the indentor method 4. Eq (4) also includes the coefficient of contact frictit~n fatigue t which varies between 0.3 and 0.5 for rolling bearing materials.
TRIBOLOGY international June 1981 137
Yampolski,
Kragelskii and Yushakov - Abrasive wear of rolling
The third group of factors K, in Eq (5) shows the influence of geometric and kinematic parameters on wear: p*, the PlPZ
where p1 and pz are radius of curvature equal to -~ PI +Pz’ the radii of curvature of rolling bodies 1 and 2 (plus and minus refer to the contact of rolling bodies with the same or different curvature); Vr ’ and V,’ are projections of linear speeds of rolling bodies 1 and 2; I/ is the absolute value of linear speed of the rolling bodies; nlc2) is the number of loadings on the rolling bodies 1 and 2 per minute (revolutions per minute). By substituting Eqs (1) (3), (4) and (5) in Eq (2) using known formulae for definition of the number n, />, , we may evaluate the abrasive wear of rolling eleme;t?in axial loadings EZ/3 RI.5 g2.5 W 1_2,3= 8x lo* K 1,2,3 nl (6) 6 1A3 H:‘:> , 3 H2 >12 9 In this equation, the subscripts 1, 2, 3 relate to the inner race, roller and outer race, respectively.
=
(Pl$
(Pl_P2
(7)
p,p,‘:XfiJP.
Pl +P2
PlP2
P2P3
P3-P2
~pZ(Pl+PZ)
(8)
30x 10 % 30-10 GGlO’
(--30x
10x50 % 5ot10
lo’+(GX? 30 tFO)
1
x 8 = 1.83
(iG&
50x 30
10(30+10)=
2.27
x 8 = 2.54
Then, according to Eq (6) we obtain the values of wear rate of the elements for the inner race x 1.83x 200 = 0.89Hm/h,
Pl
)p,
(9) p2p3
Pl
According to Eq (6) the wear of rolling bearings depends mostly on the hardness of contact surfaces. Besides elasticity and coefficient of contact friction, fatigue plays a very important role. The influence of these different factors on the abrasive wear of rolling bearings may be used in solving a number of engineering problems eg the prediction of bearing assembly life and optimization of geometric and kinematic bearing parameters.
international June 1981
12’3x 0 05”s x 302.5 ’ x2.27x 200=1.11 pm/h 4°.5 x 6OOr.’ x 600’ -
and for the outer race
+P2
From Eq (6) we know that the abrasive wear of rolling bearings depends mostly on the concentrations, size and hardness of abrasive elements rather than on the loading conditions. Contact stress is defined only by the mechanical stability of abrasive particles under loads which intensively crush them. Bearing wear is determined by the total number of revolutions and not by the frequency of rotation.
x 600
for the roller
‘~’
where p1 , p2 and p3 are the radii of the inner race, roller and outer race respectively and P is the number of rollers.
TRIBOLOGY
30x10 % 30-10 50 36x1o)(3o+1o) 30+10) (
Kr =(
W2=8x102
P2P3 )I/i,s+P2)(
K3= (---
138
p1 =
at an abrasive content of the lubricant E = l%, with an average particle size of R = 0.05 mm with mechanical strength u = 30 kg/mm2. The bearing element materials have the following physico-mechanical properties HI = Hz = H3 = 600 kg/mm2 (Brinel); 6 = 4%; fatigue coefficient f = 0.5 and speed of inner race IZ~ = 200 rev/min. From Eqs (7)-(9) we may determine kinematic indices for the inner race K1, roller K2 and outer race K3.
qa5 x 600”’
and for the outer race
P3-P2
rolling bearing with characteristics
12’3x 0.05”5 x 302*5
P3Pl
+Pz
A heavy-loaded
30 mm, p2 = 10 mm, p3 = 50 mm, P = 8 is subject to wear
W1 =8x102
for the roller
LPl
Example
10x 50 % 50+10 K3 =(---loxso) 50-10) (
For the inner race K1
bearings
W3=8xlO*
12’3x 0 051.5 x 302.5 x 2.54x 200=1.27 urn/h. _ ’ 4’.’ x 6001.’ x 600
References 1. Moore D.F. Principles
and Applications
of Tribology.
Dublin,
19 75, 488 2. Pinegin C.V. Contact Machinery,
Strength
and Rolling
Resistance.
1972, 172
3. Yampolsky
G.Ya. and Kragelskii 1.V. Investigation of Abrasive Wear in a Pair of Elements of Rolling I:riction. Wear, 1972, 21, 231-262
4. Kragelskii
I.V., Bobyuchin of Calculations for Friction
M.N. and Kombalov VS. Basic Data and Wear. Machinery, 1977, 526
P. Paper of American Society of Mechanical Engineers. NWA/lu h. -2 7, 196 7
5. Eschmann
6. Yampolsky
G.Ya. and Kragelskii Wear in a Pair of Rolling Friction 64
I.V. Investigation of Abrasive Elements. Science, 1973.