When designing an application, the design engineer must consider proper bearing lubrication. The lubrication method affects the proper operation of the equipment and the cost of maintaining it. Once the lubrication method is determined, selection of the proper lubricant oil viscosity is vital for prolonging the life of the equipment’s rolling element bearings. Rolling element bearings work best when they operate in a lubrication condition called elastohydrodynamic lubrication (EHL). Bearing life is extended when a rolling element bearing operates with complete separation of the rolling elements from the raceways. Formation of a fully developed EHL layer between the rolling elements and the raceway depends on the speed of rotation, the bearing size and type, and the operating viscosity of the lubricant. Sufficient available oil volume is also necessary for the development of the EHL layer. The film parameter (Λ) evaluates and optimizes this separation given a particular set of application conditions. This article discusses a relatively simple method for calculating the film parameter, with an understanding of the factors that affect it and how to apply it to a design project.
To optimize the lubrication of a bearing, proper oil viscosity selection is essential.
01/22/2014
Figure 1. Oil film and surface roughness
Since the scale of the EHL oil film thickness is of the same order of magnitude as the surface roughness, lubricating conditions cannot be determined without considering surface roughness. Given an average oil film thickness, a spectrum of conditions may occur depending on the surface roughness—from complete separation of the two surfaces by the oil film (see Figure 1a) to metal contact between the surface asperities (see Figure 1b) resulting in lubricant degradation and surface damage.
Λ = h / σ Equation 1
Where:
h = EHL oil film thickness
σ = Combined roughness ( √σ12 + σ22 )
σ1, σ2 = Root mean square (rms) roughness of each contacting surface
The oil film parameter is correlated to the formation of the oil film as shown in Figure 2, and the degree of lubrication can be divided into three zones (see Figure 2). When Λ is large (around 3.0), bearing life is dominated by sub-surface fatigue. As Λ decreases, surface-originated flaking becomes dominant, reducing the life of the bearing.
Figure 2. The effect of oil film on bearing performance
Table 1. Value T
The equation is in terms of factors that the design engineer knows: oil viscosity η0 in millipascal-second (mPa∙s) or centipoise (cp), speed n (rpm), bearing bore diameter d in millimeters (mm) and type. The following procedure can be used to calculate Λ:
Determine T from the bearing type with Table 1.
Determine R from n (rpm) with Figure 3.
Determine A from the absolute viscosity (mPa∙s, cp) and oil type in Figure 4. Generally, the kinematic viscosity ν0 (square millimeters per second, centistokes) is used and the conversion is shown in Equation 5.
Figure 3. Speed term, R
Figure 4. Lubricant viscosity term, A
η0 = ρ • ν0 Equation 5
Where:
ρ = the density (grams per cubic centimeter) and is approximated below:
Mineral oil: ρ = 0.85
Silicone oil: ρ = 1.0
Diester oil: ρ = 0.9
If the users are unsure if the mineral oil is napthenic or paraffinic, they should use the paraffin mineral oil curve shown in Figure 4.
Determine D from the diameter series and bore diameter d (mm) using Figure 5. The product that results from Equation 4 is the oil film parameter.
Figure 5. Bearing specifications term, D
A few examples of the EHL oil film parameter calculation are described in this section.
Determine the oil film parameter for a 6,312 deep groove ball bearing operating with a paraffinic mineral oil (ηo = 30 mPa∙s, cp) at speed n = 1,000 rpm.
d = 60 mm and D = 130 mm, from the bearing catalog
T = 1.5 from Table 1
R = 3.0 from Figure 3
A = 0.31 from Figure 4
D = 1.76 from Figure 5
Therefore, Λ = 2.5
Calculate the oil film parameter for an NU240 cylindrical roller bearing operating with paraffinic mineral oil (η0 = 10 mPa∙s, cp) at speed n = 2,500 rpm.
d = 200 mm and D = 360 mm, from the bearing catalog
T = 1.0 from Table 1
R = 5.7 from Figure 3
A = 0.13 from Figure 4
D = 4.8 from Figure 5
Therefore, Λ = 3.6
Figure 6. Oil film thickness reduction factor, Hi, because of shearing heat generation
By multiplying the oil film parameter determined in the previous section by this reduction factor, Hi, a version of the oil film parameter is obtained that includes shearing heat generation (see Equation 6). Note that it is assumed that the pitch diameter (Dpw) is the average of the bore and outside diameters of the bearing.
Λ = Hi • T • R • A • D Equation 6
Under the conditions in Example 1, dmn = 9.5 x 104 and η0 = 30 mPa∙s, cp, and Hi is nearly equivalent to 1 (see Figure 6). Therefore, almost no effect occurs because of shearing heat generation. In Example 2, dmn = 7 x 105 and η0 = 10 mPa∙s, cp, and Hi = 0.76, smaller than in Example 1 by about 25 percent. Accordingly, Λ is actually 2.7, not 3.6.