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Calculation examples

Example 1: Basic rating life and SKF rating life

An SKF Explorer 6309 deep groove ball bearing is to operate at 3 000 r/min under a constant radial load Fr = 10 kN. Oil lubrication is to be used, the oil has an actual kinematic viscosity ν = 20 mm2/s at normal operating temperature. The desired reliability is 90% and it is assumed that the operating conditions are very clean. What are the basic and SKF rating lives?
a) The basic rating life for 90% reliability is

Example 1 a): formula

From the product table for bearing 6309, C = 55,3 kN. Since the load is purely radial, P = Fr = 10 kN (→ Equivalent dynamic bearing load). Therefore, in million revolutions

Example 1 a): equation 1

or in operating hours

Example 1 a): equation 2

Example 1 a): equation 3
b) The SKF rating life for 90% reliability is

Example 1 b): formula
  • As a reliability of 90% is required, the L10m life is to be calculated and a1 = 1 (table 1).
  • From the product table for bearing 6309, dm = 0,5 (d + D) = 0,5 (45 + 100) = 72,5 mm
  • From diagram 1, the rated oil viscosity at operating temperature for a speed of 3 000 r/min, ν1 = 8,15 mm2/s. Therefore, κ = ν/ν1 = 20/8,15 = 2,45
  • From the product table Pu = 1,34 kN and Pu/P = 1,34/10 = 0,134. As the conditions are very clean, ηc = 0,8 (table 2) and ηc (Pu/P) = 0,107. With κ = 2,45 and using the SKF Explorer scale in diagram 2, the value of aSKF = 8 is obtained. Then, according to the SKF rating life equation, in million revolutions

    Example 1 b): equation 1

    or in operating hours using

    Example 1 b): equation 2

    Example 1 b): equation 3

Example 2: Check contamination conditions

An existing application has to be reviewed. An SKF Explorer 6309-2RS1 deep groove ball bearing with integral seals and standard grease fill is working under the same conditions as described in example 1 (κ = 2,45). The contamination conditions of this application have to be checked to determine if it is possible to use a more cost-effective bearing for a minimum requisite life of 3 000 hours of operation.
  • Considering grease lubrication and integral seals, the level of contamination can be characterized as high cleanliness and from table 2, ηc = 0,8. With Pu/P = 0,134, ηc (Pu/P) = 0,107, using the SKF Explorer scale in diagram 1 and κ = 2,45, aSKF = 8.

    Example 2: equation 1

    in operating hours.
  • A more cost-effective bearing arrangement would use a shielded SKF Explorer 6309-2Z bearing. The contamination level can be characterized as normal cleanliness, then from table 2, ηc = 0,5. With Pu/P = 0,134, ηc (Pu/P) = 0,067, using the SKF Explorer scale in diagram 2 and κ = 2,45, aSKF ≈ 3,5.

    Example 2: equation 2

    in operating hours.

Conclusion: This application would be able to take advantage of a more cost-effective solution by replacing the sealed bearing with a shielded bearing.

Example 3: Verify dynamic and static load conditions

The duty cycle of a sealed SKF Explorer spherical roller bearing 24026-2CS2/VT143 used in heavy transportation equipment of a steel plant has the operating conditions listed in table 3.
The static load of this application is determined with reasonable accuracy by taking into account the inertial loads that occur during loading and the shock loads that can occur if something is accidentally dropped.
It is required to verify the dynamic and static load conditions of this application, assuming a required L10mh operating life of 60 000 hours and a minimum static safety factor of 1,5.

From the product table and introductory text:
  • Load ratings:
    C = 540 kN; C0 = 815 kN; Pu = 81,5 kN
  • Dimensions:
    d = 130 mm; D = 200 mm,
    therefore, dm = 0,5 (130 + 200) = 165 mm
  • Grease fill:
    Extreme pressure grease with a lithium thickener and mineral base oil, of NLGI consistency class 2, for a temperature range of –20 to +110 °C (–5 to +230 °F) and a base oil viscosity at 40 and 100 °C (105 and 210°F) of 200 and 16 mm2/s, respectively.

The following calculations are made or values determined (table 4):
  1. ν1 = rated viscosity [mm2/s] (diagram 1) – input: dm and speed
  2. ν = actual operating viscosity [mm2/s] (diagram 3) – input: lubricant viscosity at 40 °C (105 °F) and operating temperature
  3. κ = viscosity ratio – calculated (ν/ν1)
  4. ηc = factor for contamination level (table 2) – “High cleanliness”, sealed bearing: ηc = 0,8
  5. L10h = basic rating life according to the equation (→ Basic rating life) – input: C, P and n
  6. aSKF = from diagram 4 – input: SKF Explorer bearing, ηc, Pu, P and κ
  7. L10mh1,2, … = SKF rating life according to the equation (→ SKF rating life) – input: aSKF and L10h1,2, …
  8. L10mh = SKF rating life according to the equation (→ Calculating life with variable operating conditions) – input: L10mh1, L10mh2, … and U1, U2, …
The SKF rating life of 84 300 hours exceeds the required operating life, therefore, the dynamic load conditions of the bearing are verified.
Finally, the static safety factor of this application is verified using

Example 3, equation 1

Example 3, equation 1

The above shows that the static safety of this application is verified. As the static load is determined accurately, the relatively small margin between the calculated and recommended static safety is of no concern.
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