Engineering Calculator for Frictional Moment, Reference Speed, and Thermal Permissible Speed

Overview

Frictional moment, reference speed (n_ref), and thermal permissible speed (n_perm) can be calculated using the NSK engineering calculator.

Calculations are based on methods outlined in ISO15312:2003, which sets the standard for reference speed (n_ref).

Frictional Moment

Frictional moment, which is used in calculating reference speed (ISO15312:2003), is calculated as follows:

     M＝M₀＋M₁

     M₀＝10^-7 f₀ (νn )^2/3 dm³

     M₁＝f₁ P₁ d_m

where,

     M : Frictional moment (N·mm)

     M₀ : Load-independent frictional moment (N·mm)

     M₁ : Load-dependent frictional moment (N·mm)

     f₀ : Coefficient for the load-independent frictional moment for the reference condition

     f₁ : Coefficient for the load-dependent frictional moment for the reference condition

     υ : Kinematic viscosity of the lubricant under the reference conditions (mm²/s)

         (depending on bearing temperature T °C)

     n :I nner ring rotating speed

     d_m : (Bore diameter d + Outside diameter D) / 2 (mm)

     P₁ : Reference load

Lubrication Methods

• Oil bath lubrication

     · Mineral oil with no EP additives

     · Bearing is submerged in oil up to the centerline of the rolling element in the lowest position

• Grease lubrication

     · Amount of grease equivalent to 30% of bearing interior space

     · Frictional moment of a bearing that is packed with a sufficient amount of grease is about two times

       of that for a bearing using oil-bath lubrication for the duration of the break-in running time (10-20 hours),

       after which the range of frictional moment is reduced from 25% to 50% with the elapse of time.

       Results of the NSK calculator include the calculation of frictional moment for conditions where a length of time has passed.

Reference Speed (n_ref)

Reference speed (n_ref), which serves as the index, is based on bearing operating temperatures as defined by ISO15312:2003.

This figure indicates inner ring rotational speed at the point where equilibrium is reached between heat generated by friction

in the bearing and heat flow emitted through the bearing seat (shaft and housing) under the following conditions:

• Reference temperature

     · Outer ring temperature at inner ring rotation or housing washer : 70°C

     · Temperature of bearing operating environment : 20°C

• Reference load

     Radial bearing (contact angle from 0° to 45°): 5% of the basic static load rating C_0r as pure radial load

• Lubrication

     · Mineral oil with no EP additives

     · Bearing is submerged in oil up to the centerline of the rolling element in the lowest position

     · Kinematic viscosity at reference temperature 70 °C: 12 mm²/s (ISO VG32)

Under the reference conditions described above, reference speed (n_ref), which results in a condition where the state of thermal equilibrium 

between reference frictional heat generated in bearing N_r and the reference heat flow emitted from bearing Φ_r, is also calculated as follows:

     N_r (others, n_ref) = Φ_r

     N_r = πn_ref M / 30000

     Φ_r = q_r A_r

where,

     A_r：Heat emitting reference surface area of bearing (mm²)

     q_r：Heat flow density when temperature difference between bearing environment and bearing is 50°C for normal applications (W/mm²)

     A_r ≤ 50000mm²  , then   q_r = 0.016

     A_r > 50000mm²  , then   q_r = 0.016 (A_r / 50000)^-0.34

• Reference speed for bearing operating under grease lubrication conditions

Bearing frictional moment fluctuates operating time elapses under grease lubrication.

Therefore, referencetemperature T=70°C is obtained after 10 to 20 hours if the following conditions are satisfied,

and if thereference speed for grease lubrication reaches the same value as that for oil-bath lubrication.

   · Lithium-soap grease and a base oil of mineral oil

   · Base oil kinematic viscosity: Reference kinematic viscosity at 40°C, 100 to 200 mm²/s (ISO VG150)

   · Amount of grease equivalent to 30% of bearing interior space

Thermal Permissible Speed (n_perm)

Thermal permissible speed (n_perm) is defined as the rotational speed where a thermal equilibrium state isreached at designated temperature T

under arbitrary conditions of load and lubrication methods. Calculationsare performed in the same manner as reference speed calculations.

Rotational speed (n_perm), which results in acondition where the state of thermal equilibrium between frictional heat generated in bearing N

and thereference heat flow emitted from bearing Φ, is also calculated. Heat flow calculations are based onreference heat flow density qr

for normal applications listed in ISO15312.

     N (others, n_perm) = Φ

Cautionary Notes

This program is applicable to most bearing operating conditions except for the following:

   1. Bearing bore diameter exceeds 1000 mm

   2. Sealed or shielded bearings

   3. Bearing not having normal clearance (CN) or angular contact ball bearings not having a zero clearance

   4. Bearings not mounted in stationary housing or horizontal rotating shaft

   5. High-speed operations exceed limiting speeds

   6. Lubrication conditions differ from reference conditions

       (i.e. oil level is higher than the center of the rolling element in the lowest position;

        amount of grease exceeds 30% of the bearing interior space; other lubrication method is used)

   7. Bearings operated in an environment that risks heavy exposure to water, debris, etc.

   8. Bearings operated under conditions of high vibrations

   9. Conditions with a large misalignment between the inner and outer rings

   10. Bearings are suffering from abnormal wear, corrosion, electric erosion, etc.

   11. Bearings operated under conditions of starved lubrication or excessively heavy or light loads

Contact NSK for further details.