How to calculate crossed roller bearing life (with various load types)
A crossed roller bearing is a type of rotary bearing that uses cylindrical rollers arranged in a crisscross pattern, with each roller oriented at a 90 degree angle relative to the one adjacent to it.
This arrangement allows crossed roller bearings to withstand radial, axial, and moment loads, so they can often replace dual-bearing arrangements, for applications with limited installation space. And because the rollers form line contact with the raceways, crossed roller designs exhibit very high stiffness and minimal deflection under load. These characteristics make crossed roller bearings ideal for rotating motion components such as rotary actuators and rotary ball splines.
Crossed roller bearing life calculation
The predicted life for a crossed roller bearing is calculated via the standard life equation for bearings that use rollers as the load-carrying elements:
See the equation here https://3l4sbp4ao2771ln0f54chhvm-wpengine.netdna-ssl.com/wp-content/uploads/2021/02/Radial-Bearing-Life-Equation.jpg
L = bearing life (revolutions)
C = basic dynamic load rating (N)
P = applied load (N)
Note that the exponent in the bearing life equation is “10/3” rather than the typical “3.” This is because crossed roller bearings use rollers rather than balls for carrying the load.
How to account for axial, moment, or combined loads
The basic dynamic load rating for a crossed roller bearing is for loads applied in the radial direction.
When a crossed roller bearing is subjected to axial and/or moment loads, the equivalent radial load must be calculated based on the combination of the applied radial, axial, and moment loads.
See the equation here https://3l4sbp4ao2771ln0f54chhvm-wpengine.netdna-ssl.com/wp-content/uploads/2021/02/Crossed-Roller-Bearing-Equivalent-Radial-Load-Equation-300x59.jpg
Pr = dynamic equivalent radial load (N)
X = radial load coefficient
Fr = applied radial load (N)
M = applied moment load (Nm)
Dp = pitch circle diameter of rollers (m)
Y = axial load coefficient
Fa = applied axial load (N)
Radial and axial load coefficients
The radial and axial load coefficients (X and Y, respectively) are commonly used for rotary bearings to account for how the loads are distributed within the bearing. Their values change based on the ratio of the axial and radial loads.
For the case of crossed roller bearings, the threshold for the axial-to-radial load ratio is 1.5, at which point the axial load begins to affect how the rollers ride within the raceways, and therefore, how the load is distributed across each roller.
For an axial-to-radial load ratio equal to or less than 1.5, the radial load coefficient is higher than the axial load coefficient (1.0 versus 0.45), meaning the radial load plays a more significant role in bearing fatigue.
Then X = 1.0
Y = 0.45
However, if the axial-to-radial load ratio exceeds 1.5, the radial and axial loads are multiplied by the same load coefficient (0.67), meaning they play an equal role in causing bearing fatigue.
Then X = 0.67
Y = 0.67
Life based on equivalent radial load
Now the equivalent radial load can be used to determine the life of the crossed roller bearing.
Factors for high temperature, shock & vibration loads, and oscillating motion
Most manufacturers also recommend incorporating factors to adjust for high temperature applications (typically those above 80° C) and for applications with moderate or severe impact loads.
See the equation here https://3l4sbp4ao2771ln0f54chhvm-wpengine.netdna-ssl.com/wp-content/uploads/2021/02/Crossed-Roller-Bearing-Life-Equation-with-Factors.jpg
ft = temperature factor (1.0 at 80° C and decreases with increasing temperature)
fw = load factor (typically 1.0 to 3.0, depending on the expected level of shock and vibration loading)
And if the application involves oscillating motion — repeated, partial rotations — the life should be reduced by the amount of the oscillation.
See the equation here https://3l4sbp4ao2771ln0f54chhvm-wpengine.netdna-ssl.com/wp-content/uploads/2021/02/Crossed-Roller-Bearing-Life-with-Oscillation-Equation.jpg
Loc = life of oscillating bearing (revolutions)
θ = angle of oscillating motion