End users must include bearing clearance as an integral part of designing or building a pump.
by Miles Woodard and Ryan Thomas

Internal clearance is one of the most important factors affecting bearing performance within pump applications. The bearing’s internal clearance is the relative movement of the outer and inner rings when they are lightly pushing in opposite directions. Movement in the diametrical direction is defined as radial clearance. Movement in the shaft’s direction is axial clearance.

Internal clearance is critical to bearing performance for multiple reasons. The amount of clearance influences the load distribution in a bearing, which ultimately affects bearing life. It also influences bearing running noise and vibration. In addition, it can influence whether the rolling elements move in a rolling or sliding motion.

Normally, bearings are installed with interference on either the inner or outer ring. This leads to its expansion or contraction, which causes a change in clearance. During operation, the bearing temperature will increase until it reaches saturation temperature. However, the temperature of the inner ring, outer ring and rolling elements are all different from each other, and this temperature difference changes the clearance (see Figure 1). In addition, when a bearing operates under load, an elastic deformation of the inner ring, outer ring and rolling elements also leads to a change in clearance. Quantifying all these changes can make calculating bearing internal clearance a complex task.

Figure 1
Figure 1. Changes of radial internal clearance of a roller bearing


Different Types of Clearances
What is the ideal clearance? Before considering this question, different types of clearance will be defined in this section.

Measured Internal Clearance (∆1)
This is the internal clearance measured under a specified measuring load and can be called apparent clearance. It includes the elastic deformation (δFO) caused by the measuring load.

∆1 = ∆0 + δFO

Theoretical Internal Clearance (∆0)
This is the radial internal clearance, which is the measured clearance minus the elastic deformation caused by the measuring load.

∆0 = ∆1 + δFO

δFO is significant for ball bearings but not for roller bearings, where it is assumed to be equal to zero, and therefore ∆0 = ∆1.


Residual Internal Clearance (∆f)
This is the clearance left in a bearing after mounting it on a shaft and in a housing. The elastic deformation caused by the mass of the shaft, etc., is neglected. Assuming the clearance decrease caused by the ring expansion or contraction is δf, then:

∆f = ∆0 + δf


Effective Internal Clearance (∆)
This is the bearing clearance that exists in a machine at its operating temperature, excluding the elastic deformation caused by load. In other words, this is the clearance when considering only the changes because of the bearing fitting δf and temperature difference between the inner and outer rings, δt. The basic load ratings of bearings apply only when the effective clearance is ∆=0.
∆ = ∆f − δt = ∆0 – (δf + δt)


Operating Clearance (∆F)
This is the actual clearance when a bearing is installed and running under load. In this situation, the effect of elastic deformation δF is included and the fitting and temperature. Generally, the operating clearance is not used in the calculation.

∆F = ∆ + δF


Importance of Effective Clearance
The most important bearing clearance is the effective clearance. Theoretically, a bearing with a slightly negative effective clearance ∆ will have the longest life. A slightly negative clearance (or preload) will actually become positive under the influence of bearing load. However, making the clearance of all the bearings the ideal effective clearance is impossible. End users must consider the geometrical clearance ∆0 to achieve a zero or slightly negative effective clearance minimum value. To calculate this value, a user needs to know the clearance reduction caused by the interference of the inner ring and outer ring δf and the clearance change caused by the temperature difference between the inner ring and outer ring, δt.


Calculating Residual Internal Clearance After Mounting
When the inner ring of a bearing is press fit onto a shaft, or when the outer ring is press fit into a housing, the radial, internal clearance will naturally decrease because of the resulting expansion or contraction of the bearing raceways. Generally, most pumps have a rotating shaft that requires a tight fit between the inner ring and shaft and a loose fit between the outer ring and housing. In these cases, only the effect of the interference on the inner ring needs to be considered.

An example calculation is shown below for a 6310, single-row, deep-groove ball bearing. The shaft tolerance used is K5, while the housing is H7. The interference fit is applied only to the inner ring.

Shaft diameter, bore size and radial clearance are the standard bearing measurements. Assuming that 99.7 percent of the parts are within tolerance, the mean value (m∆f) and standard deviation (σ∆f) of the internal clearance after mounting (residual clearance) can be calculated. Measurements are given in millimeters (mm).