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8. Internal Clearance of Bearings

Internal Clearance and Standard Values

Internal Clearance of Bearings

Internal clearance is the space among a bearing’s outer ring, inner ring, and balls. Generally speaking, the amount of vertical movement of the outer ring with the inner ring fixed is called the “radial internal clearance,” and the amount of horizontal movement is called the “axial internal clearance.” The amount of internal clearance during the bearing’s operation is an important factor that impacts performance such as noise, vibration, heat generation, and fatigue life.

Deep groove ball bearings are usually classified by their radial internal clearance. In the actual clearance measurement, a designated load is applied to achieve stable results. As elastic deformation of the bearing occurs during the measurement, which makes the results larger than the true clearance, a correction (reduction) is made to obtain the true clearance.

Radial internal clearance of small/miniature bearings

Remarks:

1. Standard clearance is MC3.
2. The correction in the following table should be made when using the values above as measurement clearance.

Remarks: The measurement load is:

1. For miniature bearings ... 2.5N(0.25kgf)
2. For small bearings ...4.4N(0.45kgf)

Radial internal clearance of standard deep groove ball bearings

Remarks:

1. Standard clearance is C0.
2. Corrections in the table above should be made when using the values above as measurement clearances.
3. For the correction of C2 clearance, be sure to apply the minimum values to minimum clearance, and the maximum values to maximum clearance.

Relation between Radial Internal Clearance and Axial Internal Clearance

The axial internal clearance is determined based on the values of ball diameter, inner/outer ring raceway radius, and radial internal clearance. It is risky to select a bearing with a small radial internal clearance or a fitting with a large interference with the aim of achieving a smaller axial internal clearance after mounting.

Selection of Bearing Clearance

Theoretically, the longest bearing life can be achieved by setting the clearance during operation to a slightly negative value. However, it is also known that the life becomes significantly shorter when the negative clearance exceeds this value, even to the slightest degree. Therefore, normal practice is to select an initial clearance so that it becomes slightly positive (away from zero). Generally, MC3 is selected for miniature/small bearings, and C0 is selected for standard bearings.

Selection criteria for radial internal clearance

Relation between Radial Internal Clearance and Angular Clearance

During the actual use of a bearing, it may receive a moment load as a result of factors such as shaft deflection due to load and the housing’s cylindricity. At this time, an inclination called the “angular clearance” is generated at the inner and outer rings. If the allowable angular clearance determined for each bearing is exceeded, this may cause an abnormal stress between the raceway and the ball, which will result in high temperatures or flaking.

Angular clearance refers to an angle that may be freely inclined when either the inner or outer ring is fixed, and when the ring that is not fixed is tilted to the left or right. The inclination around the center of the bearing is defined as θ₁, and the inclination around the center of the bottom ball is defined as θ₂. θ₁ is significantly larger than θ₂. The angular clearance must be taken into account when designing the device and installing the bearing.

θ₁=2×tan^-1 (2×(Δ_r×(r_o+r_i-D_w)) ^0.5/dm)
θ₂=2×tan^-1((Δ_r×(r_o+r_i-D_w)) ^0.5/dm)
θ₁=Angular clearance around the center of the bearing
θ₂=Angular clearance around the center of the bottom ball
dm=Pitch circle diameter (mm); generally dm = (D+d)/2

Calculation of Clearance

(1) Operating clearance: Δ

Operating clearance refers to a clearance with elastic deformation caused by load and fitting during bearing operation at a constant temperature.

Δ=Δ₁- (δ_t+δ_f) +δ_w (mm)

(2) Decreased clearance due to temperature difference between inner and outer rings: δ_t

Under normal operating conditions, the balls will have the highest temperature, followed by the inner ring, with the outer ring at the lowest temperature. It is difficult to measure the temperature of the balls, which is deemed to be identical to that of the inner ring for the sake of practical convenience.

δ_t≒a×ΔT×D_a (mm)

(3) Decreased clearance due to fitting: δ_f

When the bearing is mounted on a shaft or the housing with interference, the outer ring will contract, while the inner ring will expand, resulting in a decrease in the bearing’s internal clearance.

δ_f=δf_i+δf_o=Δd_b×d/d_b× ((1-(d_o/d)²)/(1-(d_o/d_b)²)) +ΔD_a×D_a/D× ((1-(D/D_h)²)/(1-(D_a/D_h)²)) (mm)

(4) Increased clearance after receiving load: δ_w

When a load is applied to the bearing, the internal clearance increases due to elastic deformation.

Meaning of symbols

Axial Load and Axial Displacement, and Change in Contact Angle

When the ball bearing receives an axial load, axial displacement takes place due to elastic deformation, and the contact angle becomes larger than the initial contact angle.

(1) Axial load: F_a

F_a=9.8×Z×sinα×D_w²×(cosα₀/cosα-1)^(3/2)×((2×m-D_w)/(C×D_w))^(3/2)(N)

(2) Axial displacement: δ_a

δ_a=C/sinα×(1/D_w)^(1/3)×(F_a/(Z×sinα))^(2/3)(mm)

Radial Clearance and Bearing Fatigue Life

Normally, the radial clearance used for calculating the life of bearings is Δ_r = 0, where the load distribution within the bearing can be represented by a load factor of ε = 0.5. In this case, almost half of the balls receive the load. The load factor and the bearing fatigue life change based on the change of the radial clearance.

In the case of a deep groove ball bearing, the following relational equation is formulated between the radial clearance Δ_r and the load factor ε, and the function F(ε). Lε can be obtained from the relation between F(ε) and the life ratio Lε/L.

F(ε)=Δ_r×D_w^(1/3)/(C×(F_r/Z)^(2/3))

As shown in the example figure below, the longest life can be achieved when the clearance value is slightly negative. The figure also shows that as the clearance increases, the number of balls that receive the load decreases, which results in a shorter life.