Purpose for Preload
The purpose of applying preload to a bearing is to improve the runout precision of the rotating axis, and to reduce vibration and noise. It is important to select the proper amount of preload and method for each application. Otherwise, bearing performance such as life, noise, and vibration will be degraded. Excessive heat could also be generated.
The necessary radial internal clearance in an assembled ball bearing may increase noise and rotational vibration in an application due to the movement of the balls inside the bearings. To combat the relative movement of the balls, an axial “preload” should be applied to the bearing, as shown in the diagram below. Preload increases the stiffness of the bearing and reduces potential noise and vibration. The appropriate preload force depends on the size of the ball bearing. Higher preload will increase the bearing stiffness but excessive preload may result in premature failures. If insufficient preload is applied, vibration and fretting wear may occur inside of the bearing.
Minebea recommends an optimum preload based on the calculation of the optimum surface stress. When the preload is applied to the ball bearing, a contact ellipse is generated as a result of elastic deformation of the contact areas between the balls and raceways. The surface stress is given by dividing the loads, Q (ball loads), which are generated in the perpendicular direction at the contacts between the balls and raceways, by the surface areas of the contact ellipses.
In Figure 2-15,below, the contact ellipse area (S) between the balls and raceways is formulated as: S = πab (a: the major axis of the contact ellipse area, b: the minor axis of the contact ellipse area). P represents the average surface stress, and Q represents the loads generated in the perpendicular direction at the contact areas between the balls and raceways.
P = Q / S [MPa]
If the preload is the dominant load applied to the bearing, the guideline to meet the noise life is as follows:
• Over 10,000 hours noise life requirement. The specific preload should not generate an average surface contact stress (P) higher than 800MPa.
• 5,000 – 10,000 hours noise life requirement (general products) The specific preload should be generating an average surface contact stress (P) of roughly 1,000MPa.
• Less than 5,000 hours noise life requirement (critical stiffness application) The specific preload should be generating an average surface contact stress (P) of roughly 1,500MPa.
Simple calculation of preload using dynamic load rating (Cr)
• Over 10,000 hours noise life requirement: 0.5/100Cr – 1/100Cr
• 5,000 – 10,000 hours noise life requirement: 1/100Cr – 1.5/100Cr
• Less than 5,000 hours noise life requirement: 1.5/100Cr – 2/100Cr
Maximum Permissible Load
In general, a permanent deformation will occur if the average surface stress generated on high carbon chromium steel is greater than 2,700 MPa. So, even for a very short period of time, the loads should not generate greater than 2,700 MPa of average surface stress. Based on our experience, the loads applied to the bearing should not generate more than 1,600 MPa of average surface stress. Besides preload, other types of loads should also be considered because they could generate surface stress.
Preload and Stiffness
There are two basic methods of preloading: Solid Preload (Figure 2-16) and Spring Preload (Figure 2-17) shown on the following pages. Solid Preload can be obtained by mechanically locking all of the rings in position. The advantages of this type of design are simplicity and high stiffness. However, expansion and shrinkage of the components due to temperature change can cause changes in preload.
The components could also wear, and eventually the preloads could be reduced.
Spring Preload (constant pressure preload) can be applied by using a coil spring, wave spring, etc. An advantage of spring preload is stability despite temperature variation. The disadvantages are complexity and low stiffness.
The preload can be applied in two directions: Duplex Face to Face (DF) (Figure 2-18) and duplex Back to Back (DB) (Figure 2-19). The stiffness is higher in DB.
When the loads are applied to the bearings, the displacement takes place at the contact points between the balls and raceways.
When the loads are applied in radial directions as shown in Figure 2-20, Q is expressed as:
(Fr, Q, and Z represent a radial load, the maximum load applied to the balls, and the number of balls, respectively.) Radial displacement at the contact points between balls and raceways is expressed below
eδ : Coefficient based on the relationship between balls and raceways
Σρ : Total major curvature In order to determine the total displacement, the displacement between the balls inner ring and outer ring needs to be summed because the balls are contacting both the inner ring and outer rings.
δr : Total radial displacement
δi : Radial displacement between balls and inner ring raceway
δe : Radial displacement between balls and outer ring raceway Total displacement is represented as follows:
Axial displacement (Fa) can be calculated in the following series of calculations: Initial Contact Angle (α0) For a bearing with the radial internal clearance (Gr) eliminated from an axial load, the initial contact angle can be calculated as follows.
Gr : Radial Internal Clearance
ri : Inner Ring Groove Radius
re : Outer Ring Groove Radius
Dw : Ball Diameter
Relationship between Initial Contact Angle (α0) and Contact Angle (α)
The relationship between the initial contact angle and the contact angle generated by applying an axial load (Fa) is expressed below. (Figure 2-21)