# About the Selection of the Groove Curvature Radius Coefficient of Deep Groove Ball Bearings

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Abstract: On the basis of ignoring bearing clearance, the geometric parameters and contact stress of deep groove ball bearings are analyzed. According to the calculation method of ultimate stress,

The Co e curves of different groove curvature radius coefficients are drawn, and how to select the groove curvature radius coefficients according to the figure is illustrated.

## 1 Ball bearing contact stress and deformation

Regardless of the bearing clearance, when the steel ball is in contact with the inner and outer grooves of the bearing, the geometric parameters near the contact point are specified as follows: dm is the diameter of the ball pitch circle, Ri and Re are the groove curvature radii of the inner and outer rings, respectively. fi , fe——the radius coefficient of groove curvature of the inner and outer rings. The curvature sum and the curvature difference function at the contact point between the steel ball and the channel are divided into the inner and outer channels. Under the action of the load, for the steel bearing, the Hertz contact deformation and the contact stress are calculated as in the formula Q – the largest steel ball Radial load, a, b — semimajor and minor axes of the contact ellipse, σmax — maximum contact stress,

## 2 Co e corresponding to different groove curvature radius coefficients

Among them, , the range of f is generally selected in China to be 0.51~0.54; the positive correlation between the groove curvature function A* and the (a* and b* are both positively related to the groove curvature function). For a certain bearing, Q can be regarded as a constant, then it can be known that σmax is only related to the change of Co e, taking as the abscissa and Co e as the ordinate, and plotting the Co e at different fi, fe and times, to obtain Figure 1. It can be observed from Figure 1 that:

(1) When γ is constant, the Co e of the inner and outer channels increases with the increase of f; this can be explained as: when the channel curvature radius coefficient is larger, the channel has a larger channel radius, The bottom of the tightness between the channel and the steel ball (that is, the contact area between the channel and the steel ball is small), under the same pressure, the pressure is large. At the same time, when γ is the same as f, the outer channel Co e is smaller than the inner channel Co e, which can also be understood as the outer ring channel stress is smaller than the inner ring channel stress, this is because: the outer channel and the steel ball are inner The cut with the inner channel is the outer cut.

(2) The Co e values of the inner and outer channels do not change linearly, but with the increase of the f value, the change becomes smaller and smaller; the Co e value of the inner channel decreases with the increase of γ, and the inner The Co e value of the channel increases with the increase of γ. Both are due to reasons (3) and (4).

## 3 Determination of the coefficient of curvature radius of inner and outer grooves

For a preliminary designed bearing, knowing the bearing load and obtaining the diameter of the steel ball used, one can first determine a groove curvature coefficient according to Figure 1, and then select another coefficient according to the principle of equal or close stress. Different interval ranges are used for different interpolation selection, and the appropriate groove curvature coefficient is selected. Considering the influence of centrifugal force when the bearing is working, it should generally be ensured that the obtained groove curvature coefficient makes the Co e value of the outer ring smaller than that of the inner ring.

When the speed is 2 000r/min, dm=65mm, the maximum rolling element load is 1 000N, Dw=12.7, regardless of bearing preload and bearing clearance, when the maximum stress is guaranteed not to exceed 1 800MPa, choose fi=0.515, f e=0.53 , the maximum stress of the inner and outer grooves is 1 766MPa and 1 705MPa respectively. When the rotational speed is increased to 40 000 r/min, if the above parameters are still used, the inner and outer ring stresses will be 1 748 MPa and 2 065 MPa respectively, the latter is not allowed under long-term working conditions. At this time, it is necessary to change the channel coefficient of the outer ring to obtain fi=0.515, fe=0.514, and Co e are equal. The calculated stresses are 1 766 MPa and 1 764 MPa, respectively.

## 4 Conclusion

The influence of fi, fe on the performance of the bearing is very important, and the choice of fi, fe is mainly to consider that the ultimate stress of the inner and outer channels of the bearing is equal to or similar to the stress, in general, choose a suitable set of fi, fe fe requires a lot of computation, and Figure 1 solves this problem intuitively. After determining the diameter of the rolling element and knowing the bearing speed, the appropriate fi and fe can be selected, so that the designed bearing can meet the requirements of use to the greatest extent.

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