ii The balls are equally spaced iii The balls in the upper half do not support

# Ii the balls are equally spaced iii the balls in the

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(ii) The balls are equally spaced. (iii) The balls in the upper half do not support any load. Figure 3.3 (a) shows the forces acting on the inner race through the rolling elements, which support the static load C 0 . It is assumed that there is a single row of balls. Considering the equilibrium of forces in the vertical direction, As the races are rigid, only balls are deformed. Suppose d1 is the deformation at the most heavily stressed Ball No.1. Due to this deformation, the inner race is deflected with respect to the outer race through d1. As shown in Fig. 3.3(b), the center of the inner ring moves from O to O through the distance 1 without changing its shape. Suppose 1 , 2 …… are radial deflections at the respective balls. Also According to Hertz’s equation, the relationship between the load and deflection at each ball is given by, Therefore From Eq. (b) and (c), In a similar way, (a) (b) (c)
Substituting these values in Eq. (a), or C 0 = P 1 M where If z is the number of balls, β = 360 z The values of M for different values of z are tabulated as follows: Z 8 10 12 15 M 1.84 2.28 2.75 3.47 z/M 4.35 4.38 4.36 4.37 It is seen from the above table that (z/M) is practically constant. Stribeck suggested the value for (z/M) as 5 or M = (1/5)z Substituting this value in Eq. (d), From experimental evidence, it is found that the force P 1 required to produce a given permanent deformation of the ball is given by, P 1 = kd 2 where d is the ball diameter and the factor k depends upon the radii of curvature at the point of contact, and on the modulii of elasticity of materials. From Eqs (f) and (g), The above equation is known as Stribeck’s equation. 3.5 Equivalent bearing load (d) (e) (f) (g)

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