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)
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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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In actual applications, the force acting on the bearing has two components—radial and thrust. It is therefore necessary to convert the two components acting on the bearing into a single hypothetical load, fulfilling the conditions applied to the dynamic load carrying capacity. Then the hypothetical load can be compared with the dynamic load capacity. The equivalent dynamic load is defined as the constant radial load in radial bearings (or thrust load in thrust bearings), which if applied to the bearing would give same life as that which the bearing will attain under actual condition of forces. The expression for the equivalent dynamic load is given by P = XVF r + YF a where, P = equivalent dynamic load (N) F r = radial load (N) F a = axial or thrust load (N) V = race-rotation factor X and Y are radial and thrust factors respectively and their values are given in the manufacturer’s catalogues. The race-rotation factor depends upon whether the inner race is rotating or the outer race. The value of V is 1 when the inner race rotates while the outer race is held stationary in the housing. The value of V is 1.2 when the outer race rotates with respect to the load, while the inner race remains stationary. In most of the applications, the inner race rotates and the outer race is fixed in the housing. Assuming V as unity, the general equation for equivalent dynamic load is given by, P = XF r + YF a In this chapter, we will use the above equation for calculating equivalent dynamic load. The
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  • Two '10
  • Ball bearing, contact bearings, Rolling Contact Bearing

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