Answer to Question #185667 in Mechanical Engineering for kibet Justine

Question

An angular contact bearing of a lathe spindle is subjected to a cyclic radial load

during a manufacturing process in an automated plant. During the cycle, the

bearing experiences a radial load of 95 N for 30 s at 2 500 rpm, 75 N for 45 s at

3 500 rpm, and 115 N at 3 100 rpm for 15 s. Assume a shaft diameter of 15 mm.

Specify an appropriate bearing that will be used for 4 000 hours life with a 98 %

reliability. Give the bearing code as well as the relative ratings and dimensions.

Answer 1

Equivalent load (P_e)

$_3\sqrt{\dfrac{N_1P_1^3 + N₂P₂³ +N_3 P_3 ³}{ N_1+N_2 + N_3}}$

$_3\sqrt{\dfrac{1250×95³ +2625 ×75³ + 775 ×115³}{ 1250 + 2625 + 775}}$

P_e = 89.71N (Equivalent load/ mean cubic load)

Life of component = 4000h.

L₁₀ Life = 6ON L₁₀H/10⁶

N = N₁ + N₂ + N₃ = 1250 + 2625 +775

N = 4650

+ ²N+IN = N

L₁₀ Life = 60 × 4650 × 4000/10⁶

= 1116 milion revolutions

so, dynamic Load carrying capacity; (c)

c = P_e (L₁₀)⅓

c = 89.71 (1116)⅓ = 930.52N