Explanation It has been assumed that the normal force per unit area is inversely proportional to r . Express the change in the bearing area due to the wear using the below expression; Δ A = r Δ θ Δ r Here, the distance between the point to the axis of the shaft is r , and Δ θ is the central angle of the sector having radius Δ r . Find the normal force exerted Δ N due to the elemental area Δ A using the relation; Δ N = k r Δ A Here, the term k is the kinetic coefficient. Substitute r Δ θ Δ r for Δ A . Δ N = k r r Δ θ Δ r = k Δ θ Δ r (1) Find the value of k using the relation. P = ∑ Δ N = ∫ d N = ∫ 0 2 π ∫ 0 R Δ N Here, the term P is the force required to make the shaft travel through the distance r Substitute k Δ θ Δ r for Δ N . P = ∫ 0 2 π ∫ 0 R k Δ θ Δ r = k [ θ ] 0 2 π [ r ] 0 R = k [ 2 π − 0 ] [ R − 0 ] k = P 2 π R Substitute P 2 π R for k in Equation (1). Δ N = P 2 π R Δ θ Δ r Find the change in friction force Δ F using the relation. Δ F = μ k Δ N Here, the term μ k represents the coefficient of kinetic friction. Substitute P 2 π R Δ θ Δ r for Δ N . Δ F = μ k P 2 π R Δ θ Δ r Find the change in moment Δ M using the relation. Δ M = r Δ F Substitute μ k P 2 π R Δ θ Δ r for Δ F

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 8.3, Problem 8.94P

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Show that the magnitude M of the couple required of a worn-out end bearing is 75 percent of that of new bearing to overcome the frictional resistance.

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Chapter 8.3, Problem 8.93P

Chapter 8.3, Problem 8.95P

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Show that the magnitude M of the couple required of a worn-out end bearing is 75 percent of that of new bearing to overcome the frictional resistance.

Solution Summary: The author demonstrates that the magnitude M of the couple required of a worn-out end bearing is 75 percent of that of new bearing to overcome the frictional resistance.

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Show that the magnitude M of the couple required of a worn-out end bearing is 75 percent of that of new bearing to overcome the frictional resistance.

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