A hollow disc (Plane stress) of inner radius a and outer radius b, modulus of Elasticity E Poisson’s ratio v ,and density p, is co-centrically placed in an otherwise rigid housing to which a frictionless bearing is attachedto its inner surface as shown in the figure. An initial clearance 8 exists between the outer surface of the elasticallydeforming rotating disc and the inner lining of the frictionless bearing.(a) Determine the angular velocity o at which the disc comes in contact with the frictionless bearing.(b) If the angular velocity is further increased to @1> @, determine the pressure that develops between thefrinctionless bearing and the outer surface of the rotating disc.RigidFrictionlessbearingE, v

given datainner radius = aouter radius = bmodulus of elasticity = EPoissons ratio = νdensity = ρ

A hollow disc (Plane stress) of inner radius a and outer radius b, modulus of Elasticity E Poisson’s ratio v, and density p, is co-centrically placed in an otherwise rigid housing to which a frictionless bearing is attached o its inner surface as shown in the figure. An initial clearance & exists between the outer surface of the elastically leforming rotating disc and the inner lining of the frictionless bearing. a) Determine the angular velocity o at which the disc comes in contact with the frictionless bearing. b) If the angular velocity is further increased to @1> @, determine the pressure that develops between the frinctionless bearing and the outer surface of the rotating disc. Rigid -Frictionless bearing a E, v

A hollow disc (Plane stress) of inner radius a and outer radius b, modulus of Elasticity E Poisson’s ratio v, and density p, is co-centrically placed in an otherwise rigid housing to which a frictionless bearing is attached o its inner surface as shown in the figure. An initial clearance & exists between the outer surface of the elastically leforming rotating disc and the inner lining of the frictionless bearing. a) Determine the angular velocity o at which the disc comes in contact with the frictionless bearing. b) If the angular velocity is further increased to @1> @, determine the pressure that develops between the frinctionless bearing and the outer surface of the rotating disc. Rigid -Frictionless bearing a E, v

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

A hollow disc (Plane stress) of inner radius a and outer radius b, modulus of Elasticity E Poisson’s ratio v ,
and density p, is co-centrically placed in an otherwise rigid housing to which a frictionless bearing is attached
to its inner surface as shown in the figure. An initial clearance 8 exists between the outer surface of the elastically
deforming rotating disc and the inner lining of the frictionless bearing.
(a) Determine the angular velocity o at which the disc comes in contact with the frictionless bearing.
(b) If the angular velocity is further increased to @1> @, determine the pressure that develops between the
frinctionless bearing and the outer surface of the rotating disc.
Rigid
Frictionless
bearing
E, v

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