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lesantik [10]
3 years ago
8

A bronze bushing 60 mm in outer diameter and 40 mm in inner diameter is to be pressed into a hollow steel cylinder of 120-mm out

er diameter. Calculate the tangential stresses for steel and bronze at the boundary between the two parts
Engineering
1 answer:
-BARSIC- [3]3 years ago
7 0

Answer:

The tangential stress for the steel at 30mm = 88.8MPa.

The tangential stress for the steel at 60mm = 35.5 MPa.

The tangential stress for the bronze at 20mm =  - 191.9 MPa.

The tangential stress for the bronze at 30mm =  - 138.6 MPa.

Explanation:

The outer radius bronze bushing = 60 mm/2 = 30 mm, the inner radius for bronze bushing = 40mm/2 = 20mm and the cylinder radius = 120mm/2 = 60mm.

Step one: The first step is to calculate or Determine the interface pressure.

The interface pressure = 0.05/ [ [ 30 × ( 1/210 ×10⁹) ] ×  [( 60² + 30²/ ( 60² - 30²) + 0.3 ] + [ 1/105 × 10⁹× [ ( 20² + 30²)/( 30² - 20²) - 0.3] ].

The interface pressure = 53.3 MPa

Step two: Determine the tangential stresses for steel and bronze as given below:

The tangential stress for the steel at 30mm = 10⁶ × 53.3 [ ( 0.06)² + (0.03)²/ ( 0.06)² - (0.03)² ] = 88.8 MPa.

The tangential stress for the steel at 60mm = 10⁶ × 53.3 × 2 × [0.03]²/  ( 0.06)² - (0.03)² ] = 35.5 MPa.

The tangential stresses for the bronze is calculated below;

=> The tangential stress for the bronze at 20mm = - [ 10⁶ × 53.3 × 2 × [0.03]² ] /  ( 0.03)² - (0.02)² ] = - 191.9 MPa.

The tangential stress for the bronze at 30mm = - [ 10⁶ × 53.3  × [ 0.03]² + (0.03)² ] /  ( 0.03)² - (0.02)² ] = - 138.6 MPa.

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This question is incomplete, the complete question is;

An air-standard Diesel cycle engine operates as follows: The temperatures at the beginning and end of the compression stroke are 30 °C and 700 °C, respectively. The net work per cycle is 590.1 kJ/kg, and the heat transfer input per cycle is 925 kJ/kg. Determine the a) compression ratio, b) maximum temperature of the cycle, and c) the cutoff ratio, v3/v2.

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b) maximum temperature of the cycle

We know that for Air, Cp = 1.005 kJ/kgK

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we substitute

925 = 1.005( T₃ - 700 )

( T₃ - 700 ) = 925 / 1.005

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Therefore, The maximum temperature of the cycle is 1893.4 K

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Since pressure is constant, V ∝ T

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we substitute

cutoff ratio S = 1893.396 K / 973 K

cutoff ratio S = 1.9459 ≈ 1.946

Therefore, the cutoff ratio, v₃/v₂ is 1.946

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