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trasher [3.6K]
3 years ago
7

A 50 mm diameter steel shaft and a 100 mm long steel cylindrical bushing with an outer diameter of 70 mm have been incorrectly s

hrink fit together and have to be separated. What axial force, Pa, is needed for this if the diametral interference is 0.005 mm and the coefficient of friction is 0.2? E (steel) = 207 x 103 MPa (N/mm2)
Physics
1 answer:
BARSIC [14]3 years ago
8 0

Answer:

The axial force is  P =  15.93 k N

Explanation:

From the question we are told that

     The diameter of the shaft steel is  d =  50mm

      The length of the cylindrical bushing  L =100mm

     The outer diameter of the cylindrical bushing  is  D =  70 \ mm

       The diametral interference is \delta _d = 0.005 mm

       The coefficient of friction is  \mu = 0.2

       The Young modulus of  steel is  207 *10^{3} MPa (N/mm^2)

The diametral interference is mathematically represented as

           \delta_d = \frac{2 *d * P_B * D^2}{E (D^2 -d^2)}

Where P_B is the pressure (stress) on the two object held together  

     So making P_B the subject

            P_B = \frac{\delta _d E (D^2 - d^2)}{2 * d* D^2}

Substituting values

                P_B = \frac{(0.005) (207 *10^{3} ) * (70^2 - 50^2))}{2 * (50) (70) ^2 }

                 P_B = 5.069 MPa

Now he axial force required is

             P =  \mu * P_B * A

Where A is the area which is mathematically evaluated as

               \pi d l

So   P  =  \mu P_B \pi d l

Substituting values

      P =  0.2 * 5.069 * 3.142 * 50 * 100

       P =  15.93 k N

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