(a)
The temperature rise in open die forging of cylinder for no friction between the flat dies and the specimen.
(a)
Explanation of Solution
Given:
The initial thickness of the specimen is
The initial radius of the specimen is
The friction coefficient is
Formula used:
The expression for the flow stress is given as,
Here,
The expression for the true strain is given as,
Here,
The expression for the final radius by equating the volume is given as,
The expression for the forging force is given as,
Here,
The expression for the average pressure is given as,
The expression for final height for
The expression for final height for
The expression forfinal height for
The expression for final height for
The expression for final height for
The expression for the temperature rise is given as,
Here
Calculation:
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
Reduction (in ) | Forging force (in ) | Area under curve (in ) |
2.1635 |
Work done can be calculated by the summation of the area under the curve.
Refer to table of properties of common engineering materials “Typical values of density and heat capacity” for annealed copper is,
Change in temperature can be calculated as,
The figure (1) shows the curve between the forging force and reduction in height.
Figure (1)
(b)
The temperature risein open die forging of cylinder for
(b)
Explanation of Solution
Given:
The initial thickness of the specimen is
The initial radius of the specimen is
The friction coefficient is
Formula used:
The expression for the flow stress is given as,
Here,
The expression for the true strain is given as,
Here,
The expression for the final radius by equating the volume is given as,
The expression for the forging force is given as,
Here,
The expression for the average pressure is given as,
The expression for final height for
The expression for final height for
The expression forfinal height for
The expression for final height for
The expression for final height for
The expression for the temperature rise is given as,
Here
Calculation:
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
The final height can be calculated as,
The final radius can be calculated as,
The true strain can be calculated as,
The flow stress can be calculated as,
Refer to table 2.2 “Typical values of strength coefficient
The average pressure can be calculated as,
The forging force can be calculated as,
For
Reduction (in ) | Forging force (in ) | Area under curve (in ) |
Work done can be calculated by the summation of the area under the curve.
Refer to table of properties of common engineering materials “Typical values of density and heat capacity” for annealed copper is,
Change in temperature can be calculated as,
The figure (2) shows the curve between the forging force and reduction in height.
Figure (2)
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