EBK MANUFACTURING PROCESSES FOR ENGINEE
EBK MANUFACTURING PROCESSES FOR ENGINEE
6th Edition
ISBN: 9780134425115
Author: Schmid
Publisher: YUZU
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Question
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Chapter 4, Problem 4.59P

(a)

To determine

The reduction in the height of the specimen.

(a)

Expert Solution
Check Mark

Explanation of Solution

Formula used:

The expressionfor the volume of the original specimen is given as,

  V=π4(do2di2)h

Here, do is outer diameter of the specimen, di is inner diameter of the specimen and h is the height of specimen.

The expression for the volume during the plastic deformation of the original specimen is given as,

  V1=π4(do2di2)h

Here, do is outer diameter of the specimen and di is inner diameter of the specimen.

Calculation:

Refer figure 4.8(a) “Charts to determine friction in ring compression test” to obtain the values as,

The outer diameter of the specimen is do=0.75in .

The outer diameter of the specimen is di=0.375in .

Height of the specimen is h=0.25in .

The value for the volume of original specimen can be calculated by substituting the values of d0 , di and h as,

  V=π4(do2di2)hV=π4(do2di2)×hV=π4( 0.752 in2 0.3752 in2)×0.25inV=0.0828in3

The value for the height of specimen is calculated as,

  V=V10.0828in3=π4(d02di2)hh=0.105( d 0 2 d i 2 )

The reduction in height of specimen is calculated by taking different values of di and d0 from the figure 4.8(a) as,

    Specimen
    (Number)

      di(in)

      d0(in)
    FormulaCalculation
      h

      1.

      0.375

      0.75
    h=0.105(d02di2)h=0.105in3( 0.752 in2 0.3752 in2)
      0.25in

      2.

      0.477

      0.97
    h=0.105(d02di2)h=0.105in3( 0.972 in2 0.4772 in2)
      0.147in

      3.

      0.282

      1.04
    h=0.105(d02di2)h=0.105in3( 1.042 in2 0.2822 in2)
      0.104in

(b)

To determine

The coefficient of the friction for the each specimen.

(b)

Expert Solution
Check Mark

Explanation of Solution

The value of coefficient is calculated from the figure 4.8(a) corresponding to the different values of percentage reduction in height and reduction in internal diameter is given as,

    Specimen
    (Number)
    % Reduction in height% Reduction in Internal diameterCoefficient of Friction

      (μ)

    1.41.2-27.20.01
    2.58.424.80.10
    3.6053.10.20

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