Chapter 5, Problem 5.92P

(a)

To determine

The three quantitative problem and three qualitative question with their answer.

The solidification time in seconds for a spherical casting.

Answer to Problem 5.92P

The solidification time is $\tau =66.66\text{s}$ .

Explanation of Solution

Given:

Let the diameter of the sphere is $d=50\text{mm}$ .

The solidification factor is $K=0.96\times {10}^6\text{s}/{\text{m}}^2$ .

Formula used:

The expression for the modulus is given as,

  $M=\frac{V}{A}$

Here, $V$ is the volume of sphere and $A$ is the surface area of the sphere.

The expression for the solidification time is given as,

  $\tau =K{M}^2$

Calculation:

The modulus can be calculated as,

  $\begin{array}{l}M=\frac{V}{A}\\ M=\frac{\frac{4}{3}\pi R^2}{4\pi R^2}\\ M=\frac{D}{6}\end{array}$

The solidification time can be calculated as,

  $\begin{array}{l}\tau =K{M}^2\\ \tau =0.96\times {10}^6\text{s}/{\text{m}}^2\times {\left(\frac{50\text{mm}}{6}\times \frac{1\text{m}}{1000\text{mm}}\right)}^2\\ \tau =66.66\text{s}\end{array}$

Conclusion:

Therefore, the solidification time is $\tau =66.66\text{s}$ .

(b)

To determine

The ratio of the volume of the pattern to that of casting.

Answer to Problem 5.92P

The ratio of volume of the pattern to the volume of the casting is $0.94$ .

Explanation of Solution

Given:

Let the volume of the cast iron block is $V_c=180\text{mm}\times 90\text{mm}\times 7\text{mm}$ .

The shrinkage allowance for the pattern is $A_s=0.02$ .

Formula used:

The expression for the volume of pattern is given as,

  $V_p=\left(1-A_s\right)V_c$

The expression for the ratio of volume of the pattern to the volume of the casting is given as,

  $R=\frac{V_P}{V_c}$

Calculation:

The volume of pattern can be calculated as,

  $\begin{array}{l}{V}_p=\left(1-A_s\right)V_c\\ V_p=\left(1-0.02\right)\times 180\text{mm}\times \left(1-0.02\right)\times 90\text{mm}\times \left(1-0.02\right)\times \text{7}\text{mm}\\ V_p=176.4\text{mm}\times \text{88}\text{.2}\text{mm}\times 6.86\text{mm}\\ V_p=106731.1{\text{mm}}^3\end{array}$

The ratio of volume of the pattern to the volume of the casting can be calculated as,

  $\begin{array}{l}R=\frac{V_p}{V_c}\\ R=\frac{106731.1{\text{mm}}^3}{180\text{mm}\times 90\text{mm}\times 7\text{mm}}\\ R=0.94\end{array}$

Conclusion:

Therefore, the ratio of volume of the pattern to the volume of the casting is $0.94$ .

(c)

To determine

The time required to fill the mold cavity.

Answer to Problem 5.92P

The required time for filling the mold cavity is $1.42\text{s}$ .

Explanation of Solution

Given:

Let the length of the sprue is $L=15\text{cm}$ .

The cross sectional area at the base of down sprue is $A=0.5\text{}{\text{cm}}^2$ .

The volume of the mold cavity is $V=500{\text{cm}}^{\text{3}}$ .

The fluid velocity is $v=175\text{m}/\text{s}$ .

Formula used:

The expression for the required time for filling the mold cavity is given as,

  $T=\frac{V}{A\times v}$

Calculation:

The required time for filling the mold cavity calculated as,

  $\begin{array}{l}T=\frac{V}{A\times v}\\ T=\frac{500{\text{cm}}^3}{0.5\text{}{\text{cm}}^2\times 175\text{m}/\text{s}}\\ T=1.42\text{s}\end{array}$

Conclusion:

Therefore, the required time for filling the mold cavity is $1.42\text{s}$ .

(d)

To determine

The purpose for the design of riser in casting process.

Explanation of Solution

The riser is designed to supply the molten metal to mold cavity for the prevention of the shrinkage. It is acts as reservoir. In the casting process the metal in the riser should not be solidify before the casting solidifies. Allowances are provided in the casting process to stop the occurrence of deformation. Lots of other allowance are also provided in casting process.

(e)

To determine

The place where lighter impurities deposited in the process of centrifugal casting.

Explanation of Solution

The casting in which centrifugal force of action is used to perform casting is known as centrifugal casting. In this process, the higher density of the particle, the higher centrifugal force acts on the particle. So they move away from the center. The lighter impurities have low density. Thus they are collected at the center.

(f)

To determine

The type of casting process which uses expandable pattern and expandable mold.

Explanation of Solution

The casting process which uses expandable pattern and expandable mold is investment casting process. This process uses lost wax pattern to make intricate shapes.