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    Metal Casting

    Metal casting is a manufacturing process where molten metal is poured into a mold cavity that represents the negative shape of a desired part. Once the metal solidifies, the mold is removed to obtain the finished casting.

    • Pattern: A replica of the final part, slightly oversized to account for shrinkage, used to make an impression in the mold.
    • Mold: The hollow cavity that the metal is poured into.
    • Core: A sand or ceramic insert used to form internal cavities in a casting.
    • Riser: A reservoir that feeds molten metal to the part during solidification to prevent shrinkage defects. The riser should cool slower than the part.

    Casting processes are chosen based on complexity, surface finish, material, and required dimensional accuracy.

    Mold Filling

    When metal is poured, smooth (laminar) flow is preferred to avoid oxide formation from turbulent flow.

    How to prevent the molten metal from splashing and oxidizing at free surface:

    • Bottom-up filling structure
    • Low viscosity (\( \mu \))
    • Low filling speed (v)
    • Short flow length (L)

    Solidification

    As metal cools, it contracts and eventually solidifies.

    Solidification Process Image

    When casting metal, you must consider the possibility of shrinkage by creating pattern shrinkage allowance where the mold is made larger than the final casting size.

    Shrinkage Allowance:

    $$ L_{\text{pattern}} = \frac{L_{\text{final}}}{1 - s} $$

    where \( s \) is the alloy’s shrinkage over the temperature change.

    Key Note

    Most alloys solidify over a temperature range rather than at a single temperature as shown in the curves.

    Example Problem: Shrinkage Allowance

    How long should the pattern be for a 100 mm aluminum casting?

    Given:

    $$ s = 0.013 (1.3\%) $$
    $$ L_{\text{pattern}} = \frac{100}{1 - 0.013} = 101.3\ \text{mm} $$

    This means the pattern should be 101.3mm long.

    Cooling Curves

    Cooling Curve of Pure Metal Image

    Cooling Curve of Alloys Image

    Chvorinov's Rule

    The total solidification time depends on size and shape of casting which is modeled by Chvorinov's Rule:

    $$ t_{TS} = C_m \left(\frac{V}{A}\right)^n $$

    where

    • \( t_{TS} \) = total solidification time
    • \( V \) = volume
    • \( A \) = surface area
    • \( n \) = exponent (typically \( n = 2 \))
    • \( C_m \) = mold constant
    • \( M = \frac{V}{A} \), thermal modulus

    Solidification time can be minimized by minimizing thermal modulus.

    Example Problem: Solidification Time

    Question: Find the solidification time of a cylindrical casting with a diameter of 75mm when mold constant is 3 \( s/mm^2 \).

    Given:

    $$ d = 75\,\text{mm},\quad h = 125\,\text{mm},\quad C_m = 3\ \text{s/mm}^2 $$
    Solution:
    $$ V = \pi\left(\frac{75}{2}\right)^2 (125) = 5.51\times 10^5\ \text{mm}^3 $$
    $$ A = \pi (75)(125) + 2\pi \left(\frac{75}{2}\right)^2 = 3.77\times10^4\ \text{mm}^2 $$
    $$ M = \frac{V}{A} = 14.6 $$
    $$ t_{TS} = 3(14.6)^2 = 640\ \text{s} \approx 10.7\ \text{min} $$

    Therefore, the solidification time of the cylindrical casting is 10.7 minutes.

    Casting Methods

    Selected based on the part design, volume, material, cost, PDS, etc.

    Temporary/Expandable Molds: Molds that are destroyed to remove the casting.

    • Sand casting: Molten metal is poured into a mold made of compacted sand; after solidification, the mold is broken to remove the part. Suitable for large or complex shapes and low-cost production.
    • Investment casting: A wax pattern is coated with ceramic to form a shell; the wax is melted out and metal is poured into the cavity, producing parts with excellent surface finish and fine detail.

    Permanent Molds: Molds that are reusable and made from durable metals such as steel or iron.

    • Gravity die casting: Molten metal flows into the reusable mold under gravity only; produces parts with better dimensional accuracy and surface finish than sand casting.
    • Low-pressure die casting: Molten metal is pushed gently into the mold using low gas pressure from below, providing smooth filling and reduced defects like turbulence and porosity.
    • High-pressure die casting: Molten metal is injected into the mold at very high pressure and speed, allowing production of thin-walled parts with excellent surface quality and tight tolerances for high-volume manufacturing.

    Selection Table

    Casting Methods Comparison

    Sand Casting

    Sand Casting Diagram

    Buoyancy

    Cores inside molds float because molten metal is typically denser. The buoyant force is:

    $$ F_b = \rho_{\text{metal}} V g $$

    and core weight is:

    $$ F_g = \rho_{\text{core}} V g $$

    Chaplets must resist:

    $$ F_{\text{top}} = F_b - F_g $$

    Bottom Chaplet Force (Prior to Filling)

    Before pouring, no buoyant force exists. The bottom chaplets must therefore support the entire weight of the core:

    $$ F_{\text{bottom, prior}} = F_g = \rho_{\text{core}} V g $$

    Example Problem: Number of Chaplets Required

    Question: Determine how many chaplets are needed to hold the core in place.

    Image

    Given:

    $$ \rho_{\text{metal}} = 2.7,\ \rho_{\text{core}} = 0.9,\ V = 4\text{ cm}^3 $$
    $$ g=9.81,\quad F_{\text{chaplet}} = 0.01\text{ N} $$
    Solution:
    $$ F_g = 0.9(4)(9.81) = 0.035\text{ N} $$
    $$ F_b = 2.7(4)(9.81) = 0.106\text{ N} $$
    $$ F_{\text{top}} = 0.071\text{ N} $$

    Chaplets needed:

    $$ \text{Top} = \lceil 0.071/0.01 \rceil = 8 $$
    $$ \text{Bottom} = \lceil 0.035/0.01 \rceil = 4 $$

    Design Advisor

    Recommended vs. Avoided Design Aspects

    Key Note

    Good casting design promotes smooth metal flow, uniform cooling, minimal coring, and easy mold separation.