## Part e: Design the Part Riser (Given: Riser Diameter = 1.75 × Riser Height) ### **Step 1 Use the Modulus Rule** - The modulus of the riser should be higher than the casting's modulus to ensure it solidifies last. - **Given:** - Modulus of casting, \(M_c = 1.68\, \text{cm}\) For a cylindrical riser: \[ \text{Modulus (M)} = \frac{\text{Volume}}{\text{Surface Area}} \] For a cylinder of diameter \(D\) and height \(H\): - Volume, \(V = \frac{\pi}{4} D^2 H\) - Surface area, \(A = \pi D H + \frac{\pi}{2} D^2\) (side + one base exposed) Set modulus of riser, \(M_r \geq 1.2 \times M_c\) (safety factor), so: \[ M_r = \frac{V}{A} = \frac{\frac{\pi}{4} D^2 H}{\pi D H + \frac{\pi}{2} D^2} \] Simplify: \[ M_r = \frac{D^2 H / 4}{D H + D^2/2} \] Given \(D = 1.75 H\): - Substitute \(D\) in terms of \(H\): \[ M_r = \frac{(1.75H)^2 H / 4}{1.75H \cdot H + (1.75H)^2/2} \] \[ = \frac{(3.0625H^3)/4}{1.75H^2 + (3.0625H^2)/2} \] Denominator: \[ 1.75H^2 + 1.53125H^2 = 3.28125H^2 \] \[ M_r = \frac{.765625 H^3}{3.28125 H^2} = .2333 H \] Set \(M_r \geq 1.2 \times 1.68 = 2.02\, \text{cm}\): \[ .2333 H \geq 2.02 \implies H \geq \frac{2.02}{.2333} \approx 8.66\, \text{cm} \] Now, \(D = 1.75 \times 8.66 = 15.16\, \text{cm}\) **Explanation:** - We calculated the minimum height for the riser using the modulus method and the given diameter-to-height ratio. - This ensures the riser solidifies after the casting. --- ### **Step 2: Final Answer** **Riser Height:** \[ \boxed{8.66\, \text{cm}} \] **Riser Diameter:** \[ \boxed{15.16\, \text{cm}} \] --- ## Part f: Sketch and Recommended Molding Condition ### **Step 1: Sketch the Molding Conditions** #### **Molding Condition 1: Horizontal Parting Line** - **Elements:** - Cope (top half), Drag (bottom half) - Riser attached on top (cope) - Sprue connects to basin, then to runner, then to the cavity - Core for internal cavity - Parting line is horizontal #### **Molding Condition 2: Vertical Parting Line** - **Elements:** - Parting line is vertical - Riser on the side - Sprue, runner, and gate aligned accordingly - Core (if necessary) positioned vertically **(You would draw these, labeling: riser, sprue, basin, cope, drag, core, parting line)** --- **Explanation:** - Two common conditions are shown: horizontal (most common, easier for complex parts, gravity helps fill) and vertical (less common, useful for certain geometries). --- ### **Step 2: Recommended Molding Condition** **Recommended:** - **Horizontal Parting Line** **Reason:** - The part's geometry is best suited for horizontal parting; easier core placement and removal, better metal flow, and easier defect control. --- ## **Final Answer Summary** **e) Riser Design:** - Riser Height = **8.66 cm** - Riser Diameter = **15.16 cm** **f) Molding Condition:** - Two methods: Horizontal and Vertical parting lines (sketch required). - **Recommended:** Horizontal parting line for this part.

# HH Project 2: Casting Design and Analysis ## Part e: Design the Part Riser ### Step 1: Use the Modulus Rule To ensure effective solidification, the modulus of the riser must be greater than that of the casting. Given the casting's modulus \(M_c\): - **Modulus of Casting:** \[ M_c = 1.68\, \text{cm} \] To find the required modulus for the riser, we use: \[ M_r \geq 1.2 \times M_c = 2.02\, \text{cm} \] For a cylindrical riser: \[ M = \frac{V}{A} \] Where: - Volume \(V = \frac{\pi}{4} D^2 H\) - Surface Area \(A = \pi D H + \frac{\pi}{2} D^2\) Substituting \(D = 1.75 H\): 1. **Volume Calculation:** \[ V = \frac{\pi}{4} (1.75 H)^2 H = \frac{\pi}{4} (3.0625 H^2) H = \frac{3.0625 \pi H^3}{4} \] 2. **Surface Area Calculation:** \[ A = \pi (1.75 H) H + \frac{\pi}{2} (1.75 H)^2 = \pi (1.75 H^2) + \frac{3.0625 \pi H^2}{2} = (1.75 + 1.53125) \pi H^2 = 3.28125 \pi H^2 \] 3. **Modulus Calculation:** \[ M_r = \frac{V}{A} = \frac{\frac{3.0625 \pi H^3}{4}}{3.28125 \pi H^2} = \frac{3.0625 H}{4 \cdot 3.28125} = 0.2333 H \] Setting \(M_r \geq 2.02\): \[ 0.2333 H \geq 2.02 \implies H \geq \frac{2.02}{0.2333} \approx 8.66\, \text{cm} \] 4. **Calculate Diameter:** \[ D = 1.75 \times 8.66 \approx 15.16\, \text{cm} \] **Explanation:** We calculated the minimum riser height \(H\) required for effective solidification using the modulus method, ensuring that the riser solidifies after the casting. ### Step 2: Final Answer - **Riser Height:** \[ \boxed{8.66\, \text{cm}} \] - **Riser Diameter:** \[ \boxed{15.16\, \text{cm}} \] --- ## Part f: Sketch and Recommended Molding Condition ### Step 1: Sketch the Molding Conditions #### Molding Condition 1: Horizontal Parting Line - **Elements:** - Cope (top half) - Drag (bottom half) - Riser attached on the cope - Sprue connects to basin, runner, and cavity - Core for internal cavity - **Parting line:** Horizontal #### Molding Condition 2: Vertical Parting Line - **Elements:** - Parting line is vertical - Riser on the side - Sprue, runner, and gate aligned accordingly - Core positioned vertically **(Sketch these elements, labeling each part clearly.)** ### Step 2: Recommended Molding Condition **Recommended:** - **Horizontal Parting Line** **Reason:** - This method is easier for complex geometries, facilitates better metal flow, and simplifies core placement and removal, leading to improved defect control. --- ## Final Answer Summary **e) Riser Design:** - Riser Height: **8.66 cm** - Riser Diameter: **15.16 cm** **f) Molding Condition:** - Two methods: Horizontal and Vertical parting lines (sketch required). - **Recommended:** Horizontal parting line for optimal casting performance.

# HH Project 2: Casting Design and Analysis ## Solutions to Parts a, b, c, d, e, and f ### Part a: Calculate Casting Volume - **Given:** Casting volume = **1530.4 cm³** ### Part b: Calculate Casting Surface Area - **Given:** Casting surface area = **910.3 cm²** ### Part c: Calculate Casting Modulus \(M_c\) - **Given:** Casting modulus = **1.68 cm** ### Part d: Calculate Solidification Time 1. **Given Parameters:** - Diameter of the cylinder = 5 cm - Height of the cylinder = 8 cm - Solidification time of the cylinder = 9.5 min - Constant \(K = 10 \text{ min/cm}^2\) 2. **Calculate the solidification time for the casting:** - Volume of casting \(V = \text{Volume of cylinder} = \frac{\pi}{4} D^2 H\) - Using \(K\) and volume to find solidification time: \[ t = K \times \left(\frac{V}{A}\right) = K \times t_{cylinder} \] Where \(A\) is the surface area of the casting. 3. **Final Calculation:** - Solidification time \(t \approx 28.2 \text{ min}\) **Explanation:** The solidification time was calculated based on the known properties of a similar cylinder and the provided constant \(K\). --- ### Part e: Design the Part Riser #### Step 1: Use the Modulus Rule 1. **Modulus of the Riser:** \[ M_r \geq 1.2 \times M_c = 1.2 \times 1.68 = 2.016 \text{ cm} \] 2. **Volume and Surface Area of Riser:** - Assume riser diameter \(D = 1.75H\). - For a cylindrical riser: - Volume \(V = \frac{\pi}{4} D^2 H\) - Surface Area \(A = \pi D H + \frac{\pi}{2} D^2\) 3. **Calculate Modulus \(M_r\):** - After substituting \(D\): \[ M_r = \frac{V}{A} \text{ and simplify.} \] - Set \(M_r \geq 2.016\): \[ H \geq 8.66 \text{ cm} \] - Calculate \(D\): \[ D \approx 15.16 \text{ cm} \] **Explanation:** The riser was designed following the modulus method, ensuring it solidifies after the casting to avoid defects. #### Step 2: Final Answer for Riser - **Riser Height:** \[ \boxed{8.66 \text{ cm}} \] - **Riser Diameter:** \[ \boxed{15.16 \text{ cm}} \] --- ### Part f: Sketch and Recommended Molding Condition #### Step 1: Sketch the Molding Conditions 1. **Molding Condition 1: Horizontal Parting Line** - Cope (top), Drag (bottom) - Riser on the cope - Sprue to basin, runner, cavity - Core for internal features - **Parting line:** Horizontal 2. **Molding Condition 2: Vertical Parting Line** - Riser on the side - Sprue, runner, and gate aligned vertically - Core positioned vertically **(Draw and label these conditions.)** #### Step 2: Recommended Molding Condition - **Recommended:** Horizontal Parting Line **Reason:** This condition is more effective for the casting's geometry, improving metal flow and facilitating core placement/removal. --- ## Final Answer Summary - **Part a:** Casting Volume = **1530.4 cm³** - **Part b:** Casting Surface Area = **910.3 cm²** - **Part c:** Casting Modulus = **1.68 cm** - **Part d:** Solidification Time = **28.2 min** - **Part e:** Riser Height = **8.66 cm**, Riser Diameter = **15.16 cm** - **Part f:** Recommended Molding Condition - **Horizontal Parting Line**