11.2 Manufacturing Processes, Machine Tools & Machining Calculations

11.2 Manufacturing Processes, Machine Tools & Machining Calculations

Manufacturing engineering converts raw materials into finished engineering components through casting, bulk forming, metal cutting, and non-traditional processing. Mastery of process parameters, material removal rates, tool speeds, and production timing is essential for optimizing manufacturing systems. This section covers fundamental manufacturing processes and machine tool calculations required for the PRC Mechanical Engineering Licensure Examination.

---

1. Casting Processes & Riser Design

Casting involves pouring liquid metal into a mold cavity containing the desired part shape, where it solidifies. The principal casting methods include:

• Sand Casting: Expendable molds made of silica sand and binders. Low tooling cost, suitable for large parts (engine blocks, valve bodies), but moderate surface roughness ($6.3 \text{ to } 25 \> \mu\text{m} \text{ Ra}$).
• Investment Casting (Lost-Wax): Slurry coating over disposable wax patterns. Produces near-net-shape components with intricate detail and tight tolerances ($0.8 \text{ to } 3.2 \> \mu\text{m} \text{ Ra}$), widely used for turbine blades.
• Die Casting: Permanent steel dies injected with molten metal under high pressure ($10 \text{ to } 175 \text{ MPa}$). High production rate for non-ferrous alloys (aluminum, zinc, magnesium).
• Centrifugal Casting: Molten metal poured into a rotating mold ($300 \text{ to } 3000 \text{ RPM}$). Centrifugal force pushes dense metal to the outer wall while impurities float to the inner core, producing high-density cylindrical tubes and pipes.

Solidification Modeling: Chvorinov's Rule

To prevent shrinkage porosity, risers must act as molten reservoirs that solidify after the main casting. Solidification time ($t$) is modeled by Chvorinov's Rule:

$$t = B \left( \frac{V}{A} \right)^2$$

where:

• $t$ = total solidification time (min or s)
• $B$ = mold constant ($\text{s/mm}^2$ or $\text{min/cm}^2$), dependent on mold material, metal properties, and pouring temperature
• $V$ = volume of the casting or riser ($\text{mm}^3$ or $\text{cm}^3$)
• $A$ = cooling surface area ($\text{mm}^2$ or $\text{cm}^2$)
• $V/A$ = modulus of cooling ($M$)

To ensure proper feeding, the riser solidification time must exceed the casting solidification time by at least $25\%$, requiring $(V/A)_{\text{riser}} \ge 1.12 (V/A)_{\text{casting}}$.

---

Worked Step-by-Step Calculation: Riser Sizing via Chvorinov's Rule

Problem: A rectangular steel casting with dimensions $100 \text{ mm} \times 200 \text{ mm} \times 50 \text{ mm}$ is cast in a sand mold with mold constant $B = 0.004 \text{ min/mm}^2$. Determine:

1. The solidification time of the casting.
2. The minimum required solidification time for a top cylindrical riser ($H = D$).

Step 1: Calculate Volume and Surface Area of Rectangular Casting

$$V_{\text{cast}} = 100 \times 200 \times 50 = 1,000,000 \text{ mm}^3$$ $$A_{\text{cast}} = 2 (100 \times 200 + 100 \times 50 + 200 \times 50) = 2 (20,000 + 5,000 + 10,000) = 70,000 \text{ mm}^2$$ $$\left(\frac{V}{A}\right)_{\text{cast}} = \frac{1,000,000}{70,000} = 14.286 \text{ mm}$$

Step 2: Calculate Casting Solidification Time

$$t_{\text{cast}} = B \left(\frac{V}{A}\right)^2 = 0.004 \times (14.286)^2 = 0.004 \times 204.09 = 0.816 \text{ min} \quad (49.0 \text{ seconds})$$

Step 3: Calculate Minimum Riser Solidification Time

$$t_{\text{riser}} \ge 1.25 \times t_{\text{cast}} = 1.25 \times 0.816 = 1.020 \text{ min}$$

---

2. Bulk Metal Forming Operations

Metal forming shapes solid metals through plastic deformation above or below the recrystallization temperature.

• Hot Working ($T > 0.5 T_m$): Deforms metal above recrystallization temperature. Requires lower forces, eliminates strain hardening, and refines coarse grain structures.
• Cold Working ($T < 0.3 T_m$): Deforms metal at room temperature. Increases yield strength and hardness through work hardening (dislocation multiplication), providing superior dimensional control and bright surface finishes.

Primary Forming Operations

1. Rolling: Reduces cross-sectional thickness between counter-rotating rolls. Maximum thickness draft per pass: $d_{\max} = h_0 - h_f = \mu^2 R$, where $\mu$ is friction coefficient and $R$ is roll radius.
2. Forging: Shapes metal via compressive impact or press forces. Divided into open-die forging, closed-die impression forging (with flash), and flashless precision forging.
3. Extrusion: Forces a billet through a shaped die orifice (direct/forward vs indirect/backward extrusion). Extrusion ratio $R_e = A_0 / A_f$.
4. Wire & Bar Drawing: Pulls solid rod through a converging die to reduce diameter. Reduction ratio $r = 1 - (A_f / A_0)$.

---

3. Turning & Lathe Machining Calculations

Lathe turning generates cylindrical surfaces by rotating a workpiece against a single-point cutting tool.

Lathe Turning Setup:
       +-------------------+  <--- Workpiece (Diameter D, RPM N)
  ======|===================|-----> Rotation
       +-------------------+ 
            ^ Tool Feed f (mm/rev)
            | [Tool]

Core Machining Formulas

1. Cutting Speed ($V$): The linear speed of the workpiece surface relative to the tool:

   $$V = \frac{\pi D N}{1000} \quad (\text{m/min})$$ $$N = \frac{1000 V}{\pi D} \quad (\text{RPM})$$

   where $D$ is workpiece diameter (mm) and $N$ is rotational spindle speed (RPM).

2. Machining Time ($T_m$): The time required to complete a single cutting pass over length $L$:

   $$T_m = \frac{L + L_o}{f N} \quad (\text{minutes})$$

   where $L$ is cut length (mm), $L_o$ is tool approach/overtravel allowance (mm), and $f$ is feed rate (mm/rev).

3. Material Removal Rate ($MRR$): The volumetric rate of metal removed:

   $$MRR = v_f \cdot d \cdot w = (f \cdot N) \cdot d \cdot (\pi D_{\text{avg}}) = 1000 \cdot V \cdot f \cdot d \quad (\text{mm}^3/\text{min})$$

   or in $\text{cm}^3/\text{min}$:

   $$MRR = V \cdot f \cdot d \quad (\text{cm}^3/\text{min})$$

   where $d$ is depth of cut (mm), $f$ is feed rate (mm/rev), and $V$ is cutting speed (m/min).

---

Worked Step-by-Step Calculation: Lathe Turning

Problem: A cylindrical steel rod of diameter $D = 80 \text{ mm}$ and length $L = 300 \text{ mm}$ is turned on a lathe at a recommended cutting speed $V = 120 \text{ m/min}$. The feed rate is set to $f = 0.30 \text{ mm/rev}$ and depth of cut is $d = 2.5 \text{ mm}$. Allowance for tool entry/exit is $L_o = 10 \text{ mm}$. Calculate:

1. The required lathe spindle speed $N$.
2. The total machining time $T_m$ for one pass.
3. The Material Removal Rate ($MRR$) in $\text{cm}^3/\text{min}$.

Step 1: Calculate Spindle Speed ($N$)

$$N = \frac{1000 V}{\pi D} = \frac{1000 \times 120}{\pi \times 80} = \frac{120,000}{251.327} = 477.46 \text{ RPM} \approx 477 \text{ RPM}$$

Step 2: Calculate Machining Time ($T_m$) Total travel length $L_{\text{total}} = L + L_o = 300 + 10 = 310 \text{ mm}$.

$$T_m = \frac{L_{\text{total}}}{f N} = \frac{310}{0.30 \times 477.46} = \frac{310}{143.238} = 2.164 \text{ min} \quad (2 \text{ min } 10 \text{ sec})$$

Step 3: Calculate Material Removal Rate ($MRR$)

$$MRR = V \cdot f \cdot d = 120 \text{ m/min} \times 0.30 \text{ mm/rev} \times 2.5 \text{ mm} = 90.0 \text{ cm}^3/\text{min}$$

---

4. Milling Operations & Feed Rate Equations

Milling uses multi-tooth rotary cutters to produce flat, contoured, or slotted surfaces. It is categorized into face milling (cutting action on periphery and face) and end milling (cutting slots/pockets with side and end teeth).

Milling Feed Rate & Table Speed ($V_f$)

The linear feed rate of the worktable ($V_f$) depends on the feed per tooth ($f_t$), number of cutter teeth ($z$), and spindle speed ($N$):

$$V_f = f_t \cdot z \cdot N \quad (\text{mm/min})$$ $$MRR = w \cdot d \cdot V_f \quad (\text{mm}^3/\text{min})$$

where $w$ is the width of cut (mm) and $d$ is the depth of cut (mm).

---

Worked Step-by-Step Calculation: Milling MRR

Problem: A $100 \text{ mm}$ diameter face milling cutter with $z = 8$ carbide teeth mills a flat steel plate of width $w = 80 \text{ mm}$ at a depth of cut $d = 3.0 \text{ mm}$. The cutting speed is $V = 150 \text{ m/min}$ and feed per tooth is $f_t = 0.15 \text{ mm/tooth}$. Calculate:

1. The spindle speed $N$ and table feed velocity $V_f$.
2. The volumetric Material Removal Rate ($MRR$) in $\text{cm}^3/\text{min}$.

Step 1: Calculate Spindle Speed ($N$)

$$N = \frac{1000 V}{\pi D} = \frac{1000 \times 150}{\pi \times 100} = 477.46 \text{ RPM}$$

Step 2: Calculate Table Feed Rate ($V_f$)

$$V_f = f_t \cdot z \cdot N = 0.15 \text{ mm/tooth} \times 8 \text{ teeth} \times 477.46 \text{ RPM} = 572.95 \text{ mm/min}$$

Step 3: Calculate MRR

$$MRR = w \cdot d \cdot V_f = 80 \text{ mm} \times 3.0 \text{ mm} \times 572.95 \text{ mm/min} = 137,508 \text{ mm}^3/\text{min} = 137.51 \text{ cm}^3/\text{min}$$

---

5. Drilling, Grinding & Non-Traditional Machining

Drilling Calculations

Drilling produces cylindrical holes using a rotating twist drill bit. The drill point angle (typically $118^\circ$) adds an approach height $h_p = 0.3 D$ to the hole depth $h$. Total drilling time is:

$$T_m = \frac{h + 0.3 D}{f N}$$

Grinding

Grinding removes small chips using abrasive grains bonded in a grinding wheel. Grinding wheel surface speed $V_g$ must be maintained between $20 \text{ and } 35 \text{ m/s}$:

$$V_g = \frac{\pi D_g N_g}{60,000} \quad (\text{m/s})$$

Non-Traditional Machining Technologies

1. Electrical Discharge Machining (EDM): Removes material via controlled electro-thermal spark erosion in a dielectric fluid (kerosene/deionized water). Machinability depends solely on thermal properties and electrical conductivity, regardless of material hardness (e.g., hardened tool steels, titanium).
2. Electrochemical Machining (ECM): Controlled anodic dissolution according to Faraday's Law ($m = \frac{I t M}{n F}$). Produces zero tool wear, zero thermal stress, and stress-free mirror finishes on hard alloys.
3. Laser Beam Machining (LBM): Focuses high-intensity coherent light to melt and vaporize thin metal or ceramic sheets.
4. Abrasive Waterjet Cutting (AWJC): Uses ultra-high pressure water ($300 - 400 \text{ MPa}$) entrained with abrasive garnets to cold-cut thick metal plates without heat-affected zones (HAZ).