18.6 Economic Optimization Strategies & Fabrication Cost Comparison

Engineering Strategies for Economic Optimization

                               OPTIMIZATION STRATEGIES

    PROCESS CONVERSION:           JOINT DESIGN:                 AUTOMATION:
    SMAW -> FCAW -> SAW           Standard V -> Narrow Groove   Mechanized Carriages
    Triples Deposition Rate       Cuts Volume by 60%            Increases OF to 60-80%

1. Process Conversion:
   • Replacing manual SMAW with semi-automatic FCAW-G or GMAW on structural assemblies increases deposition rates from $2.5\text{ lb/h}$ to $9.0\text{ lb/h}$ while doubling the operating factor from $20%$ to $40%$. Total labor hours drop by over $70%$.
   • Converting from solid wire (GMAW) to metal-cored wire (GMAW-C) eliminates post-weld deslagging, supports higher travel speeds on mill scale, and increases duty cycles.
2. Narrow-Groove Joint Preparation (NGW):
   • On plate thicknesses exceeding $2\text{ in}$ ($50\text{ mm}$), substituting a standard $60^\circ$ single-V groove preparation with a narrow-gap joint ($10^\circ\text{ to }15^\circ$ included angle with a backing shoe or oscillating tandem GMAW/SAW) reduces total deposited weld metal volume by $60%\text{ to }70%$.
3. Fit-up Gap Elimination:
   • In fillet-welded T-joints, a root fit-up gap of $2\text{ mm}$ ($1/16\text{ in}$) requires increasing the fillet leg by $2\text{ mm}$ to maintain the design effective throat, triggering a $40%$ surge in filler metal consumption.

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Comprehensive Worked Engineering Example: Shop Fabrication Cost Comparison

Problem Statement

A heavy steel bridge fabricator must weld $500\text{ meters}$ ($500,000\text{ mm}$) of continuous, equal-leg fillet welds on stiffener-to-web connections. The structural drawings specify an $8.0\text{ mm}$ leg fillet weld ($w = 8.0\text{ mm}$). Assume zero root gap, flat weld profile (no excessive convexity), and steel density $\rho = 7.85 \times 10^{-6}\text{ kg/mm}^3$.

The Welding Engineer is conducting a rigorous financial comparison between two candidate processes:

• Option A: Manual SMAW utilizing $4.0\text{ mm}$ AWS A5.1 E7018 electrodes.
• Option B: Semi-Automatic FCAW-G utilizing $1.2\text{ mm}$ AWS A5.20 E71T-1M wire with $75%\text{ Ar} / 25%\text{ CO}_2$ shielding gas.

+---------------------------------------------------------------------------------------------------+
|                                 PROCESS ECONOMIC PARAMETERS                                       |
+---------------------------------------+---------------------------+-------------------------------+
| Parameter                             | Option A: SMAW (E7018)    | Option B: FCAW-G (E71T-1M)    |
+---------------------------------------+---------------------------+-------------------------------+
| Deposition Rate ($DR$)                | $1.80\text{ kg/h}$        | $4.50\text{ kg/h}$            |
| Deposition Efficiency ($\eta_{\text{dep}}$)| $0.60$ ($60\%$)       | $0.85$ ($85\%$)               |
| Operating Factor ($OF$)               | $0.20$ ($20\%$)           | $0.40$ ($40\%$)               |
| Fully Burdened Labor Rate ($R_L$)     | $\$75.00\text{ / hour}$  | $\$75.00\text{ / hour}$       |
| Filler Metal Unit Price ($P_F$)       | $\$4.50\text{ / kg}$      | $\$6.20\text{ / kg}$          |
| Shielding Gas Flow ($Q_G$)            | None ($0\text{ m}^3\text{/h}$) | $1.20\text{ m}^3\text{/h}$ (20 L/min) |
| Shielding Gas Unit Price ($P_G$)      | None                      | $\$14.00\text{ / m}^3$        |
| Electrical Power Parameters           | $24\text{ V}, 160\text{ A}$| $28\text{ V}, 260\text{ A}$   |
| Power Source Efficiency ($\eta_{\text{pwr}}$)| $0.80$             | $0.88$                        |
| Industrial Electricity Price ($P_{\text{kWh}}$)| $\$0.15\text{ / kWh}$ | $\$0.15\text{ / kWh}$   |
+---------------------------------------+---------------------------+-------------------------------+

Calculate for both options:

1. Total deposited weld metal mass ($M_{\text{total}}$).
2. Arc-on time ($t_{\text{arc}}$) and total paid labor hours ($t_{\text{labor}}$).
3. Direct labor & overhead cost ($C_{\text{labor}}$).
4. Consumable filler metal cost ($C_{\text{filler}}$).
5. Shielding gas cost ($C_{\text{gas}}$) and electrical power cost ($C_{\text{power}}$).
6. Total project welding cost and cost per linear meter.
7. Total financial savings and labor hours saved by selecting FCAW-G.

Step-by-Step Engineering Solution

Step 1: Calculate Deposited Weld Metal Mass ($M_{\text{total}}$)

• Fillet weld cross-sectional area: $A = \frac{1}{2} w^2 = \frac{1}{2} (8.0\text{ mm})^2 = 32.0\text{ mm}^2$
• Total weld volume for $500\text{ m}$ ($500,000\text{ mm}$): $V = A \times L = 32.0\text{ mm}^2 \times 500,000\text{ mm} = 16,000,000\text{ mm}^3$
• Total deposited weld metal mass: $M_{\text{total}} = V \times \rho = 16,000,000\text{ mm}^3 \times 7.85 \times 10^{-6}\text{ kg/mm}^3 = 125.6\text{ kg}$

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Step 2: Option A (Manual SMAW) Cost Breakdown

1. Arc-On Time and Labor Hours: $t_{\text{arc}} = \frac{M_{\text{total}}}{DR} = \frac{125.6\text{ kg}}{1.80\text{ kg/h}} = 69.78\text{ hours}$ $t_{\text{labor}} = \frac{t_{\text{arc}}}{OF} = \frac{69.78\text{ h}}{0.20} = 348.9\text{ paid labor hours}$

2. Labor & Overhead Cost ($C_{\text{labor}}$): $C_{\text{labor}} = 348.9\text{ h} \times \$75.00\text{/h} = \$26,167.50$

3. Consumable Mass and Cost ($C_{\text{filler}}$): $M_{\text{purchased}} = \frac{M_{\text{total}}}{\eta_{\text{dep}}} = \frac{125.6\text{ kg}}{0.60} = 209.33\text{ kg}$ $C_{\text{filler}} = 209.33\text{ kg} \times \$4.50\text{/kg} = \$941.99$

4. Shielding Gas Cost ($C_{\text{gas}}$): $C_{\text{gas}} = \$0.00 \quad (\text{Self-shielded via electrode flux})$

5. Electrical Power Cost ($C_{\text{power}}$): $\text{Arc Power} = \frac{24\text{ V} \times 160\text{ A}}{1000} = 3.84\text{ kW}$ $\text{Input Power} = \frac{3.84}{0.80} = 4.80\text{ kW}$ $\text{Total Energy} = 4.80\text{ kW} \times 69.78\text{ h} = 334.94\text{ kWh}$ $C_{\text{power}} = 334.94\text{ kWh} \times \$0.15\text{/kWh} = \$50.24$

6. Total Cost for Option A (SMAW): $C_{\text{total, SMAW}} = \$26,167.50 + \$941.99 + \$0.00 + \$50.24 = \$27,159.73$ $\text{Cost per Meter (SMAW)} = \frac{\$27,159.73}{500\text{ m}} = \$54.32\text{ / meter}$

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Step 3: Option B (Semi-Automatic FCAW-G) Cost Breakdown

1. Arc-On Time and Labor Hours: $t_{\text{arc}} = \frac{M_{\text{total}}}{DR} = \frac{125.6\text{ kg}}{4.50\text{ kg/h}} = 27.91\text{ hours}$ $t_{\text{labor}} = \frac{t_{\text{arc}}}{OF} = \frac{27.91\text{ h}}{0.40} = 69.78\text{ paid labor hours}$

2. Labor & Overhead Cost ($C_{\text{labor}}$): $C_{\text{labor}} = 69.78\text{ h} \times \$75.00\text{/h} = \$5,233.50$

3. Consumable Mass and Cost ($C_{\text{filler}}$): $M_{\text{purchased}} = \frac{M_{\text{total}}}{\eta_{\text{dep}}} = \frac{125.6\text{ kg}}{0.85} = 147.76\text{ kg}$ $C_{\text{filler}} = 147.76\text{ kg} \times \$6.20\text{/kg} = \$916.11$

4. Shielding Gas Cost ($C_{\text{gas}}$): $\text{Gas Volume} = t_{\text{arc}} \times Q_G = 27.91\text{ h} \times 1.20\text{ m}^3\text{/h} = 33.49\text{ m}^3$ $C_{\text{gas}} = 33.49\text{ m}^3 \times \$14.00\text{/m}^3 = \$468.86$

5. Electrical Power Cost ($C_{\text{power}}$): $\text{Arc Power} = \frac{28\text{ V} \times 260\text{ A}}{1000} = 7.28\text{ kW}$ $\text{Input Power} = \frac{7.28}{0.88} = 8.273\text{ kW}$ $\text{Total Energy} = 8.273\text{ kW} \times 27.91\text{ h} = 230.9\text{ kWh}$ $C_{\text{power}} = 230.9\text{ kWh} \times \$0.15\text{/kWh} = \$34.64$

6. Total Cost for Option B (FCAW-G): $C_{\text{total, FCAW}} = \$5,233.50 + \$916.11 + \$468.86 + \$34.64 = \$6,653.11$ $\text{Cost per Meter (FCAW)} = \frac{\$6,653.11}{500\text{ m}} = \$13.31\text{ / meter}$

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Step 4: Comparative Financial Summary

+---------------------------------------------------------------------------------------------------+
|                                 ECONOMIC COMPARISON RESULTS                                       |
+-----------------------------+-------------------------+-----------------------+-------------------+
| Cost Category               | Option A: SMAW          | Option B: FCAW-G      | Absolute Savings  |
+-----------------------------+-------------------------+-----------------------+-------------------+
| Total Paid Labor Hours      | 348.9 hours             | 69.8 hours            | **279.1 hours**   |
| Direct Labor & Overhead     | $26,167.50 (96.3%)      | $5,233.50 (78.7%)     | **$20,934.00**    |
| Consumable Filler Metal     | $941.99 (3.5%)          | $916.11 (13.8%)       | $25.88            |
| Shielding Gas               | $0.00 (0.0%)            | $468.86 (7.0%)        | -$468.86          |
| Electrical Power            | $50.24 (0.2%)           | $34.64 (0.5%)         | $15.60            |
+-----------------------------+-------------------------+-----------------------+-------------------+
| **TOTAL PROJECT COST**      | **$27,159.73**          | **$6,653.11**         | **$20,506.62**    |
| **COST PER LINEAR METER**   | **$54.32 / m**          | **$13.31 / m**        | **$41.01 / m**    |
+-----------------------------+-------------------------+-----------------------+-------------------+

• Bottom-Line Impact: Converting from SMAW to FCAW-G yields a $75.5%$ reduction in total project welding cost and frees up $279\text{ hours}$ of skilled labor to work on other structural modules.
• Note that although FCAW-G wire costs more per kilogram ($$6.20$ vs. $$4.50$) and requires shielding gas, the higher deposition efficiency ($85%$ vs $60%$) resulted in lower total consumable expenditure, completely refuting the notion that stick welding is cheaper due to lower upfront supply costs.

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Industrial Scenarios & Certified Welding Engineer Exam Pitfalls

Real-World Field Disaster Scenario

A rail car manufacturing plant bid on a contract to produce 400 hopper cars. The estimating department based labor hours on an assumed Operating Factor of $45%$ for manual GMAW. However, the shop layout was congested, requiring welders to wait an average of 25 minutes per shift for overhead crane picks to rotate car bodies, and welders had to fetch their own wire spools from a distant central warehouse. An audit by a Certified Welding Engineer revealed the true shop Operating Factor was only $18%$. Because labor costs are inversely proportional to operating factor ($C_L \propto 1/OF$), the actual labor cost per car was $45 / 18 = 2.5$ times higher than estimated—a $150%$ cost overrun that eradicated company profits and resulted in a $2.8 million contract loss.

Common Exam Traps

Exam Trap 1: Applying Operating Factor to Consumable Weight An exam question will ask: "If the operating factor increases from 25% to 50%, what happens to the weight of filler metal required to complete the joint?" A common trap is assuming the consumable requirement drops by half. The correct answer is: Consumable weight is completely unchanged. Operating factor affects labor time only. Deposited joint volume and mass depend strictly on joint geometry and plate thickness.

Exam Trap 2: Linear vs. Quadratic Overwelding Cost Scaling Questions frequently present a scenario where a fillet weld leg is increased by $25%$ (e.g., from $8\text{ mm}$ to $10\text{ mm}$) and ask for the resulting cost impact. Candidates intuitively guess that costs increase by $25%$. The true cost increase is governed by $(1.25)^2 - 1 = 1.5625 - 1 = +56.25%$. Always square the leg dimension ratio when calculating fillet weld volume and cost!

Exam Trap 3: Inverting Deposition Efficiency in Cost Formulas When calculating filler metal procurement mass, candidates often multiply deposited mass by $\eta_{\text{dep}}$ instead of dividing. To deposit $100\text{ kg}$ of metal using a process with $\eta_{\text{dep}} = 0.80$, you must purchase $100 / 0.80 = 125\text{ kg}$ of wire. Multiplying by $0.80$ would give $80\text{ kg}$, resulting in a severe material shortfall.