This paper presents a precision control methodology for pre-installing steel casting components of inclined dual-axis rudder systems during block construction stage, effectively resolving traditional challenges including low efficiency, safety risks, and prolonged cycles in conventional erection-phase installations.
1. Precision Control Strategy for Steel Casting Pre-installation
The positioning requirements for steel casting components are mathematically expressed as:
$$ \Delta_{total} = \sum_{i=1}^{n} (\delta_{thermal} + \delta_{weld} + \delta_{assembly}) $$
Where:
$\Delta_{total}$ = Total permissible deviation (≤2mm)
$\delta_{thermal}$ = Thermal deformation factor
$\delta_{weld}$ = Welding shrinkage coefficient
$\delta_{assembly}$ = Assembly tolerance
| Component | Longitudinal Compensation | Transverse Tolerance | Vertical Compensation |
|---|---|---|---|
| Stern Casting (ED11P/S) | 0-3mm | ±1mm | 3-5mm |
| “I” Frame (AG02C) | 4mm (forward) | ±1mm | 3-5mm |
| “V” Frame (AG03C) | 5mm (aft) | 5mm offset | 5mm |
| Rudder Bush (AG01C) | 0-1mm | ±1mm | 3-5mm |
2. Implementation of Steel Casting Precision Control
The concentricity control equation for axis alignment:
$$ C = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} \leq 2\text{mm} $$
Where $(x_1,y_1)$ and $(x_2,y_2)$ represent coordinate pairs of axis endpoints.
Welding deformation compensation model:
$$ \delta_{comp} = k \cdot \frac{Q}{v} \cdot \alpha \cdot L $$
Where:
$k$ = Material constant (0.8-1.2 for steel castings)
$Q$ = Heat input (kJ/mm)
$v$ = Welding speed (mm/s)
$\alpha$ = Thermal expansion coefficient
$L$ = Weld length
| Process Stage | Measurement Frequency | Tolerance Limit | Control Method |
|---|---|---|---|
| Sub-assembly | Every 30cm weld | ±1.5mm | Laser Tracker |
| Block Assembly | Hourly | ±1mm | Total Station |
| Erection | Real-time | ±0.5mm | 3D Metrology |
3. Deformation Monitoring Data
| Component | Pre-weld (mm) | Post-weld (mm) | Deviation |
|---|---|---|---|
| AG02C Longitudinal | -1 | -2 | 1 |
| AG03C Transverse | 2 | 2 | 0 |
| AG01C Vertical | 1 | -1 | 2 |
4. Results and Discussion
The implementation demonstrated significant improvements:
$$ \eta = \frac{t_{traditional} – t_{new}}{t_{traditional}} \times 100\% = \frac{28 – 15}{28} \times 100\% ≈ 46.4\% $$
Where:
$\eta$ = Efficiency improvement
$t_{traditional}$ = Conventional installation time (days)
$t_{new}$ = Optimized process time (days)
Key achievements in steel casting installation:
– Concentricity error reduction from 3.2mm to 1.5mm
– Welding deformation control within 1.8mm/m
– Positional accuracy improvement by 62%
5. Conclusion
The precision control methodology for steel casting components in inclined dual-axis systems effectively addresses manufacturing challenges through:
$$ \sigma_{total} = \sqrt{\sigma_{position}^2 + \sigma_{weld}^2 + \sigma_{measure}^2} \leq 2\text{mm} $$
Where:
$\sigma_{position}$ = Positioning error
$\sigma_{weld}$ = Welding deformation
$\sigma_{measure}$ = Measurement uncertainty
This approach establishes technical benchmarks for steel casting applications in marine propulsion systems, providing valuable data references for complex shafting installations in various vessel types.