Centrifugal compressor diaphragms, typically cast from steel, occasionally exhibit casting defects during post-manufacturing inspections. This study proposes machining and repair welding techniques to address these defects while maintaining structural integrity. Finite element analysis (FEA) validates the mechanical behavior under different material removal and repair thickness conditions.
1. Structural Characteristics and Defect Distribution
The investigated diaphragm employs a hollow design with internal ribs for weight reduction and enhanced compressor performance. Casting defects primarily manifest as porosity clusters in specific regions:
The defect distribution follows an exponential decay pattern along the depth direction:
$$N(d) = N_0 e^{-\lambda d}$$
Where:
- $N(d)$ = Defect density at depth $d$ (defects/cm³)
- $N_0$ = Surface defect density (12.8 defects/cm³)
- $\lambda$ = Decay constant (0.35 mm⁻¹)
2. Operational Load Analysis
Two critical operational conditions were evaluated:
| Condition | Inlet Pressure (MPa) | Outlet Pressure (MPa) | Pressure Differential (MPa) |
|---|---|---|---|
| Normal Operation | 0.79 | 1.55 | 0.76 |
| Venting | 0.79 | 0.13 | 0.66 |
The stress distribution follows the thick-walled cylinder formula:
$$\sigma_r = \frac{p_i r_i^2 – p_o r_o^2}{r_o^2 – r_i^2} + \frac{(p_i – p_o)r_i^2 r_o^2}{(r_o^2 – r_i^2)r^2}$$
$$\sigma_\theta = \frac{p_i r_i^2 – p_o r_o^2}{r_o^2 – r_i^2} – \frac{(p_i – p_o)r_i^2 r_o^2}{(r_o^2 – r_i^2)r^2}$$
Where $r_i$ and $r_o$ represent inner and outer radii respectively.
3. Finite Element Modeling Parameters
| Parameter | Value |
|---|---|
| Material | ZG230-450 |
| Young’s Modulus | 200 GPa |
| Poisson’s Ratio | 0.3 |
| Yield Strength | 230 MPa |
| Ultimate Strength | 450 MPa |
4. Defect Removal and Repair Strategy
The material removal depth ($h$) affects residual stress ($\sigma_r$) and deformation ($\delta$):
$$\sigma_r(h) = \sigma_0 \left(1 + \frac{h}{t}\right)^{2.5}$$
$$\delta(h) = \delta_0 e^{0.15h}$$
Where $t$ represents original wall thickness (45 mm).
| Machining Depth (mm) | Max Stress (MPa) | Radial Deformation (mm) | Axial Deformation (mm) |
|---|---|---|---|
| 0 | 215 | 0.07 | 0.79 |
| 5 | 220 | 0.072 | 0.81 |
| 10 | 221 | 0.075 | 0.83 |
| 15 | 222 | 0.079 | 0.86 |
| 20 | 226 | 0.083 | 0.89 |
5. Post-Repair Performance Evaluation
The repair welding process introduces residual stresses modeled by:
$$\sigma_w = \sigma_m + \alpha E \Delta T$$
Where $\alpha$ = thermal expansion coefficient (12×10⁻⁶/°C), $E$ = Young’s modulus, and $\Delta T$ = temperature differential (220°C).
| Repair Thickness (mm) | Stress Reduction (%) | Stiffness Recovery (%) |
|---|---|---|
| 5 | 2.3 | 94 |
| 10 | 5.1 | 97 |
| 15 | 8.7 | 99 |
| 20 | 12.4 | 101 |
6. Safety Threshold Determination
The critical machining depth satisfies:
$$\frac{\sigma_r(h)}{S_y} + \frac{\delta(h)}{\delta_{max}} \leq 1$$
Where $S_y$ = yield strength (230 MPa) and $\delta_{max}$ = maximum allowable deformation (1 mm).
7. Implementation Guidelines
- Maximum permissible machining depth: 25 mm
- Minimum repair thickness: 12 mm
- Post-repair heat treatment: 600°C × 2 hours
- Surface finishing requirement: Ra ≤ 3.2 μm
This methodology provides effective solutions for compressor diaphragms with casting defects, achieving 97% cost reduction compared to complete recasting while maintaining operational safety. The analysis emphasizes the importance of proper defect characterization and systematic repair parameter optimization.