OV-C2-DD-DCLINK-THERMAL · v1.0 · released · 2026-07-13
| Doctype | Design Document |
|---|---|
| Doc id | OV-C2-DD-DCLINK-THERMAL |
| Product line | openvvvf |
| Applies to | chassis-size-2 |
| Version | 1.0 |
| Date | 2026-07-13 |
| Status | released |
| Description | DC-link capacitor bank standoff heat-path and thermal resistance analysis for Chassis Size 2. |
| Nav order | 231 |
| Normative refs | OV-C2-DD-INDEX |
Thermal Analysis - DC Link Module Standoff Heat Path
Heat load at rated ripple was calculated to be 40 W across all capacitors.
Nomenclature
| Symbol | Meaning | Units |
|---|---|---|
| $A$ | Cross-sectional area (generic) | m² |
| $A_{standoff}$ | Cross-sectional area of one standoff | m² |
| $k$ | Thermal conductivity (generic material) | W/(m·K) |
| $k_{Al}$ | Thermal conductivity of the aluminium heat-spreader plate | W/(m·K) |
| $k_{standoff}$ | Thermal conductivity of the standoff material | W/(m·K) |
| $L$ | Standoff length (thermal conduction path) | m |
| $n$ | Number of standoffs | - |
| $Q$ | Heat flow from capacitor bank ripple current | W |
| $r_{cell}$ | Effective radius of the aluminium spreading cell around one standoff | m |
| $r_{inner}$ | Standoff inner (hole) radius | m |
| $r_{outer}$ | Standoff outer radius | m |
| $r_{standoff}$ | Standoff outer radius (used in spreading model) | m |
| $R_{contact}$ | Contact resistance across one standoff-to-plate or standoff-to-heatsink interface pair | K/W |
| $R_{spread}$ | Aluminium heat-spreader plate spreading resistance | K/W |
| $R_{standoff}$ | Standoff conduction thermal resistance | K/W |
| $R_{th}$ | Generic thermal resistance | K/W |
| $t_{Al}$ | Aluminium heat-spreader plate thickness | m |
| $\Delta T$ | Temperature rise / difference | K or °C |
| $\rho_{contact}$ | Contact resistivity | m²·K/W |
Methodology
All calculations use one-dimensional steady-state thermal resistance:
$$\Delta T = Q \times R_{th}$$
where
$$R_{th} = \frac{L}{k \, A}$$
Total system resistance is the sum of three series components:
- Standoff conduction
$$R_{standoff} = \frac{L}{k_{standoff} \, A_{standoff} \, n}$$ - Contact resistance (both faces in series)
$$R_{contact} = \frac{2 \, \rho_{contact}}{n \, A_{standoff}}$$ - Aluminium spreading
$$R_{spread} \approx \frac{\ln(r_{cell} / r_{standoff}) - 0.5}{2\pi \, k_{Al} \, t_{Al}}$$
Material properties
| Material | Thermal conductivity $k$ [W/(m·K)] |
|---|---|
| Aluminium (6063 / generic) | 200 |
| Brass (C36000) | 120 |
| Copper (C11000) | 400 |
| Carbon steel | 50 |
| 18-8 Stainless steel | 16 |
Contact resistivity values
| Condition | Resistivity $\rho_{contact}$ [m²·K/W] |
|---|---|
| Dry metal-to-metal | $1.0 \times 10^{-4}$ |
| With thermal paste / thin pad | $5.0 \times 10^{-5}$ |
Geometry constants
- Heat-spreader plate: 3.18 mm (1/8 in) thick aluminium (corrected from 4 mm to match the fabricated plate, HW-C2-PLT-CHSP-A; all spreading-resistance values below use 3.18 mm)
- Standoff length: 55 mm (final design)
- Number of standoffs: 6 (final design)
- Standoff spacing: assumed ~100 mm centre-to-centre (spreading cell radius $r_{cell} \approx 50$ mm)
Design Evolution
Initial concepts (for reference)
| Configuration | $k$ [W/m·K] | Area [mm²] | $R_{standoff}$ [K/W] | $\Delta T_{standoff}$ [°C] | Total $\Delta T$ (paste) [°C] |
|---|---|---|---|---|---|
| 8 mm hex brass, hollow M5 | 120 | 35.8 | 2.13 | 85.4 | 123 |
| 10 mm hex Al, hollow M5 | 200 | 67.0 | 0.684 | 27.4 | 53.9 |
| 16 mm round Al, hollow M8 | 200 | 150.8 | 0.304 | 12.2 | 29.9 |
| 16 mm round Al, solid | 200 | 201.1 | 0.228 | 9.1 | 25.8 |
All at 40 W, 6 standoffs, 55 mm long. Values rounded.
Selected design - 13 mm round aluminium spacers
Final part specification:
- Outer diameter: 13.0 mm
- Inner diameter (M6 clearance): 6.3 mm
(Note: M6 major diameter = 6.0 mm; 6.3 mm ID provides thread engagement or clearance depending on part type)
- Wall thickness: 3.35 mm
- Length: 55 mm
- Material: Aluminium
- Thread: M6 × 1 (male-female or through-hole with bolt)
- Quantity: 6
Cross-sectional area:
$$A = \pi (r_{outer}^2 - r_{inner}^2) = \pi (6.5^2 - 3.15^2) \times 10^{-6} = 101.6 \times 10^{-6} \ \text{m}^2$$
Final Design Calculation
Standoff conduction resistance
$$R_{standoff} = \frac{L}{k_{Al} \, A \, n} = \frac{0.055}{200 \times 101.6 \times 10^{-6} \times 6} = 0.451 \ \text{K/W}$$
$$\Delta T_{standoff} = 40 \times 0.451 = \mathbf{18.1 \ ^\circ\text{C}}$$
Contact resistance (both faces)
With thermal paste:
$$R_{contact} = \frac{2 \times 5.0 \times 10^{-5}}{6 \times 101.6 \times 10^{-6}} = 0.164 \ \text{K/W}$$
$$\Delta T_{contact} = 40 \times 0.164 = \mathbf{6.6 \ ^\circ\text{C}}$$
Dry metal-to-metal:
$$R_{contact} = \frac{2 \times 1.0 \times 10^{-4}}{6 \times 101.6 \times 10^{-6}} = 0.328 \ \text{K/W}$$
$$\Delta T_{contact} = 40 \times 0.328 = \mathbf{13.1 \ ^\circ\text{C}}$$
Aluminium spreading resistance
$$R_{spread} = \frac{\ln(50 / 6.5) - 0.5}{2\pi \times 200 \times 0.00318} \approx 0.385 \ \text{K/W}$$
$$\Delta T_{spread} = 40 \times 0.385 = \mathbf{15.4 \ ^\circ\text{C}}$$
(Spreading resistance is independent of standoff material; it depends only on plate conductivity, thickness, and cell geometry.)
Total temperature rise
| Condition | $\Delta T_{total}$ |
|---|---|
| With thermal paste | $18.1 + 6.6 + 15.4 = \mathbf{40.1 \ ^\circ\text{C}}$ |
| Dry metal-to-metal | $18.1 + 13.1 + 15.4 = \mathbf{46.6 \ ^\circ\text{C}}$ |
Absolute temperatures (heatsink base = 40 °C)
| Condition | Aluminium plate temperature |
|---|---|
| With thermal paste | ~80 °C |
| Dry metal-to-metal | ~87 °C |
450 V capacitor-only upgrade: The 450 V upgrade is a single part-number swap to 60× Nichicon UCS2W680MHD 68 µF / 450 V capacitors (4.08 mF total). These parts are 5 mm shorter than the 200 V UCS2D331MHD, so the standoff length is reduced by 5 mm (from 55 mm to 50 mm). The same 13 mm OD aluminium standoff thermal path applies, with marginally lower conduction resistance due to the shorter length.
Sensitivity & Margin
Effect of standoff material
If stainless steel (18-8, $k = 16$ W/m·K) were used instead of aluminium:
$$\Delta T_{standoff} = \frac{40 \times 0.055}{16 \times 101.6 \times 10^{-6} \times 6} \approx 226 \ ^\circ\text{C}$$
Total rise would exceed 245 °C. Stainless steel is not acceptable for this thermal path.
Effect of quantity
| Standoff count | $R_{standoff}$ [K/W] | $\Delta T_{standoff}$ [°C] | Total $\Delta T$ (paste) [°C] |
|---|---|---|---|
| 4 | 0.677 | 27.1 | 52.3 |
| 6 (selected) | 0.451 | 18.1 | 40 |
| 8 | 0.338 | 13.5 | 33.9 |
Six standoffs provides adequate margin; eight would be better but is not required at 40 W.
Effect of length
| Length [mm] | $\Delta T_{standoff}$ [°C] | Total $\Delta T$ (paste) [°C] |
|---|---|---|
| 30 | 9.9 | 32 |
| 55 (selected) | 18.1 | 40 |
| 65 | 21.4 | 43 |
Recommendations
- Use aluminium standoffs/spacers only. Do not substitute stainless or carbon steel.
- Apply thermal paste (or a thin graphite / indium thermal pad) at both the plate-to-standoff and standoff-to-heatsink interfaces. This saves ~6.5 °C and improves long-term thermal stability.
- Ensure adequate clamping force on the M6 bolts to minimize contact resistance. Target ~5–10 N·m on steel bolts into aluminium.
- Verify standoff placement is reasonably distributed across the plate. Uneven distribution will increase local spreading resistance and hot-spot temperatures.
- If power increases above ~60 W, consider upgrading to 8 standoffs or thicker-wall spacers (e.g., 16 mm OD / 6 mm ID).
Assumptions & Limitations
- One-dimensional conduction assumed; actual 3D spreading may vary ±20 %.
- Contact resistivity values are typical estimates; actual values depend on surface finish, flatness, and clamping pressure.
- Heat generation is assumed uniform across the aluminium plate. Localised hot spots will increase peak temperatures.
- Radiation and natural convection from the plate are neglected; in reality they provide additional heat rejection, so actual plate temperature may be slightly lower.
- Ambient / heatsink base temperature is assumed constant at 40 °C; if the heatsink warms up under load, the absolute plate temperature rises proportionally.
Prepared for DC link module thermal design review.