Arrhenius Lifetime Plot: Cable Aging Test Method
1. Required Equipment and Setup
To perform a cable aging test, the following equipment is needed:
✔ Heated Ovens / Aging Chambers: To expose cables to high temperatures.
✔ Thermocouple Sensors: To monitor real-time cable temperature.
✔ Timer and Data Logger: To track test duration.
2. Cable Aging Test Procedure
- Step 1: Selecting Test Samples
- Different insulation materials are chosen (PVC, XLPE, EPR, etc.).
- Cables are cut into equal lengths for consistency.
- Step 2: Defining Aging Conditions
- Cables are exposed to different elevated temperatures (e.g., 60°C, 90°C, 120°C).
- Cables are kept in the aging chamber for a specified duration:
- 90°C for 2000 hours
- 120°C for 500 hours
- Step 3: Electrical & Mechanical Testing
- Tan Delta (Tan δ) Test: Measures insulation loss factor.
- Dielectric Strength Test: Applies high voltage to determine failure point.
- Mechanical Tests: Checks insulation flexibility and crack formation.
- Step 4: Recording Failure Time
- The time taken for insulation to fail is noted.
- Example:
- 120°C → 500 hours
- 90°C → 2000 hours
- 60°C → Lifetime needs to be estimated.
3. Lifetime Estimation Using Arrhenius Equation
The formula for predicting cable lifetime at lower temperatures:
ln t = ln t₀ + (Ea / RT)
Where:
- t = Estimated cable lifetime at temperature T
- t₀ = Known lifetime at a reference temperature
- Ea = Activation energy (J/mol)
- R = Gas constant (8.314 J/mol·K)
- T = Absolute temperature in Kelvin (K)
4. Example Calculation
Given test data:
- 90°C → Cable lasted 2000 hours
- 120°C → Cable lasted 500 hours
- Find lifetime at 60°C
- Step 1: Convert Temperature to Kelvin
T₁ = 120 + 273.15 = 393.15K
T₂ = 90 + 273.15 = 363.15K
T₃ = 60 + 273.15 = 333.15K
- Step 2: Calculate 1/T
1/T₁ = 1 / 393.15 = 0.002544
1/T₂ = 1 / 363.15 = 0.002754
- Step 3: Compute Lifetime Logarithm
ln(500) = 6.2146
ln(2000) = 7.6009
- Step 4: Find Activation Energy (Ea)
Ea = (7.6009 - 6.2146) * (8.314 / (0.002754 - 0.002544))
Ea = 54883 J/mol
- Step 5: Estimate Lifetime at 60°C
ln t₃ = ln 2000 + (Ea / R) * (1/T₃ - 1/T₂)
ln t₃ = 7.6009 + (54883 / 8.314) * (0.002998 - 0.002754)
ln t₃ = 9.2125
t₃ = e^9.2125 = 10000 hours
- Final Answer:
- Cable lifetime at 60°C is 10,000 hours (~1.14 years).
- If this value is too low, insulation type or operating temperature should be adjusted.
5. Applications of Cable Aging Tests
✔ Predicting the lifetime of medium and high-voltage cables.
✔ Evaluating the long-term reliability of underground or subsea cables.
✔ Determining insulation resistance at different temperature conditions.
✔ Helping manufacturers define warranty periods based on real test data.
Conclusion
The Arrhenius method allows engineers to accelerate aging tests in controlled environments and extrapolate real-world performance.