Arrhenius Lifetime Plot: Cable Aging Test Method

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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.

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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. 

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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) 

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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.

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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. 

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Conclusion

The Arrhenius method allows engineers to accelerate aging tests in controlled environments and extrapolate real-world performance.