# Estimating Cable Life

Estimating cable life is complex and will on give results within some statistical variance. A key determinant in cable life is the temperature at which the insulation is operated. IEC standard 60216 gives guidance on estimating the thermal endurance of insulation based on measurements on test samples. For any particular cable, it is probably best to discuss with the manufacturer.

## Arrhenius Equation

The Arrhenius equation is often used to predict the lift span of insulation materials:

$k=A{e}^{E/RT}$

*k* - expected life in hours

*A* - pre-exponential factor

*E* - activation energy

*R* - Boltzmann constant

*T* - temperature in K

To put the equation in a more useful form, we can take the natural logarithm and rearrange the terms:

$\mathrm{ln}k=\mathrm{ln}A-\left(\frac{E}{R}\right)\times \left(\frac{1}{T}\right)$

Since A, E, and R are constants, this becomes a straight line with a negative slope of (E/R) plotted against the inverse of temperature (1/T).

## Rule of Thumb and Application Example

A sometimes adopted rule of thumb is that for every 10 °C rise in temperature, the life of insulation is halved. Inversely a 10 °C decrease in temperature will double the life of the insulation. The Rule is based on the Arrhenius Equation of chemical reaction time vs temperature.

The image below illustrates a typical cable performance as provided by the manufacturer:

From the Arrhenius equation, we know that relation ship is that of a log-linear straight line:

$\mathrm{ln}(y)=mx+b$

with the slope *m*, given by: * ( ln(20,000) - ln(5,000) ) / (125 - 145) = 0.0693*

and the x-axis intercept, *b* by:* ln(20,000) - m * 125 = 18.5678*

giving:

$\mathrm{ln}(y)=-0.0693x+18.5678$

and, for example at 110 °C, the estimated life span would be:

$y=\mathrm{exp}(-0.0693\times 110+18.5678)=56,500\text{(or6}\text{.5years)}$