Unlock the Secrets of Fuse TCC: Calculate Melting Time in 3 Easy Steps

작성자: calcany

Do you know how to calculate the melting time of fuses? Understanding the concepts of logarithms and exponents plays a crucial role in interpreting Fuse Time Current Curves (TCC), thereby enhancing the safety of electrical systems. Additionally, the exponential interpolation method enables accurate prediction of values between known points on a logarithmic scale, making it a versatile tool applicable across various domains.

ⓘ This post was written after studying with lots of information like books, internet sites, etc. Except in some cases where it is specifically stated, images are made by R & Python using RStudio or VS code.

Exponents and Logarithms

Exponents and logarithms are closely related. Exponents represent raising a number to a power, while logarithms are the inverse operation.

For example, if 2^3 = 2 \times 2 \times 2 = 8, then \log_2 8 = 3. This means that 2 raised to the 3rd power is 8, and the logarithm of 8 with base 2 is 3.

exp.graph
log.graph

Exponential graphs curve upwards, with the slope increasing sharply. In contrast, logarithmic graphs have a gradual downward curve.

Linear and Log Scales

A linear scale represents numbers increasing at equal intervals. However, a log scale can represent exponentially increasing values at uniform intervals.

For example, 1, 10, 100, 1000 are spaced equally on a log scale. This is useful when dealing with values that have a wide range.

linear_log.graph

Fuse Time Current Curve

A fuse is a device used to protect electrical circuits from overcurrent. The Time Current Curve is a graph that shows how quickly a fuse melts at different overcurrent levels.

tcc time current fuse

This graph plots current on the y-axis and time on the x-axis, both on a log scale. At high current levels, the fuse melts quickly, while at lower currents, it takes longer. The graph is a simplified representation of the TCC. It can be interpreted that the fuse is designed to blow in approximately 1 second when a current of 10A flows through it.

Calculate Melting Time with Exponential Interpolation

The Melting Time is the average time it takes for a fuse to melt when exposed to a specific current. To calculate this, the exponential interpolation method is used.

Exponential interpolation is a method to approximate values between two data points on a log-log scale. It is used to interpolate the time for a given current value on the Time Current Curve.

Suppose we have two known data points (I₁, t₁) and (I₂, t₂). The time t for our desired current I can be calculated as:

\log(t) = \log(t_1) + (\log(t_2) - \log(t_1)) \times \frac{\log(I) - \log(I_1)}{\log(I_2) - \log(I_1)}

This formula can be used to find the melting time for any desired current value.

calculate melting time with exponential interpolation

Example Calculation

In the example shown in the image:

  • ( ( I_1, t_1) = (10, 1) )
  • ( ( I_2, t_2) = (100, 10) )
  • ( I = 50 )

Let’s use the formula to find ( t ) when ( I = 50 ).

1. Calculate logarithms:

  • \log(t_1) = \log(1) = 0
  • \log(t_2) = \log(10) = 1
  • \log(I_1) = \log(10) = 1
  • \log(I_2) = \log(100) = 2
  • \log(I) \approx \log(50) \approx 1.69897

2. Substitute values into the formula:

  • \log(t) = 0 + (1 - 0) \times \frac{\log(50) - 1}{2 - 1}
  • \log(t) = 0 + 1 \times (1.69897 - 1)
  • \log(t) = 1.69897 - 1 = 0.69897

3. Convert back from logarithmic scale:

  • t = 10^{0.69897} \approx 5

Therefore, the correct melting time ( t ) when ( I = 50 ) is approximately 5 seconds.

The graph shows the (50, 5) point lying on the curve passing through the two data points. This demonstrates how exponential interpolation can accurately approximate values between two points on a log-log scale.

By using the Fuse Time Current Curve and exponential interpolation, the melting time can be accurately calculated. This plays a crucial role in ensuring the safety and reliability of electrical systems.

You can find the average fuse blowing time through the three easy steps above. However, if you try to do it manually, you will find that it takes more time than you think. So Calcany prepared a solution for you. If you press the button or post box below, you can automatically obtain the fuse blowing time through several settings. Welcome to a new world.

Fuse Melting Time Calculator(FMTC)
Ultimate Fuse Melting Time Calculator: Your 1-Minute Guide to Precision

Conclusion

By using the Fuse Time Current Curve and exponential interpolation, the melting time can be accurately calculated. This plays a crucial role in ensuring the safety and reliability of electrical systems. You can find the average fuse blowing time through the three easy steps above. However, if you try to do it manually, you will find that it takes more time than you think. So Calcany prepared a solution for you. If you press the button or post box below, you can automatically obtain the fuse blowing time through several settings. Welcome to a new world.

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