# How to calculate natural frequency of timing belt

• friscoboya
In summary, to calculate the natural frequency of a timing belt in order to avoid resonance, it is important to consider the tension in each side of the belt and calculate the likely resonant frequencies for both sides. It may also be helpful to think about possible drivers at or near those frequencies and to research the maximum speed and pulley rotational speed limits for timing belts. Some useful starting points for this research include websites such as roymech.co.uk and optibelt-usa.com, which provide equations and information on timing belt specifications. Additionally, a formula for calculating the maximum belt speed based on pulley diameter, drive rpm, and belt length can be found on mromagazine.com.
friscoboya
Hello

I am designing a shaft and it will be powered via belt pulley system. The ideal RPM of the shaft is 8000 RPM. How do I calculate the natural frequency of the timing belt to ensure resonance is never met? From what I read online it has to do with belt pretension, but even then I am little lost. Equations and links would be helpful.

Thank you

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Not really my field but if I had to approach this problem I would look at this...

https://en.m.wikipedia.org/wiki/String_vibration

Treat each unsupported length of belt as a potentially vibrating string. Remember the tension in each side is different when its running. Calculate likely resonant frequencies for both sides.

Then think about possible drivers at or near those frequencies? For example the rate at which teeth engage or disengage with the ends of an unsupported length? Perhaps the pulley speeds (in revolutions per second) or perhaps the whole belt speed (in revolutions per second)?

But perhaps there is a more formal method?

32 000 000 hits from a search using: https://www.google.com/search?&q=max+speed+timing+belt

A quick look shows you might find these useful starting points in your search.
http://www.roymech.co.uk/Useful_Tables/Drive/Timing_belts.html

Some sites indicate maximum belt speeds around 25 to 50 m/s, and pully rotational speed limits based on pulley construction.

## 1. What is the natural frequency of a timing belt?

The natural frequency of a timing belt refers to the frequency at which the belt naturally vibrates when it is not being driven or influenced by external forces. It is usually measured in Hertz (Hz) and is dependent on the belt's material properties, length, and tension.

## 2. How do you calculate the natural frequency of a timing belt?

The natural frequency of a timing belt can be calculated using the formula: f = 1/2π√(T/m), where f is the natural frequency in Hz, T is the tension in Newtons, and m is the mass per unit length of the belt in kg/m.

## 3. What factors can affect the natural frequency of a timing belt?

The natural frequency of a timing belt can be affected by various factors such as the belt's material properties (such as density and stiffness), length, tension, and the presence of any external forces or vibrations.

## 4. Why is it important to know the natural frequency of a timing belt?

Knowing the natural frequency of a timing belt is important because it can help determine the belt's potential for resonance, which can cause excessive vibration and wear. It can also aid in selecting the appropriate belt material and tension for specific applications.

## 5. Are there any safety precautions to consider when calculating the natural frequency of a timing belt?

Yes, it is important to follow proper safety precautions when handling timing belts, such as wearing protective gear and ensuring the belt is properly tensioned. It is also recommended to consult a professional or refer to manufacturer guidelines for accurate calculations and proper belt installation.

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