# How to calculate energy density of mainspring?

• lightspd
In summary, the person is looking for help in calculating the energy density of a main-spring or motor-spring, specifically for materials like steel. They have found some material properties online and are interested in experimenting with different materials, but are unsure of how to measure the properties and incorporate them into the energy density formula. They are also seeking recommendations for resources on this subject.
lightspd
Hi,

How do I calculate the energy density of either a main-spring (like in a clock) or a motor-spring?
Can someone show me values put into the correct formula for something like steel?

I did find some material properties like this: http://www.engineeringtoolbox.com/young-modulus-d_417.html

The motor-spring I am interested in is a type like this: http://www.sdp-si.com/Gateway/D220-T183.htm

Secondly, I would like to experiment with various materials (composites especially). If I make a plank of this material, how can I measure its properties to be able to put it into the correct formula for energy density of such a spring (if made into a spring)? I would have to take into account the breaking-point of the material of course (i.e. I bend the plank and at some point it either snaps or buckles).

I did study mech. engineering for a coupple of years but it is 20 years ago and I am rusty ;-)
I have googled and read a lot but am still stuck. Most stuff only relates to compression-springs but I need to work out spring constant of basically a beam (?) and not sure of to work out the breaking point (of the clockspring) when I know that a certain material will snap when it is deflected a certain amount.

Thanks a lot.

Regards

A concrete example I would very much like to see is something like this:

Take an acrylic ruler. it is 30 cm long, 3 cm wide and 2mm thick. It weighs 20grams (just estimated for this example).
Acrylic has Youngs Modulus of 3.2 GPa and ultimate Tensile Strength of 70 Mpa (according to the page I posted ealier).

If I took this material and used 500cm of it and turned it into a mainspring (or motor-spring), then:

a) What is the energy density of the spring?

b) If I didn't have Youngs Modulus and Ultimate Tensile Strength, how could I work these out (and any other values that I might need)?Thanks and regards

Bump!

Sorry I have cross-posted this in the coursework forum, many reads but no answers :-(
Is no one able to help me with this?
When I google, I only find articles related to compression springs. Why is it so difficult to find stuff on main-springs?

Can someone recommend a good book on the subject? Not interrested at all in compression-springs, only main-springs and tensator springs and the like.

Thanks.

## 1. How do you calculate the energy density of a mainspring?

The energy density of a mainspring can be calculated by dividing the total energy stored in the spring by its volume. This can be represented by the equation: Energy density = Energy stored/Volume.

## 2. What is the formula for calculating the energy stored in a mainspring?

The formula for calculating the energy stored in a mainspring is: Energy = 1/2 x Spring constant x (Spring extension)^2. The spring constant can be determined experimentally or by consulting the manufacturer's specifications.

## 3. Can the energy density of a mainspring be increased?

Yes, the energy density of a mainspring can be increased by either increasing the spring constant or increasing the spring extension. However, increasing the spring extension beyond its elastic limit can result in permanent deformation of the spring.

## 4. What units are used to measure energy density?

The energy density of a mainspring is typically measured in Joules per cubic meter (J/m3). However, other units such as kJ/cm3 or N/m can also be used.

## 5. How does the energy density of a mainspring affect its performance?

The higher the energy density of a mainspring, the more energy it can store and release. This can result in a more powerful and efficient performance, as the spring can deliver more energy with each oscillation.

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