Spring constants from the physical dimensions of a spring

In summary, the conversation discusses the calculation of the spring constant (k) for coil springs based on their physical dimensions. The speaker shares their own experience of using a coil spring and observing its oscillation period to estimate the spring constant to be around 65. They also mention the relevant dimensions of the spring and share a resource, the Handbook of Spring Design from the Spring Manufacturers Institute, which provides comprehensive information on spring design. Additionally, they suggest using an online calculator specifically designed for calculating spring stiffness. The conversation also touches upon the type of alloy typically used for coil springs.
  • #1
Alen_Esterling
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I’d like to know if anyone has formulas for calculating the spring constant (k) of coil springs, from their physical dimensions. I bought a coil spring, suspended a 0.6 kg mass to it, observed its oscillation period at very close to 0.6 seconds, and so believed the spring constant “k” to be about 65. The spring has a 19mm coil diameter, 22 active coils, the wire is 1mm diameter. Not sure of the shear modulus, but I believe it’s just spring steel. Can’t seem to find a formula that comes out even close to agreement, or even a place that tells the units of measure for their formulas.
 
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  • #2
Everything you want to know about spring design, and more, is in the Handbook of Spring Design from the Spring Manufacturers Institute: https://smihq.org/store/ListProducts.aspx?catid=550000&ftr=. It has a hundred pages of spring goodness. Here is an online calculator that should do the job for you: https://www.acxesspring.com/spring-stiffness-calculator.html.

Your spring alloy is most likely music wire.
 
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1. What is a spring constant?

A spring constant, also known as a force constant, is a measure of the stiffness of a spring. It represents the amount of force required to stretch or compress a spring by a certain distance.

2. How is the spring constant calculated?

The spring constant can be calculated by dividing the applied force by the resulting displacement of the spring. It can also be determined by dividing the elastic potential energy stored in the spring by the amount of stretch or compression.

3. What are the units of spring constant?

The units of spring constant depend on the units used for force and displacement. In the SI system, the units are newtons per meter (N/m). In the imperial system, the units are pounds per inch (lb/in).

4. How do the physical dimensions of a spring affect its spring constant?

The spring constant is directly proportional to the cross-sectional area and inversely proportional to the length of the spring. This means that a thicker and shorter spring will have a higher spring constant than a thinner and longer spring.

5. Can the spring constant change?

Yes, the spring constant can change if the physical dimensions of the spring are altered. For example, if a spring is stretched or compressed beyond its elastic limit, its spring constant may change. Additionally, the material of the spring can also affect its spring constant.

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