Calculating Torsion Spring Constant | 20 Turns, 6mm Mean Dia, ASTM A228 Material

In summary, the conversation is about calculating the spring constant of a torsion spring with given parameters such as turns, mean diameter, wire diameter, and material. The homework equation used is k=Ed^4/10.8DN and with the given values, the calculated spring constant is 2.556 Nm/revolution. The conversation also discusses the calculation of the force applied by the spring with a deflection of 1/4 revolution and a free arm length of 25mm, resulting in a force of 25.56N.
  • #1
evo_vil
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Homework Statement



I need to calculate the spring constant of a torsion spring.

Turns : 20
Mean Diameter : 6mm
Wire Diameter : 2mm
Material : ASTM A228
Arm Length : will be negligible, as they will be fixed
Orientation : Arms inline

Homework Equations



[itex]k=\frac{Ed^4}{10.8DN}[/itex]

The Attempt at a Solution



Subbing values in i get a spring constant of 1.944 Nm/revolution

Does this look correct to you?
Am i using the right equation?

If the one arm is fixed and the other is rotated (with arm length 25mm) 1/4 revolution does this result in 1.944/4*0.025 = 0.01215 N or 1.944/4/0.025 = 19.44 N at the end of the arm?
 
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  • #2
I'm not exactly sure what modulus you used but ASTM A228 is music wire so E≈207GPa. With that value the spring constant I found was:

[tex] \kappa = \frac{Ed^4}{10.8DN} = \frac{(207GPa)(2mm)^4}{10.8(6mm)(20)}=2.556Nm/rev [/tex]

As for your question, to calculate the force the spring will apply you need to multiply the spring constant by the deflection and then divide the resulting torque by the moment arm (arm length). Therefore if the spring is deflected a quarter turn and the free arm is 25mm long:

[tex] F=\frac{\kappa \delta}{L}=(2.556Nm/rev)*(0.25rev)/(0.025m)=25.56N [/tex]

Hope that helps.
 
  • #3
Yes that help alot... Thank you... I was being stupid at the end and not thinking about the units... Newton meters divided by meters provides Newtons... Duh... After redoing the number i get your value... Thanks

(sorry bout the formating, done on my phone)
 

1. What is a torsion spring constant?

A torsion spring constant, also known as spring rate or spring stiffness, is a measure of the amount of force required to twist or rotate a torsion spring by one unit of distance. It is a characteristic property of the spring and is typically measured in units of force per distance, such as newtons per meter (N/m) or pounds per inch (lb/in).

2. How is the torsion spring constant calculated?

The torsion spring constant is calculated by dividing the torque (rotational force) applied to the spring by the angular deflection (twist) of the spring. In mathematical terms, it can be expressed as K = T/θ, where K is the spring constant, T is the torque, and θ is the angular deflection.

3. What factors affect the torsion spring constant?

The torsion spring constant is affected by several factors, including the material and dimensions of the spring, the number of coils, and the type of winding used. The type of material used, such as steel or titanium, can greatly impact the stiffness of the spring. Additionally, a larger spring with more coils will typically have a higher spring constant compared to a smaller spring with fewer coils.

4. How does the torsion spring constant affect the performance of a spring?

The torsion spring constant is an important factor in determining the performance of a spring. A higher spring constant means that the spring will require more force to twist or rotate, making it stiffer and more resistant to deformation. On the other hand, a lower spring constant allows for more flexibility and a smoother response to applied forces. The appropriate torsion spring constant for a specific application will depend on the desired level of stiffness and flexibility.

5. Can the torsion spring constant be changed?

Yes, the torsion spring constant can be changed by altering the design or material of the spring. For example, increasing the wire diameter or number of coils can result in a higher spring constant, while using a different type of material can also impact the stiffness of the spring. It is important to carefully consider the desired characteristics and application of the spring when making changes to the torsion spring constant.

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