# Torsion constant of a bent spring

• Piyush Hatwalne
In summary, the torsion constant (Kt) of a spring that is bent while being rotated along its axis will not change. This is because the variables involved in calculating Kt, such as linear stiffness (K) and distance from center of rotation (r), remain constant. The only exception would be if the bend deforms the spring to the point where it can no longer rotate freely, resulting in a lower torsional stress limit.
Piyush Hatwalne
How do I find torsion constant (Kt) of a spring which is bent, as shown in the image below

#### Attachments

• piyush1.jpg
9.1 KB · Views: 665
$$K_t= \frac{T}{\theta}= \frac{Fr}{\frac{x}{r}}= \frac{F}{x}r^2= Kr^2$$

Where $K$ is the linear stiffness of the spring and $r$ is the distance between the spring and the center of rotation.

Hello,
May be I wasn't clear in previous post. The spring is being rotated along its axis, while being kept in a curved position. In this case how will the torsion constant change ?

I'm going to let other chimes in, but I don't think it change anything for the torsional stiffness; Just like the bent doesn't change anything to linear stiffness (for example, the way I thought you were using the spring). The torsional stiffness is:

and none of these variables should change if the spring is bent. The exception would be if the bent deformed the spring so much that it doesn't allow the spring to freely rotate. For example, if the bent is so pronounced that it looks like 2 springs side by side joint by a wire, you will probably end up with 2 independent springs with half the active coils of the initial spring (i.e. twice the initial spring torsional stiffness).

However, because there is an initial deformation, the torsional stress limit that it can withstand will be lower.

## What is the torsion constant of a bent spring?

The torsion constant of a bent spring, also known as the spring constant or spring rate, is a measure of the stiffness of a spring. It is defined as the torque required to twist a spring by one unit of angle, usually expressed in units of newton-meters per radian (Nm/rad) or inch-pounds per degree (in-lb/deg).

## How is the torsion constant of a bent spring calculated?

The torsion constant of a bent spring can be calculated by dividing the applied torque by the angular deflection of the spring. It can also be calculated using the formula k = (Gd^4)/(32L), where k is the torsion constant, G is the shear modulus of the material, d is the diameter of the spring wire, and L is the length of the spring.

## What factors affect the torsion constant of a bent spring?

The torsion constant of a bent spring is affected by the material properties of the spring, such as its shear modulus and diameter, as well as its physical dimensions, such as its length and cross-sectional area. It can also be affected by external factors, such as temperature and stress.

## Why is the torsion constant of a bent spring important?

The torsion constant of a bent spring is important because it determines the amount of torque required to twist the spring by a certain angle, and thus affects the spring's ability to store and release energy. It is also used in the design and engineering of various mechanical systems and devices that utilize springs.

## How can the torsion constant of a bent spring be measured?

The torsion constant of a bent spring can be measured using a torsion balance or a torsion pendulum, which applies a known torque to the spring and measures its angular deflection. It can also be calculated using experimental data from a torsion test, where torque and deflection measurements are taken at different points along the spring's length.

• Mechanical Engineering
Replies
1
Views
670
• Mechanical Engineering
Replies
2
Views
1K
• Mechanical Engineering
Replies
4
Views
631
• Mechanical Engineering
Replies
3
Views
2K
• Mechanical Engineering
Replies
8
Views
3K
• Mechanical Engineering
Replies
4
Views
2K
• Mechanical Engineering
Replies
25
Views
7K
• Mechanical Engineering
Replies
2
Views
180
• Mechanical Engineering
Replies
1
Views
2K
• Mechanical Engineering
Replies
2
Views
2K