# Torsion Spring

Written by Jerry Ratzlaff on . Posted in Fastener

### Tortion springs are helical springs that store mechanical energy to exert a torque or rotary force.  Compression springs and extension springs work with pulling and pushing forces, but tortion springs work with twisting forces.  After being twisted a porportional force to the applied force is exerted in the opposite direction.

The ends of the spring are attached to other components and rotated around the spring center as the spring pushes back to its origional position.

### Torsion Spring Bending Stress formula

$$\large{ S_b = \frac{ 32 \; \tau }{ \pi \; d^3 } }$$

Where:

$$\large{ S_b }$$ = bending stress

$$\large{ \pi }$$ = Pi

$$\large{ G }$$ = shear modulus of material

$$\large{ \tau }$$  (Greek symbol tau) = torque

$$\large{ d }$$ = wire diameter

### Torsion Spring Force formula

$$\large{ F = \tau \; M }$$

Where:

$$\large{ F }$$ = force

$$\large{ M }$$ = moment arm

$$\large{ \tau }$$  (Greek symbol tau) = torque

### Torsion Spring Mean Coil Diameter formula

$$\large{ D = ID + d }$$

Where:

$$\large{ D }$$ = mean coil diameter

$$\large{ ID }$$ = inside diameter

$$\large{ d }$$ = wire diameter

### Torsion Spring Number of Active coils formula

$$\large{ n_a = n_t + \frac{ L_l }{ 3 \; \pi \; d } }$$

Where:

$$\large{ n_a }$$ = number of active coils

$$\large{ L_l }$$ = leg length

$$\large{ n_t }$$ = number of total coils

$$\large{ \pi }$$ = Pi

$$\large{ d }$$ = wire size

### Torsion Spring Rate formula

$$\large{ n_s = \frac{ \lambda \; d^4 }{ 10.8 \; n_a \; D } }$$

Where:

$$\large{ n_s }$$ = spring rate

$$\large{ \lambda }$$  (Greek symbol lambda) = elastic modulus

$$\large{ D }$$ = mean coil diameter

$$\large{ n_a }$$ = number of active coils

$$\large{ d }$$ = wire diameter

### Torsion Spring Torque formula

$$\large{ \tau = n_s \; N }$$

Where:

$$\large{ \tau }$$  (Greek symbol tau) = torque

$$\large{ N }$$ = number of turns or revolutions

$$\large{ n_s }$$ = spring rate

Tags: Equations for Spring