The image above represents shaft length.

To compute for shaft length, four essential parameters are needed and these parameters are **Applied Torque (T), Length of Shaft (L), Modulus of Rigidity (G)** and **Diameter of Shaft (D).**

The formula for calculating shaft length:

θ = ^{T x L x 32}/_{G x π x D4}

Where:

θ = Shaft Length

T = Applied Torque

L = Length of Shaft

G = Modulus of Rigidity

D = Diameter of Shaft

Let’s solve an example;

Find the shaft length when the applied torque is 8, the length of shaft is 12, the modulus of rigidity is 4 and the diameter of shaft is 10.

This implies that;

T = Applied Torque = 8

L = Length of Shaft = 12

G = Modulus of Rigidity = 4

D = Diameter of Shaft = 10

θ = ^{T x L x 32}/_{G x π x D4}

θ = ^{(8) x (12) x 32}/_{(4) x π x (10)4}

θ = ^{3072}/_{(4) x π x (10000)}

θ = ^{3072}/_{125663.7}

θ = 0.024

Therefore, the **shaft length **is **0.024 m.**

**Calculating the Applied Torque when the Shaft Length, the Length of Shaft, the Modulus of Rigidity and the Diameter of Shaft is Given.**

T = ^{θ x G x π x D}^{4} / _{L x 32}

Where;

T = Applied Torque

θ = Shaft Length

L = Length of Shaft

G = Modulus of Rigidity

D = Diameter of Shaft

Let’s solve an example;

Find the applied torque when the shaft length is 10, the length of shaft is 5, the modulus of rigidity is 4 and the diameter of shaft is 2.

This implies that;

θ = Shaft Length = 10

L = Length of Shaft = 5

G = Modulus of Rigidity = 4

D = Diameter of Shaft = 2

T = ^{θ x G x π x D}^{4} / _{L x 32}

T = ^{10 x 4 x π x 2}^{4} / _{5 x 32}

T = ^{40 x π x 16} / _{160}

T = ^{2010.6} / _{160}

T = 12.56

Therefore, the **applied torque **is **12.56 m.**

Continue reading How to Calculate and Solve for Shaft Length | Ball Mill Sizing