How to Calculate and Solve for Mass of Cylindrical Shaft | Material Selection

The image above represents mass of cylindrical shaft.

To compute for mass of cylindrical shaft, five essential parameters are needed and these parameters are Factor of Safety (N), Twisting Moment (M), Length of Shaft (L), Density (ρ) and Shear Stress at Fracture (τf).

The formula for calculating mass of cylindrical shaft:

m = (2NM)2/31/3L)(ρ/τf2/3)

Where:

m = Mass of Cylindrical Shaft
N = Factor of Safety
M = Twisting Moment
L = Length of Shaft
ρ = Density
τf = Shear Stress at Fracture

Let’s solve an example;
Find the mass of cylindrical shaft when the factor of safety is 4, the twisting moment is 2, the length of shaft is 7, the density is 6 and the shear stress at fracture is 10.

This implies that;

N = Factor of Safety = 4
M = Twisting Moment = 2
L = Length of Shaft = 7
ρ = Density = 6
τf = Shear Stress at Fracture = 10

m = (2NM)2/31/3L)(ρ/τf2/3)
m = (2(4)(2))2/3 (π1/3(7)) (6/102/3)
m = (16)2/3 ((1.46)(7)) (6/4.64)
m = (6.349) (10.25) (1.29)
m = 84.14

Therefore, the mass of cylindrical shaft is 84.14 kg.

Continue reading How to Calculate and Solve for Mass of Cylindrical Shaft | Material Selection

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

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 D4 / 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 D4 / L x 32
T = 10 x 4 x π x 24 / 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