Strength of Materials | Beam Stress Deflection
Mechanics and Machine Design, Equations and Calculators

Cylindrical Torsion spring with torque applied design equations and calculator

Symbols used:
D_o = Outside diamater of rubber bushing, (mm, in)
D_i = Inside diamater of rubber bushing, (mm, in)
P = Loading Force, (N, lbs)
L = Rubber thickness, (mm, in)
T = Torque ( N-mm, lb-in)
θ = Angle of Twist Radians
G = Shear modulus

Design equations:

Maximum Shear Stress τ_m = 2 T / π L D^2_i
Angle of Twist θ = T ( 1 / D²_i - 1 / D²_o ) / ( π L G )
where G = shear modulus.

Modulus and strength of rubber
G = 0.3 to 1.2MPa
E = 0.9 to 3.6 MPa
Allowable shear stress = 0.2 to 0.4 MPa
Deflection limited to 10% to 20% of free height.