Keys and Coupling
• Many Types of Keys and couplings, however
understand how Torque is transferred in
between each, and forms shearing stresses
Shaft Coupling
• Sometimes, join 2 shafts together
• Flanged couplings
• Torque in Shaft  Torque in Couplings  Shear in
bolts
• Similarly keys
Bolt circle
Flanged Couplings
Bolt
Shaft
Design of Shaft
Torque applied, TA = ∏ τ d3 / 16
» Where,
τ = shear stress in shaft
d = shaft dia.
Design of bolts
Torque resisted,
TR = Shear Stress Area x Radius of bolt circle
TR = n . (∏/4) . db2 . τ b . (D/2)
Where, τ b = shear stress in bolt
db = bolt dia.
D = Diameter of bolt circle
n = number of bolts
TA < TR
Design of Shaft
Torque applied, TA = ∏ τ d3 / 16
» Where,
τ = shear stress in shaft
d = shaft dia.
Design of keys
Torque resisted,
Tk = Shear Stress Area .x Radius of shaft
Tk = l b τ k (D/2)
Where, τ k = shear stress in key
db = bolt dia.
D = Diameter of bolt circle
n = number of bolts
TA < Tk
Springs and Stiffness
Stiffness of spring
Load required to produce a unit deflection in spring.
K = F/x
x=unit deflection
Under gravity,
W=F
Springs
Types of spring
1. Bending / leaf / laminated spring
2. Torsion / helical spring
1.
Close Coil helical spring
2.
Open Coil helical spring
Springs
Uses of Springs
1. Storing energy, used in watch
2. Shock absorbers
3. Seismic isolation
4. Spring balance
5. Cycle seats
Closed Coiled helical springs subjected to axial loads
R = radius of the coil
d = Spring wire diameter
W= axial load on spring
N = number of coils/turns
δ = deflection
τ, θ, G,
Torque produced by axial load
T=WR
Also
T = ∏ τ d3/16
Thus,
∏ τ d3/16 = W R
Length of wire = no. of coils x length of one coil
Or,
l = n 2∏R
T = Gθ
J
l
θ = 64 WR2 n
Gd4
δ = R. θ = 64 WR3 n
Gd4
Stiffness, s = W =
Gd4
δ
64 R3 n
Energy Stored in a spring, U = (1/2) W δ
Combined Bending and Torsion
Find how Tanθ = 2 τ / f = T /M
Where
• T = Torsion,
• M = Bending Moment
• τ = Shear Stress
• M = Bending Stress
Tutorial- 2
1. Sketch 5 examples of use of springs
2. List differences between closed and open coil
springs. Provide one sketch minimum
3. Answer Q.1. from Rethalia’s exercise on
Helical Springs. pp. 72
4. Answer Q.1. to Q.7 from Rethalia’s example
exercise