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

Flanged Couplings

Shaft

Bolt circle

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 circlen = 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 keysTorque 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 circlen = number of bolts

TA < Tk

.

Springs and Stiffness

Stiffness of springLoad required to produce a unit deflection in spring. K = F/xx=unit deflectionUnder gravity,W = F

SpringsTypes of spring1. Bending / leaf / laminated spring

2. Torsion / helical spring

1. Close Coil helical spring

2. Open Coil helical spring

SpringsUses of Springs1. Storing energy, used in watch2. Shock absorbers3. Seismic isolation4. Spring balance5. Cycle seats

Closed Coiled helical springs subjected to axial loads

R = radius of the coild = Spring wire diameterW= axial load on springN = number of coils/turnsδ = deflection τ, θ, G,

Torque produced by axial load

T = W R

Also T = ∏ τ d3/16

Thus, ∏ τ d3/16 = W R

Length of wire = no. of coils x length of one coilOr, l = n 2∏R

T = G θJ l θ = 64 WR2 n Gd4

δ = R. θ = 64 WR3 n Gd4

Stiffness, s = W = Gd4

δ 64 R3 nEnergy 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 springs2. List differences between closed and open coil

springs. Provide one sketch minimum3. Answer Q.1. from Rethalia’s exercise on

Helical Springs. pp. 724. Answer Q.1. to Q.7 from Rethalia’s example

exercise