NUMBER OF BOLTS REQUIRED FOR A FLANGE COUPLING?

We were discussing shear stress produced in a circular shaft subjected to torsion, torque transmitted by circular solid shaft and derivation of torsional equation in our previous posts.

Today we will see here the basic concept of flanged coupling and the calculations of number of bolts for transmitting the desired torque from one shaft to other shaft.

So let us first understand here the basic concept of flanged coupling

Flanged coupling is usually used to connect two shafts via nuts and bolts or fasteners for transmitting the desired torque from one shaft to another shaft.

There will be two flanges in one flanged coupling, one flange hub will be connected with one shaft with key and second flange hub will be connected with second shaft with the help of key.

We will see the detailed information about the various types of flanged couplings in our another post, today we will be interested to find here the appropriate formula for calculation of number of bolts for transmitting the desired torque from one shaft to other shaft.

We must have to understand here that there will be shear stress acting over the bolts during the transmitting of torque between two shafts connected with flanged coupling.

Following figure, displayed here, indicates the flanged coupling connecting two shafts.

We have following information from above figure as mentioned here.

τ = Shear stress in the shaft

q = Shear stress in the bolt

d = Diameter of bolt

D = Diameter of the shaft

D₀ = Pitch circle diameter of the flange bolts

n = Number of bolts

Let us first determine the load resisted by one single bolt

Load resisted by one bolt = Shear stress x area of cross-section of one bolt

Load resisted by one bolt = q x (П/4) x d²

Now, we can determine here the torque resisted by one bolt and we have following equation as mentioned here

Torque resisted by one bolt = Load resisted by one bolt x pitch circle radius

Torque resisted by one bolt = [q x (П/4) x d²] x D₀/2

Torque resisted by n bolt = n x [q x (П/4) x d²] x D₀/2

Let us recall the concept of torque transmitted by a circular shaft and we will have following equation for torque transmitted by the shaft

T = (П/16) x τ x D³

Now as we know that Torque resisted by n bolts will be equal to the torque transmitted by the shaft and therefore we will have following equation to determine the number of bolts for transmitting the desired torque from one shaft to other shaft.

n x [q x (П/4) x d²] x D₀/2 = (П/16) x τ x D³

n x q x d² x D₀ = (1/2) x τ x D³

From above equation, we can secure the value of n i.e. number of bolts for transmitting the desired torque from one shaft to other shaft.

Do you have suggestions? Please write in comment box.

We will now discuss another topic, in the category of strength of material, in our next post.

Reference:

Strength of material, By R. K. Bansal

Image Courtesy: Google

Also read

Bending stress in beams
Shear stress distribution diagram 

Basic concept of shear force and bending moment

Strain energy stored in body 

Beam bending equation

Bending stress of composite beam