concept of centrifugal tensionexplain concept of

Question

Concept of centrifugal tension:

Explain concept of centrifugal tension in any belt drive. What is main consideration for taking maximum tension?

Sol: The belt continuously runs over both the pulleys. In tight side and slack side of belt tension is increased because of presence of centrifugal Tension in belt. At lower speeds centrifugal tension can be ignored but at the higher speed its effect is considered.

The tension caused in the running belt by the centrifugal force is known as centrifugal tension. Whenever particle of mass 'm' is rotated in circular path of radius 'r' at uniform velocity 'v', a centrifugal force is acting outward radially and its magnitude is equal to mv²/r

i.e.,        F_c = mv²/r

The centrifugal tension in belt can be computed by considering forces acting on an elemental length of the belt(that is length MN) subtending an angle dq at the center as shown in the given figure

Let

v = Velocity of belt in m/s

r = Radius of pulley over which belt run. M = Mass of elemental length of belt.

m = Mass of belt per meter length

T₁ = Tight side tension

T_c = Centrifugal tension acting at points M and N tangentially

F_c = Centrifugal force acting radially outwards

The centrifugal force R which is acting radially outwards is balanced by components of Tc acting radially inwards. The elemental length of belt is

MN = r. δθ

Mass of belt MN = Mass per meter length X Length of MN M = m X r X δθ

Centrifugal force = F_c  = M X v²/r = m.r.δθ.v²/r

Now by resolving force horizontally, we get

T_c.sinδθ/2  + T_c.sinδθ/2 = F_c

Or       2T_c.sinδθ/2 = m.r.δθ.v²/r

At the angle δθ is very small, thus = sinδθ/2 = δθ/2

Then above equation becomes as

2T_c.δθ/2 = m.r.δθ.v²/r or  

T_c= m.v²