We know that the belt continuously runs over both the pulleys. In the tight side and slack side of the belt tension is increased due to presence of centrifugal Tension in the belt. At lower speeds the centrifugal tension may be ignored but at higher speed its effect is considered.
The tension caused in the running belt by the centrifugal force is known as centrifugal tension. When ever a particle of mass 'm' is rotated in a circular path of radius 'r' at a uniform velocity 'v', a centrifugal force is acting radially outward and its magnitude is equal to mv2/r.
i.e., Fc = mv2/r
The centrifugal tension in the belt can be calculated by considering the forces acting on an elemental length of the belt(i.e length MN) subtending an angle δθ at he center as shown in the fig,
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 the belt per meter length
T1 = Tight side tension Tc = Centrifugal tension acting at M and N tangentially
Fc = Centrifugal force acting radially outwards The centrifugal force R acting radially outwards is balanced by the components of Tc acting radially inwards. Now elemental length of belt.
MN = r. δθ
Mass of the belt MN = Mass per meter length X Length of MN
M = m X r X δθ
Centrifugal force = Fc = M X v2/r = m.r.δθ.v2/r
Now resolving the force horizontally, we get
Tc .sinδθ/2 + Tc .sinδθ/2 = Fc
Or 2Tc .sinδθ/2 = m.r.δθ.v2/r
At the angle δθ is very small, hence = sinδθ/2 = δθ/2
Then the above equation becomes as
2Tc .δθ/2 = m.r.δθ.v2/r
or Tc = m.v2
1. From the above equation, it is clear that centrifugal tension is independent of T1 and T2. It depends upon the velocity of the belt. For lower belt speed (i.e., Belt speed less than 10m/s) the centrifugal tension is very small and may be neglected.
2. When centrifugal tension is to be taken into consideration then total tension on tight side and slack side of the belt is given by For tight side = T1 + Tc For slack side = T2 + Tc
3. Maximum tension(Tm) in the belt is equal to maximum safe stress in the belt multiplied by cross sectional area of the belt.
Tm = σ (b.t)
σ = Maximum safe stress in the belt
b = Width of belt and
t = Thickness of belt
Tm = T1 + Tc ---- if centrifugal tension is to be considered
= T1 ------- if centrifugal tension is to be neglected