(^688) A Textbook of Engineering Mechanics
33.17.CONDITION FOR TRANSMISSION OF MAXIMUM POWER
We have already discussed in Art. 33·13 that the power transmitted by a belt,
P=(T 1 – T 2 ) v ...(i)
where T 1 = Tension on the tight side,
T 2 = Tension on the slack side, and
v= Velocity of the belt.
We have also discussed in Art. 33·14 the ratio of tensions,
1
2
T
T =e
μθ or 1
2
T
T
eμθ
= ...(ii)
Substituting the value of T 2 in equation (i),
P=
1
11
1
–1–
T
TvT v
eeμθ μθ
⎛⎞×=⎛⎞×
⎜⎟⎜⎟
⎝⎠⎝⎠
= T 1 × v × C ...(iii)
where C=
1
1–
eμθ
⎛⎞
⎜⎟
⎝⎠
We know that tension in the tight side,
T 1 =T – TC
where T= Maximum tension in the belt in newtons, and
TC= Centrifugal tension in newtons.
Substituting the value of T 1 in equation (iii),
P=(T – TC) v C = (T – mv^2 ) v C = (Tv – mv^2 ) C
We know that for maximum power, differentiating the above equation and equating the same
to zero,
T – 3 mv^2 = 0 ...(iv)
T – 3TC= 0 ...(Substituting mv^2 = TC)
or T=3TC
It shows that when the power transmitted is maximum^1 rd
3
of the maximum tension is
absorbed as centrifugal tension.
33.18.BELT SPEED FOR MAXIMUM POWER
We have already discussed in Art. 33·17 that for maximum power transmission
T – 3 mv^2 =0
or 3 mv^2 =T
∴ v=
3
T
m
where v= Speed of the belt for maximum transmission of power,
T=*Maximum tension in the belt, and
m= Mass of the belt for unit length.
Note: The power transmitted when 1/3 of the maximum tension is absorbed as centrifugal
tension (condition of last article) at belt speed for maximum power (condition of the above article) is
known as absolute maximum power or in other words, maximum power which can be transmitted
under any conditions.
- Maximum tension in the belt is equal to sum of tensions in tight side (T 1 ) and centrifugal tension (TC).