Derive the relationship between mechanical advantage, velocity ratio and effeciency of a machine. Name the term which will not change for a machine of a given design?
Derive the relationship between mechanical advantage, velocity ratio and effeciency of a machine. Name the term which will not change for a machine of a given design?
The said relations will be given in context of the gear.
Let us consider two cogwheels of radius r1 and r2 are transmitting power P. Let Ï„ 1 and Ï„ 2 be the torque of the driver wheel and driven wheel.
By conservation of energy
P = τ1ω1 = τ 2ω2
Ï„ 2/ Ï„ 1 = M.A.
Thus M.A. = τ 2/ τ 1 = ω1/ω2
ω2/ω1 = velocity ratio (V.R)
So M.A = 1/V.R.
Efficiency = output work / input work
= τ 2ω2/ τ1ω1
Now if no energy is lost then Efficiency = 1.
For practical gears the efficiency is lesser than but close to 1.
Detail relationship of practical gear efficiency expression is difficult and involves property of the material that makes the gear. So it is beyond the scope of your standard.
In gear of given design gear ratio, mechanical advantage and velocity ratio remains same.
The said relations will be given in context of the gear.
Let us consider two cogwheels of radius r1 and r2 are transmitting power P. Let Ï„ 1 and Ï„ 2 be the torque of the driver wheel and driven wheel.
By conservation of energy
P = τ1ω1 = τ 2ω2
Ï„ 2/ Ï„ 1 = M.A.
Thus M.A. = τ 2/ τ 1 = ω1/ω2
ω2/ω1 = velocity ratio (V.R)
So M.A = 1/V.R.
Efficiency = output work / input work
= τ 2ω2/ τ1ω1
Now if no energy is lost then Efficiency = 1.
For practical gears the efficiency is lesser than but close to 1.
Detail relationship of practical gear efficiency expression is difficult and involves property of the material that makes the gear. So it is beyond the scope of your standard.
In gear of given design gear ratio, mechanical advantage and velocity ratio remains same.
