Calculation of gear-box

What is a gear box?

Ans. Gear box is a combination of shaft, gears, dog clutch, intermediate shaft, counter shaft, drive shaft etc. The main purpose of a gear box is to vary torque and range of speed requires at different conditions.
     

         Let 

                                N₁ = No of teeth of the driving gear.

                                N₂= No of teeth of the driven gear.

                                Gear ratio (R) =N2/N1

If P= Power develop by the engine

T= Toque produce by engine

ω = angular velocity.

P= T*ω

If N₁ < N₂

Power is constant for both the gear

T₁*ω ₁ =T₂*ω ₂  …………….(1)                                       ω=(2*pi*n)/60

                                                                                            n = rpm

Since N₁ < N₂

ω ₁> ω ₂

Therefore from eqn. (1)

T₁<T₂

T is directly proportional to N

R=(ω _1/ω _2)=(N2/N1)

But maximum speed of the vehicle doesn't depend upon the gear ratio of the drive line. It depends on the power of engine that can push the vehicle to overcome all the resistant.

Let a 10 hp engine vehicle have drive line efficiency 80%. Therefore power available at wheel is 8 hp.

Aero dynamic drag+ rolling resistant + gradient resistant= 8 hp ……………..(2)

Aerodynamic drag=.5*c* v³

Rolling drag= F_r*v

Gradient resistant= F_g*v

Where c = coefficient of drag.

v= velocity of the vehicle.

The velocity calculate from the eqn. (2) is the maximum velocity that the vehicle can push by the engine.