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.

Drive-train/Transmission of vehicle

What is Drive train or Transmission line of a vehicle?
Ans.  The drive line of a car includes the flywheel, clutch, drive shaft, gear box, differential  and axle shaft along with necessary universal joints. Drive line transmits power from engine to wheel through all these parts.

      When drive line transmits power from engine to Front Wheel it is called Front Wheel Drive, when power delivers to Rear wheel it is called Rear Wheel drive and in some vehicle power is delivers to all the four wheel it is called All Wheel drive or Four Wheel Drive.
      
What is Drive train efficiency?
Ans. The power develop by the engine is delivers to wheel through drive line. But practically it is observed that the power available at wheel is less than that of power develop by the engine. There is loss of power in the drive line. The loss is mainly due to the inertia of all rotating part like flywheel, clutch, drive shaft, gears etc. Some amount of torque needed to rotate all these part and the loss is more  when no. of rotating parts and mass of the rotating part is more.