## Tuesday, 26 December 2017

### How does gear ratio affect Torque?

While moving into this topic, first of all we have to recall some topics. They are Gear ratio , Speed ratio, torque etc., Image Courtesy : Google

Gear ratio :
Gear ratio is found by "dividing the number of teeth in the output gear (gear being driven) by the number of teeth in the driving gear". In simple words, gear ratio defines the relationhip between the number of teeth of multiple gears.
Gear Ratio = Output gear #teeth/ Input Gear # teeth
Speed Ratio:
The ratio of gear train is defined as, "it is the ratio of the angular velocity of the driver (Input gear) to the angular velocity of driven gear (Output gear)", it is alo called speed ratio of gear train.
Gear ratio is directly proportional to the number of teeth of gear, so
Torque:
"Torque is the force that tends to turn or rotate objects about its axis or fulcrum or pivot".
"To calculate the torque, we just multiply the force by the perpendicular distance from an axis (Fulcrum or Pivot) to the line of action of force (moment arm)"
Torque = Force multiplied by Distance
τ = F X D
From the above eqation we can say that the torque acting on the gear wheel 1 is the multiplication value of force (F1) acting on gear wheel 1 and the distance of application of force (Teeth end of gear) D1.
When gear wheel 1 is rotating it transfer the force to gear wheel 2. so the force is same on both the gears F1 = F2.
F1 = τ1/D1 = F2
The torque in gear 2 is τ2  = F2 X D2.
τ2  = (τ1/D1) X D2           (since F2 =  τ1/D1 F1 )

Since D2 > D1
T2 > T1

Case 1: If Gear 1 and 2 will have same radii and same number of teeth then there will no gain in turning effect (Torque) nor speed. Image Courtesy : Google

Case 2: If Gear 1 has smaller radious and lesser number of teeth than Gear 2 then Gear 2 will gain Torque but looses number of rotation (rpm).
This is the principle used by cyclist by going up hill. When they go uphill they need to apply a turning effect in this case they change the bicycle chain from a gear having smaller radius to gear having having large radius with more number of teeth by this they loose speed but they gain torque, this will help them to go uphill.

By this we can say that Gear ratio will effect the Torque.