A gearbox is a mechanical device that is used to provide speed and torque conversions from a rotating power source to output shaft.

  • It is works on principle of meshing of teeth which result in the transmission of motion and power from input shaft to output shaft.
  • Gearbox is widely used in automobile, machine tools like lathe machine, drill press, turbines and also in material handling equipment and in earth moving equipment.
  • The process of gearbox design is very vast and critical area and difficult to mesh the gears. In machine tool application, variety of speed is must required because of cutting parameters mainly cutting speed ,feed and depends upon work piece material and also surface finish.

In multi speed gearbox,

Fixed single input speed, the output speed obtained in between Nmax & Nmin.

To select discrete steps of speed between two extreme value of speed, three laws are proposed.

  1. Arithmetic progression
  2. Geometric progression
  3. Harmonic progression

Here, the Geometric progression method is commonly used in machine tool drives due to

  • Constant loss of economic cutting speed,
  • Better gearbox design features

This Example is based on a developed gearbox for a machine tool having speed Variation from 100 rpm to 1120 rpm in 8 steps by the use of 12 gears and 4 shafts.

Design procedure

  • Power transmitted:-15kw
  • maximum speed:-1120 rpm
  • minimum speed:-110 rpm

Initial specification of gearbox

Calculation of geometric progression ratio

= 1.41

From design data-book Ø = 1.41 (R10 series) we get 12

standard speeds as under :


N2=N1* ϕ1=100*(1.41)1=141≈140 rpm

N3=N22=100*(1.41)2=198.81 ≈200 rpm

Likewise we found speed variation as under

N4= 280 rpm

N5=400 rpm

N6=560 rpm

N7=800 rpm


Structural formula

Z=P1(x1)*P2(X2)*P3(X3) Z= 2(1)*2(2)*2(4)

P1,P2,P3 represent the no. of transmission

X1 represent main transmission group (always 1) X2 represent 2nd transmission group =P1= 2

X3 represent 3rd transmission group=P1*P2= 4

from the structural formula,

-between shaft 1 & 2 there is one group with two transmission,

– between shaft 2 & 3 there is two group with two transmission each,

– between shaft 3 & 4 there is four group with two transmission each,

Transmission range between shaft 1 & 2

= ø1

  Transmission range between shaft 2 & 3

= ø2

Transmission range between shaft 3 & 4

= ø4

Structural Diagram


Here the power is Supplied to the input shaft by an electric motor, running at 1000 rpm, through a belt drive having a speed reduction of 1.6:1.

so speed of input shaft= 1000/1.6 =625 rpm.

Determination of number of teeth on gears

The transmission I1,I2 ,I3 ,I4 ,I5 ,I6 and I7 are indicated by rays.

Speed Chart

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1 Comment

  • Itís difficult to find educated people in this particular topic, however, you seem like you know what youíre talking about! Thanks

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