Gears & gear trains worksheet with answers

Free printable Gears & gear trains worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
A = 24B = 30C = 60

Gear A (24 teeth) turns at 1500 rpm and drives an idler gear B (30 teeth), which in turn drives gear C (60 teeth). All three gears are on separate shafts. Find the speed nC of gear C.

NA = 24NB = 30NC = 60nA = 1500 rpm
nC = rpm
2.Easy
N1​ = 20N2​ = 45

A driving gear with 20 teeth turns at 1440 rpm and meshes with a gear with 45 teeth. Find the speed n2 of the driven gear.

N1 = 20N2 = 45n1 = 1440 rpm
n2 = rpm
3.Medium
N1​ = 16, m = 3 mm

A 2.2 kW motor running at 1440 rpm drives a pinion with 16 teeth and a module of 3 mm. Find the tangential force Ft on the pinion teeth.

P = 2.2 kWn = 1440 rpmN1 = 16m = 3 mm
Ft = N
4.Medium
N1​ = 20, m = 5 mm

A 4 kW motor running at 1450 rpm drives a pinion with 20 teeth and a module of 5 mm. Find the tangential force Ft on the pinion teeth.

P = 4 kWn = 1450 rpmN1 = 20m = 5 mm
Ft = N
5.Hard
A = 16B = 72C = 20D = 25

A 4 kW motor at 1440 rpm drives gear A (16 teeth), which meshes with gear B (72 teeth). Gear C (20 teeth) on the same shaft as B drives gear D (25 teeth) on the output shaft. Each gear mesh has an efficiency of 96%. Find the output torque Tout.

P = 4 kWnin = 1440 rpmA = 16B = 72C = 20D = 25ηmesh = 96%
Tout = N·m
6.Hard
A = 25B = 50C = 15D = ?

In a compound gear train, gear A (25 teeth) on the input shaft turns at 960 rpm and drives gear B (50 teeth). Gear C (15 teeth) is fixed to the same shaft as B and drives gear D on the output shaft. The output must turn at 450 rpm. How many teeth ND must gear D have?

nin = 960 rpmA = 25B = 50C = 15nout = 450 rpm
ND =

Answer key

  1. 1. nC = 600 rpm
  2. 2. n2 = 640 rpm
  3. 3. Ft = 607.9 N
  4. 4. Ft = 526.9 N
  5. 5. Tout = 137.5 N·m
  6. 6. ND = 16

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