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
N1​ = 50N2​ = 72

A driving gear with 50 teeth turns at 1000 rpm and meshes with a gear with 72 teeth. Find the speed n2 of the driven gear.

N1 = 50N2 = 72n1 = 1000 rpm
n2 = rpm
2.Easy
d1​ = 125 mmd2​ = 400 mm720 rpmn2​ = ?

A motor turning at 720 rpm drives a 125 mm pulley. A belt connects it to a 400 mm pulley. Assuming no slip, find the speed n2 of the driven pulley.

n1 = 720 rpmd1 = 125 mmd2 = 400 mm
n2 = rpm
3.Medium
N1​ = ?N2​

Two parallel shafts are 120 mm apart. They must be connected by a pair of spur gears with a module of 2 mm and a speed reduction of 4 : 1. How many teeth N1 must the pinion have?

a = 120 mmm = 2 mmi = 4
N1 =
4.Medium
N1​ = 15N2​ = 18

A 2.2 kW motor running at 1500 rpm drives a pinion with 15 teeth, which meshes with a gear with 18 teeth. The gear pair has an efficiency of 98%. Find the output torque T2 on the gear shaft.

P = 2.2 kWn1 = 1500 rpmN1 = 15N2 = 18η = 98%
T2 = N·m
5.Hard
A = 16B = 50C = 16D = 30

A 7.5 kW motor at 2900 rpm drives gear A (16 teeth), which meshes with gear B (50 teeth). Gear C (16 teeth) on the same shaft as B drives gear D (30 teeth) on the output shaft. Each gear mesh has an efficiency of 96%. Find the output torque Tout.

P = 7.5 kWnin = 2900 rpmA = 16B = 50C = 16D = 30ηmesh = 96%
Tout = N·m
6.Hard
A = 32B = 50C = 15D = 20

In a compound gear train, gear A (32 teeth) on the input shaft turning at 960 rpm drives gear B (50 teeth). Gear C (15 teeth) is fixed to the same shaft as B and drives gear D (20 teeth) on the output shaft. Find the output speed nout.

nin = 960 rpmA = 32B = 50C = 15D = 20
nout = rpm

Answer key

  1. 1. n2 = 694.4 rpm
  2. 2. n2 = 225 rpm
  3. 3. N1 = 24
  4. 4. T2 = 16.47 N·m
  5. 5. Tout = 133.4 N·m
  6. 6. nout = 460.8 rpm

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