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​ = 80N2​ = 36

A driving gear with 80 teeth turns at 1200 rpm and meshes with a gear with 36 teeth. Find the speed n2 of the driven gear.

N1 = 80N2 = 36n1 = 1200 rpm
n2 = rpm
2.Easy
A = 25B = 50C = 36

Gear A (25 teeth) turns at 1440 rpm and drives an idler gear B (50 teeth), which in turn drives gear C (36 teeth). All three gears are on separate shafts. Find the speed nC of gear C.

NA = 25NB = 50NC = 36nA = 1440 rpm
nC = rpm
3.Medium
Tw​ = ?z = 3, 960 rpm

A 1.5 kW motor at 960 rpm drives a worm with 3 start(s). The worm wheel has 40 teeth and the drive has an efficiency of 75%. Find the output torque Tw on the wheel shaft.

z = 3Nw = 40n = 960 rpmP = 1.5 kWη = 75%
Tw = N·m
4.Medium
d1​ = 120 mmd2​ = 500 mm960 rpmT1​ = 1500 NT2​ = 600 NP = ?

A belt runs on a 120 mm driving pulley at 960 rpm. The tension is 1500 N on the tight side and 600 N on the slack side. Find the power P transmitted, in kW.

d1 = 120 mmn1 = 960 rpmT1 = 1500 NT2 = 600 N
P = kW
5.Hard
A = 30B = 50C = 16D = 48

In a compound gear train, gear A (30 teeth) on the input shaft turning at 3000 rpm drives gear B (50 teeth). Gear C (16 teeth) is fixed to the same shaft as B and drives gear D (48 teeth) on the output shaft. Find the output speed nout.

nin = 3000 rpmA = 30B = 50C = 16D = 48
nout = rpm
6.Hard
A = 15B = 48C = 20D = 24

In a compound gear train, gear A (15 teeth) on the input shaft turning at 1440 rpm drives gear B (48 teeth). Gear C (20 teeth) is fixed to the same shaft as B and drives gear D (24 teeth) on the output shaft. Find the output speed nout.

nin = 1440 rpmA = 15B = 48C = 20D = 24
nout = rpm

Answer key

  1. 1. n2 = 2667 rpm
  2. 2. nC = 1000 rpm
  3. 3. Tw = 149.2 N·m
  4. 4. P = 5.429 kW
  5. 5. nout = 600 rpm
  6. 6. nout = 375 rpm

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