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​ = 30N2​ = 20

A driving gear with 30 teeth turns at 1200 rpm and meshes with a gear with 20 teeth. Find the speed n2 of the driven gear.

N1 = 30N2 = 20n1 = 1200 rpm
n2 = rpm
2.Easy
N1​ = 30N2​ = 12

A driving gear with 30 teeth turns at 1800 rpm and meshes with a gear with 12 teeth. Find the speed n2 of the driven gear.

N1 = 30N2 = 12n1 = 1800 rpm
n2 = rpm
3.Medium
d1​ = 120 mmd2​ = 315 mm1450 rpmT1​ = 600 NT2​ = 300 NP = ?

A belt runs on a 120 mm driving pulley at 1450 rpm. The tension is 600 N on the tight side and 300 N on the slack side. Find the power P transmitted, in kW.

d1 = 120 mmn1 = 1450 rpmT1 = 600 NT2 = 300 N
P = kW
4.Medium
N1​ = 40N2​ = 48

A 1.1 kW motor running at 1440 rpm drives a pinion with 40 teeth, which meshes with a gear with 48 teeth. The gear pair has an efficiency of 96%. Find the output torque T2 on the gear shaft.

P = 1.1 kWn1 = 1440 rpmN1 = 40N2 = 48η = 96%
T2 = N·m
5.Hard
Ns​ = 20ring fixedNp​ = 18nc​ = ?

In a planetary gear set the sun gear has 20 teeth and each planet gear has 18 teeth. The ring gear is held fixed and the sun is driven at 1800 rpm. Find the speed nc of the planet carrier.

Ns = 20Np = 18ns = 1800 rpm
nc = rpm
6.Hard
A = 15B = 16C = 12D = 18

A 15 kW motor at 2900 rpm drives gear A (15 teeth), which meshes with gear B (16 teeth). Gear C (12 teeth) on the same shaft as B drives gear D (18 teeth) on the output shaft. Each gear mesh has an efficiency of 97%. Find the output torque Tout.

P = 15 kWnin = 2900 rpmA = 15B = 16C = 12D = 18ηmesh = 97%
Tout = N·m

Answer key

  1. 1. n2 = 1800 rpm
  2. 2. n2 = 4500 rpm
  3. 3. P = 2.733 kW
  4. 4. T2 = 8.403 N·m
  5. 5. nc = 473.7 rpm
  6. 6. Tout = 74.36 N·m

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