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
N = 45, m = 2.5 mm

A gear with 45 teeth and a module of 2.5 mm turns at 2900 rpm. Find the pitch-line velocity v of its teeth.

N = 45m = 2.5 mmn = 2900 rpm
v = m/s
2.Easy
N1​ = 18N2​ = ?

A pinion with 18 teeth is driven at 1440 rpm. The driven gear must turn at 1080 rpm. How many teeth N2 must the driven gear have?

N1 = 18n1 = 1440 rpmn2 = 1080 rpm
N2 =
3.Medium
N1​ = 20N2​ = 48

A 2.2 kW motor running at 1440 rpm drives a pinion with 20 teeth, which meshes with a gear with 48 teeth. The gear pair has an efficiency of 95%. Find the output torque T2 on the gear shaft.

P = 2.2 kWn1 = 1440 rpmN1 = 20N2 = 48η = 95%
T2 = N·m
4.Medium
N1​ = 16N2​ = 60

A 1.5 kW motor running at 1500 rpm drives a pinion with 16 teeth, which meshes with a gear with 60 teeth. The gear pair has an efficiency of 96%. Find the torque T1 on the motor shaft.

P = 1.5 kWn1 = 1500 rpmN1 = 16N2 = 60η = 96%
T1 = N·m
5.Hard
d1​ = 200 mmd2​ = 450 mm1450 rpmC = 600 mmT1​ = 600 NT2​P = ?

An open belt connects a 200 mm driving pulley at 1450 rpm to a 450 mm pulley; the centres are 600 mm apart. The coefficient of friction is 0.3 and the tight-side tension may not exceed 600 N. Find the largest power P the belt can transmit without slipping, in kW (ignore centrifugal effects).

d1 = 200 mmn1 = 1450 rpmd2 = 450 mmC = 600 mmμ = 0.3T1 = 600 N
P = kW
6.Hard
A = 12B = 40C = 18D = 20

A 1.1 kW motor at 960 rpm drives gear A (12 teeth), which meshes with gear B (40 teeth). Gear C (18 teeth) on the same shaft as B drives gear D (20 teeth) on the output shaft. Each gear mesh has an efficiency of 95%. Find the output torque Tout.

P = 1.1 kWnin = 960 rpmA = 12B = 40C = 18D = 20ηmesh = 95%
Tout = N·m

Answer key

  1. 1. v = 17.08 m/s
  2. 2. N2 = 24
  3. 3. T2 = 33.26 N·m
  4. 4. T1 = 9.549 N·m
  5. 5. P = 5.084 kW
  6. 6. Tout = 36.57 N·m

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