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​ = 45N2​ = 40

A driving gear with 45 teeth turns at 900 rpm and meshes with a gear with 40 teeth. Find the speed n2 of the driven gear.

N1 = 45N2 = 40n1 = 900 rpm
n2 = rpm
2.Easy
d1​ = 100 mmd2​ = 450 mm1450 rpmn2​ = ?

A motor turning at 1450 rpm drives a 100 mm pulley. A belt connects it to a 450 mm pulley. Assuming no slip, find the speed n2 of the driven pulley.

n1 = 1450 rpmd1 = 100 mmd2 = 450 mm
n2 = rpm
3.Medium
N1​ = 32N2​ = 45

An 11 kW motor running at 1440 rpm drives a pinion with 32 teeth, which meshes with a gear with 45 teeth. The gear pair has an efficiency of 98%. Find the output torque T2 on the gear shaft.

P = 11 kWn1 = 1440 rpmN1 = 32N2 = 45η = 98%
T2 = N·m
4.Medium
Tw​ = ?z = 1, 2900 rpm

A 1.5 kW motor at 2900 rpm drives a worm with 1 start(s). The worm wheel has 45 teeth and the drive has an efficiency of 70%. Find the output torque Tw on the wheel shaft.

z = 1Nw = 45n = 2900 rpmP = 1.5 kWη = 70%
Tw = N·m
5.Hard
d1​ = 80 mmd2​ = 315 mm2880 rpmC = 600 mmT1​ = 600 NT2​P = ?

An open belt connects an 80 mm driving pulley at 2880 rpm to a 315 mm pulley; the centres are 600 mm apart. The coefficient of friction is 0.25 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 = 80 mmn1 = 2880 rpmd2 = 315 mmC = 600 mmμ = 0.25T1 = 600 N
P = kW
6.Hard
d1​ = 80 mmd2​ = 450 mm1450 rpmC = 800 mmθ = ?

An open belt connects an 80 mm pulley and a 450 mm pulley whose centres are 800 mm apart. Find the angle of wrap θ on the smaller pulley, in degrees.

d1 = 80 mmd2 = 450 mmC = 800 mm
θ = °

Answer key

  1. 1. n2 = 1013 rpm
  2. 2. n2 = 322.2 rpm
  3. 3. T2 = 100.5 N·m
  4. 4. Tw = 155.6 N·m
  5. 5. P = 3.596 kW
  6. 6. θ = 153.3 °

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