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 = 16, m = 4 mm

A gear with 16 teeth and a module of 4 mm turns at 1500 rpm. Find the pitch-line velocity v of its teeth.

N = 16m = 4 mmn = 1500 rpm
v = m/s
2.Easy
A = 25B = 45C = 15

Gear A (25 teeth) turns at 1440 rpm and drives an idler gear B (45 teeth), which in turn drives gear C (15 teeth). All three gears are on separate shafts. Find the speed nC of gear C.

NA = 25NB = 45NC = 15nA = 1440 rpm
nC = rpm
3.Medium
N1​ = 24N2​ = 72

An 11 kW motor running at 1450 rpm drives a pinion with 24 teeth, which meshes with a gear with 72 teeth. Ignore losses. Find the output torque T2 on the gear shaft.

P = 11 kWn1 = 1450 rpmN1 = 24N2 = 72η = 100%
T2 = N·m
4.Medium
N1​ = 15N2​ = 18

A 0.75 kW motor running at 1450 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 torque T1 on the motor shaft.

P = 0.75 kWn1 = 1450 rpmN1 = 15N2 = 18η = 98%
T1 = N·m
5.Hard
A = 50B = 80C = 15D = 40

In a compound gear train, gear A (50 teeth) on the input shaft turning at 3000 rpm drives gear B (80 teeth). Gear C (15 teeth) is fixed to the same shaft as B and drives gear D (40 teeth) on the output shaft. Find the output speed nout.

nin = 3000 rpmA = 50B = 80C = 15D = 40
nout = rpm
6.Hard
d1​ = 150 mmd2​ = 315 mm1500 rpmC = 800 mmT1​ = 1500 NT2​P = ?

An open belt connects a 150 mm driving pulley at 1500 rpm to a 315 mm pulley; the centres are 800 mm apart. The coefficient of friction is 0.3 and the tight-side tension may not exceed 1500 N. Find the largest power P the belt can transmit without slipping, in kW (ignore centrifugal effects).

d1 = 150 mmn1 = 1500 rpmd2 = 315 mmC = 800 mmμ = 0.3T1 = 1500 N
P = kW

Answer key

  1. 1. v = 5.027 m/s
  2. 2. nC = 2400 rpm
  3. 3. T2 = 217.3 N·m
  4. 4. T1 = 4.939 N·m
  5. 5. nout = 703.1 rpm
  6. 6. P = 10.35 kW

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