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​ = 12N2​ = 48

A driving gear with 12 teeth turns at 720 rpm and meshes with a gear with 48 teeth. Find the speed n2 of the driven gear.

N1 = 12N2 = 48n1 = 720 rpm
n2 = rpm
2.Easy
N = 60, m = 4 mm

A gear with 60 teeth and a module of 4 mm turns at 960 rpm. Find the pitch-line velocity v of its teeth.

N = 60m = 4 mmn = 960 rpm
v = m/s
3.Medium
N1​ = 50N2​ = 80

A 15 kW motor running at 2900 rpm drives a pinion with 50 teeth, which meshes with a gear with 80 teeth. The gear pair has an efficiency of 98%. Find the torque T1 on the motor shaft.

P = 15 kWn1 = 2900 rpmN1 = 50N2 = 80η = 98%
T1 = N·m
4.Medium
N1​ = 16, m = 4 mm

A 5.5 kW motor running at 2900 rpm drives a pinion with 16 teeth and a module of 4 mm. Find the tangential force Ft on the pinion teeth.

P = 5.5 kWn = 2900 rpmN1 = 16m = 4 mm
Ft = N
5.Hard
A = 40B = 50C = 25D = 45

In a compound gear train, gear A (40 teeth) on the input shaft turning at 1440 rpm drives gear B (50 teeth). Gear C (25 teeth) is fixed to the same shaft as B and drives gear D (45 teeth) on the output shaft. Find the output speed nout.

nin = 1440 rpmA = 40B = 50C = 25D = 45
nout = rpm
6.Hard
A = 20B = 36C = 18D = ?

In a compound gear train, gear A (20 teeth) on the input shaft turns at 2880 rpm and drives gear B (36 teeth). Gear C (18 teeth) is fixed to the same shaft as B and drives gear D on the output shaft. The output must turn at 1200 rpm. How many teeth ND must gear D have?

nin = 2880 rpmA = 20B = 36C = 18nout = 1200 rpm
ND =

Answer key

  1. 1. n2 = 180 rpm
  2. 2. v = 12.06 m/s
  3. 3. T1 = 49.39 N·m
  4. 4. Ft = 566 N
  5. 5. nout = 640 rpm
  6. 6. ND = 24

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