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​ = 48N2​ = 60

A driving gear with 48 teeth turns at 720 rpm and meshes with a gear with 60 teeth. Find the speed n2 of the driven gear.

N1 = 48N2 = 60n1 = 720 rpm
n2 = rpm
2.Easy
N1​ = 60N2​ = ?

A pinion with 60 teeth is driven at 1200 rpm. The driven gear must turn at 6000 rpm. How many teeth N2 must the driven gear have?

N1 = 60n1 = 1200 rpmn2 = 6000 rpm
N2 =
3.Medium
N1​ = 20N2​ = 60

A 0.75 kW motor running at 1440 rpm drives a pinion with 20 teeth, which meshes with a gear with 60 teeth. Ignore losses. Find the torque T1 on the motor shaft.

P = 0.75 kWn1 = 1440 rpmN1 = 20N2 = 60η = 100%
T1 = N·m
4.Medium
N1​ = 18N2​ = 40

A 7.5 kW motor running at 960 rpm drives a pinion with 18 teeth, which meshes with a gear with 40 teeth. The gear pair has an efficiency of 95%. Find the torque T1 on the motor shaft.

P = 7.5 kWn1 = 960 rpmN1 = 18N2 = 40η = 95%
T1 = N·m
5.Hard
A = 15B = 18C = 18D = ?

In a compound gear train, gear A (15 teeth) on the input shaft turns at 1450 rpm and drives gear B (18 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 1088 rpm. How many teeth ND must gear D have?

nin = 1450 rpmA = 15B = 18C = 18nout = 1088 rpm
ND =
6.Hard
A = 24B = 30C = 18D = 40

A 5.5 kW motor at 1440 rpm drives gear A (24 teeth), which meshes with gear B (30 teeth). Gear C (18 teeth) on the same shaft as B drives gear D (40 teeth) on the output shaft. Each gear mesh has an efficiency of 97%. Find the output torque Tout.

P = 5.5 kWnin = 1440 rpmA = 24B = 30C = 18D = 40ηmesh = 97%
Tout = N·m

Answer key

  1. 1. n2 = 576 rpm
  2. 2. N2 = 12
  3. 3. T1 = 4.974 N·m
  4. 4. T1 = 74.6 N·m
  5. 5. ND = 20
  6. 6. Tout = 95.33 N·m

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