Understanding the difference between simple and compound gear trains and the gear ratios

Simple Gear Train

Each shaft in a simple gear train is attached to one spur gear only.

Shaft

Compound Gear Train System

Two or more spur gears added together to the same shaft form a compound gear. The different gears that make a compound gear all rotate at the same speed. Gear trains with compound gears are called compound gear trains.

What’s the advantage of compound gear train over simple gear train ?

30 TeethDriven

120 TeethDriver

60 Teeth

A B C

Simple Gear Train

If gear A is running at 100 revs/min, gear B will run at 200 revs/min. This is because the no. of teeth is inversely proportional to the speed. The smaller the gear the faster it turns. Similarly gear C turns at 400 revs/min as Gear C is twice as small as gear A. The gear ratio (velocity ratio) for the gear train above is Velocity of Gear A(Driver): Velocity of Gear C(Driven) which is 1:4. This gear ratio means that the driven gear is 4 times faster than the driver gear.

Compound Gear Train

If gear A is running at 100 revs/min, compound gear B will run at 200 revs/min as it has twice the teeth and will be twice as slow (inversely proportional). The larger teeth gear in compound gear B (120 teeth) is attached to Gear C (30 teeth), which is 4 times smaller and therefore 4 times faster. Gear C’s speed will be 800 revs/min. The strategy here to mesh the smaller gear (30 teeth) in compound gear B to A and the larger(120 teeth) to C to achieve the greatest increase in speed. This is the advantage of a having a compound gear.

The gear ratio (velocity ratio) for the gear train above is Velocity of Gear A(Driver): Velocity of Gear C(Driven) which is 1:8 as A is running at 100 revs/min and C is running at 800 revs/min. You get 2 times better output speed compared to the simple gear train used just now.

120 Teeth

30 Teeth

60 Teeth

A

BC

Now compare the space taken up by the simple gear train and compound gear train

A B C

AB

C

Simple Gear Train

Compound Gear Train

Look at the compound gear train, it has one more 30 teeth gear, and the other 3 gears are the same. Yet the length occupied by the compound gear is less, this is because of the overlap of A with B. So you have 2 advantages, takes up less space and at the same time achieves a better speed increase or reduction (in above case its speed increase of course). No wonder watches use compound gear trains as a great speed reduction is needed within a small space !!

Worm Gear

Worm Gear systems always has a gear ratio of No. of tooth in worm wheel : 1. And worm gears are used to reduce speed. The worm gear is the driver and the worm wheel is the driven. The driver rotates 1 full turn just for the worm wheel to move 1 teeth.

In the above example the worm gear rotates 12( since there are 12 teeth in worm wheel) times for the wheel to turn once. Hence gear ratio (velocity ratio) is 12: 1.