Multiple gearsMECH1200

The Speed of any driven gear is determined by calculating the gear ratio using the driven gear as the output gear along with the input gear and ignoring all other gears in between

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Whether an extra gear in a gear train is an idler or drives an extra shaft,The method to determine speed and torque remains the same.

Idler gears do not affect torque or speed of the driven shaft

If you calculate the gear ratio by multiplying the ratios of each pair of neighboring gears together, the effect of the idle gears is canceled out

The number of teeth of both the idler gears is used twice in the formula. They cancel each other out.

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The gear shown has three output gears, each of which drives a separate shaft with a separate load. It has one true idler gear.

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The speed of each output shaft can now be calculated separately using its own gear ratio.

The idler gear has no effect on the speed of any output shaft.

The speed of one output shaft has no effect on the speed of the other output shafts because they act like idlers with respect to the other shafts.

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Torque Review

Torque Total Torque

MECH1200Gear Ratio Review

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MECH1200Torque

Compound Gears MECH1200

A compound gear drive is a type of gear train that has two or more gears mounted on one shaft

The gears can be mounted anywhere on the shaft, either next to each other or on opposite sides of the shaft.

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Two applications of compound gears are:Driving two output shafts at different speeds and driving an output shaft that is offset from the driver shaft.

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A third application of compound gear drives is to create a gear reduction between two shafts which are located on the same axis.

This is call a reverted gear drive.

MECH1200Compound Gear Drive Speed

Similar to calculations from before except the gear ratio of any gears that are mounted on the same shaft must be included in the calculation.

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These also are the same as simple gear drives except that they are multiplied by the gear ratio of the compound gears.

Idlers still have no effect.

Overall Gear Ratio is found using same driven/driver formulax x ………. or Rtot = R1 x R2 x R3 x R4 x …..x RN

This is similar to overall efficiency:ηtot = η1 x η2 x η3 x η4 x …….. x ηN

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Gear Ratio: Driven to Driver

R = 30:10 = 3:1

Gear Ratio: Compound GearsR = 10:20 = 1:2

Compound Gear Ratio = 3:2

𝑅=𝑆 𝑖𝑛𝑝𝑢𝑡

𝑆𝑜𝑢𝑡𝑝𝑢𝑡

3 :2=1800𝑆𝑜𝑢𝑡𝑝𝑢𝑡

𝑆𝑜𝑢𝑡𝑝𝑢𝑡=18003 :2

=1200

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Compound Gear Drive Torque

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What is the driven shaft’s speed?

MECH1200What is the torque of the driven shaft?

MECH1200What is the driver’s shaft speed?

MECH1200

What is the torque of the driver shaft?

MECH1200What is the driver’s shaft speed?

MECH1200What is the torque of the driver shaft?