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Gear trains
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Virtual Machine Shop Forum  |  Machine Tool Technology  |  Questions, answers, ideas  |  Topic: Gear trains « previous next »
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Geo.
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« on: October 18, 2016, 12:17:01 PM »

Compound gearing is also known as a ¡§Gear Train¡¨ 
 
            
 Gear A (24t) is the Drive Gear, Driven Gear B (44t) shares a common shaft and is Keyed to Gear C (24t), which drives gear D (68t)

„«   To find the RPM or Number of teeth of any driven gear Divide the product of the driving gears by the product of the Driven gears

Example 1
To find Output RPM:
If gear A rotates at 100 rpm what speed does gear D rotate at?
(Input RPM * driver * driver / driven * driven = output RPM)
100 * 24/44 * 24/68 = 19.25 rpm

Exercise 1
If gear A rotates at 75 rpm what speed does gear D rotate at?
75* 24 * 24 / 44 * 68 = 14.5 (14.43 Rounded)

Example 2
To find number of Teeth
(Input RPM * driver * driver / driven * output RPM = number of output teeth)
100 x 24/44 x 24/19.25 = 68 teeth

Exercise 2
Find the number of teeth of the output gear
If gear A makes 75 revelations how many teeth does gear D need to make 14.5 Rpm? 
75 * 24 * 24 = 43200
44 * 14.5 = 638
43200 / 638 = 68 (67.7 Rounded)


Example 3
To Find Input RPM
19.25 * 68 * 44 / 24 * 24 = 100

Exercise 3
How many RPM must gear A make if gear D is required to make 45 RPM?
(Output RPM * driven * driven / driver * driver = input RPM)
45 * 68 * 44 = 134640
24 * 24 = 576
134640 / 576 = 233.75

„«   Finding Gears that will transmit motion at a given Ratio
3/7 = 2/3.5 * 1.5/2 = (2 * 12) / (3.5 * 12) * (1.5 * 16) / (2 * 16)
(The Multipliers used are ones that will produce an available set of gears)
 = 24/42 ¡V 24/32
A = 24t input Drive / B = 42t driven ¡V C = 24t Driver / D = 32t Driven output = 3/7th ratio
 
            
Proving: 3 / 7 of 100 = 42.8
100 (rpm)* 24 * 24 = 57600
42 * 32 = 1344
57600 / 1344 = 42.8
Note: The Multipliers can be changed to produce a set of available gears that will complement the center distances needed 

„«   Worm and worm wheel
To fine the output speed of a worm wheel we need to know the input speed, the number of starts (threads) of the worm and the number of teeth on the worm wheel
Note: the worm is considered a gear with 1 tooth if it is a single lead, 2 teeth if it is a double lead, 3 teeth if a triple lead, and so on, so to find the rpm of the worm wheel, the worm rpm is multiplied by the number of leads (starts) and divide by the number of teeth on the worm wheel
If the input speed is 100 RPM, the worm has 2 starts (double thread) and the worm wheel has 60 teeth
The formula is: 100 * 2 / 60 = 3.3 rpm

„«   Bevel gears
Bevel gear ratios and speeds are treated as spur gears, and problems are solved using the same formulas as spur gears

„«   Mixed gear trains
In this problem we have a set of spur gears driving a set of bevel gears that drive a worm set
Input is 300 rpm to spur gear A (20t) driving gear B (32T) that shares a common keyed shaft with bevel gear C (21t) driving bevel gear D (26t) which drives a 4 lead worm with a 60 tooth wheel
(300 * 20 * 21 * 4) / (32 * 26 * 60) = 10 RPM
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