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Design a two-speed transmission with output-to-input speed ratios of approximately 1:4.2 and 1:1. Many possible designs will satisfy this requirement. (Suggestions: Use a computer to evaluate possible...

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Design a two-speed transmission with output-to-input speed ratios of approximately 1:4.2 and 1:1. Many possible designs will satisfy this requirement. (Suggestions: Use a computer to evaluate possible solutions. Consider a simple planetary train with 18 to 20 sun gear teeth and 19 to 21 planet gear teeth. Use three or four planet gears.)

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Answered 22 days After Dec 04, 2021

Solution

Subhashis answered on Dec 26 2021
136 Votes
Solution
    There are many possible solutions. Since we have just considered planetary transmissions, let us attempt to use a simple planetary transmission of the type shown in assignment Figure. We will try sun gears with 18 to 20 teeth and planet gears with 19 to 21 teeth, using either three or four planet gears (18 possible combinations).
    The number of teeth in the ring gear is given by NR = NS + 2NP.
    We want to consider only balanced planetary trains, in order to avoid lateral loads on the sun and ca
ier shafts. The train can be balanced with equally spaced planet gears if
    (NS + NR)/(the number of planets) = an integer.
    An IF statement and modulo (remainder) function may be used. The test for a balanced train is based on the statement
    If(MOD[(NS + NR)/(number of planets)) < 10^-6 , “yes’’, “no’’) [Mod is a remainder function in excel]
    which returns “yes” if the remainder is zero (within a small round-off e
or). If the test returns “no,” the train cannot be assembled with equally spaced planets, and we reject that combination of gears.
    Let the sun gear be integral with the input shaft, and...
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