Question

Aroad grader has 36" diameter wheels which are driven by a two-stage planetary gear train as shown below. All gears have 20 teeth except for the fixed ring gear which has 60 teeth. If the road speed of the grader is to be 20 mph, calculate the required rotational speeds of the output shaft and input shaft. Determine the overall input to output ratio. Input 20 mph Output Note, choose one or more than one of the following MC answers and then type the letter (s) corresponding to the question number in the essay section of this problem with supporting calculations contained on the scratch sheet. If the answer requires "the correct answer is_ _"type that in the essay section as well. 3a) Rotational speed of output shaft is: a)-27 in/s b) -187 RPM c) 16 d) -19.6 rad/s e) All of the above f) None of the above, the correct answer is: 3b) Rotational speed of input shaft is: a)-352 in/s b) - 4500 RPM c) - 100 d)-313 rad/s e) All of the above f) None of the above, the correct answer is:

Answer 1

Before solving this problem, the basic thing to understand here is that output shaft is connected to the arm of the sun and planetary gear system and the sun gear is connected to the input shaft.

Now let us start solving the problem ::

SunCrear Input Shaft suffint shaft Planet Crears Ring Ayon Gear w=2amph (to Teeth) Gronea - 12 inen 18* 0,1254 m +0.957rm Wasm 63 = frown Diagram it is clear that but Win = sun 1609.344 m N = 20 mph - 20 11 zo Hour 3toa S V 8.340 8 m/s o Wont mis 8.9 408 anys (Nant 8.9408 0,4572 19.55 rond ainu 19.6 rar (d) 316) - Want Ethern Warm 19.6 rand Arm sun Planet Ring when Arms Assumed fired X (let) / 1-- (2)* )-- External Gearing Direction of Rotation Reverses Internal gearing 3 Direction of Rotation Remains same when Armas yller) Kty -xty xlm Moring

Wring c C - 3 g ty = D e - 3 за Wsun = 44 ne ty (34) + 5 = = y ronal 19.6 y = Coasm Court = Jarin W sum=44 4(19.6) = 78.4 rond Winput
for the (c) part of the question, both option (a) and (d) seems feasible, but for option (a) you must open the whole transmission system and change the expansive gearing arrangements, so it might cost more...

But instead, for (d), you just have to change the wheels that is an external components, so if you add the total cost of all the components, and the servicing charges etc. Then it might be more feasible to change the wheels.

So to me , option (d) seems more promising.

Hope you got the concept well...!!!