Calculating Simpson Compound Planetary Ratio
Calculating Simpson Compound Planetary Ratio
(OP)
I am trying to calculate the first gear ratio of a compound Simpson gear set. Power is transmitted thru the front planetary ring gear (66 tooth). The output shaft is splined to the rear planetary ring gear (66 tooth) and the front planetary carrier. The sun gear is common (34 Tooth on each end). Also the rear planetary carrier is held with a one-way sprag. Any help would be appreciated.





RE: Calculating Simpson Compound Planetary Ratio
I have another paper that gives the overall kinematic eqn for this drive as
(1+2alpha)ws = (-alpha^2)(wr1)+{(1+alpha)^2)wc2 where alpha is ring teeth/sun teeth. w is angular velocity, or rpm.
So for this first gear, the overall eqn reduces to
(1+2(Nr/Ns)rpmsun=(-(Nr/Ns)^2)(rpmring1)
solve for the rpmsun. Then output = rpmsun x Ns/Nr.
Example
60 teeth ring, 18 tooth sun. Then I get 2.52 as first gear ratio.
Please someone check for errors.
RE: Calculating Simpson Compound Planetary Ratio
(1+alpha1 x alpha2)ws =
(-alpha1xalpha2)(wr1)+[(1+alpha1)(1+alpha2)]wc2
RE: Calculating Simpson Compound Planetary Ratio
Both planetary are the same tooth counts. 66 Ring gear and 34 tooth sun gear.
Thank you for the quick reply.
RE: Calculating Simpson Compound Planetary Ratio
RE: Calculating Simpson Compound Planetary Ratio
RE: Calculating Simpson Compound Planetary Ratio
Using the first paper,
(1+2(Nr/Ns)rpmsun=(-(Nr/Ns)^2)(rpmring1)
solving for rpm sun using 34-16-66 teeth, gives
rpm sun = .772 rpm ring, and the inverse is 1.295.
As a check, looking at building a superposition table.
Carrier1 Sun planet1 ring1 carrier2 planet2 ring2
+1 +1 +1 +1 +1 +1 +1
0 a b c -1 0
sum +1 1+a 1+b 1+c 0
a = -1(100/34) = -2.941 = planetary gear ratio
b = (34/16)a = 2.125a =
c = (34/66)a = .5151a = 1.514
ratio of sun to ring1 = (1+a)/(1+c) = -1.941/2.514 = .772
So we have a check.
RE: Calculating Simpson Compound Planetary Ratio