Talk:Sun and planet gear

Talk

I believe that the role in steam engine is wrong its more a Crank-slider (see Linkage (mechanical)). 80.185.8.102 16:50, 1 January 2006 (UTC)[reply]

Steam locomotive

I am taking this out because the sun and planet motion played no role in the development of the locomotive. The 2 : 1 action would considerably reduce the power at the wheel tread to no avail.--John of Paris 11:41, 25 February 2007 (UTC)[reply]

Why not...

mention that it was resorted to because of patent issues (assuming that's true)? --Crimson30 20:19, 25 June 2007 (UTC)[reply]

Animation

I think there is a fault with the animation. The sun wheel is not going round. Biscuittin (talk) 23:27, 2 February 2008 (UTC)[reply]

It is, but I think it's just suffering from the wagon-wheel effect so it looks like it isn't. 136.176.100.22 (talk) 03:58, 19 February 2008 (UTC)[reply]

I see it as oscillating back and forth rather than going round at the wrong speed. Also, the spokes of the sun gear seem to be going round with the flywheel just fine, so I don't think its any kind of Fresnel interference with the display scan (ie 'wagon wheel' effect). There definitely seems to be something up with the animation. SpinningSpark 01:21, 14 March 2011 (UTC)[reply]

See "Better animation" below --Roly (talk) 14:38, 14 February 2013 (UTC)[reply]

Rotation Mathematics

Previous caption on the animation: "Notice that the sun and flywheel rotate twice for every rotation of the planet." I believe this is wrong; the rotation of the sun and flywheel is based on the proportion of the "planet" relative to the size of the "sun" (more specifically, the number of teeth on those gears), like all other Epicyclic gearing. The rotation of the sun will only be twice the rotation of the planet if they are the same size. In extreme (and theoretical) cases of great size difference, the rotation of the sun per rotation of the planet will range from 1 (small planet, large sun) to unlimited (large planet, small sun). I'm changing this hoping I'm not crazy. 67.142.130.18 (talk) 22:30, 21 February 2009 (UTC)[reply]

Moment of Inertia Multiplication

Using a sun and planet system rather than just a crank increases the effectiveness of the flywheel compared with a crank system. Suppose the number of teeth in the sun and planet gears are $s$ and $p$ respectively. If the sun gear and thus the flywheel rotate at angular speed $\omega _{s}$ which, for simplicity, we assume to be constant and the axis of the planet rotates around that of sun at angular speed $\omega _{c}$ , it can be shown that

\omega _{s}=\left(1+{\frac {p}{s}}\right){\bar {\omega }}_{c}

Because the planet gear 'rocks' about its axis as it rotates around the sun, $\omega _{c}$ is not constant; ${\bar {\omega }}_{c}$ is its average value for a complete cycle.

We see that when, as mentioned in the article, the two gears have the same number of teeth, a doubling of speed occurs.

If the moment of inertia of the flywheel is $I$ , the kinetic energy stored in it is

{\tfrac {1}{2}}I\omega _{s}^{2}={\tfrac {1}{2}}I\left(1+{\frac {p}{s}}\right)^{2}{\bar {\omega }}_{c}^{2}={\tfrac {1}{2}}I_{c}{\bar {\omega }}_{c}^{2}

where

I_{c}=I\left(1+{\frac {p}{s}}\right)^{2}

This kinetic energy is just that which would be stored in a crank system with a flywheel of moment of inertia $I_{c}$ rotating at angular speed ${\bar {\omega }}_{c}$ . Thus, in a sun and planet system, a given flywheel has an energy storage capacity which is a factor $\left(1+{\frac {p}{s}}\right)^{2}$ times what it would have in a crank system. When the gear wheels have the same number of teeth, this factor is, of course, 4.

This moment of inertia multiplication effect is well known elsewhere but I have never seen it mentioned in any discussion of sun and planet gearing. Is it known whether Murdoch and Watt were aware of it? IanHH (talk) 08:23, 7 July 2011 (UTC)— Preceding unsigned comment added by IanHH (talk • contribs) 08:31, 6 July 2011 (UTC)[reply]

It's an over-simplification to rely on this multiplication of moment of inertia. The flywheel inertia is needed for two reasons: to even out the delivery of a single-cylinder steam engine but also to act as a reserve of inertia against a varying load. As the flywheel is still coupled to the output shaft, then the inertia in terms of the load is just the same between a crankshaft and a sun & planet gear. If the load has a high starting torque, or needs a considerable reserve (rolling mills would be one example), then flywheels are just as large and heavy. Only in the case of a light load, or many light loads that are distributed so as to remain relatively constant, can the flywheel be reduced in weight and size (the Lap engine is a good example). In this case the flywheel is only needed to even the engine delivery, not to act as a load reserve, so the major constraint is reduced by the gearing and thus the flywheel can be too. Andy Dingley (talk) 08:40, 7 July 2011 (UTC)[reply]

If the output is taken from the shaft to which the flywheel is attached, the moment of inertia multiplication effect is indeed of no use in reducing the effects of load variation. However, if we were to take the output from a shaft driven by the arm on which the planet gear is mounted, the multiplication effect applies to the load also. The latter option would, presumably, not been available to Watt because of the patent issue. — Preceding unsigned comment added by IanHH (talk • contribs) 16:50, 2 December 2011 (UTC)[reply]

Better animation?

I've created an alternative animation, which is not as neat as the current one but shows the action better. Any comments? Should I replace the existing one?

Roly (talk) 11:52, 27 January 2013 (UTC)[reply]

No comments on this so I've made the change. --Roly (talk) 14:34, 14 February 2013 (UTC)[reply]