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A planetary gear is a gear that rotates not around an axle but around another gear known as a sun gear, or star gear. I have designed prototype systems in the past that used a single planetary gear rotating around a rotating gear. However since then almost every system I've seen using planetary gears have used multiple gears, most commonly in sets of 3, 4, 5 and 6.

What is the mechanical advantages and disadvantages of using multiple planetary gears and what is the optimum number of gears?

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  • $\begingroup$ You don't mean compound, right? $\endgroup$
    – HDE 226868
    Commented Mar 7, 2015 at 23:25
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    $\begingroup$ Optimum number of gears for what? In terms of cost, the answer's probably something trivial like "just one." But you would need at least three for the gears themselves to resist in-plane displacement, for example. What application are you concerned with? $\endgroup$
    – Air
    Commented Mar 7, 2015 at 23:48
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    $\begingroup$ @ChrisMueller upload.wikimedia.org/wikipedia/commons/d/d4/… $\endgroup$
    – Air
    Commented Mar 8, 2015 at 0:50
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    $\begingroup$ @ChrisMueller: Actually, if axis of all - the sun, the carrier and the annular gear are fixed against lateral displacement (=mounted in bearings nearby), one gear would perfectly suffice if the load is low enough. 3+ gears provide a bearing functionality without actual bearings, and much better load capacity. $\endgroup$
    – SF.
    Commented Mar 8, 2015 at 2:08
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    $\begingroup$ 3 is the minimum that will provide a balanced locating force $\endgroup$
    – Russell McMahon
    Commented Mar 8, 2015 at 2:58

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Advantages

I'll start off by quoting from the "Benefits" section of the Wikipedia article:

The load in a planetary gear train is shared among multiple planets, therefore torque capability is greatly increased. The more planets in the system, the greater the load ability and the higher the torque density.

The more the merrier. The same idea is covered here:

Torque Splits
When considering torque splits one assumes the torque to be divided among the planets equally, but this may not be a valid assumption. Member support and the number of planets determine the torque split represented by an “effective” number of planets. This number in epicyclic sets constructed with two or three planets is in most cases equal to the actual number of planets. When more than three planets are used, however, the effective number of planets is always less than the actual number of planets.

Let’s look at torque splits in terms of fixed support and floating support of the members. With fixed support, all members are supported in bearings. The centers of the sun, ring, and carrier will not be coincident due to manufacturing tolerances. Because of this fewer planets are simultaneously in mesh, resulting in a lower effective number of planets sharing the load. With floating support, one or two members are allowed a small amount of radial freedom or float, which allows the sun, ring, and carrier to seek a position where their centers are coincident. This float could be as little as .001-.002 inches. With floating support three planets will always be in mesh, resulting in a higher effective number of planets sharing the load.

The single-planet arrangement doesn't change the torque capability, but the multiple-planet arrangement does. You can increase the number of planets without limit and still continue to increase it.

Another advantage of using more planets is less energy loss. Wikipedia claims that there is an energy loss of only about 3% per stage, but it doesn't back that up with an inline citation, nor does it specify the number or arrangement of planets. This gives the same feature as a "typical energy loss."

Disadvantages

The obvious one here is that the more planets you add, the more complex the system becomes. If there's a major failure, it could be amplified by having more planets (alternatively, it could be argued that some arrangements provide redundancy).

Is there an optimal number of gears? It really depends on your application. Complexity can be a huge issue, and with complexity comes cost. Repairs, in turn, can be expensive if something goes drastically wrong. If the application involves a great load and torque, then more gears can be helpful.

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  • $\begingroup$ Fantastic answer this really clarified the situation well. $\endgroup$
    – Sam Weston
    Commented Mar 8, 2015 at 0:32
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    $\begingroup$ I think extra gears may also increase the friction losses. More planets, each with friction of own axis. $\endgroup$
    – SF.
    Commented Mar 8, 2015 at 2:21
  • $\begingroup$ @SF. - but the force on each gear (on its teeth and on its axle) is reduced by a corresponding amount, so in a first-order approximation, it should all cancel out. Only second-order effects, such as lubricant viscosity, would matter. $\endgroup$
    – Dave Tweed
    Commented Jan 16, 2017 at 13:39
  • $\begingroup$ @DaveTweed: Yes, but while for high loads (torque, axial or radial load) the load distribution is beneficial (less stress=losses per element), with low loads these second-order effects are dominant. Say, you want to speed up a propeller fan (low torque, only weak air friction) with an in-line motor; the planetary gear will generally be a poor choice, and one with more "planets" increasingly so. OTOH if you use a high-torque motor to drive an even higher torque device, extra gears will be helpful. $\endgroup$
    – SF.
    Commented Jan 16, 2017 at 14:27

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