How does a planetary gear work? | Design and operating principle simply explained

0:01this video explains the structure and

0:03operating principle of a planetary

0:04gearbox in more detail let us first look

0:07at a socalled stationary gearbox which

0:09is characterized by the fact that the

0:11gears have stationary axis of rotation

0:14the animation shows a yellow drive gear

0:16that first drives a blue idler gear this

0:18in turn sets the red output gear in

0:20Motion in principle this is a two-stage

0:24gearbox the yellow drive gear and the

0:26blue intermediate gear form the first

0:28gear stage the gear ratio of this gear

0:30stage results as indicated from the

0:32ratio of the number of teeth of the two

0:34gears the second gear stage is formed by

0:37the blue idler gear and the red output

0:39gear the gear ratio of this gear stage

0:41also results as indicated from the ratio

0:44of the number of teeth of the two gears

0:46the total transmission ratio of this

0:48two-stage stationary gearbox therefore

0:50also called stationary transmission

0:52ratio is calculated by multiplying the

0:54individual gear ratios i1 and I2 it can

0:57now be seen that only the number of

0:59teeth of the output gear and the input

1:01gear are relevant for the overall

1:02transmission ratio the number of teeth

1:04of The Idler gear has no influence on

1:07this this fact will become important

1:09later

1:10on in principle an internal gear can be

1:13used instead of the external gear as

1:16long as the ring gear has the same

1:17number of teeth as the external spur

1:19gear the overall transmission ratio will

1:21not change only the direction of

1:23rotation of the output gear is reversed

1:26usually the rotational axis of the input

1:29and output shaft shafts are not aligned

1:31but are offset however by properly

1:33selecting the diameter and therefore the

1:35number of teeth of The Idler gear it is

1:37possible to ensure that the input shaft

1:39of the yellow gear and the output shaft

1:40of the red ring gear are aligned on a

1:42common axis of rotation at this point we

1:45use the previously explained fact that

1:47the number of teeth of The Idler gear

1:48has no influence on the overall

1:50transmission ratio anyway and can

1:52therefore be chosen as desired if the

1:54input and output shafts are to be

1:56coaxial on a common axis of rotation the

1:58pitch diameter of the inter immediate

2:00gear must be equal to the difference

2:01between the pitch Circle radi of the

2:03output and input gear since the number

2:05of teeth is directly proportional to the

2:07pitch diameter the number of teeth can

2:09be used instead of the pitch diameter

2:12therefore the number of teeth of The

2:13Idler gear must be half the difference

2:15between the number of teeth of the ring

2:17gear and that of the input gear in this

2:19case the red ring gear has 48 teeth and

2:22the yellow drive gear has 12 teeth this

2:24results in a number of 18 teeth for the

2:26intermediate gear so that the axis of

2:28rotation of the ring gear and drive gear

2:30are

2:31aligned a disadvantage of this gearbox

2:33is that the output shaft and the input

2:35shaft are subjected to bending due to

2:37the one-sided flank force of The Idler

2:39gear in the animation f is the force of

2:42The Idler gear acting on the flank of

2:43the ring gear however bending stress can

2:46be avoided if several intermediate gears

2:48are arranged symmetrically so that the

2:50flank forces compensate each other in

2:52their bending effect in the case of

2:54three idler gears the drive and output

2:56shafts are no longer subjected to

2:58bending but only to torsion

3:00at the same time the circumferential

3:02Force generated by the torque of the

3:04drive shaft is distributed over a total

3:05of three gears reducing the flank forces

3:08of each gear this significantly

3:10increases the maximum torque that can be

3:13transmitted in principle this gearbox is

3:16already the preliminary stage of a

3:18planetary gearbox in the final stage The

3:21Idler gears are mounted on a so-called

3:23carrier the carrier in turn is connected

3:26to a shaft and is guided coaxially

3:28through the output shaft which is

3:30designed as a hollow shaft the planetary

3:32gearbox is now complete in principle in

3:35this operating state it has the

3:37transmission ratio already derived the

3:40mode of operation does not yet differ

3:42from that of the stationary gearbox

3:44described at the beginning however this

3:46changes when the planetary gear is used

3:49in a different way the output does not

3:51always have to be on the ring gear it is

3:53now possible to use the carrier as the

3:55output while the ring gear is firmly

3:57locked in this case the in put gear

4:00drives The Idler gears around the fixed

4:02ring gear The Idler gears rotate around

4:04the central input gear like the planets

4:06around the Sun hence the name planetary

4:09gearbox the transmission ratio of this

4:11planetary gear is now different to that

4:13of the stationary gear considered before

4:16the gears previously referred to as

4:18idler gears are generally also known as

4:20Planet gears the externally toothed

4:22Central gear is called The Sun Gear the

4:25internally toothed ring gear is also

4:26referred to as annulus here too the need

4:30for a symmetrical arrangement of the

4:31planet gears becomes apparent as

4:33otherwise enormous unbalance forces

4:35would occur at high

4:37speeds with a planetary gear it is not

4:40only possible to lock the ring gear and

4:42have the output take place using the

4:44carrier there are many other possible

4:46variants which we will go into in more

4:48detail in a moment and which each result

4:50in a different transmission ratio this

4:52makes the planetary gearbox particularly

4:54suitable for shiftable transmissions

4:56such as in Hub Gears of bicycles or in

4:58automatic transmission of Motor Vehicles

5:01the advantage of a planetary gear

5:03compared to a conventional stationary

5:04gearbox is the compact design and the

5:06advantage that all shafts are arranged

5:08coaxially for very large transmission

5:11ratios several planetary gearboxes can

5:14also be connected in

5:15series various transmission ratios can

5:18be realized with a planetary gear

5:20depending on which shaft is used for the

5:22input or output the various gear ratios

5:25are explained using the example of the

5:27planetary gear shown here with a Sun

5:28Gear with 12 12 teeth and a ring gear

5:30with 48 teeth in this case the largest

5:33transmission ratio of five is achieved

5:35if the Sun Gear is used as the input and

5:37the carrier as the output when the ring

5:39gear is locked interchanging the input

5:41and output results in the smallest

5:43possible transmission ratio of 0.2 as a

5:46reciprocal value the direction of

5:48rotation of the input and output shafts

5:51Remains the Same in both

5:53cases the second largest transmission

5:55ratio of four results in the present

5:57case if the Sun Gear is still used for

5:59the input but this time the carrier is

6:01firmly locked and the ring gear is used

6:02for the output the second lowest

6:04transmission ratio is again obtained by

6:06interchanging the input and output

6:08shafts and is then

6:100.25 however the direction of rotation

6:13between the input and output shafts is

6:15different in both cases mathematically

6:18the transmission ratio in such a case is

6:20also given as a negative value a reverse

6:23gear can therefore be created with such

6:25a transmission ratio another way of

6:27using the planetary gearbox is to blck

6:29The Sun Gear and have the ring gear as

6:31the input and the carrier as the output

6:33in this case the transmission ratio is

6:361.25 while the direction of rotation is

6:39maintained interchanging the input and

6:41output results in a reciprocal

6:43transmission ratio of

6:460.8 with shiftable gearboxes in

6:48particular it should not be forgotten

6:50that a so-called direct drive is also

6:52possible in this case all components of

6:55the planetary gearbox are firmly locked

6:57together in this case the transmission

7:00ratio is one such a direct drive is used

7:03for example in three-speed Hub gears as

7:05the second

7:06gear the various possible gear ratios

7:09are summarized in the table the

7:11transmission ratios with the input and

7:13output reversed are shown in Brackets

7:16negative signs indicate a reversal of

7:18the direction of rotation the derivation

7:21of the formulas given for determining

7:22the transmission ratios is explained in

7:24detail in another video however it

7:27should be noted that the number of teeth

7:28of the planet gears has no influence on

7:30the transmission ratio for any

7:32configuration the shifting of the

7:34various transmission ratios is carried

7:36out in shiftable gear Boxes by so-called

7:38clutches which enable the Locking of

7:40individual components depending on the

7:42desired transmission ratio for

7:44constructive reasons not all

7:46transmission ratios listed in the table

7:48can be realized with a single planetary

7:50gearbox however by combining several

7:53individual planetary gear sets the

7:55possible transmission ratios can be

7:57increased considerably in practice up to

8:00three planetary sets are common in a

8:02gearbox