It’s no secret that planetary gears have many uses. As a result, they are widely used to get various speed reductions (or increases). In this video, we will show how small changes can make large differences in the speeds of the same planetary gear set.
Welcome to the Mentored Engineer. In this video, we’re going to talk about planetary gear systems and specifically two different ways of getting multiple speed power transmissions using the same gear sets and only making small changes in between each one. So let’s look at this video. And in each case, the arm is moving one revolution. Yes, the carrier is only moving one revolution, but the output is different.
So why is that? Hey, keep watching this video and you’ll find out. Hey, if you like what you see so far, please be sure to smash that like button and subscribe and click that notification bell so I can annoy you at least once a week. So let’s look at the gear apparatus.
In the apparatus, we have three different sun gears mounting on the same shaft. We also have three different sized planetary gears and three different sized internal ring gears. All right. So how does all this work together? Well, first of all, all the ring gears are essentially bolted together.
Somehow they’re they’re bolted, glued, you got roll pans, whatever, keeping them all together. So they all turn at the same rate. Now, the sun gears aren’t actually attached to the shaft. They’re just circling on it. The planetary gears are then sized accordingly, just to say on the same shaft of the carrier.
So in the first stage with the smallest sun gear, that’s going to be 24 teeth on both the sun and the planet. And the ring will have 72. We can use our simple equation to find out that we need a 72 tooth ring gear. to make all this work. On our second stage, we have 30 teeth on the sun gear, 18 teeth on the planet and 66 teeth on the ring gear.
So in all these cases, we had to keep the same physical distance between the center of the sun and the radius of the carriage the same so that we could mount all of the planets on one single straight pin. If the planet size was varying differently with that, we’d have, you know, step pins and I really don’t know how you design, manufacture and assemble that. So we kept the same diameter there. As a result, the second stage ring gear is actually six teeth smaller than the first stage at 66 teeth.
As we go to the third section now, we’re going to have 36 teeth on the sun, 12 teeth on the planet and 60 teeth on the ring gear. All right, so we have three different ratios at play here. Now, I bring this up because a lot of high end bicycles will actually use a internal planetary gear style transmission instead of having the typical chain derailleur where you have multiple size sprockets and then the chain goes over it and then you have the little derailleur to pull it side to side. Those are you know, it’s a proven technology, but they do have their quirks and their problems, and they need to be calibrated from time to time.
However, if we make this simple change here, we can get three gear ratios out of this. And what happens is we will lock a sun gear in each one of those cases. Now let’s look at this from the manufacturer, Shimano, of one of these internal gears, and they will show you a little bit about how they interlock with the shaft. Within the gear carrier are three sun gears of varying size and matching stepped planetary gear sets. These planetaries drive a ring gear on which is mounted a roller clutch which transmits power to the hub shell.
Going back to the introduction, the larger the sun gear in relation to the ring gear, the greater the differential in speed between the units. The sun gears are engaged by means of rising pawls, which are actuated by the shifter through an actuation arm. In order for power to be transmitted to the ring gear, one of the sun gears must be coupled to the axle to become the fixed reactionary gear. Sun gears not coupled to the axle are free to rotate and will not function as a reactionary element. So that’s a really cool idea.
I would have never thought of that on my own. So kudos to Shimano and everybody else that’s doing that. So let’s talk about our system here. And we are inputting on the carriage arm and we’re outputting on the ring gear. So let’s look at the details of our first section here with the smallest sun.
When we lock that, we’re going to notice that as we input one revolution in the carriage, we actually get 1.33 revolutions on the ring. Now, if we were to back drive this and drive the ring as the power input and the carriage as the output, we would get the inverse of that. So it’d be 1.33 input revolutions to one output revolution. When we lock the second sun, we actually get a 1 to 1.45 output. And when we lock the third one, we get a 1 to 1.6 output.
So each time as the sun gets bigger, we actually get a step up in our output ratio. That can be useful. Now in the bicycle example here, there’s a lot more complication and generally you want more than three speeds. All right, so the first thing is, is you got a back drive. uh or coast at least so if you’re not pedaling you don’t want the pedals be you know forcing you to move your legs uh that’s a good way to get an injury or you know cause an accident or something like that
so you got to be able to back drive or just not pedal coast all right the other thing is is there’s actually a secret fourth gear Yes, secret fourth gear. The fourth gear comes in to play as if you have another mechanism there that locks the carriage and the ring together. This can be done a number of ways. If you simply lock the planetary gear from rotating, great.
Now you’ll have to release the sun gears from being locked as well, otherwise you’re going to bind the whole thing up and, you know, parts are going to fly everywhere. So that’s the first type of transmission. All right. So all that is good and well on a bicycle. It’s a little bit different on a car.
Car transmissions have to be more robust, heavier duty, and it’s really hard to lock the sun on a shaft that’s really small. So cars treat it differently. First of all, their input is going to be the sun and their output is going to be the carrier. And they’re going to use the rings to control the speeds. So the rings are all necessarily just free floating in the automobile when nothing is happening.
Alright, what’s going to happen is there’s going to be clutch pads on each ring gear that will lock the rotation of the ring so it won’t be able to move. So the outside can of the transmission is going to force the ring to be stationary and then that’s going to cause motion through the transmission. So you can see here from this picture, there’s another difference in how these automatic transmissions work compared to the bicycle one. And you can see in the three stages here, the ring gear is driven by the planets in front of them.
So the carriage output of one ring system is now the the the input on the ring. And that allows us to have multiple speeds as well. So let’s look at how the system is constructed. You can see here that there are three sun gears mounted to the input shaft. So you have a ring gear that’s not mounted to anything.
But the next stage, the planets are mounted to the ring gear. And consequently, this third stage after that has the planets mounted to the ring gear. So when we look at how this transmission functions, our gears are going to go from right to left. So when we engage the rightmost clutch, that’s first gear. But we’re going to get a speed ratio here of one to a quarter revolution .
So one revolution input, one quarter of a revolution output. When we go to the second gear here, we’re going to clutch the middle ring and stop that from rotating, and we’re going to get a ratio of one to 0.44. So our speed is increased. That’s going to be second gear. and on our third one we’re going to break the left most ring and that is going to cause us to have our highest ratio which is 1 to 0.58 revolutions so as each time we’re going we’re increasing our speed now also with this we have a secret fourth gear where we could actually lock the input shaft to the output shaft and get a one-to-one and we can do that variety of ways, locking the planetary rotation and not having any of the clutches in there.
But most automatic transmissions don’t do that. They have their gears timed specifically for the values that they want. now obviously this is not all of an automatic transmission because you have generally you know four to five gears plus a reverse uh some transmissions have you know 12 speeds now so there’s a lot more that goes into it than this but this is the basics of how you get three different distinct gears by simply making a few changes Hey, well, thank you for watching this video on planetary gear systems. I hope it was informative and please give it a like.
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