How to model Planetary Gears; Requirements, Gear Ratios, Helical/Herringbone (Gears pt 5/7)

hi everyone in today's video i would like to show you how to make a planetary gear set which will allow you to transmit high amounts of torque at a relatively high ratio in a very compact package i would like to start today by showing you how to model the red ring gear i'll do it once first to show you the basic idea of how to do it but it will lead to a few inaccuracies so i will do it a second time to show you how to correct for those starting from an empty file the first thing i'm going to do is create a gear with the same parameters that i want for my eventual ring gear so metric with a 20 degree pressure angle i'll take a module of two millimeters with 56 teeth i'll leave the backlash at zero to show you the inaccuracies later on um a root fillet radius also of zero for now i'll make it 20 millimeters thick and i don't want a hole so there we have a gear and now i'll activate this new component and create a sketch on this top surface here and then i'll hit c for circle and let's just make this 126 millimeters in diameter finish the sketch e for extrude and i'll select both of these profiles and then i'll drag these down by minus 20 millimeters and i'm going for operation new body click ok and once that's done computing modify combine a cut the target is the large cylinder the tool is the gear and then you can click ok and then under the spur gear component we'll have one body left and that's our ring gear i want to show you how this ring gear interacts with a regular gear and for that i first want to create a supporting bracket so i'll activate the root component and create a new component that i will call bracket and then i will create a sketch on this bottom plane here make a circle of let's say 100 millimeters and then i'll make another circle that is 19 and a half millimeters and i will ensure that that thing is vertically above the origin and that it is 36 millimeters above the origin then finish the sketch and then i'll extrude the main bit three millimeters upward and then i'll unhide the sketch and extrude this bit 20 millimeters upwards we can now set up our first joint so i'm going to hide the sketch we no longer need it and activate the root component and i'm going to right click the bracket and select ground so that it can no longer move and then i'm going to create a joint i'm going to the underside here and i want to join this ring gear so i hold ctrl so i can select the center of the ring gear and i'm going to join it to the center of the bracket so it's the good revolute joint right now so i'm going to flip it up and then i'm going to press animate to double check that it's good and that looks pretty good the next thing i'm going to do is create the pinion gear that is supposed to mesh with this thing so i'm going to create a spur gear and i'm going to create it with 20 teeth and i'm going to give this one a whole diameter of 20 millimeters and then i'm going to create a second joint which is a revolute joint between this pinion here and this little shaft knob over there i'm going to flip this and just animate it again to be safe that looks pretty good so now our joints are set up and now we need to set up a motion link before i do that i would first like to give some names to my joints so if i look under joints here and i click this one i see that it is this joint in the center so i will call that ring gear and then the other one is the revolution of the pinion and i do this because the order in which i click these joints matters so under assemble we go to motion link and i want to link the rotation of the ring gear to the pinion and then i want to ask myself if i rotate the ring gear 360 degrees how much does the pinion rotate well the ring gear had 56 teeth and the pinion had only 20 and of course the pinion would have to turn faster than the ring gear because it has fewer teeth so if i just take that gear ratio and multiply it by the same 360 degrees we should get the right ratio and if i reverse this now you see that it indeed matches up now that we have the motion link set up we can take a closer look at how well these gears mesh there will be a little bit of interference here and i want to make that more obvious by creating an offset plane off the top of this ring gear just drag this down a little bit and then do a section analysis on that new plane and then i'm going to hide the plane and then these colored hatchings will better show the interference so if i now zoom in we see first of all that the fit here is extremely tight and this is because we selected zero backlash on both of the gears but if i rotate this orange gear a little bit now we see over here that these two lines are sticking into each other so here we can see them intersect and this is a little bit of interference now between the pinion and the ring gear the second issue if i rotate them back a little bit is that the outer diameter of this pinion here sticks all the way into the inner diameter of the ring gear and if i rotate them one tooth over then we see exactly the same problem with the tooth of the ring here going all the way into the trough of the pinion now if we look at the meshing of a regular set of spur gears we see that that's not supposed to happen so there is a little bit of clearance here between the tooth tip and the trough of the mating gear the problem here is that if we look at the pitch diameter or the pitch circle of this left gear we see that it has a radius of 30 millimeters and the outer diameter has a radius of 32 millimeters so between this circle here and the outer diameter we have a total distance of two millimeters but this inner diameter over here is almost two and a half millimeters smaller than this 30 millimeter circle so here we have the addendum of two millimeters which we've discussed in video four compared to a d-dandim of nearly two and a half millimeters but what happened is when we did that combined cut to make the ring gear we flipped around the addendum for the d-dendum which causes this too tight fit over here so let's start over from scratch let's model a new ring gear but this time we will add some backlash and we will also fix up the inner and outer diameters to ensure that we don't get this tip to trough interference i've got the gear generator open again in a new blank file and i'm going to make the same base gear as before the difference here is that i'm going to enter a backlash of minus 0.2 millimeters so usually if you have the normal sized gear teeth and you add a positive backlash the gear teeth become a little bit narrower but the idea now is that by entering a negative backlash we make the gear teeth a little bit wider and then by doing the combined cuts later on the resulting gear teeth on the ring gear will be a little bit narrower which corresponds to the backlash that we want so let's click ok on this let's now fix up the addendum indeed endem and for that i will unpack this group here on the timeline by pressing this little plus and then i'll take my history marker and roll it back by two positions so that it is before the circular pattern here i'm going to take the press pull command and i'm going to press pull this face here and i'll press pull it outwards and i want to point out here that under offset type modify existing feature and automatic both will not work it has to be new offset and how much are we going to offset it well originally it's one time the module for the addendum but we want this now to be the later dedendum so it has to be 1.25 times the module and the difference there is then one 0.25 times the module 0.25 times 2 and then hit enter and then we can roll the history marker back forward and then we see that if we look at the gear teeth only the gear tooth that we offset ourselves is lengthened the rest is unchanged so now we go into the circular pattern feature right click edit feature and then under objects we will also select this offset face that we just made and then click ok and this takes a moment to compute and now we see that all of the gear teeth have been lengthened and so now we want to fix the d-dendem and for that we'll go into the first sketch of the gear so right click edit sketch and all we have to do is adjust this diameter so the diameter that we want this to have is 112 minus one time the module that is the addendum that we want to have later which will be the d-denim now but we want to have that on this side of the gear but also on this side of the gear so we'll have to do this twice and that'll be 108 millimeters and then finish the sketch the final thing we can do now is activate the component to make sure that we're working inside of it and then we'll do the sketch again make sure we're in the origin 126 millimeters and so the other way to proceed from this point forward is to take only the outer profile here extrude it downward by 20 millimeters and then under operation select new body press ok and then inside of the component you can remove the original body and that will leave you with a ring gear i've created a new bracket now and i'm about to make the pinion and there are two things i want to point out first it's important that you don't forget to turn the backlash back into a positive backlash second i'm going to make this particular gear 15 millimeters thick for reasons that will become clear later on i've set up the motion links again and now if we take a look at it from the top we see that we have clearance all around the gear teeth and that is still the case as we rotate the gears around like this a mechanism like this would be commonly used in for example a tower crane to slow the boom around and it is also used in for example tanks to traverse the turret what i'd like to do now is convert this mechanism into a planetary gear set the first thing i'll do is go into the bracket and then edit this sketch and i'm going to do a few things first i'm going to add an extra circle here and i will give that a spacing of let's say two millimeters and i'm also going to create a similar type of construction in the center here and i'll make that equal to the shaft for the planet and that will be the shaft to carry the sun gear the final thing we'll do i'll finish the sketch we'll unhide the sketch e for extrude i can just press continue here and then i press and hold until i can select the profile and this one is coming up by 20 millimeters that will be a join and the other thing that we'll do is also extrude up this profile over here this little ring and we'll also extrude that ring over there up and we'll extrude those up by five millimeters and we'll make that a join again and these little rings now create a little bit of a shoulder here on which the gears can rise so that the flat surface of the gear doesn't ride against the flat surface of the planet carrier and this at least somewhat minimizes friction and wear and the final thing that we'll do now is go into a circular pattern so under create pattern circular pattern and then we're going to make a pattern of type features and i want the shoulders and i want this extrude over here and i want to have that patterned around that center shaft and then for the quantity i want to have three planets for now so click okay on this and now we have three shafts and the final thing we have to do now is create the sun gear so we could just go under tools add in scripts and designs again spur gear and here we're going to need a sun gear of 16 teeth it has to be 16 teeth in this case so i'd like to go up to the white board now to show you why that is the case here i have two gears in mesh and one convenient way to think about gears is to picture them as cylinders that roll against each other without slipping and the diameters of these cylinders then equal the pitch diameters of these gears and this mental image will also come in handy when we talk about bevel gears now when looking at a planetary gear set this actually shows quite quickly that the diameter of the ring gear needs to be equal to the diameter of one planet plus the sun plus another planet but because the pitch diameter is equal to the module times the number of teeth and all these gears have the same module that also means that the relationship holds for the tooth counts and going back to our example here if we have 56 on the ring and 20 on both of these planets then the sun must be 16 teeth i now like to change up the joints to turn this thing into a planetary gear set the first thing i'll do is take this bracket and rename it to planet carrier and i will unground it and then i will ground this component over here and i'll call it the ring gear now after doing this if we rotate the planet carrier around we see that the joints and the motion link for the planet is still fine so what we need to do now is joint up the sun and give that the right ratio so i make a joint for this sun and i'm going to joint it to the ring gear because the ring gear is stationary it's different if you jointed to the planet carrier because then you're going to couple a rotating object to another rotating object which will complicate things later on so i'm going to move this thing up by five millimeters so that it matches up there and then i also need to rotate it so that it measures correctly and this is going to be 180 degrees divided by 16 16 the number of teeth and then it lines up like that so what we need to do now is create the final motion link so assemble motion link and we want to link this rotation of the of the planet carrier this now has the wrong name to this rotation of the sun so if the planet carrier advances one revolution then that means that the planet itself has advanced by 56 teeth and so if the planet advances 56 teeth then you could say that the sun gear should advance 56 divided by 16 teeth so 16 being the number of teeth of the sun itself but if we do that though we see that it doesn't quite work out and the reason for that is the planet is not only spinning around its own axis it's also orbiting around the sun and as it orbits the sun in that way it actually creates an additional rotation of the sun so it is 56 over 16 rotations for the spin of the planet plus one extra rotation to account for the orbit of the planet so we now have the beginnings of a working planetary gear set and if we have the sun as an input and the planet carrier as an output we now see that the gear ratio is the number of teeth on the ring gear divided by the number of teeth on the sun gear plus one so in this case it's 56 divided by 16 which is three and a half plus one so this is a one to four and a half gear ratio what i'd now like to do is get two more planets in there because i want three planets and so for this you can simply do a circular pattern and then the type is going to be components this component over here and then we'll just select this axis over here and one extra thing that i'd like to show you is that if i go for four planets in this case you see that all of the planets immediately line up with the ring gear and i'll get into that a little more later on but going back to three planets we now see that the gears don't line up so what we have to do now is joint these planets to the rest of the model so this planet to this shaft flip that back and now it is in the correct orientation here and i'll also do that over here flip it okay and then to complete the motion links the easiest thing to do here because now the other two planets aren't linked the easiest thing to do is to choose motion link not this one i want to link that one to that one and just one to one and i also want to motion link this one to this one also again one to one so now we have all of our motion links set up so if we go to for example the sun gear rotation so let's call this sun gear rotation and if i now right click it and do animate model we can see the entire gear set moving like this and so the downside here is that um every 360 degrees the entire thing resets so that's causing a little bit of jumpiness so one of the things you can do is instead of that so this is now actually the joint for the planet carrier and if we animate this one if it rotates a full 360 degrees it comes back to where it started so in this case it is nice and continuous but it is also pretty fast so pick your poison in a way and then the final thing we can do is apply some appearances so click a for appearances and so here we have a mostly finished model the final thing i'm going to do to this model is create some small little cylinders for the planet carrier and the sun gear and then also extrude this up 20 millimeters and that just gives me two little cylinders that i can use to manually manipulate these gears now here's the planetary gear set fully 3d printed and what i'd like to do now is add this little indicator to the sun gear and i'll screw that down and i'll also make a mark on this planet over here and what i'll do now is rotate the sun nine times and that should cause the planet carrier to rotate twice one so as you can see this is indeed a four and a half to one reduction or nine to two and i want to point out that if you want to achieve the same reduction with a 16 tooth pinion then you will need a 72 tooth gear to mesh with it in an ordinary gear set and not only that not only is it much larger the contact here is split across three planets and yet in this arrangement the contact will be just one gear to the next now the contact ratio here is higher than in these meshes here because this gear has more teeth and the sharing of the load across the planets is never quite perfect however despite that i do estimate this gear set to be about two to two and a half times stronger than this arrangement here here i have a planetary gear set where i did not correct the addendum nd dendon and because of this the ring gear is now constricting the planet gears into the sun and so if i just lift this setup by the ring gear you see that the planets and the sun don't fall out on their own and the unfortunate consequence of this is that if i try to rotate this gear set i feel rather a lot of friction here and even some resistance as some of the teeth start to bind so it's really important that you do take the backlash and add in them indeed then them into account i'd now like to go over the requirements that you need to meet for a planetary gear set to work the first requirement we've seen before says that the sun gear and two planet gears together have to fit inside the ring gear the second requirement only applies if you want your planets to be equally spaced so before i continue i want to convince you that really you want them to be equally spaced in video two i showed you that when you have two gears in mesh like this there is a force in this direction that transmits the torque but there is also a force in this direction that will tend to drive the gears apart now if we look at a planetary gear set these forces will tend to cancel out if the planets are equally spaced but if i take this force here and this guy here and i move them for example closer to each other we see now that the forces no longer cancel out and there is going to be a net force on the sun that will push the sun that way but as these planets rotate around these forces will too so the sun will tend to wobble around like this and that will cause vibrations furthermore if the sun is pushed into this direction then it will move away from these two planets and closer to this planet which is detrimental for the load sharing between the planets there are other configurations than just a regular polygon that will equally share the load and that will not cause a force like this but you do have to take this into account this gear set that we made before had the tooth counts of 56 20 and 16 teeth and so from this you can quite easily see that we meet requirement number one at number two specifically we had 56 plus 16 up here that's 72 and divided by 3 is 24 and that's a whole number now if you meet these two requirements here simultaneously then not only do the planets fit they will also point in the same direction they will be in phase with each other so for three planets that doesn't work out for the gear set that i had because both of these numbers are not divisible by three but in fusion 360 when i went to four planets you saw that the planets immediately fell into place and that is because both 56 and 16 are divisible by four i don't know if this phenomenon is useful to anyone but it is a true fact regardless this third requirement here checks whether there is enough space in the planetary gear set for all the planets so when i take this planetary gear set here i could have also selected 6 planets to comply with requirement 2 because after all 72 is divisible by 6. but if i were to try that i would quickly notice that there just isn't enough space for that extra planet to go in between here and that is what this third requirement checks for now i won't go into it in too much detail but notice on the left side here that this is essentially just the outer diameter of a planet and on the right side here we have the pitch diameter of the sun plus the pitch diameter of a planet multiplied by this sign over here notice also that because the module appears on both sides of the equation you can simply drop the module when computing it it just makes it a little more intuitive to see what's actually going on here if you don't want to do math you can also check the fit of the planets in fusion 360 using a sketch so here i have simply the outer diameter of a planet as the diameter of the circle and the circle is 36 millimeters away from the center which is the pitch radius of the sun plus the pitch radius of the planet so if i now create a circular pattern of this circle around the center we see that three planets will fit fine four planets will also fit but in the case of five planets we will get interference and going back to the math this is the left side of the equation that i showed you before and this distance between these two points is the right hand side of that equation these are the gear ratios for a planetary gear set when the ring sun or carrier gear are held stationary respectively so this formula here we sort of derived in fusion 360. and the one at the bottom here is obvious to some degree because in that case the planet gears are just stationary idlers now it is possible that all three gears are rotating at the same time and in that case you'll have to use this more general formula at the bottom you can find more about this formula in the links below now as far as i can tell the most popular variety is to have a fixed ring gear and that has two reasons one it has the highest possible reduction out of these three options and second by fixing the ring gear you can also fix the ring gear to the outer housing or even make it a single part which is a lot more convenient than having the ring itself rotate around and then having another housing around it finally i wish to point out that using a higher pressure angle on your gears can be very beneficial because it will make your gear teeth stronger the two downsides are that first the force driving the gears apart like this will increase but if you have equally spaced planets then those forces will cancel out and it shouldn't cause you any problems the second problem is that you will get an increased backlash but in many applications like driving tanks that doesn't really matter finally i should also point out that in the fixed ring case you will get a higher reduction if you have a smaller number of teeth on the sun but you can only do that up to a point before you start running into undercutting but having a higher pressure angle also mitigates undercutting starting from an ordinary planetary gear set like this it's quite easy to construct a helico or herringbone gear set the first thing i'll do is remove those two cylinders that i made as handholds so let's roll back the history marker four positions and then delete all features after the h3 marker i'll activate the ring gear and then create a sketch on this vertical plane over here and then p for project i project the outer ring into the sketch l for line and then i'm going to look for this midpoint constraint here and then we go up 20 millimeters finish the sketch and then under create sweep and we're going to sweep this profile along this path over here and then we are going to enter a twist angle of 5.483 degrees and that will give us a helix angle of 15 degrees for the calculation on this look back at video 3. the operation is going to be new body and then click ok and then if we go into the ring gear we can take this old body and remove it so now we'll do the same to the other gears like so and one of the issues that i did run into is that the sun gear wouldn't cooperate with the sweep if i didn't have the hole plugged in the middle so it would sweep it but it wouldn't apply the twist angle so what i did is i added this empty sketch here on the top face of the sun gear and then i just twisted the entire sun gear profile without its hole that being done we can go into the separate components and remove all the bodies so remove it from the sun and from the planets and the planets are linked to each other so you only need to do that once and there we have a helical set i do wish to point out that every sweep command here requires a different angle so for this sweep command for the sun gear we use an angle of 19.19 degrees which is very different from the five degrees and a little bit that we used for the ring gear also notice that for the sun gear the twist angle is negative so the ring gear and the planet gears have the same handedness and then the sun gear has opposite handedness to the rest finally turning this helical gear set into a herringbone gear set is quite easy all we have to do is activate the components so let's start with the ring gear and then under create mirror mirror this body over this mirror surface and then relatively recently the ability came here to select operation join so we can just click ok on this and then it's immediately finished we don't have to come in with a separate modify combine to join up the two halves so that's very convenient that's the ring gear done so let me do the planets and the sun gear now and that's a finished planetary herringbone gear set all of the joints on this model are still functional so if we go under joints and for example animate the model on the pinion we see that everything still works fine the only thing that is a little strange is that the planet carrier hasn't moved from where we left it so we can go to modify move copy and then move this guy up by well not 20 millimeters because we have those shoulders here but if we move it by 15 millimeters at least the planet carrier will line up with the planets and then you can lengthen the shafts on the planet carriers all the way upwards if you like so that is a completed planetary gear set with herringbone gears finally i wish to warn you that if you use helical gears for a set like this each gear will experience an axial thrust that you will have to take into account for a herringbone set like this you won't get an actual thrust but assembly can be somewhat complicated and one of the tricks people use to make assembly possible at all for a set like this is to create splits in the ring gear so i'll activate the ring gear and then isolate it and then i'll create a sketch on one of the vertical planes and then i will create a projection of the trough that is directly parallel to the plane that i just selected so project those into the sketch with l for line and l for construction then i'm going to make a construction line down the middle of this projection and then i will use regular lines now parallel to the construction line on both sides next i will take these two lines and make them symmetric around the center line and then finally i will make a distance constraint here of let's say 0.3 millimeters finish the sketch then e for extrude we select both of these profiles and we extrude them to distance all and that will create a cut right down the middle of the trough here and so this single trough allows you to take this ring gear and essentially force it open with your hands you can also create two cuts like this so you can bring the ring gear together like this that's all i have for you today i will leave the files for this planetary gear set down in the description below there are two more topics that i would like to cover on planetary gears first i would like to make a practical planetary gear set because this one has gears riding directly on 3d printed shafts and there's no real way to mount it to anything so i want to create a planetary gear set where all the gears are riding on bushings now conceptually that's not a very difficult thing to do but it is quite difficult to make sure that you can get all the parts in there and that you can assemble everything and i'm hoping to mount it to a nema 23 stepper motor like this one and i'm hoping to create some pretty serious torque with it the other topic i would like to cover is compound planetary gear sets which allow you to reach some pretty insane reduction so a two-stage reducer could do a hundred to one or more finally i wish to point out that i've been recording the whiteboard sections of this video with my new lavalier microphone and i'm hoping to see some improvement in the sound quality but the main thing i'm hoping to do is to get better rejection of all sorts of ambient noise so i used to be recording with this shotgun microphone here or cardioid and because that is mounted on the camera it's a fair distance away from me and that allows all sorts of outside noises that come in so right now it's actually quite windy and it rains a little bit and i can hear that quite clearly because that's all happening on this roof behind me but i'm hoping that most of that will be rejected relatively speaking to the loudness of my voice finally i also wish to cover at some point bevel gears though i'm not quite sure when i'll be able to do that this video has already taken quite a lot longer to produce than i had hoped i've already done my first editing pass now and it's already at 35 minutes which is longer than i expected um so i guess there was a bit more content there than i had anticipated with that i'd like to thank you very much for watching and have a great day because i finished filming in the daytime for once

Channel: Antalz

Views: 12,787

Rating: 4.9791665 out of 5

Keywords:

Id: 71dn-eVdSmc

Length: 38min 17sec (2297 seconds)

Published: Mon Nov 16 2020

Reddit Comments

[u/MrSaltz]

I want to have a need to learn this skill... but I don’t have the need. Lol

Maybe I’ll make a tank? 🤔

[u/josnik]

Definitely going to check this out thanks.

[u/trackedpackage]

Saving this so I can learn how to do this for my local astronomy club events!

[u/gmara13]

Actually a fantastic application of this for those that like diy home projects is to create smart blinds. The planetary gear and a stepper motor fit within the tub of the blind. Been noodling this project for a while since they’re so god damn expensive.

[u/Aenaeus]

Very interesting video, great explanation. I will check out your other videos as well. Thanks!