How to model Helical and Herringbone Gears; pros and cons (Gears pt 3/7)

hi in today's video i would like to talk about helical and herringbone gears and to start i'm first going to create a regular spur gear so you've seen how to do this before and there we have a spur gear i'll now activate the new component that i've got i'm going to create a sketch and i'm going to put that sketch on one of these two upright planes and if you're having trouble selecting them you can left click and hold and then this dialog pops up and you can easily select either of the two i hit p for project and i project the top plane of the gear into my sketch reset the view via the view cube l for line and i'm just going to draw a line floating out here i'm going to take the end point of the line and make that coincident with the projected line and i'm also going to make the line itself coincident with the origin now you could have made a midpoint constraint as well but because this projected line consists of all these line elements you may end up having your line slightly off kilter the final thing is d for dimension and i'm going to make this gear 20 millimeters tall finish the sketch and then under create we go to sweep the profile is the face of this gear the path is the line that we made and then under the twist angle we are going to enter 57.296 degrees and i'll explain where that angle comes from later and then under the operation we are going to select new body and then click ok and then if you open up the component here you can see these two bodies and so we can take the original body and remove it and there we have a helical gear from here you can use all of the techniques that i've showed you in video 1 to attach this gear to a shaft and you can use all the mathematics from video 2 without any changes what i'd like to do now is turn this gear into a herringbone gear and to do that we will go to create mirror we are going to mirror a body specifically this one and we're going to mirror it across the top face of the gear and then click ok and there we have basically a herringbone gear but if i look now under my component i see that i have two bodies so i'm going to modify combine click both of the bodies and once this is computed that will join them up operation join into a single body and that completes the herringbone gear and this is in general a very convenient way of making symmetric objects you just make one half and then you mirror it across a flat face to make the other half i want to go back a few steps and show you something different so i'll select the combine and mirror on the timeline and press delete and what i'll do now is create a sketch on the top surface of the gear c for circle and i'm going to make this circle as large as the inner diameter of the gear finish the sketch e for extrude and let's pull this up by 10 millimeters and then i'm going to construct mid plane which i use so often that i have it pinned to my bar and i'm going to put it between the end of the helical gear and the top of this cylinder click okay then create mirror as before i'm going to take this body and mirror it across the plane that we just made and then modify combine as before the two bodies join them and click ok and so this is basically the same thing as we had a moment ago but instead of the two helical gears really meeting tip to tip at the center there is this space in between and this is known as a double helical gear and i'll go into the reasons why you would want a double helical gear instead of a herringbone gear later on let's first take a look at that angle that we put in the sweep command imagine you take a gear like this and you cut it open and then you lay it flat like this what you then have is a rectangle and the long end is equal to the diameter times pi the circumference of the circle and in this case it's specifically the pitch diameter times pi which is also equal to the module times the number of teeth times pi in a regular spirit gear the teeth would go upright like this but in a helical gear they will go off at an angle and that angle between the helical teeth and upright is beta which is the helix angle now these helical teeth cover a horizontal distance and that horizontal distance is equal to this expression over here so it's theta over 360 degrees and theta is that angle that we put into the sweep command and this part essentially represents how much of a complete revolution the sweep has turned and then these three numbers are simply the circumference of the circle so it is how much of a complete revolution have you made times how long is a complete revolution so if you remember your high school trigonometry you will know that the tangent of beta is the opposite divided by the adjacent which is this expression over here this horizontal bit divided by the vertical bit which is simply the height of the gear but this gives us beta if we know what we put into the sweep command but we want that the other way around so we need to rewrite this this is fairly straightforward you multiply both sides by h and by 360 and you divide by module number of teeth and pi and what you get is that theta is equal to 360 times h times the tangent of the helix angle divided by marginal number of teeth and pi and in the specific example that i did a moment ago in fusion 360 i had a helix angle of 45 degrees and the tangent of 45 is one so we get 360 times 20 times 1 divided by 2 times 20 times pi and that is equal to 7200 divided by 40 pi which is a little bit less than 60 aka that 57 and a little bit degrees that we put in so that is how you get the correct helix angle or rather what you need to put into the sweep command to get the helix angle that you want i've so far entered only positive values for the twist angle in the sweep command but you can also enter negative values so i'll activate this component here on the right and then create sweep and then i'll sweep it the same way as before with a positive twist angle of 57.296 degrees and as before the operation will be new body and then on the other gear i will do the same kind of sweep but this time i will give it an angle of negative 57.296 and again for the operation we'll do new body and then as before i can remove the old bodies that were the spur gears themselves and i've set up motion links between these components so that they rotate together and as you can see by having this opposite twist angle these two gears mesh together correctly and these two gears are said to have opposite handedness if you look from the top you see here that these gear teeth tend to veer off to the right and these go off to the left and so the left gear is left-handed and the right gear is right-handed and for parallel axes like these you need opposite-handedness in the gears and you can achieve this by entering negative twist angles in the sweep command but what you can also do is mirror the gears because the left gear here is the mirror image of the right gear and so you can of course do that under create mirror but you can also mirror the components or the stls really inside of a slicer like cura or cruiser there are quite literally two different ways of looking at a helical gear called the transverse and the normal systems i'd first like to show you the transverse system which is essentially what we've been doing all this time so for this i'll activate this component on the left and create an offset plane and i'll just drag that down some random distance and then i'm going to split the body so modify split body split this thing along this plane and then i have these two bodies and then i'll just remove the top one and then if we look at the section that we've just made we have essentially just another section of the spur gear that we've started out with so this is kind of a natural consequence of how we model these gears in the first place but let's now look at the normal system so i'm going to activate the other component and hide this plane so here i have made this helix here and i've made it specifically so that this path here follows this tooth here in the gear and so i'll go to construct plane along a path and then i'll drag that to about here and then i'll do the same thing modifying split body this body on this plane and then i'll again remove the top bit and i'll also hide the helix and the plane and then if we look at this section here we see that it is essentially just a spur gear but the teeth form is a little different so if you look here at the thickness of this tooth roughly speaking it's about two and a half millimeters you can see here but if we look at this gear here and we check how far these are apart we see that it's uh 3.3 millimeters a little bit more than that and so the thickness of the teeth quite literally depends on what angle you use to look at them and so this gear on the right now is the transverse system with the transverse module and this transverse module is larger for the same gear than the normal module which is what we have here on the left and so you can use some formulas to translate between the two but the most important thing is that if you're using the transverse system then the center to center distance and the pitch diameters all follow the same rules that we've seen before for regular spur gears so that's a very easy and convenient way to go for the normal system you have to do a little bit more math to figure out the center to center distance the normal system however is very natural if you want to cut gears from blanks and the reason is because this normal system this path here along this helix is basically the path that you have to push a gear cutter through a blank to make a gear like this so you will find that most commercial gears actually follow the normal system which is arguably a bit inconvenient but you can also definitely purchase gears in the transverse system as we've just seen for two helical gears to mesh on parallel shafts they should have the same helix angle but opposite handedness and in general the formula for the shaft angle sigma is that it is equal to the sum of the helix angles and so it is most convenient really to regard these two as having the same helix angle but opposite sign so one is plus 45 degrees the other is negative 45 degrees and so if i bring these two together the shaft angle is zero but if i take another gear with the same helix angle and handedness then they won't mesh on parallel shafts but 45 degrees and 45 degrees is 90 degrees so if i twist this gear 90 degrees it goes into mesh now in general for parallel shafts if the shaft angle is zero then you should have equal and opposite handedness and that is your only choice really but for non-parallel shafts i recommend that you use the same beta and the same handedness for both gears you can choose to use a different helix angle a different data for each gear but in such a case you must ensure that the normal module of the gears match and that also means that the transverse module will not match and you have to keep this in mind when you're modeling i would now like to talk about some of the advantages and disadvantages of using spur gears versus helical gears and herringbone gears and perhaps one of the surprising parts is that there are reasons to use a spur gear besides just cost the first thing i'd like to show you is that helical gears produce an axial force which straight spur gears and herringbone gears do not so let's take a closer look at this here i have a set of regular spur gears and as we've seen before these spur gears produce a force in this direction to transmit the torque but because of the pressure angle on the teeth they also produce a force in this direction which drives the gear apart now that is still true for helical gears but helical gears have an additional complication the force generated by these gears is always perpendicular to the teeth because it is a normal force and for the spur gears that's simply in this plane perpendicular to the gear teeth but that's still the case for the helical gears but here the force points in that direction so if i drive this green gear i will start pushing the blue gear in this direction and because the blue gear produces an equal and opposite reaction force the green gear will be pushed in this direction now that force is proportional to 1 over the cosine of the helix angle so it'll get much more serious as the helix angle grows larger to hold this force you have to ensure that the mounting methods that you use to put these gears on the shaft can hold the force and you must also ensure that the bearings supporting the shaft can hold the force now regular ball bearings can take a little bit of thrust force but if you have a very extreme helix angle or you are transmitting a lot of torque then you must probably upgrade to something more exotic like a tapered roller bearing or an angular contact bearing now for herringbone gears they don't actually have this problem because the force generated on the top end here is compensated by the equal and opposite force generated at the bottom so these two balance each other out so that net they don't produce an axial force like the helical gears do the next thing i want to show you is that you cannot slide herringbone gears into mesh like you can with spur gears or helical gears so let's take a closer look at this too if i take two regular spur gears like these i can slide them in to mesh across the direction of their axes like this and if i take a set of helical gears i can do the same thing the only difference is that as they go together one of the gears has to spin but if i take a look at herringbone gears i run into a bit of a problem because these two gears are supposed to mesh together like this and that means that these two upper bits mesh and these two lower bits but if i put the gears like this or like this they won't go together so if i approach the gears along the directions of the shafts then they won't go into mesh like this because these two parts cannot mesh and i get the same problem if i come in from the other side and so the only way to put these gears together is by approaching them from the sides like this and so two things that you can do is first put them together in mesh like this and then put them on their shafts and the other thing you can do is put them on the shafts put the bearings on the shafts as well and then put the bearings into the bearing housings from the side but this does require that you have bearing housings that you can open and close from the side if you really want to get a physical feel for this problem i recommend that you download and print the emmett gear bearing really drives home nicely how this problem works the next thing i want to discuss is the handedness of the gears so it is quite obvious now that spur gears don't have a handedness and helical gears do but a lot of sources will claim that a herringbone gear does not have a handedness to it and i'd like to show you that honestly in most cases they do and you really have to look out for this here i have that set of herringbone gears again and as you can see they won't go into mesh like this but now someone might come around and say well all you have to do is turn one of the gears around and they are correct if i turn them around they go into mesh like this but my problem is this mounting hub is now up here and i don't want the hub here i want it down here and so if i want these mounting hubs in the right positions i do have to ensure that these two ears have opposite handedness and in fact if you do anything that is not symmetric with respect to this plane over here you will reintroduce a handedness to the gears that you should be mindful of one of the big advantages of helical gears and herringbone gears over regular spur gears is that they have a much higher contact ratio and because of this they tend to run much smoother so let's take a closer look at this i have marked one of the teeth on both of these spur gears so that we can track them as they go into mesh so if i rotate these two gears then right around here the two marked teeth first contact each other and if we look at the same teeth at the other side we see that they go into contact at the same time so the entire tooth goes into contact all at the same time and this is very different for helical gears so if i turn these two together then right around here the marked teeth going to mesh and yet if i look at the same teeth on the other side we see that they are nowhere close to meshing so in general helical gears spread the load that they are transmitting through more teeth however each tooth is only partially in contact with its mating tooth and how many teeth are participating in this transmission of the load is called the contact ratio and if you have a higher contact ratio then you have a smoother running gear generally speaking we've also seen in video 2 that if you have more gear teeth then you have a higher contact ratio as well so that is again why if you have more teeth to your spur gear you have a smoother running set next let's talk about machining these gears now for a straight spur gear it is relatively easy but you do still need some equipment you need a mill you need a dividing head and you need an appropriate set of gear cutters what you do is you mount the blank on the dividing head and then you run the gear cutter through the blank and then every time you do that you can rotate the blank by the appropriate amount of degrees which is determined by how many teeth the gear has and then as you keep doing that you will form all the teeth and make the gear for a helical gear it's much more complicated because you need to rotate the head to match the helix angle and you must also rotate the blank as you're pushing the gear cutter through to create the helix and for the herringbone gear it's basically impossible because it's very difficult to form that part where the two helices of the herringbone gear meet and so you need specialized machinery to do that in contrast to all that all three of these types of gears are very easy to 3d print equally easy now the reason you might want to use a double helical gear is because those are still relatively easy to machine compared to making herringbone gear so it's easier to make two helical gears and put those together than it is to make a herringbone gear the trade-off there is that you need a little bit of space between the helical gears to ensure that the tooth tips don't interfere with each other there are two more things that i'd like to show you first is the difference between what you get from a helical gear generator and what you get from the method that i've shown you at the start of the video so if you go to tools add-ins into the fusion 360 app store you can download a bunch of add-ins and one of the most popular ones is a helical gear generator so once you have that installed and running if you go to create helical gear you get this dialog so you can go for normal or radial system and radio is the same as transverse and you can enter everything else the one thing that's missing here is the root phillip radius which you can enter into the spirit gear generator and the other thing that is a bit annoying about this generator is that if you go for a low number of teeth then it says that undercut is required which is true but it doesn't create the undercut for you so you cannot create gears with a very low number of teeth because you don't get the undercutting that you need nevertheless if you do make gear with this i have made two here so one is based off of a spirit gear using the method that i've shown you before and the other comes out of a helical gear generator so if we look at these two in detail we see two slight differences so the first difference well first let's notice that the teeth the shape here is completely the same and we'll see that that's really true in just a second but here at the root of the teeth we see two slight differences first we see that the inner diameter of the two gears differs by about 0.05 millimeters and second we have this root fillet here that is part of the spur gear based gear but is not present in the helical gear so if i hide this one you see that there is no root fillet here so if i put this back i can go to modify combine and we've used this before to join two bits together and what we're going to do now is cut two things away from each other so i'm going to take the spur gear based helical gear and from that i'm going to remove the helical gear from the generator so here we can see all of the parts that are in the spur gear based gear but that are not present in the helical gear generator based gear so this takes a little while to compute this is fairly complicated geometry and we press ok a little bit more waiting and here we have the difference so what you can see is this little part here again this difference in inner diameter and the presence or absence of the root fillets but there is nothing here of the teeth themselves so the tooth form is exactly the same so that is the difference between the two and i both of these methods will work fine for generating the gear the root fillets do add a little bit of strength to the teeth but the difference isn't that large the final thing i'd like to show you is another small advantage of using a double helical gear over a pair of herringbone gears so if i rotate these two gears together like this we notice that the contact first happens at these tips in the center and then the contact gradually moves outward along the teeth now if i reverse the rotation direction and i also look at that from the other side we see the reverse we see that the contact first happens on the outsides and then gradually moves inwards now if you have some grease or some dirt on these gears then this action will tend to pull that grease and dirt inside these little crevices here and if you have a double helical gear instead you have this space where the grease can escape so that it can continue circulating or where dirt can escape so that it doesn't act like grinding dust inside of your gear set i hope you found that interesting and useful this video really did take a little bit too long to make of course the thing that happened at the start of 2020 happened which did slow me down a little bit and it also prompted me to start work on a ventilator specifically this guy so you can find some videos on some of the individual pieces of that ventilator on my channel and i've also created a longer video covering the entire system and how it all goes together in my last video we assembled this drive unit for my remote control tank and in the next video we're going to put those drive units into the tank going to clean up the insides a little bit fix some of the electronics and hopefully that'll make it ready for a test drive i don't know yet where i'm going to test drive it because my favorite testing field has been turned into a construction site which is mildly inconvenient i'm also going to be working on part 4 of this series on ring gears and racks that part hopefully will come out a bit quicker than this one i'm quite hopeful in that respect because the material in that video should be a little bit simpler than the material of this one with that i'd like to thank you very much again for watching and have a great night

Channel: Antalz

Views: 24,688

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Id: re8-kYZjjyY

Length: 30min 6sec (1806 seconds)

Published: Thu Jul 30 2020

Reddit Comments

[u/CrispyDragonz]

Excellent video. Thanks.