Force Distribution on Sprockets

[TorqueWrench]

I have been looking into exactly how a sprocket is loaded in order to refine our FEA a bit and couldn't find any info on the forum about this.

The main thing I am struggling to find is force distribution across the teeth. Machinist Handbook states that the teeth where the chain first wraps is under lower loads than average and the teeth where the chain leaves the sprocket are under higher than average loads. Does anyone know how much of a difference there is among the teeth?

[Conor]

Order a sprocket from Sprocket Specialists and they'll do all the lightening work for you for a darn good price.

[Thrainer]

What will your sprocket be made of and what size chain?

For a rough start, I would load about five teeth and see what happens.

[TorqueWrench]

Sprocket is going to be 7075 to deal with fatigue issues. Sprocket is 428 chain, 52 tooth.

I have figured out in Solidworks what the minimum number of teeth that are going to be wrapped is, but I know the force isn't evenly distributed along those.

[Hector]

I will say only that the answer is definitely out there. About a year ago I came up with a model to describe the forces that each tooth on a sprocket sees (to be more specific, the force that each LINK in the CHAIN sees, hint hint). After searching for a way to validate my model I came across a book that had my model in it, which also recommended a technical paper put out by ASME (originally published by SAE, interestingly enough) which is needed to accurately calculate forces.

The book is Standard Handbook of Chains and the technical paper is ASME B29.10.

Hope this helps.

[Conor]

I have trouble understanding why you're so concerned about the loading on your sprocket unless you're trying to build your own. If that's the case, why go through all the extra time and effort when you can just call up a company, give them the tooth count and type, and they'll custom build you one and have it shipped in a matter of days. Does your team really have that much extra time to waste on such details??

[Hector]

Does your team really have that much extra time to waste on such details??

Yes.

It helps when the material is donated and you have access to a good CNC mill, too. I've seen sprockets go from conception>design>FEA/iteration>finished product in the period of a weekend.

At the end of the day is an engineering competition. Most parts suppliers, even racing parts suppliers, tend to greatly overbuild components, at least in terms of the loads that we see in FSAE. Some may feel that they can out-engineer a company like Sprocket Specialists and produce a lighter, more effective sprocket. Like all engineering decisions, that choice must balance time, cost, resources, etc. If you have the time, money, and resources, why not do it? Is designing your own sprocket the best use of time? Maybe, maybe not. Let the team engineers make the call, and the scores will sort out the good choices from the bad.

[TorqueWrench]

Thanks Hector. I'm gonna look into those books today and see if I can get an answer out of it.

Yes, we will be building our own sprocket. The time required to do it is not as extreme as you may think. The sprocket itself took maybe an hour to do and this will be day two of actual analysis. In my opinion, its well worth the two days to design something myself, learn something along the way, and, in the end, have something that only I am to blame for if it fails.

[Conor]

Forgive me for over estimating your capabilities. My experience was ladden with poor machines and no CNC access so I tend to think towards that direction when it comes to making components. I would still much rather buy a sprocket and save my time for vehicle testing.

[J.R.]

Well, if it's 10 degrees and two feet of snow outside then you cannot test! http://fsae.com/groupee_common/emoticons/icon_smile.gif Plus if you chassis is being welded, you also cannot test! And yes if that over-FEA'd sprocket fails....

[rjwoods77]

Chris,

Are you planning on machining the teeth as well? If you are going off of my old model I cannot guarentee that the tooth profile is correct since I found something off the internet that I don't know if I could completely trust.

[Conor]

[QUOTE]Originally posted by J.R.:
Well, if it's 10 degrees and two feet of snow outside then you cannot test! http://fsae.com/groupee_common/emoticons/icon_smile.gif[QUOTE]

You can get lots of dyno time... that will really test your sprocket.

[TorqueWrench]

Originally posted by Conor:
[QUOTE]Originally posted by J.R.:
Well, if it's 10 degrees and two feet of snow outside then you cannot test! http://fsae.com/groupee_common/emoticons/icon_smile.gif[QUOTE]

You can get lots of dyno time... that will really test your sprocket.

That would work if we had a working dyno that I could be doing engine work on. Unfortunately, ours broke last year...

[Conor]

Man, that certainly is tough then. Do you engine tune with an engine dyno then?

[TorqueWrench]

Originally posted by Conor:
Man, that certainly is tough then. Do you engine tune with an engine dyno then?

Last year we tuned fuel using the load cell from the dyno, but spark went untuned. This year we have a local snowmobile shop with a rolling road/trail dyno that is willing to give us time to do our tuning work on. Somehow, they have a setup to tune spark through a CVT. Most people would say that is impossible, but I think I know how they have it rigged up...

[VFR750R]

It's absolutely a good idea to make your own sprocket once you've done the calculations to show that laps times are sensitive to the weight/inertia of available sprockets.

The best way to apply the load in FEA is by also modeling the chain. The stiffer the links of the chain the more spread out the load will be.

A 428 chain has lighter (hence less stiff) links then a 520 chain, but the rollers are more closely spaced then 520 chain. The first roller in full contact will handle the most load of rollers in contact with the load falling off steeply with each succesive roller.

Good luck with constraining the chain to the sprocket correctly.

[Conor]

Originally posted by VFR750R:
It's absolutely a good idea to make your own sprocket once you've done the calculations to show that laps times are sensitive to the weight/inertia of available sprockets.

The best way to apply the load in FEA is by also modeling the chain. The stiffer the links of the chain the more spread out the load will be.

A 428 chain has lighter (hence less stiff) links then a 520 chain, but the rollers are more closely spaced then 520 chain. The first roller in full contact will handle the most load of rollers in contact with the load falling off steeply with each succesive roller.

Good luck with constraining the chain to the sprocket correctly.

I'm very intrigued by this. Do you have any data/plots for this type of comparison? I'm under the impression that the inertia would considered neglible unless the rest of the entire car is tuned extremely well. Getting the engine and suspension to this level of performance is quite an obstacle for many teams.

[VFR750R]

It was meant to be facetious. I'd get to sprocket design after I optimized every other rotating component that adds more substantial inertia to the system.

I see a common desire to 'do it yourself' in FSAE. I think I was alot like that in college too. But working with outside suppliers is just as much 'engineering' as designing the part yourself. It's always good to understand your suppliers methods for coming up with a solution, and compare multiple suppliers to see where you can get your best product. In the event that no supplier can meet your demands or goals, in house designing may be required. Remember that specialized suppliers have already learned all the 'tricks of the trade' so to speak.

In fact, many of you will go to work as engineers for 'outside' suppliers. On second thought, I'd do it myself too. http://fsae.com/groupee_common/emoticons/icon_wink.gif

[Conor]

Nicely stated. I didn't know what the intentions of your post were so I asked for hard evidence just in case http://fsae.com/groupee_common/emoticons/icon_wink.gif. Sure would have been interesting had you produced a plot for the comparison...

[Mark R.]

You're not the only one designing and machining your own sprocket. We run a press fit between the diff and the sprocket so the bolts don't load in shear and break. It allows us to reduce complexity and rotational inertia. Its not a common design, and we have material donated so from our actual budget it works out better than buying one and probably modifying the design or the sprocket to fit.

I've been approximating the load spread evenly across the teeth (based on a static analysis I did last year assuming worst case scenario was a bind), and it didn't break (with a safety factor ~k=2). A better understanding of loading conditions would improve the design.

[ibanezplayer]

We do a bit of designing and a bit of buying.....

Sprocket Specialists will sell you a blank with the number of teeth / pitch you want, we then take that, using our FEA (which I know nothing about) and our design criteria to CNC out the centre.

[TorqueWrench]

Originally posted by Mark R.:
I've been approximating the load spread evenly across the teeth (based on a static analysis I did last year assuming worst case scenario was a bind), and it didn't break (with a safety factor ~k=2). A better understanding of loading conditions would improve the design.

Thats pretty much what I have been doing, but using tire data to get the maximum forces possible and shock loading scenarios. The thing is, the even loading is not 100% accurate and hence my concern.

If you are doing an even spread on teeth, I would suggest testing the design with both all radial forces (chain skipping teeth) and all of them at maximum pressure angle (brand new, really tight chain). I even went further to apply all the forces onto 5 or 6 teeth to make sure it wouldn't fail if the load distribution was as severe as some were making it sound.

[Hector]

Sprocket Specialists will sell you a blank with the number of teeth / pitch you want, we then take that, using our FEA (which I know nothing about) and our design criteria to CNC out the centre.

If you're going to CNC the inside, you might as well CNC the teeth, too. A quick site that I've found that gives a correct tooth profile is Gizmology (http://www.gizmology.net/sprockets.htm). If you set it up right, all you need to do is model one tooth and save it as a template. Then, just change the angle of that one tooth and do a circular pattern for whatever size sprocket you may design in the future.

Can someone accurately weigh a Sprocket Specialists sprocket and post the weight? I'd be very interested to see how much they weigh in comparison to our home-cut units. Regardless, we will continue to cut our own since the material is donated and we have CNC access, but by visual inspection I'm going to wager that ours are a bit lighter than their "Ultra Lite" option.

[rjwoods77]

That is what I modeled the sprocket off when I did it at UB. I just don't know how much I trust that method of doing it if you were going to go cut your own teeth. I never looked into it to see if that is the real way of doing it. A blank from Sprocket Spec. cost 35 bucks for an aluminum sprocket and you get exactly what you want and also extra things like beveled teeth edges and such . They even throw in an internal cut profile for you for a couple dollars more.

[Hector]

I've cut six or seven sprockets using that profile and it works perfectly, actually a little too perfectly, resulting in a line fit that made it very hard to wrap a chain around. Taking off .002-.003" X-Y stock fixes the issues. The chain links fit perfectly between the teeth with no issues. Beveled teeth are easily cut with a profiling tool (how we do it now) or can be quickly beveled with a sanding wheel (old-school). Total machine time: around 15 minutes.

We have the stock, so cutting a sprocket is still free < $35.

Still waiting to hear on weights.

[Mark R.]

I don't use the tooth design from gizmology. There's a good profile in the Machinery's Handbook. Its around in the roller chain section. Its a little complicated at first, but if you work through all their numbers, the teeth work like a charm and aren't as tall / transfer the forces at a better angle.

[rjwoods77]

Hector,

Weight is really a null issue. They sell the lightened sprockets as is but if you send a dwg/dxf file to Randy he will cut the inner profile the way you want it for a couple extra bucks. UB has had Sprocket Spec. make our sprockets. They even hobbed a 10 tooth 428 steel gear for us with a pilot bore of our choice. It is made out of 8620 I think with a 30 thou case hardening on it if I remember correctly.

[rjwoods77]

Mark,

I just noticed the profiles in there. Very good call. I cant believe I never saw them before. Do you have any idea what the "metric" motorcycle chain profiles are or where they are located?

Rob Woods

[A Richards]

That profile from Gizmology works fine, thats what I designed our laser cut sprokets from. I took 0.04mm off the diameter though, which probably makes little or no difference. Only thing that i would advise is that you take the sharp point of the top of the tooth as it does catch, oh and also machine chamfers on the edges. I really cant see how you could design the profile any differently, its just a series of semi-circles of diameter equal to the rollers and seperated by the pitch after all, hummm, maybe im just vague.

[Hector]

Yeah, the Gizmology sprocket profile does work fine, but like Rob, I never noticed the profile in Machinery's Handbook. After checking it out last night I definitely like the teeth tips a lot better. I may have to try that for the next sprocket we make.

How did that 10-tooth gear work? What kind of torque/speeds was it seeing?

[TorqueWrench]

The ten tooth gear worked fine for its application. Max torque on that engine was somewhere around 45 ft-lbs and the redline was a hair over 6000.

[jdstuff]

For what it's worth.....

I used the Machinery'd handbook tooth profile a few years back for the rear drive sprocket (~49T if I recall correctly), with our own internal design. Then mounted the finished sprocket on a lathe to cut the tooth chamfer. Worked beautifully....

[Paul Achard]

Hi guys,

I've been wondering for a few days now why sprocket designs tend to place bracing in compression. Check out the following album for examples (keep in mind that bike sprockets are on the left side of the wheel).
http://imgur.com/a/DRQwN#0

Another example is Wisconsin's sprocket design from 2012 (I BELIEVE the spokes were also loaded in compression):
https://www.facebook.com/photo...08843&type=3&theater (https://www.facebook.com/photo.php?v=398611056823668&set=vb.141092665908843&type=3&theater)

To me this concept makes little sense as you expose the bracing to buckling failure; placing the bracing in tension (i.e. flipping all those sprockets I showed) seems like a safer, more stable design as far as I can tell.

Am I missing something fundamental?

Cheers,

[Pete G]

I'm assuming it has something to do with fatigue.

[Mark R.]

It's possible it is in tension under the most severe loading conditions. Which one's worse? Acceleration or engine braking? Don't forget ALL of your potential loading conditions.

I've seen differential mounts designed for accel fail because nobody thought about engine braking. I'm pretty sure the sudden stops are actually worse than the accel loads.

[Z]

Paul,

My guess...

If the spokes are in tension, like the spokes on a bicycle wheel, then the circular rim of the sprocket is in compression. If this compression becomes too great, then the sprocket rim buckles, like an overloaded bicycle wheel (the rim ends up looking like the edge of a potato crisp).

Having the spokes in compression puts the rim in tension, and this acts to keep the rim in a circle that lies in a flat plane. Large circular saw discs (eg. in timber mills) often have their centres "expanded" by hammering or heavy-press-fit hubs. This puts the rim into tension, with perhaps the whole disc adopting a slight conical shape. This forces the rim with its teeth into a flat circle, which is good for straight cuts. Shrinking the centre of the disc (perhaps by excessive welding near the centre) can turn the disc into that potato crisp shape, which is not good for straight cuts! http://fsae.com/groupee_common/emoticons/icon_smile.gif

(Nerd note: Flat disc = Euclidian space. Potato crisp shape = hyperbolic space (= excess of material around any point). Conical shape = elliptic space (= deficit of material around any point).)

Z

[Paul Achard]

Z,

Thanks for the insight, I had never visualized it that way.

[Slim]

Paul,
My take on it is that you want to react the chain forces as directly as possible to use the material as efficiently as possible. I see many teams with both tension and compression spokes (triangles) but found in my FEA that a compression only spokes was the lighter option. Seems like Wisconsin thinks the same from that cool video. The closer the angle of the 'spoke' matches with the incoming load, the less the bending in the spoke will be.
I never tried angling the spokes the other way past vertical, but with how the loads are coming in I can't see anything other than a large amount of bending of the spokes happening, requiring a much heavy sprocket.

See attached the picture of the distributed loads used in our FEA last year. http://i.imgur.com/s4F35WF.png

Regards,
Slim
Waterloo Formula Motorsports