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Fasttrack
07-17-2008, 02:56 AM
Its late... or early... and I'm having trouble coming up with what I need to figure this out. Maybe I'll have it worked out by the time I wake up, but I thought I'd post it here bfore going to bed.

Ook - I've got a sprocket that threads onto a hub. The thread is 24 TPI with a major diameter of 1.685. I accidently chipped my carbide tool and did not notice it for the last two runs, so the root is a little wider than I had wished for, however the thread still engages fine but lets call it only a 50% engagement. The sprocket only engages 5-6 threads at a time. Call it 3/16 for the length of engagement.

I'd like to find out the maximum amount of torque that the sprocket can handle before destroying the threads. I crunched some numbers doing some "home-brew" math (thats by way of saying I had no formulas) and came up with about 2000 ft-lbs, which seems way too high.

davidh
07-17-2008, 08:18 AM
one of my customers was looking for a torque multiplier for tightening grade 8 or better bolts, 1-1/4 diameter coarse thread, and needed a total of 1800 foot lb capacity to do it properly. just for your reference. . . .

wierdscience
07-17-2008, 08:34 AM

Evan
07-17-2008, 09:11 AM
I'd like to find out the maximum amount of torque that the sprocket can handle before destroying the threads. I crunched some numbers doing some "home-brew" math (thats by way of saying I had no formulas) and came up with about 2000 ft-lbs, which seems way too high.

I make it about 30 inches of thread that needs to be sheared off at once. 2000 ft lbs doesn't seem out of line to me. It takes a lot to shear a thread on a large diameter.

A.K. Boomer
07-17-2008, 09:21 AM
Could be time to chuck the books bro, Youv tightened enough fasteners in your day already --- Look at the big picture, take into consideration the material grade of both friction units, their hardness - the thread pitch and diameter like you state, the inherent flaws like you state, what its up against for its service life in the future, Is much of the stock torque specs due to them not wanting it to vibrate off? then maybe some locktite?
Sounds like allot of torque, get a rock solid cheater so you cant be fooled and pay attention to the elasticity of the materials, once you "bump up" the tension to movement curve should snowball like your hitting a wall, then pour the coals to it with great attention to detail with the elasticity so you dont go overboard, rough figure your weight on the cheater length to get to ballpark but more importantly is the "feel" for it, in no way shape or form should it ever get "easier" or even "break even" unless its an expansion bolt of some kind or some setup with a crush bushing -- use your head, you got a good one:)

I use a torque wrench on rods and mains and head bolts - thats about it anymore, Iv saved myself allot of grief because of it, many things one can make exceptions for, a few things you cant, or at least shouldnt.

Some things I know I torque over factory specs, other things not so,
Factory specs dont tell you a damn thing about how a vehicle will hold together after a decade of use, thats where a good mechanic who pays attention can out-trump the book smart engineers who don't have a clue, and believe me, many times they don't, Over the years it has become quite obvious that many lack the foresight to take all the variables into consideration.

Fasttrack
07-17-2008, 01:10 PM
Interesting, using the equation on that website or a similiar in machinery's handbook, I get a maximum shear strength of 15.27 tons. Now I just need to figure out how to get that to a torque measurment. I think I saw some graphs somewhere that show what happens as far as torque and clamping force.

Am I correct to assume that the 15.27 tons would be the maximum "clamping force" before failure? Then I could convert to torque pretty easily using a formula in machinery's handbook.

Thanks for help!

p.s. Thanks for the advice AK. Unfortunantly, I don't have any factory specs. I'm actually using a #41 sprocket from a bike as a drive sprocket on a go-kart. It was one of the rear sprocekts on a 10 speed that thread onto the free-wheel mechanism. After I finished making my part, it occured to me that it may not handle the torque developed from a 7 hp engine after going through "low-hole" in a transmission.

Fortunantly, it threads up against a shoulder, so as you deliver more torque to the sprocket, it tightens itself against that shoulder and the resulting increase in normal force means a greater force of friction between those two mating services. That, of course, means that it will handle more torque than the threads alone can handle.

edit: I skipped the torque part and just figured out how much torque could be delivered based on the force of friction generated by tightening the sprocket. Correct me if I've made a mistake in my reasoning: I figure that the maximum clamping force is 15 tons so I call this the normal force between the two mating sufaces. Then, I find that the static coeficient of friction for steel-steel is .8. Multiplying this with the 15 tons gives me a force of friction. I then use the inside diameter of the ring to give me a torque value. I arrived at 1850 ft-lbs. Sound reasonable?

Evan
07-17-2008, 05:21 PM
Sound reasonable?

It may sound good but that doesn't necessarily mean it is. Especially at low to zero relative movement between surfaces there aren't any accurate ways to quantify friction for most material combinations. It's very non-linear in terms of how much force it takes to break free and begin moving. Stick-slip is the problem and it cannot be well described mathematically.

Fasttrack
07-17-2008, 06:20 PM
LOL ... so basically its "try and find out"...

I don't need an exact answer, I just need a rough answer to find out whether or not a bicycle sprocket/hub can handle the torque from a 6.5 horse engine after a 6.5:1 increase in torque without frying the threads.

Well I've already got the part made so I guess crunching numbers is just "quibbling". I'll just have to see what happens when I mash down on the throttle for the first time :D

edit: stick/slip should only be an issue as the applied force nears the force of static friction. If I have correctly figured on the amount of torque it can theoretically handle (ignoring the stick slip issues) then I'll at least be able to make a comparison. If the torque value coming out of the transmission was 1500 ft-lbs (that would be sweet :D), I might need to worry but if 1800 ft-lbs really is correct in at least magnitude, then I've got nothing to worry about. My little engine, even after the gearing, won't produce near 1000 ft-lbs ;)

Evan
07-17-2008, 06:31 PM
As you are aware I have been messing about with bike parts of late. It's amazing how strong the parts like freewheels and sprockets are. They are hard, really hard and tough too. I don't know what material they are but it sure isn't mild steel. I tried hard turning one piece and it was like the unstoppable force meeting the immovable object except the immovable object won. Well, it did until I set up the tool post grinder. :D

BTW, I should point out that the static friction values do not scale according to force applied. That's where the non-linear part comes in to play. With some materials the coefficient of friction can even go down with applied force, ice being an example.

Fasttrack
07-17-2008, 06:49 PM
:D Yep! I tried turning a sprocket hub from a single speed bike. It was going to be my driven sprocket and man is that stuff hard! I got it turned down and welded in place but I worried about how it was going to weld. When I turned it, I was throwing sparks. The chips were burning off instead of curling off the carbide! (And this was a cheap kids bike from china)

I think steel on steel is a fairly simple friction mechanism. I looked up a graph for mild steel and the coeficient is constant until extremely high pressures where it increases. I expect that is the galling or friction welding point. My physics teacher in high school said something about static coeficients of friction and about how increased normal force always correspond to an increased force of friction. I argued. In the end he revised his statement and I got 10 points extra credit :)

I was hoping you might chip in on this post. I knew you had been working with bike components lately. You reckon they'll handle my incredible 75 ft-lbs of torque? :D

I thought last night that those threads looked awfully wimpy, but, like you pointed out, the large diameter helps alot. With a lawnmower engine rated at 7 gross ft-lbs of torque, I'm not too worried about it. I was going to make up a replacement to have on hand, but I don't think I will bother.

A.K. Boomer
07-18-2008, 12:38 AM
I'm actually using a #41 sprocket from a bike as a drive sprocket on a go-kart. It was one of the rear sprocekts on a 10 speed that thread onto the free-wheel mechanism.

Wow that must be going back aways, all the freewheels on multi speeds i know of have kinda an offset spline setup and the entire cluster of sprockets are held on by one end spline nut, the gland nut is not extremely strong but it doesnt have to be as the splines take the drive forces,
Can you buddy up another smaller sprocket with fresh threads, lock them together some (on the freewheel for thread meshing reference) and then drill and rivet them together, My XTR rear cluster freewheel on my C-dale is actually riveted together so all sprockets have each others splines involved -- much nicer.
Your right about the hardness of those dang parts, and the inside sprags and engagement teeth are like dowel material -- exceptin even harder.

Rich Carlstedt
07-18-2008, 12:57 AM
Its late and I can't explain,
but calculations show 250 Ft/pounds to shear point.
More tomorrow
Rich

Evan
07-18-2008, 02:08 AM
I think steel on steel is a fairly simple friction mechanism. I looked up a graph for mild steel and the coeficient is constant until extremely high pressures where it increases. I expect that is the galling or friction welding point.

Extremely high pressures are easy to obtain when large diameter very low helix angle threads are in use. 24 tpi at a diameter of 3/8" gives a helix angle of about 2 degrees. At 1.6" it is only about 0.45 degrees. That acts as a ~4 times multiplier of the tensile stress produced (rule of small angles) by the same applied ft lbs of torque, ignoring friction considerations. Taking friction into account it can easily reach the non-linear range in a fastener that size. That's why large bolts usually use acme or other similar thread forms. They are much stronger than a vee thread.

Fasttrack
07-18-2008, 12:55 PM
Evan - interesting ... I hadn't thought of that. I can see how the pressure on the threads could be quite large, but the clamping force between the two faces is not, and that was what I meant when referencing the graph.

Looking forward to hearing where I went wrong, Rich! Post when you get a chance. Even at 250 ft-lbs, that should be ok. The engine puts out a whopping 7.5 ft-lbs and even after gearing, i'm still only looking at about 70 ft-lbs.

AK - Yeah its an oldie alright. It looked like a bike from the '50s before it hit the scrapyard. There are five sprockets, three of them have four "splines" and the two smallest are threaded. The splined ones have a larger ID and I plan on using them as my "driven" sprockets. I thought about trying to pin two of them together, but the two threaded ones are just to small. There is no meat to get a rivet, bolt or other through them. I had really hoped to pin the sprocket to the hub and do away with the threads, but like I say... just too small!

A.K. Boomer
07-18-2008, 03:30 PM
FT im going with a two thumbs down;) Im starting to get a little "picha" of whats going on over at the farm:p
Yes iv been wrong before so this is just a "for what its worth"
The very fact that they had the larger cogs on this rear cluster splined and the smaller ones just threaded speaks volumes to me, it means they were already having to compensate with having the larger rear gears splined because they receive more torque than the smaller ones, the biggest factor is that this is occurring on a humanoid powered machine, while we are high torque power plants muscles dont have a fraction of a small percentage of the radical spike curves that the IC engine has and also dont cover no where near the range (our high RPM is only about twice that of our effective low RPM) Muscles can be more compared to powerful rubberbands when it comes to drivetrain talk, Your 7 HP all steel construction piston pumping flywheel storage apparatus is about to create spikes that that little hub never even dreamed of, If its way geared for low then your doing that for a reason (you want torque!) If its geared for high speed then you have a chance but lugging can then work against you and create ungodly forces in the drivetrain as the steady momentum of the bike clashes with the pulsating mechanical apparatus...
I see trouble a brewin, go for it and let us know what breaks and how long it took - Id like to be wrong in this instance.
Keep in mind this, that you have a constant hammering in one direction to keep tightening --- its like taking an air hammer to it:eek: if your even close to its rating its days are numbered.

Fasttrack
07-18-2008, 04:06 PM
I see trouble a brewin, go for it and let us know what breaks and how long it took - Id like to be wrong in this instance.

:D Thats how I look at all my go-karts. They are not an entertaining diversion from life but rather an experimental vehicle platform for testing certain mechanical devices. At least thats what I told our homeowners association when they complained about my go-karts. This is back at home, not on the farm ;)

I consider every homemade component on the go-kart an experiment and am waiting to see what breaks and how long it took!

Incidently, the whole reason I posted here was because of the fact that three of them were splined. I thought it was suggestive too, and I began to worry what happen trying to drive a go-kart with a few piddly threads...

A.K. Boomer
07-19-2008, 08:20 AM
I consider every homemade component on the go-kart an experiment and am waiting to see what breaks and how long it took!

Fasttrack I like your style, thats why you have such an incredible learning curve happening, all failures are mini - successes - if one pays attention, Its why I asked you to post the results, I wanna learn too:)

From my very early mini bike days of running pieces of a peanut butter and jelly sandwich down the carb of my 3.5 hp briggs, rapping it out with the frame high centered on a railroad tie - full throttle - My Dad walking past shaking his head:p
I learned that sandwiches (baloney too) although may contain carbohydrates and therefore BTU's don't atomize very well in the combustion cycle of an IC engine. I also learned that baloney smells terrible - and can plug up a muffler with burnt animal flesh...

Rich Carlstedt
07-19-2008, 10:59 PM
repost by mistake

Paul Alciatore
07-20-2008, 11:33 AM
Hey,

Install it and use it.

If it strips, weld it.

Rich Carlstedt
07-20-2008, 04:14 PM
Fast track
finally had a chance to get back
Sorry about the 250 number, I was tired and had rough numbers .
Rich

Before I start, I want everyone to know this is a theorietical calculatiion and can have many
different answers based on numerous unknowns.
We do not know the material and strengths
We do not know the true thread profile.
What I would like to do is walk you through these to
see how such calculations can be done IN A SIMPLE WAY .
Threads strip for a number of reasons, foremost is "Shear" failure
Given two perfect threads of the same material, the smaller Root Diameter part which is normally called
the screw, will strip first. This means that Female threads are more forgiving for dimensional errors !

With that said, we need to know the thread thickness at the pitch center of the screw (1.6") and the T ( tensile) of the material.
I will assume it is mild steel because I have no other info.!
Mild steel has a T of 65,000 , and shear = 75 % of T, or 49K~
Material shear forces are a function of thickness, so if we know diameter and thickness and material, we can get
the strength of the joint, that being the thickness of the tooth ( at PD)
Normal 24 pitch threads have a tooth thickness of .021at the pitch diameter
If Fasttrack cut the thread with a .012 flat on the tool end, and went to the prescribed tooth depth of .036,
he would have a truncated thread as shown. This thread has only .009 thickness at the critical point .
So we will look at that.
Therefore .009 times diameter, times PI gives us one thread, times the number of turns (5) , times shear strength, will give total strength.
.009 x 1.6 x 3.1416 x 5 x 49,000 = 11,083 pounds ( of force required to "shear"
If we look at the thread pitch, we see it as a 1.6 diameter, but lets unroll that, and lay it flat.
You now have a 5 inch long line, and since one turn of a 24 pitch thread moves .041",
we can say that the slope of the 5 inch line rises .041 inches and that is a "leverage" of 5/.041=122 to one.
Now that means that the screw thread gives us a 122 advantage over the shear, so 11,083/122= 90 pounds at the pitch center
Since the pitch diameter has a 1.6 diameter, the pitch radius is .8 inches.
Since .8 is 4/5 ths of ONE INCH , we invert and get 90 / 5 x 4= 72 inch pounds
Summary, so the forces required to shear is 72/12= 6 foot pounds

I hope these numbers help to understand the dynamics of threads. Obviously, many factors affect thse such as, friction forces, and 60 degreee thread angle.