Output Shaft

[Joepro9]

ve seen it here before, but I cant find it...(search does not coorperate)

Anyway, A friend and U have been debating if it id harder on the engine putput shaft with a smaller or larger sproket. If anyone know the explanation to this or where I can find it, please help me out, thanks.

 

[jmics19067]

If the final dive ratio is the same and the chain adjusted properly it shouldn't matter

 

[Joepro9]

I am just saying for example, you go from a 13 to an 11. or a 13 to 15, which would technically be harder on the shaft? chain adjusted but the same rear sproket, we are just debating, I dont know why. :)

 

[jmics19067]

actuallyI dont think it would matter any gear any gearing.

If your engine made a certain amount of torque and the rear wheel had a certain amount of rolling resistance those forces would remain constant no matter what ratio of gearing you would have. .All the gearing would do is change how the engine rpm reacts to the rolling resistance or for a given engine rpm it would change the torque and speed of the rear wheel.
However there would be more twisting of the output shaft if you happen to be riding in the trans gear set closest to the clutch than the gear sets closest to the sprocket .

 

[Jaybird]

I hate these things, they keep me up at night.  :)
Lets do some math. I will state some constants for the sake of ease.

20HP @ 5000 Engine RPM's
1st gear ratio of 15:29(1.93:1 ratio) which means at 5000rpm our CS is turning 2591rpm's (5000/1.93)

To figure torque of shafts, we need to first figure chain speed and working load.
The formula for figuring chain speed is:
Number of Teeth x RPM's / Pitches per Ft.

(I will figure for an 11t x 44t [4:1 ratio] and a 13t x 52t [4:1 ratio] on a 520 chain)

11t x 2591= 28,501
28,501 / 19.2(# of pitches per ft.) = 1484 Ft. per Min.

13t x 2591= 33,683
33,683 / 19.2 = 1754 Ft. per Min.

Now that we know the Ft. per Min of each sprocket we can now figure the Working Load of the two.
Working load is figured as follows:
HP x 33,000 / Ft. per Min.

(11t) 20 x 33,000 =660,000 / 1484 = 444.74 in. lbs. working load
(13t) 20 x 33,000 =660,000 / 1754 = 376.28 in. lbs. working load

Now we know the working load of each sprocket, we can figure the shaft torques.
Shaft torque for driving shaft (or CS) is as follows:
HP x 63,000 / RPM = CS shaft torque (expressed in in. lbs.)
20 x 63,000 = 1,260,000 / 2591 = 486.3 in. lbs. (this remains constant )

Shaft torque for driven shaft (or rear) is as follows:
Working Load x Pitch Radius = Driven Shaft Torque
(11t) 444.74 x 4.3805 (pitch rad. of 44t) = 1948.18 in. lbs. torque
(13t) 376.28 x 5.1755 (pitch rad. of 52t) = 1947.43 in. lbs. torque

What we see when we do the math using engineering formulas is that torque on the CS remains constant with a constant output of horse power. We also see that the torque on the rear shaft remains virtually the same between the two drive set-ups at the same ratio.

What we see different is the working load that each set-up creates. THIS is where the problem lies in going to a smaller CS. The additional working load is directly transferred to the chain links, and as a result, a smaller CS sprocket puts a greater load on the chain. We also have a lesser number or sprocket teeth to accomplish the same amount of work, so both the chain and the sprocket teeth have to work harder, and as a result, wear out faster with the smaller set-up.

I don't have an engineering degree, I'm just a geek who reads and thinks too much, so if any engineers want to correct me, please feel free. :)

 

[jmics19067]

Jay,

I believe he is asking about the output shaft itself not the sprocket if you change the final drive ratio by changing the countershaft sprocket.

I am thinking<dangerous I know> that if you locked the rear wheel made everything indestructable except the shaft itself and put a huge torque wrench on the crank shaft of the engine. The output shaft will fail at the same torque wrench reading no matter what the final drive is.


ehhh the second part of that was just plain stupid so I got rid of it.

 

[Jaybird]

jamics, I think I understand his question and torque on the shafts is what I am talking about.
As long as the output HP remains constant from the motor, the driver shaft torque remains constant no matter what you do after that fact.
You mentioned in your first post "if the drive ratio is the same", so my example was calculated using a 11-44 and a 13-52 (both 4:1 ratio) set-ups.
The engine does not have torque, it is created after the output HP is reduced by a transmission, then that reduction is what puts torque on the driver shaft.
After that, the final drive gearing(looked at as another transmission reduction) indeed effects the torque on the rear.
My example shows that the torque remains constant on the CS, and if the final drive gearing is the same ratio wise, the torque on the rear shaft remains virtually the same.
My example was to show that no matter what sprockets are used to creat the same final ratio the torque remains constant, however the working load does indeed change.

If the question is simply: does a change of CS sprocket effect the torque placed on the CS, then you can look at the formula for figuring driver shaft torque and the answer is no.

 

[jmics19067]

I'm sorry I misunderstood you , yes you indeed stated that it was the same on the countershaft, but different on teeth of the sprocket and the chain.

A thousand apologies my all seeing,sage, soothsaying friend. :confused:

 

[Joepro9]

that is a sweet response, exactly what I was looking for.

 

[motometal]

if you compare two bikes traveling at the same GROUND SPEED with different final drive ratios (different front sprockets), if the HP is constant, wouldn't the torque on the output shaft be less for the example with the smaller sprocket?

since HP = torque * RPM (times some constant), the smaller sprocket would have to spin faster, so if HP is constant torque must be less???

Jaybird, have I clouded my cells with this half empty beer? :scream:

 

[jmics19067]

Moto,

although the torque recquired to accomplish the job may vary it would not change the failing rate of the output shaft.

the worst scenerio you could do to try and twist an output shaft is too put it in first gear, front wheel against a wall, rev it up and dump the clutch. if that doesn't twist something up no changing of sprockets would matter while riding. You would either lose traction, stall the engine ,burn up the clutch or just go forward

 

[Jaybird]

The HP in my example is created prior to getting to the "driver" shaft.
We know that the HP is 20. With a 15:29 gearing in 1st, we also know that RPM is 2591 on the CS with 5000 RPM on the crank.
HP x 63,000 / RPM = Torque placed on driver shaft.
The sprocket on the shaft changes things after the fact of the torque placed on the driver shaft. Since we haven't changed the final drive ratio (4:1) the end result is the same on the "driven" shaft with both 11-44 and 13-52.

Look at the chain speed of each sprocket above....notice the 13t front set-up makes the chain travel at 270 fpm faster than the 11t does.
The output shaft is traveling at the same RPM (2591) yet the end result is the very same speed at the rear wheel for both sprockets. Thus the same HP at the rear.
Only if you change the final gearing will torque on either shaft change, and then only on the rear. Only "FPM" and "Working Load" changes with similar ratio final drive set-ups.

 

[motometal]

jmics, I wasn't suggesting anything was going to fail, this is more of a mathematical model. Actually, put a poor quality sprocket on a big bike and watch the splines wear out! That's not cool! (I have an XR650 with "iffy" splines on the output shaft because some knucklehead put a cheap sprocket on it).

Jaybird, I think what I was trying to suggest was that your mathematical model was very good, but it may be more realisitic to look at a model where the ground speed was equal (load) and the output shaft had to turn faster with a smaller sprocket to compensate. This is more of a real world comparison, to answer the question "does a smaller front sprocket put less torque (and thus less potential for wear) on the output shaft and front sprocket" and I think the answer is "yes". You made a good point regarding the mechanics of how a smaller sprocket is less ideal for other reasons, harder on the chain, etc. so I suppose the two effects somewhat cancel each other out.

The power on the output shaft should be equal on the output shaft of both examples, negating friction in the drivetrain (because power is independant of speed). Like you say, changing the final drive ratio changes the torque.

Another way of thinking of it....there is no torque unless there is a load. Assuming a constant load at a constant ground speed (lets say we are climbing a hill), with lower final drive gearing we have more mechanical advantage and therefore it takes less torque to do the job.

 

[jmics19067]

You would have more mechanical advantage at the outside edge of the sprocket not the inside the mounting of the sprocket stays constant the diameter of the shaft stays constant so the work load on the countershaft stays constant whether in low speed torque or high rpm horsepower.

If you have two similar vehicles to travel at 60 mph the same amount of energy is going to be recquiered to accomplish the same job, whether at full throttle light load or at idle hard load from the gearing.

lets say you have a 3/8 bolt you need to torque 30 ft.lbs whether you use a 2 ft long torque wrench and work twice as much or a 1 ft torque wrench and work twice as hard the end result will be a bolt that is torqued to 30 ft lbs. or....

lets say you need to lift something heavy so you have a piece of rope, pulleys and tackle blocks to help make the load easy for you by using mechanical advantage. If the rope isnt strong enough to lift the load all it is going to do is make it easier for you to break the rope, but the rope will still break at the same point in the lifting stage relative to the load.

The amount of work would be the same for a given load the only thing that changes is the amount of time it takes to accomplish it. On your ill fitting sprocket it would not matter if if it was a hard load stripping out the splines from lousy contact points or a light load wearing out a loose spline. The end result will be the same just the amount of time to reach it would change.

In the case of a complete bike the amount of energy needed to accomplish a task would be constant the amount energy produced by the engine would be the same the only thing you are doing by changing gearing is changing the RPM of the engine to hopefully in its peak operating range. You are not creating any more energy by the engine and you are not needing any more energy to ride and the only thing that would take away energy would be the possible friction losses from either running a chain too tight around a small sprocket or the amount of contact the chain would have from going around a large sprocket.

 

[motometal]

this is getting to the point where it has almost graduated to the engineering forum, eh?

first, I must correct my last post. I in that situation, the sprocket splines would show less wear on a smaller sprocket because the load is constant and less torque. But the wear on the actual teeth isn't so simple to determine. Even though there is less torque, a given tooth contacts the chain more frequently, so it's probably a wash (plus whatever additional wear from the effects Jaybird mentioned). I thought of this right after I left for work this morning (to late to fix my post).

jmics, you are correct that the same amount of energy is required, but remember that energy = power = hp. Hp = torque x rpm. If we are assuming wear or force on the ouput shaft is proportional to torque, there would be less of this if the final drive gearing is lower due to mechanical advantage...with less torque and more speed, the same work is done.

Regarding your rope/tackle blocks, think of the output shaft as the rope you pull on. If you use more pullies, more mechanical advantage, you could use a thinner rope (aka less torque) but you would have to pull the rope further/faster to accomplish the same work per time unit.

Gotta go for the evening, maybe i'll think of better examples for next post.

 

[jmics19067]

this is a great discussion for me because I have no education except for too many years in the school of hard knocks. It gives me a chance to learn if what I perceived to be true is actually true. Of course one good semester of physics would probably do a lot to dispel what I thought heh.

On the rope , tackle , and load situation wouldn't the end of the rope that is fixed closest to the load see the complete weight of the load? So if the rope wasnt rated for the load straight up wouldn't it fail?

Also if the piece in question can handle a particular amount of of energy to do a certain amount of work indefinetly then no matter how you slice it up it should last no matter what leverage ratio you use to do the same work. The only thing you are changing is amount of time it takes to do the work..or the amount of time it takes for something to fail.
I believe that this can only hold true if friction is zero, fitment of things is perfect and everything involved could last forever . We know that any is extremely difficult if not impossible to do, but for all intents and purposes of what is available to put on a bike and the possible loads that can be placed on it the wear/stress over time on the output shaft of the trans is going to be negligable if all the above is within reason.

I finally figured out now that the whole point of this discusion is at what time is it not negligible. If one was to ask how can I get my countershaft to last 30 years you could answer put a smaller sprocket on,never go above half throttle and keep it in 2nd gear and change your chain every two hours.
Which could be a decent answer, might last 50 years, except don't expect to be able to change the countershaft sprocket or into 3rd gear after 5 years because because they imbedded themselves to the shaft :confused:

Plus You know that if you have to 2 similar bikes with different gearing they are not going to be going at the same speed. I know I would be roosting whoever If I had the numerically higher gearing in every turn or blowing past him on the straights the other way around. That is of course if both riders were of equal caliber :)

Ok I know I just got silly but I would like the converstaion to continue on the serious points I discussed/asked about.

 

[motometal]

on the block and tackle example, this is an excellent comparison.

remember we are talking about changing the gear reduction ratio on the bike AFTER the output shaft, so the "equivalent" rope in your example would be one of the ropes before the pullies. The rope connected to the load would equate to anything between the rear sprocket and the dirt.

 

[jmics19067]

I am not quite following you on that one. The block and tackle I am thinking of would be one piece or rope fed thru a series of pulleys.One end you pull one end is fixed. I am not sure if you are talking about a gear reduction chain hoist but anywho...... back to the bike

if you are saying that the output shaft is at a disadvantage from a bigger countershaft sprocket Couldn't similar forces be applied from the other direction by using a lower gear in the transmision at a lower speed highload situation? Cruising along in high gear compared to climbing a hill in second.
climb the hill in second fine, climb the hill in 1st increasing mechanical advantage for the engine you over speed the engine or lose traction, in third increasing mechanical advantage of the rear tire you lug the engine possibley burning your clutch, in fourth you stall the engine or burn out the clutch.

Now you might see quicker wear on a dual sport bike at highway speeds but because of time<more probable to spend more time doing 60 on the street then in 2nd gear on a hill > and friction not because of energy and loads.
The drivetrain will not see any more torsional stress than it takes to stall the engine<load exceeding energy> or spinning the rear tire<energy exceeding load>

what does the countershaft of your dual sport bike look like? are the external ridges of the splines thinner where the sprocket rides ? is the whole shaft twisted?or the area where the sprocket rides notched back ?

 

[motometal]

I know what you mean with the rope, for our example let's tie another rope on to the end where we are pulling. This piece we tie on could be much thinner, and still not break, if we use more pullies and thus more mechanical advantage.

As long as the load and the force on the output shaft are constant, it doesn't matter what gear we are in. Notice that this is a change in mechanical advantage BEFORE the output shaft. Back to your torque wrench example, it doesn't matter how long the ratchet handle is, you are going to tighten to tighten the bolt to the same torque.

Away from the theoretical and back to the real world, on my XR i suspect this sprocket originally fit tight, but was made from soft or non-heat treated material. As the splines started to wear back and forth, it got even worse and put some wear on the shaft too. To describe the wear, the splines are worn part way through right where the sprocket rides. There is no twisting that I can see. Due to the weight of this bike and the jarring of the street riding, part of the drive train leads a hard life. I have never seen significant wear on the spline of a counter shaft on any other bike. In fact, generally I don't even look closely at it when I replace sprockets...but I will now!

 

[jmics19067]

"As long as the load and the force on the output shaft are constant, it doesn't matter what gear we are in. Notice that this is a change in mechanical advantage BEFORE the output shaft. Back to your torque wrench example, it doesn't matter how long the ratchet handle is, you are going to tighten to tighten the bolt to the same torque."


My point exactly but would it matter to the splines where the countershaft sprocket rides on where your mechanical advantage/disadvantage is?

If the bolt you are tightening<countershaft> was supported by a bearing and you tightened the nut with a wrench would it matter to the torque wrench on the head of the bolt? Only by the friction of the bearing would be my guess.

 

[motometal]

You're losing me...I thought we were talking about torque on the countershaft with various final drive ratios...

regarding your question "would it matter to the splines..." the force on the splines would be less with a smaller countershaft sprocket because they are between the power source (gearbox) and the load (rear wheel), and are BEFORE the final gear reduction (chain and sprockets).

 

[jmics19067]

ok sorry let me see if I can clarify myself.

the countershaft is supported by bearings so any torsional loads created on it would be transfered to whatever would react easiest to it. whether it would be engine rpm/stalling or the rear tire breaking loose. Plus or minus the friction of the bearings depending where you start your measuring from.

Since the counter shaft itself is not being modified whatever changes you make to the final drive would only be transferred thru the countershaft to the transmision/clutch /engine.

 

[Jaybird]

I just got back from an out-of-towner so I'm a little fuzzy...

First, on the block and tackle, which is something I have Wayy too much experience with... It's obvious where the pull end of the rope is, but the other end of the rode is not affixed to the load. Rather, it is affixed to the apparatus itself, so the rope does not need to be rated for the entire load. It only needs to be rated for the reduction that you have set up. Not precise, but in simple terms a load of 500 lbs being lifted with a 4 part line will need rope rated for approx 125 lbs.

On splines...in a perfect world the spline fit to the sprocket would not have any slop and would not enter into the equasion. However, if there is slop, then assuming the final gearing ratio is the same, and using two differnt sprocket set-ups to accomplish it, the splines should in theory wear exactly the same no matter which CS sprocket is used. It is before the fact of the sprocket teeth, and since we know by our math that the torque on the driver shaft does not change with different size sprockets(but staying same final drive ratio) it shouldn't matter what CS sprocket is used...the splines will wear the same as long as there is equal amounts of slop in each.

Y'all are getting way too deep for me. :)

 

[jmics19067]

"Y'all are getting way too deep for me. "

yeah I have been spewin some hip boot material


thanks for clearing up the block and tackle for me.


how about changing final drive ratios? Does that increase wear?

I believe that you cannot place anymore stress on the countershaft then when the engine stalls or the rear wheel spins. I think that if you can climb a hill in a lower gear and dont break the countershaft then bumping up the final drive for the high speed cruising won't be any more stress. Only the time under load increases, increasing wear. How far am I off in that thinking? try and reread the complete conversation if you have time and straighten us out please.

 

[Jaybird]

I have no formula's to refer to that will figure for slop in a mechanical apparatus, so lets not try to speculate on it yet....(but once we understand in our head how torque works from start to finish in our drives we can come to some pretty clear conclusions)

Now, remember the formulas for figuring torque are different for driver shaft and driven shaft(all you need to figure driver shaft torque is HP and RPM, more variables are involved for driven shaft). And remember that the torque will remain virtualy constant on each the driver and the driven no matter what gears you use to obtain the final ratio.

Now, if you change the final drive ratio say from 4:1 to 4.15:1, then you will see a change of chain speed and working load, thus a change of torque on the rear(or driven). But to know what that driven torque is, you have to know what gearing you are using to obtain the 4.15:1 ratio, yet no matter what that final drive gearing is, the torque will be the same on both the driven and the driven for that particular final ratio, only the chain speed and working load will change with a change of tooth set-up.

Plug in some of your own figures and test it.