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Any mathematicians? Torque, mass and broken gearboxes
Jesus-Ninja - 2/9/08 at 10:09 PM

It's no secret that is torque that kills gearboxes, especially big launches and low gears due to the effect of overcoming inertia.

But it's not torque alone, as mentioned, inertia has an effect too. What's the relationship between the torque, the mass of the vehicle and the breaking point?

Consider a car weighing a tonne will break it's gearbox with 300lbft of torque delivered from a standstill.

What amount of torque will be required to break the gearbox if the car weighs half a tonne?


watsonpj - 2/9/08 at 10:59 PM

If you talking about a catastrophic failure due to the shock load it will depend on if the tires spin up on the lighter car. If they don't then the failure will also most likely occur at the same 300lbft of torque, this is because the failure point within the gearbox will suffer the same stress in either case. If the lighter car doesn't bog down however you will probably not get this kind of failure but will head towards a fatigue type failure. This failure type takes many repeatative cycles and as the stress goes down so does the number of repeatition in a non linear way as in the graph below



Image deleted by owner


Jesus-Ninja - 2/9/08 at 11:02 PM

Now that's the kind of answer I was looking for!


smart51 - 3/9/08 at 06:59 AM

Or put simply, the 1 tonne car and the 0.5 tonne car both put the same load on the gearbox as the 300 lbft of torque does work accelerating the mass of the vehicle, however, the 1 tonne car accelerates half as quickly off the line, so the load is applied to the box for twice as long. You might therefore expect 1st gear to live half as long on the heavier car.


dhutch - 3/9/08 at 07:50 AM

quote:
Originally posted by watsonpj
If you talking about a catastrophic failure due to the shock load it will depend on if the tires spin up on the lighter car. If they don't then the failure will also most likely occur at the same 300lbft of torque, this is because the failure point within the gearbox will suffer the same stress in either case.

If the engine delivers 300lbft, the box will receave that. And if the box it in whatever gear, that will pass a certain torque onto the diff, etc, through to the load (wheels).

As you say, if the wheels lgiht up, break traction, then the load drops a lot, and so does the torque.

If the wheels dont spin up, and you maintain 300lbft thoughout accelleration it doesnt, on paper, matter on the weight of the car as you say.

However with a lighter car, if you do still maintain 300lbft it will accelerate faster as said, so will do so for less time.

Alternativly you may actaully find that the torque is less, becuase the car is lighter.
Ie, If you put the same power down, the 1/2ton car will accerate in half the time. But if in practice the half ton car only accelerates 50% faster than the one ton car, the acutall power put down will be less.

There is also the case of shock loading. Where by you rev the engine up and drop the clutch. Or have a bad gear change. Which is quite likely when you would get a catastophic failure. In which case agian, the lighter car wins.


Daniel


watsonpj - 3/9/08 at 08:00 AM

Smart51 if you look at the graph you'll see its more likely to be less than 1/2 as long.

cheers

Pete


82 Locost - 3/9/08 at 09:12 AM

Also, from the graph I'm not sure that Torque relates directly to Stress and that Cycles relates to Duration.

Cycles relates to the number of applications of Stress, and would therefore depend where the Stress were measured. For example, a spinning gear would experience Stress on the teeth everytime they were engaged/disengaged, i.e. up to 7000 times per minute (assuming 7000 RPM redline). However, the shafts would experience a single long-duration Stress with much less damaging results as there is only 1 Cycle.

I'd estimate something like Life being a function of Power Squared, i.e doubling the torque would reduce the lifespan to a quarter, trebling it would reduce the lifespan to a ninth. 10 times power = a hundredth of the life.


alistairolsen - 3/9/08 at 09:15 AM

also depends which bit of the box youre talking about.

Everything deforms, if elastically youre ok, if plastically your box is f**ked.

Imagine a driveshaft, it will twist slightly when you accelerate.

If the torque applied is the same in bth cases, the car weighing half as much will twist it less for a given rate of change of torque.

(If you bury your foot, one car will accelerate while the other twists up the shaft and snaps it in an extreme case)

apply this to your input shaft, mainshafts, prop, driveshafts...



[Edited on 6-9-08 by Fozzie]


MikeRJ - 3/9/08 at 09:52 AM

quote:
Originally posted by alistairolsen
Imagine a driveshaft, it will twist slightly when you accelerate.

If the torque applied is the same in bth cases, the car weighing half as much will twist it less for a given rate of change of torque.


For the same applied torque the driveshaft will twist exactly the same amount. The lighter car will accelerate faster though.

The problem with heavy cars is the peak (rather than sustained) loadings tend to be higher, since you can push more torque through the drivetrain without breaking traction (which is like a safety valve in this case).


richardlee237 - 3/9/08 at 10:04 AM

The torque that the engine can supply is not just that derived from the steadystate operation of the engine, but in addition the inertias of moving parts of the engine, particularly the flywheel. These inertias will supplement the torque if you try to slow down the engine.
So the situation you have is dependant very much upon how fast you try to change things. These torque peaks are what break things.
By the time the rear tyres are slipping the damage has already been done.
For example Formula one engines have little or no flywheel and very low inertias so they can accelerate very quickly and the transmission can be built for less "over" torque but it also means that it is very easy for the car to "bog down" at the race start as the stored energy is small.


Ivan - 3/9/08 at 10:06 AM

It also depends on what the weak part of the box is - ie in fith gear you can stress the casing as much as in first - and a light car won't relieve stress by wheelspin in fith so is as likely to burst the box as a heavy car.


alistairolsen - 3/9/08 at 11:29 AM

quote:
Originally posted by MikeRJ
quote:
Originally posted by alistairolsen
Imagine a driveshaft, it will twist slightly when you accelerate.

If the torque applied is the same in bth cases, the car weighing half as much will twist it less for a given rate of change of torque.


For the same applied torque the driveshaft will twist exactly the same amount. The lighter car will accelerate faster though.

The problem with heavy cars is the peak (rather than sustained) loadings tend to be higher, since you can push more torque through the drivetrain without breaking traction (which is like a safety valve in this case).


right! course it will!

imagine a straight shaft with an engine on one end and a flywheel on the other, let the clutch in and measure the twist.

now double the mass of the flywheel and you will have more twist!

I agree if you take both of them, side by side, and examine them while accelerating under constant torque that the twist will be the same. The inital twist as the shaft tries to accelerate the flywheel from stationary will give evry different results however!


Jesus-Ninja - 3/9/08 at 11:47 AM

So, long story short: My gearbox will likely live longer for being in a lighter car....?


MikeRJ - 3/9/08 at 12:06 PM

quote:
Originally posted by alistairolsen
I agree if you take both of them, side by side, and examine them while accelerating under constant torque that the twist will be the same. The inital twist as the shaft tries to accelerate the flywheel from stationary will give evry different results however!


Another good reason to get a lighter flywheel


alistairolsen - 3/9/08 at 12:11 PM

reduce inertia from rotating and linear accelerative loadings, reduce shock loadings by driving sympathetically and it should last considerably longer then in a larger car of the same power/torque in my opinion.


richardlee237 - 3/9/08 at 12:39 PM

Very simply

The more mass you have either rotating or linear, the more inertia you have and the more torque required to achieve the same acceleration.
The more acceleration you want the more torque you need for given masses.
Put the 2 together and you can see that torque required will rise rapidly if you want both a heavier car and more acceleration.
Inertia is nothing more than the force opposing change which is produced if you try to change the system and is generally proportional to the masses in the system and the acceleration rquired.
The point to realise is that these forces do not exist until you impose change and then the size of the forces is dependent on the speed of change (acceleration) and the mass of the system


iank - 3/9/08 at 01:18 PM

Also be aware that a lighter car will lose some of its safety factor if fitted with super sticky slicks as they won't spin up as easily.


Jesus-Ninja - 3/9/08 at 02:38 PM

quote:
Originally posted by MikeRJ
Another good reason to get a lighter flywheel


I hadn't really thought about the flywheel as a factor, but of course it makes sense. Hmm, I wonder if fidanza do them for Saabs.....


Jesus-Ninja - 3/9/08 at 02:45 PM

quote:
Originally posted by Jesus-NinjaI hadn't really thought about the flywheel as a factor, but of course it makes sense. Hmm, I wonder if fidanza do them for Saabs.....


...apparently not...

[Edited on 3/9/08 by Jesus-Ninja]