# Moment of inertia of a gearbox

SevenToFive
I just want to check to see if I am on the right path, I have to calculate the moment of inertia of a gearbox for an application. I was thinking of breaking down the input shaft/worm into different size cylinders since the shaft has different diameters for the the input and bearings. And then the moment of inertia of the input bearings and adding them together. I would then take the output shaft, gear, and output bearings add all of those values together, and then combine the output combined total with the input combined total.

Would this be a good approach or is there an easier way? Thanks for the advice

Homework Helper
Gold Member
2022 Award
It probably doesn't make sense to simply add them together. Not all thecomponents will rotate at the same rate.
You need to think about how you are going to use this "total inertia". If you want to compute how quickly it will be accelerate under a given torque, each component gets a different acceleration. Total torque = ΣIiαi. If you are interested in acquired KE, that would be different again.

Homework Helper
Gold Member
I just want to check to see if I am on the right path, I have to calculate the moment of inertia of a gearbox for an application. I was thinking of breaking down the input shaft/worm into different size cylinders since the shaft has different diameters for the the input and bearings. And then the moment of inertia of the input bearings and adding them together.

Ok so far.

I would then take the output shaft, gear, and output bearings add all of those values together

Ok so far.

.. and then combine the output combined total with the input combined total.

How do you plan to combine them? This might help..
http://www.engineersedge.com/motors/gear_drive_system.htm

Dr.D
There are really two different problems here:
(1) finding the MMOI of each gear or other rotating element with respect to its own axis of rotation,
and
(2) combining all the individual MMOI values to obtain an effective MMOI for the whole gear box.

For the first part, breaking each individual component into cylinders and rings, finding the MMOI for each subpart and then adding directly is correct and not difficult to accomplish.

For the second part, you must first define what shaft rotation you want to use in the MMOI definition. Typically this is (a) the input shaft, or (b) the output shaft. Choose one and stick with it. Then, in terms of the chosen shaft speed, write the speed of every other rotating part, based on gear ratios, etc. The write the total kinetic energy of the system in terms of the chosen shaft speed. Factor out that shaft speed^2 and the (1/2), and what is left is the effective MMOI for the gear box.

If you choose a different reference shaft, you will get a different effective MMOI value.

HowlerMonkey
Do you really need to get that close of an estimate or can you simply weigh the part.

The Porsche 944 had an "input shaft" (they call it driveshaft) that is 5 feet long.

That is a considerable amount of inertia and certainly not optimum but it worked for the road cars well out of the warranty period.

Dr.D
And after you have weighed the part, then what? In your Porsche example, you give a prime example why the distribution of that mass makes literally all the difference in the world. Once you have the weight, you have exactly nothing unless, of course, you happen to have the radius of gyration for the object shape and an value for gravity.

SevenToFive
Thanks Dr.D.
It was a rather lengthy exercise in math, another engineer at work suggested making 3D models of the parts and letting Solidworks determine the moment of Inertia.

Thanks everyone for the input.

HowlerMonkey
Have you seen an input shaft?...actually held one in your hand?

The porsche 944 "input shaft" weighs at least 6 times what most every other automobile input shaft weighs.

While you're arguing the "radius of gyration", have you forgotten the clutch disc which has to be included in the computation of an input shaft mass and "radius of gyration"?

My point is that, unless you are designing a formula one box or one like our riccardo straight cut gearbox that sits behind our 2700hp engine turning over 10,000 rpms, then the extra diameter of the gear on the input shaft and the inner race/balls of the bearing will likely be unbelievably small and a drop in the bucket as compared to a 944 shaft that likely weighs 17 pounds.

Dr.D
While you're arguing the "radius of gyration", have you forgotten the clutch disc which has to be included in the computation of an input shaft mass and "radius of gyration"?

It is really not necessary to forget anything to try to get the whole thing correct. One piece at a time is usually the best way to proceed if you want the final result to be correct. By the way, there really is no need for scare quotes around "radius of gyration;" it is a perfectly good term among those who actually do analysis.

xxChrisxx
Have you seen an input shaft?...actually held one in your hand?

The porsche 944 "input shaft" weighs at least 6 times what most every other automobile input shaft weighs.

While you're arguing the "radius of gyration", have you forgotten the clutch disc which has to be included in the computation of an input shaft mass and "radius of gyration"?

My point is that, unless you are designing a formula one box or one like our riccardo straight cut gearbox that sits behind our 2700hp engine turning over 10,000 rpms, then the extra diameter of the gear on the input shaft and the inner race/balls of the bearing will likely be unbelievably small and a drop in the bucket as compared to a 944 shaft that likely weighs 17 pounds.
...
and if one is doing the exercise to calculate a mass elastic system for mode extraction, or reflected inertia and stiffness for vibration/deflection analysis, or just for practice?

As much as including bearings may or may not be overkill, it's certainly more correct than just weighting something to try and gauge it's inertia.

OP asked how to achieve what he wants, not for a critique of the motivation nor the level of detail he wants to consider. Oh and I'm sure he was absolutely fascinated about the aside on torque tube shafts on transaxle Porsches.

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xxChrisxx
How come I can't edit the post above? The stray apostrophe is annoying me.

HowlerMonkey
My point is that an "input shaft" weighing over 16 pounds worked fine for a production car to make it way out of the warranty period.

That's at least 6 times the mass of almost every modern production car input shaft that doesn't have the mass of the 944's configuration.

You're worrying about a few ounces when it's proven that 6 times the mass did not have a significantly detrimental effect to the 163,000 944s sold...not to mention the corvette c5, c6, and c7s running around with a similarily heavy torque tube that is counted as input shaft mass.

I just don't think this is an area to spend a huge amount of time contemplating when there are other issues that are likely more important.

Your complaint about the comma tells me you spend too much time worrying about something that really may not need to be addressed.

Time is money.

Spend it wisely.

Gold Member
I just don't think this is an area to spend a huge amount of time contemplating when there are other issues that are likely more important.

You have not understood the question and everything you have posted so far is either incorrect or irrelevant .

The actual question relates to design of rugged relatively slow rotating gear boxes for heavy industrial equipment . Determining the MoI's of the substantial components involved is certainly a worthwhile thing to do .

The torques required to accelerate some of these substantial components up to running speed can be high enough to cause problems if not properly taken into account .

Hard to explain exactly why to someone with no technical knowledge but a definite example of where large component MoI's cause difficulty is in the motor torque needed to start something like a big rolling mill . The motor torque needed to start the mill turning can often exceed the motor torque needed to keep the mill running at full load . Motor installed has to be higher power than just needed for full load conditions or a scheduled slow start up procedure has to be employed to limit motor torque to safe values .

Dr.D
My point is that an "input shaft" weighing over 16 pounds worked fine for a production car to make it way out of the warranty period.

Almost everything you have posted in this thread seems to totally confuse weight and MMOI. They are not at all the same thing, but that seems to have escaped you. Please try to understand the difference.

xxChrisxx
My point is that an "input shaft" weighing over 16 pounds worked fine for a production car to make it way out of the warranty period.

That's at least 6 times the mass of almost every modern production car input shaft that doesn't have the mass of the 944's configuration.

You're worrying about a few ounces when it's proven that 6 times the mass did not have a significantly detrimental effect to the 163,000 944s sold...not to mention the corvette c5, c6, and c7s running around with a similarily heavy torque tube that is counted as input shaft mass.

There is clearly a massive disconnect here. Why do you think he wants to know the inertia of the system in this instance?

HowlerMonkey
The actual question relates to design of rugged relatively slow rotating gear boxes for heavy industrial equipment . Determining the MoI's of the substantial components involved is certainly a worthwhile thing to do .

Funny...how are you privy to information that should have been in the first post of this thread and does not even exist within this topic before you mentioned it?

Now a new random poster shows up with the most important information...THE APPLICATION...which has everything to do with my contributions to this thread since I assumed it was an automobile "gearbox".

Then he insults me?

That is known as changing the rules after the fact and trying to enforce them retroactively.

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xxChrisxx
Funny...how are you privy to information that should have been in the first post of this thread and does not even exist within this topic before you mentioned it?
That is known as changing the rules after the fact and trying to enforce them retroactively.

https://www.physicsforums.com/threa...mum-gearbox-input-torque.916771/#post-5777636

It wasn't in the OP. Then again OP didn't state that it was a car gearbox either, you jumped to that conclusion. The question was purely about calculating referred inertia through a gear ratio. The question is application agnostic.

HowlerMonkey
Again...that information never existed on ghis thread...where the question was posted.

Sadly, I don't have the seemingly endless downtime that allows me to hover my finger over the PF alerts dialog box like you or

xxChrisxx
Steady on, no ones's having a pop at you or trying to devalue your knowledge. The responses were just so disconnected from the thread it was very confusing. Now we know why.

Even if we take context out of it, it doesn't quite resolve why you think that accurately knowing the inertia of a specific system is irrelevant. I'd value your input as to why you think we'd want to calculate the inertia of a vehicle transmission.

HowlerMonkey
The responses are only disconnected in this thread because a separate thread carried information necessary to this topic.

Since I was working on the assumption that this thread was about an automobile transmission input shaft, then my mentioning cases where input shaft weight six times the norm not causing problems is more of a "fermi estimation" ...but it was based on information not existing within this topic.

If it were an automobile gearbox other than an extreme application such as formula one, my suggestion would have saved time.

My job is to fix engineering oversight on ultra high
performance automobile systems.

I'm billing trial lawyer labor rates so knowing what time consuming tasks to eliminate is what my customers expect on the road toward a solution that will net them world records and victory.

xxChrisxx
If it were an automobile gearbox other than an extreme application such as formula one, my suggestion would have saved time.

My job is to fix engineering oversight on ultra high performance automobile systems.

I'm billing trial lawyer labor rates so knowing what time consuming tasks to eliminate is what my customers expect on the road toward a solution that will net them world records and victory.

Would you care to elaborate how it would have saved time? What issue would it have discounted? Would weighing vs calculating the inertia of a system miss any particular issues? It's not really answering the question of why you think calculating the inertia of the system is a waste of time.