Author Topic: Flywheel calculations  (Read 6045 times)

Offline MJM460

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Flywheel calculations
« on: February 28, 2023, 02:25:10 AM »
At last, the promised thread on flywheels.  A little delayed by all the normal distractions of the summer holiday period, plus severe falls by two of the older relatives which led to additional travels.  Both on the long road to recovery now.

A flywheel is a large component that dominates the appearance of many of the engines we build.  Thus for a scale model of a full size prototype, the proportions of the model should be to scale, or the engine will look wrong.  But when material availability or machine limitations dictate a deviation from the plan dimensions, it is relatively simple to calculate alternative dimensions which will have the same critical properties as the specified dimensions, so the engine will run as expected.

This thread was prompted by a question in another thread about whether the other  dimensions of a flywheel could be changed to compensate for a necessary change in diameter as the available lathe was too small for the specified flywheel.  In my observation, it is not an uncommon question.

Of course the very question implies two assumptions, first that the flywheel size is somewhat critical, and second that the plan dimensions have been selected to achieve that right dimension. 

In practice, there is a very wide range of flywheel sizes that will be quite satisfactory, even though they might look very different.  In most cases, a dimensional change can be made to suit our circumstances without any effect on the engine operation. 

Any reciprocating engine has a torque characteristic that fluctuates.  For a single cylinder single acting oscillating engine, such as those many of us build as a first engine, the torque is negative for half the revolution, and a flywheel of some sort is necessary for the engine to run. 

For a double acting engine, the torque is zero twice per revolution, but never really negative, a much smaller flywheel will be adequate.  For a multi cylinder engine, where the torque is clearly positive throughout the complete revolution, a flywheel is strictly not required, though one is often included to reduce the speed fluctuation throughout each revolution.  In all cases, a wide range of flywheel sizes will give satisfactory performance.

I would suggest that “too small” would mean the flywheel is unable to store sufficient energy to carry past any zero or negative torque angles that occur in a particular engine.  Too large would mean the engine is unable to accelerate the engine through the positive torque angle, sufficiently for its momentum to carry through the minimums.  In between these two extremes, a larger flywheel reduces the variation in speed through each revolution when compared with a smaller one, without there being a particular “right size”.

Separate from the issue of the “right size”, the inertia of the flywheel to the plan dimensions can be calculated, and alternative dimensions can be selected which will have the same flywheel effect as the plan specified dimensions, perhaps best described as an equivalent flywheel.  But there are some basic concepts to grasp before we start the calculations.

Enough words for today.  Tomorrow, two fundamentally different types of motion and relevant flywheel properties.

I hope this is of interest, and that I can provide some help to the understanding of flywheels.

MJM460


The more I learn, the more I find that I still have to learn!

Offline RReid

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Re: Flywheel calculations
« Reply #1 on: February 28, 2023, 02:41:41 AM »
Thank you for doing this. I think it will be quite interesting, and am looking forward to following along. :ThumbsUp:
Regards,
Ron

Online Kim

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Re: Flywheel calculations
« Reply #2 on: February 28, 2023, 05:11:57 AM »
I'll certainly be following along!  Thanks for taking the time to do this MJM!  :popcorn:

Kim

Online Jo

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Re: Flywheel calculations
« Reply #3 on: February 28, 2023, 08:41:05 AM »
 This is going to be really interesting  8)

Jo
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Offline john mills

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Re: Flywheel calculations
« Reply #4 on: February 28, 2023, 09:02:16 AM »
I  will be following
John

Offline deltatango

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Re: Flywheel calculations
« Reply #5 on: February 28, 2023, 10:05:12 AM »
And me!
There was a suggestion that the Wyvern flywheels were too light for the purpose, it would be good to know what is really needed there.

David
Don't die wondering!

Offline Jasonb

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Re: Flywheel calculations
« Reply #6 on: February 28, 2023, 01:08:14 PM »
I'll be following along too.

Though knowing what is needed when an engine does not perform or when starting from scratch is a bit different to making sure an alternative will give the same or better performance to an known working original.

I'll keep it to the James Coombes thread but this thread prompted me to look at the difference between a Stuart flywheel and the one I have just describes, quite interesting and it's only a click or two of the mouse in CAD to see the figures for the two.


Offline AVTUR

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Re: Flywheel calculations
« Reply #7 on: February 28, 2023, 03:54:35 PM »
I will also follow with interest. I dug out my college notes from 50+ years ago and did the sums for a couple of designs, both single cylinder, one IC and the other steam, a few years ago.

AVTUR
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Offline MJM460

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Re: Flywheel calculations
« Reply #8 on: March 01, 2023, 08:52:25 AM »
Thank you for the positive response to the first post on this topic.  It’s a privilege to have you all following along.  Thanks also to all those who have simply looked in.

I am sure some of you could easily write the thread, so please feel free to look over my shoulder and correct or clarify as necessary.  It’s to all our advantage to have the  information as complete as possible and reliable for those who come along later.

Jason, does your programme actually calculate the moment of inertia for your flywheels?  Or have I misunderstood your meaning?

So, on to the  fundamental concepts.  It is necessary to understood what properties of a flywheel determine its effective size.

The “size” property of a flywheel is termed its inertia.  Strictly, it’s the second moment of mass.  But it’s usually abbreviated to Moment of Inertia, or just Inertia, which corresponds to our intuitive ideas associated with movement and momentum.  Moment of inertia is a property associated with rotational motion as opposed to linear motion. 

For linear motion, momentum and kinetic energy are determined by the mass and velocity.  The mass distribution or shape of the moving object is relatively unimportant. 

For rotation, mass is important as you expect, but even more important is the distribution of the mass, in particular, the distance of the mass from the axis of rotation.   The relevant velocity is the angular velocity or rotational speed.

Rotation and translation (or linear motion) both are similar but separate and independent motions in physics, and the differences lead to some cool concepts.  But we will get to that later.  First the requested calculation of inertia of a flywheel.

The “second moment” part of the definition means that the distance is squared, and hence has more than the proportionate effect on the result, thus it is not only the mass, but how that mass is distributed around the axis of rotation is important for the flywheel.

So for any small object, at distance r from its axis of rotation, the Inertia, I, is equal to the mass, m, times the radius, r, squared.  Small in this context, means dimensions small enough that all parts of the object can be considered to be at the same radius from the axis of rotation.

Written as an equation,
   I = m x r^2

For a larger object, the Inertia can be calculated by dividing the larger object into very small parts, multiplying the mass of each part by its radius squared, and adding all the results to get the inertia of the whole.  You can easily see from this equation that some mass located in the hub of a flywheel makes a much smaller contribution than the same mass located in the rim.  Similarly, a flywheel of larger diameter, will have a larger inertia, even when the rim dimensions are trimmed to have the same overall mass.

This calculation could be a tedious process, but the mathematics study called calculus makes it considerably easier.  Don’t worry, I don’t propose going through the detailed mathematical procedure.  Every student who has ever done more than a couple of years of calculus has already done all the examples we are interested in, and the results are tabulated in many maths and engineering text books for us to use.

Time for a break while that sinks in.   Tomorrow, we should look at how the flywheel moment of Inertia relates to kinetic energy and momentum before getting to the detailed calculation for typical flywheels.

Thanks to everyone for looking in,

MJM460
The more I learn, the more I find that I still have to learn!

Offline Jasonb

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Re: Flywheel calculations
« Reply #9 on: March 01, 2023, 04:09:44 PM »
This is what Alibre gives me, as you can see it is possible to spin the flywheel on any of the three X,Y & Z axis but the best value as one would hope is on XX which is the one through the middle of the central bore. As the results are mm2kg that would seem to be radius in mm squared x mass in kg. This is for the 200mm dia flywheel used on the James Coombes I'm currently describing and is almost 4 times greater that what a standard Stuart 7" flywheel give. No wonder it runs so smooth at very low revs ;D

Offline derekwarner

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Re: Flywheel calculations
« Reply #10 on: March 01, 2023, 11:30:08 PM »
Following on  MJM :atcomputer: ....at the end, will see if I can reverse apply the engineering in the calculation 'result' on the flywheel of my Saito Y2DR engine

Derek
« Last Edit: March 01, 2023, 11:40:52 PM by derekwarner »
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Offline Don1966

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Re: Flywheel calculations
« Reply #11 on: March 02, 2023, 03:08:56 AM »
Very interesting I wil follow also.

Offline MJM460

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Re: Flywheel calculations
« Reply #12 on: March 02, 2023, 09:44:57 AM »

Hi Don and Derek, good to have you on board.

Jason, that’s really cool, that Alibre does the calculation for you.  I assume that fusion 360 and other programs also do it.  It’s up there with the pipe stressing programs that calculate the natural frequencies as a byproduct that has its own uses.

It’s also interesting for another reason.  As you have pointed out, the moment of inertia for spinning around the axis of the flywheel is the largest, thus is the one we want.  Note also that the other two principle axis nearly, but not quite, add up to the moment of the principle axis perpendicular to the plane of the flywheel.  The theory as outlined in the maths texts I am familiar with say this should be exact. 

Now the theory is based on the assumption that the flywheel is in a single plane so is a two dimensional object.  The calculations for a true three dimensional object are much more complex.  It is possible, even likely, that the program does a true three dimensional calculation.  A simpler explanation may be that the two dimensional axis are slightly displaced from the centre of the flywheel on the x axis.

In practical terms, three significant figures are more than adequate, and two probably enough.

The other thing to notice is that the moment about Y-Y and Z -Z are not quite equal.  This is expected because the flywheel pictured has six spokes, so the axis that lines up with two spokes is slightly less than the other due to the difference in spoke location with respect to the axis.  They should be equal with four or eight spokes.  The small differences also illustrate that the spokes themselves make a quite small difference to the total. 

Never the less, the figures given are more than adequate to compare different flywheels as you have done.  And you can see how the bit larger diameter flywheel is much more effective without being hugely heavier.  It would be interesting to see the actual figures for the Stewart flywheel.

I had intended to discuss kinetic energy, momentum and angular momentum but this post is getting long enough, so I will continue tomorrow.

Thanks to everyone looking in.

MJM460
The more I learn, the more I find that I still have to learn!

Offline Jasonb

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Re: Flywheel calculations
« Reply #13 on: March 02, 2023, 10:41:30 AM »
I had a look at F360 but don't get that option with the free version, best I can do is ctr of mass

The slightly displaced figures could simply be a bit of rounding up or down somewhere though I generally use the symmetry and mirror functions so should be right.

I did make a bit of a boob with the comparrisson between the JC and the Stuart as I had not specified the material for the Stuart so it is actually about half the valve not 1/4

This is what I get for the Stuart, and looks like I drew that correctly as no slight offsets, drawn with ZZ as the central axis of rotation. Out of interest if I supress the spokes the figure drops slightly to 4740mm2kg so could almost be left out of the maths if a quick and dirty answer was needed

Offline steam guy willy

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Re: Flywheel calculations
« Reply #14 on: March 02, 2023, 04:27:13 PM »
Hi John , interesting article and info ..... Is there a reason for solid cranks as used in the crankshaft gear for this engine  ?? lots of extra metal being used ?

Willy
« Last Edit: March 02, 2023, 04:30:56 PM by steam guy willy »

 

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