Jan Ridders Coffee Cup Stirling

[pgk pgkParticipant @pgkpgk17461]

My school math is out of date too and biased towards biology so we never got involved in calculus. You can probably track the area of each pulse so long as the Y axis is geater than zero by sampling and accumulating tiny triangles and the rectangles beneath the previous one…?

[Michael GilliganParticipant @michaelgilligan61133]

Posted by SillyOldDuffer on 25/03/2016 22:58:36:

… Anyway, here's the question. The area outlined by the curves drawn in the Indicator Diagram reveal how much power the engine develops. Is anyone able to explain to a dunce like me how to calculate this area from the data used to produce the graph? At the moment I can guesstimate it from the number of grid squares enclosed by the curves, but it would be more satisfying to have a numerical solution. My program is written in Python3 which has good support for scientific and engineering number crunching. Unfortunately my mathematical skills aren't good enough for me to even identify a suitable function or algorithm in the available modules. Should have paid more attention at school but it's too late now!

.

Dave,

Others may contradict me [not an infrequent occurrence] but here's my take:

If the curves were mathematically precise, it would be simple [but not particularly informative] to calculate the 'area under'. … BUT, in fact they are complicated and therefore ANY method of estimating the 'area under' will come down to square-counting; however clever it may appear, and however small those squares might be.

Have faith in what you are doing … it's good !!

MichaelG.

Edited By Michael Gilligan on 26/03/2016 10:21:03

[AjohnwParticipant @ajohnw51620]

I think you will have to count squares too. Integrals need a function – wish you luck on that aspect.

I did do pure maths for a while but it didn't suite my brain. As wonderful as some aspects where it wasn't clear what they could be used for. From memory one way of seeing if a function could describe some results is difference tables. You might find details on the web. I'm pretty sure it wouldn't work in this case.

John

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[maurice bennieParticipant @mauricebennie99556]

Hi ,Have been interested in hot air engines for many years,tried to make them work with mixed results. There is a museum in Hereford , " The waterworks museum" . which has a large collection of full size engines,in steam sometimes. well worth a visit . Keep up the good work .

best wishes Maurice.

[Gordon WParticipant @gordonw]

Count the squares- the smaller the square the more accurate it will be, I'm sure you know that. Any mathmatical formula just does the same thing but with tiny imaginary squares. Well done getting the diagrams in the first place, I'm looking to make a brake of some kind, there is lots on the net and am slowly getting my head round it.

[Ian S CParticipant @iansc]

Here's some Proney Brake photos, the motor is my latest flame licker. The beam on the brake is 5" long, with notches every 10th of an inch, the weight hanger weighs .250 oz, and the total weight of the weight in the photo is 1 oz.

Ian S C

[SillyOldDufferModerator @sillyoldduffer]

Thanks to everyone who advised on the area problem. The examples of integral calculus I found being used to solve similar "area under a curve" problems are way out of my league. Now I don't think I have a practical alternative to counting squares. And it's always a good idea to "Keep It Simple Stupid".

Thanks also to Maurice for the pointer to the Hereford museum: I shall go when the weather's better.

I'll probably contact Jan Ridders when my results are a bit more reliable. At the moment the engine is temperamental as is my experimental software. And I'm still picking your brains!

Next picture is the indicator diagram from the last time the engine worked. You've guessed it – I've since broken it again!

The picture shows the diagrams of about 20 superimposed cycles. You can see that a few cycles have large areas, but that about half degenerate into a much smaller loop. Not good – the engine is defective.

Given that all the other seals are OK, my interpretation is that the power piston is leaking. This is entirely possible because I've had to polish the piston and cylinder several times to remove corrosion. (I think the corrosion is being caused by acetic acid fumes released by the sealant as it cures, made worse by heat. )

Although the piston still just about passes the 'pop' test, the fit is noticeably looser than it was when new. Making a new piston is my next priority.

Cheers,

Dave

Edited By SillyOldDuffer on 27/03/2016 21:28:53

[SillyOldDufferModerator @sillyoldduffer]

Hi Ian,

Mucho thanks for your Prony Brake photos. A picture paints a thousand words and I can certainly see me making something like that.

My own thoughts haven't reached the practical stage yet. Something like this:

Or perhaps a torsion bar made from a metal strip stolen from a windscreen wiper blade? The strip would link the flywheel axle to a rotating load. The flywheel and load would both have magnets aligned at tdc when stopped. It wouldn't be too difficult to derive the torque from the time difference between tdc detected at the flywheel and tdc detected at the load when the engine is working to turn the load by twisting the strip.

Setting up an Arduino as a kind of stopwatch to do the job seems straightforward compared with the delicate precision needed of a mechanical brake intended to measure very low power outputs.

You'll appreciate I suggest these ideas with all the confidence of a man who hasn't thought any of it through properly, let alone actually tried to do it! The real world can be so cruel…

Cheers,

Dave

[Ian S CParticipant @iansc]

I did make a rope brake with one end with a fixed weight (1 oz I think), and the other end attached to a see saw to put the weight to be read on the platform of my little digital scales, I used it on a rescently improved Ringbom motor, the readings I got were about half of those from the Proney Brake, too much friction in the see saw part of the link, I think. My motors are no ornaments (some may say b***** ugly). To get the full story I really should metre the fuel, to get uniform heating, measure barometric pressure, etc, etc, but I have enough with what I have to see any major improvement.

All but one of my motors are high temperature types, and I don't really see how a brake can work on a LTD motor that has a hard enough job rotating, without any other impediment, I want to see if you can do something.

Ian S C

Edited By Ian S C on 28/03/2016 09:49:39

[pgk pgkParticipant @pgkpgk17461]

If not aiming for an absolute measure of work but just soemthing to be relative to previus performance then i see two issues. Firstly a tiny enough work load and secondly a way to decouple it until the motor is running.

How about something like two tiny balancing magnets on your flywheel and then measure how close you can offer a steel disc before it stalls?

[Michael GilliganParticipant @michaelgilligan61133]

Dave,

So far as I am aware: Everything they sell is [several] orders of magnitude too big for your requirements, but I recommend a browse around the Magtrol website. They make great products, and have good information available.

pgk is probably on the right lines …

MichaelG.

Edit: Here is [I think] their smallest offering.

Edited By Michael Gilligan on 28/03/2016 10:24:50

[AjohnwParticipant @ajohnw51620]

I would have thought that given the nature if the beast speed would be sufficient. Increase that and it represents an improvement.

To give it a controllable amount of work to do a fan might be ideal. Super light and an adjustable pitch. This might mask other effects if speed is used as an indication.

John

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[SillyOldDufferModerator @sillyoldduffer]

I spent the afternoon making and finishing a new power piston. The engine is working again and although it's not on top form I hope it will improve with use. Then I can start measuring again.

I find using a lathe to be most therapeutic. It helps me think about stuff too, almost sub-consciously.

As a result of my metal mangling cogitations I'm warming to the idea of trying to make a very sensitive dynamometer based on measuring the twist in a springy strip. The strip (something like the inside of a wiper blade) would connect the shaft of the engine to a second wheel. The second wheel would run inside a trough. Adding water or some other viscous fluid to the trough would provide a very light brake, one that should be easy to control. Magnets are an interesting possibility too, thanks pgk. Electromagnets would make it possible for the Arduino to apply braking just short of a stall.

Sorry about the crudity of the drawing, but the apparatus would be something like this:

I optimistically guess that the main problem would be friction in the bearings of the second wheel. As Ian says it doesn't take much to stop these little engines dead.

Nice kit on the Magtrol website. I'm frightened to look at their prices though!

Cheers,

Dave

[pgk pgkParticipant @pgkpgk17461]

The problem with anything attached to the flywheel.. as in shafts or bands.. is that you need the starting flickover to overcome that and then allow it to resettle to a steady state. The additional energy stored in any spring system will work against you and that energy will vary with the power of your initiating flick. … Why I suggested the magnets as a non-contact method. And why i decided against things like fan blades or vanes…

If you can find a way of coupling after the flywheel has reached steady state then you overcome that.

[AjohnwParticipant @ajohnw51620]

Jan does do one version that has a fan fitted. Just seemed simpler to me. It can be adjusted to a level that provides a very light load and if some mod speeds it up the power has been increased. Speed seems to be a common metric from what I have seen on the web. Temperature variations will play a part as well. One persons answer to that was to monitor the temp of the hot and cold ends so that he could control the differential that was providing the power.

There are some power calculations of a sort about by a person called Schmidt. Google along with stirling engine will find them. They calculate the theoretical power that is available but may lead to a method of calculating it from Dave's plot. The same search will bring up other ideas on this general area. Lots are rather complicated when it comes down to calculating power even trying to incorporate fluid flow effects but there may be other more useful info about.

John

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[SillyOldDufferModerator @sillyoldduffer]

Thanks for the comments from Messrs pgk pgk and John.

John first, I'm not doing particularly doing this to improve the engine (though that would be good), Rather I'm experimenting with modern technology and 19th century physics to see if I can determine the engine's efficiency.

I've always been interested in the principles behind engine design. Answering questions like how much heat is needed to produce a given power output or how big should a flywheel be tickle my fancy. The work is only original in so far as I'm applying it to a very low-powered engine using my equally low-powered brain!

I looked up Schmidt after you helpfully mentioned him in an earlier post. It seems that in the 1870s Professor Schmidt studied a Hot Air Engine made by Lehmann and used the analysis to derive a general theory of Stirling Engines. I'm sure Schmidt knew how to calculate cylinder power because the method was decades old by then – it is one of James Watt's genius ideas. The limitation in Schmidt's work is that his calculations assume that the piston and displacer movements are truly sinusoidal, which in a real engine they never are. Nonetheless, Schmidt seems to be the best starting point for an engine design.

I've had reasonable success producing the Indicator Diagrams needed to the calculate power being developed inside the engine. Counting squares will give a result.

The next step is to try and measure the actual power output available at the flywheel. The theory of Dynamometers is well known and the mechanics quite simple. Unfortunately, a Dynamometer sensitive enough to work with the Coffee Cup Stirling may well be beyond my skills. I'm enjoying the challenge of finding that out at the moment!

Which brings me to pgk pgk's remarks. Yes, I fear you are right. My proposal would add significant friction to the system before any braking is applied. If it works at all it will read low by an unknown amount. And the energy used to start the engine has to be considered too. Oh dear, it's time for another think!

I spent the afternoon making a model torsion Dynamometer out of Meccano. It's a proof of concept to test the software I haven't written yet so no problem there then! Assuming I get the code to work, it will be interesting to see if this crude Dynamometer gives a reasonable power output measurement from my Meccano electric motor. Whether or not the method can be successfully applied to the Coffee Cup engine is now moot thanks to pgk pgk's input.

Back to the drawing board,

Cheers,

Dave

[AjohnwParticipant @ajohnw51620]

I had the impression that at least some of Schmidt's work maybe all of it was based around what the maximum power could be given the temperature differential that is used so if the output can be measured it can be used to determine the efficiency. There are some comments around about that – usually fairly low.

I was interested in design aspects but as nothing really offers them I lost interest in this direction and came to the conclusion that it's all very add hoc with some basic broad principle such as the one JR mentions concerning compression ratio's and temperature differentials.

I can't help looking at design aspect – that's what I am as varied as my career has been. It all really related to design of one sort or another – even tool maker training.

John

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[SillyOldDufferModerator @sillyoldduffer]

Isn't it annoying when domestic issues interfere with important things like hobbies!

After various unexpected delays I was finally able to complete a "proof of concept" dynamometer made out of Meccano and use it today to get a reasonable result from a test Meccano electric motor.

The electric motor is considerably more powerful than a Coffee Cup Stirling engine but I think I'm on the right track: it does seem possible to make a sensitive dynamometer using the torsion bar principle. (The technique is normally used at the other end of the power range to measure the beefy Shaft Horse Power delivered by a ship's engine.)

Here's the set-up:

The Arduino measures the angular displacement between the flywheel and the brake as well as the rpm of the motor. The connecting cable isn't shown but in operation data is sent to a PC for analysis through the Arduino's USB port.

The torsion bar is calibrated by attaching a horizontal balanced arm across the brake wheel and measuring how far it is deflected by slowly adding known weights to a bag suspended from the end of the arm. I got this nice straight line graph for Torque = mass x distance.

With the Arduino switched on and the PC collecting data, I laid a weighted nylon cord across the end pulley of the brake. Work is done by the motor in trying to lift the weight and in the brake's "bearings". (There's a lot of friction because Meccano doesn't have proper bearings.)

The work twists the torsion bar and because the Arduino can detect how much the brake is out of phase with the flywheel, I can determine how much the torsion bar is twisting.

After loading the data into a spreadsheet, I crunched about 100 readings to find the average deflection at average rpm. It was 1.8 degrees of twist at 365 rpm. From the calibration graph this corresponds to a torque of 0.00678 kg/m

And: Power = Torque * 2 pi * N / 60 (where N is rpm)

If I got the calculation right (oh dear!), the measured output is about 0.25W

As the input to the motor was about 1W (1.75V at 550mA), we have a motor efficiency of about 25%. This is in the right ball park for a small DC motor. Below is a graph of Torgue, Efficiency, Volts and Amps as provided by the maker of a real motor. It seems that 25% efficiency isn't unusual.

 

There's still a long way to go with this. Interested readers will have noticed that the readings come from the extreme sensitivity end of the Meccano dynamometer. The accuracy must be very suspect. Therefore a torsion bar set-up to measure a Coffee Cup engine will need to be better engineered: I don't think I can get the necessary improvement in sensitivity from standard meccano parts.

In the hope of getting more consistent operation from the engine I've also built an "electric hot-plate" to heat the Coffee-cup engine. Actually it's a 25W 22ohm wire-wound resistor mounted in a hole gouged into half a reflective insulating brick. It's much more controllable than a mug of boiling water.

20W is sufficient to reach operating temperature reasonably quickly and 10-15W keeps the engine going. My engine is still unreliable and it may well be possible to do better than this.

As I was advised earlier in the thread, I had to replace the ball bearings with a quality type. Cheap ones just about worked but reducing friction by removing their dust-guards eventually caused the bearings to stiffen due to unconstrained up and down thrust from the crankshaft. I don't think it's good when miniature bearings start making crunchy noises!

The engine runs noticeably faster with better bearings but I still have a friction problem. It may be that the steel piston is binding in the brass cylinder due to unequal expansion as the engine warms up. I'm suspicious that the odd bit of "brass" I used to make the cylinder is actually bronze. Would bronze be bad news in a cylinder?

Cheers,

Dave

Edited By SillyOldDuffer on 07/04/2016 16:36:48

[AjohnwParticipant @ajohnw51620]

Neat piece of work Dave. Maybe a plastic shaft might get the sensitivity up. I'll tuck your ideas away in case I ever feel the need for one.

I had a strange thought on these engines from Brian's experiences. If I have read correctly power on ones such as the Phillips engine is boosted by increasing the pressure in the engine, even a pump added to increase / control it. Not sure on that point. They seem to need the entire thing pressurising, in other words the entire engine enclosing so that the surrounding gas is also at the same pressure. I think in real terms this applies to the "open" end of the power piston.

Going of from this and assuming this is correct small engines may have a bit of a problem. Heat is applied which will cause the air in the engine to expand and the pressure will increase to higher levels than the surrounding air. Maybe in real terms they need a sort of controlled leak. It might explain some of the sometimes works sometimes doesn't.

As I mentioned though I am not entirely clear on this subject.

Edit. On the piston and cylinder I wouldn't have thought brass or bronze would make any difference. There are indications that carbon power pistons do make a difference.

John

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Edited By Ajohnw on 09/04/2016 12:18:11

[Michael GilliganParticipant @michaelgilligan61133]

A great job there, Dave

If you need to reduce the torsional stifness; maybe try a flat strip instead of round … The extreme version being the Torsional pendulum in a 400 day clock … You could try strips of GRP or Carbon Fibre, for example.

Keep at it … You're on to a winner!

MichaelG.

[SillyOldDufferModerator @sillyoldduffer]

Very many thanks for the encouragement, Michael and John. I need some TLC at the moment because the engine has stopped working again!

I suspect that the power piston and cylinder bind when the engine is hot: certainly the polished piston ends up marred by fine scratches after 30 minutes or so. It also gets rusty on the inside face.

Originally I put the corrosion down to acetic acid from the sealant, but I'm still getting rust even though the sealant is long since cured and there's no smell. Possibly moisture in the air is repeatedly condensing and evaporating on the piston as the pressure alternates.

In the circumstances a graphite piston sounds like a very good idea. Thank goodness I can keep the cost of this endeavour secret!

John's suggestion that the engine might work better if pressurised is interesting: I shall have to do some more research. I don't really understand how the engine works either. On one level I think I get it, but it's not difficult to upset my mental apple-cart. For example I can't explain why the piston and displacer operate 90 degrees out of phase rather than any other angle.

Michael's suggestion of using plastic strip in the Mk2 dynamometer feels right too. I have some strip that might do if only I can find it. I have to get the engine working reliably before making a start on that though.

I made some changes to the program I wrote to analyse the data. Unfortunately the code that produces indicator diagrams has gone gaga and everything I've done to fix it has made the problem worse. Any computer experts reading this won't need to ask if I took a copy of the last working version: the professionals know that only wimps take backups.

On the other hand I think my earlier question asking how to calculating the area of an indicator diagram was based on a misunderstanding, so that's a bit of accidental progress. The pioneers needed to do it that way because their indicator diagrams were produced mechanically. I have the advantage of modern technology that captures many actual pressure readings throughout the cycle. It's easy to calculate the average pressure when you have actual numbers: I don't need to draw an indicator diagram to obtain the information needed to calculate Indicated Horse Power. IHP is derived from average pressure, piston face area, and the stroke length. My unchecked calculation using this approach suggests that the IHP of the Coffee Cup Stirling is a little under half a watt, which might even be about right!

Indicator diagrams are still worth producing because the shape and consistency of the curves say much about the health, or otherwise, of the engine.

In the workshop I snapped two M2 taps in improved pillars for the engine due to clumsy over-enthusiaism.  One of them jammed in the pillar so I will be following advice from the thread that recommended Alum as a way of dissolving the tap,

Cheers,
Dave

 

 

 

 

Edited By SillyOldDuffer on 09/04/2016 21:53:18

Edited By SillyOldDuffer on 09/04/2016 21:55:40

[AjohnwParticipant @ajohnw51620]

I've dreamed up a new rule for metric taps. Measure it, subtract the pitch and add on another 0.1mm in small sizes and maybe more as the size goes up. I'm not sure why I have never broke one. Might be because I don't do m2 very often. Usually M3 but having measured some – mostly supplied by Ketan – I am going to start increasing the tap drill size based on the od by 0.1mm.

Not that I am being critical of Ketan's taps. They are generally over sized and in fact a number of his were on size.

I always reverse every 1/3 of a turn max though except being a bit more casual with spiral ones which I hardly ever use. I do have a couple some where.

John

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[Ian S CParticipant @iansc]

John you are right, in a pressurised engine the engine is pressurised on both sides of the piston (the tricky bit is sealing the crankshaft where it exits the crankcase).

You could pressurise an LTD motor, but you would run out of heat (I mean HEAT not temperature).

I think your .5 W is optimistic.

I'v got an electric mug warmer, 18W, after 20 minutes it will run my 6" LTD motor at 25rpm, normal speed on boiling water 120rpm. On a motor the size of the Coffee Cup motor it would probably be better.

I'v got a LTD motor to the design of Myford Boy, it has a displacer cylinder in the form of a tin sweets container, and uses a diaphragm, some repairs needed, then I'll see what it will do.

Good luck with the electronic instrumentation Dave, sorry can't help with that.

Ian S C

[SillyOldDufferModerator @sillyoldduffer]

Don't tell the foreman but I discovered this morning that the bloke who drilled the pillars for an M2 tap used a 1.5 mm drill thinking it was 1.6 and he didn't bother to check. No wonder the taps were a bit stiff, doh! When the replacement taps arrive I'll try 1.7 clearance as John suggests: no doubt plenty strong enough for this application.

Ian: do you know what the advantage of pressurising a Stirling engine is? Is it just that you can get more heat into a working fluid when it's more dense? Also, do you have a suggestion for what the IHP of a Coffee Cup engine might be. Anything I calculate is highly accident prone and it helps me very much to know roughly what the right answer is in advance! I wasn't too unhappy with 0.5W IHP from a 10 to 15W input, and of course the power that actually reaches the flywheel will be very much lower again.

The results you get from an 18W mug warmer and boiling water are very interesting. In comparison my engine starts at about 80C and it works noticeably better when the room temperature is low, say 12C. Central heating and warm days are very unhelpful.

My engine doesn't speed up as expected with increased temperature. I've had the lower plate up to 105C only to unexpectedly see the engine speed up as it cooled off after the test. It works best at about 88C with the top-plate 50-60C lower.

I'm pretty sure these odd results are because my engine still has faults, not least that the piston rubs when the engine gets hot. At one point it was chuffing like a baby steam engine and that's definitely not right. I ordered some graphite rod today in the hope of fixing that problem.

Back to the workshop! At least I'm getting my money's worth out of all that tooling, until I break it that is…

Cheers,

Dave

 

Edited By SillyOldDuffer on 10/04/2016 13:30:29

[AjohnwParticipant @ajohnw51620]

It would be possible to pressurise a LTD. Stick it all in a sealed bell jar and pump it up. Just waiting for the shrieks about suggesting that but people who try it are expected to have some sense.

Worse still fill it with hydrogen as that will work a lot better than air. Helium next and I suspect any gasses that are lighter than air.

I thought the gain in power with pressure is down to the pressure changes with temperature being higher. Again not totally sure.

Needing a leak is an interesting point though, Say Brian in steam engine mode managed to get the temperature up to 300 – 400C. Not going to check my school days recollection of the maths but doesn't that mean >2bar in the engine – 1 bar or more over the external air pressure and nothing like that occurring in the engine to cause the power piston to move back from being forced out. It isn't going to hold this sort of pressure but it wouldn't take much to stop the engine from running.

There are video's of the Phillips engine on youtube, even showing it liquefying air when driven backwards with an electric motor.

John

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