Steam Engine Governors

Warning - despite being imperial in the previous post, I'm now going mostly metric, just to show even handedness.

Another factor is consider is the type of flow, laminar or turbulent? Why does this matter? If I understand the theory correctly laminar flow in pipes tends to lead to a pressure drop proportional to velocity. But for turbulent flow the pressure drop is proportional to the square root of the velocity, so should be lower all other things being equal.

My engines will run at a maximum pressure of 170psi gauge, and at that pressure the speed of sound in steam is 505m/s. My calculated speed above translates to 15.05m/s. That is well below the speed of sound, so the steam flow can be treated as non-compressible, which simplifies the equations.

To determine the type of flow we need to calculate the Reynolds number. This is a dimensionless number, basically the ratio between inertial forces and viscous forces. It is defined by:

Re = (p x u x D)/µ

p is the density, for steam at 170psi it is 6.48kg/m³

u is the velocity, 2963ft/min equals 15.05m/s

D is the diameter, 9/16" equals 0.0143m

µ is the dynamic viscosity in Pa.s, for steam at 170psi it is 1.539x10^-5 Pa.s

Putting all that together we get a value for the Reynolds number of:

90616

This is well into the turbulent regime. The transition from laminar to turbulent flow occurs for Reynolds numbers in the mid to high thousands.

So all is well, or course the above could just be a load of nonsense. Of course the only thing that really matters is how the engine performs.

Andrew

For short passageways the pressure lost by friction against the walls is likely to be low, what is of more importance is pressure lost going round bends, through changes of section etc. This is dependant on the velocity squared.

is called the head, which working in SI has units of metres, multiply by density and you get pressure in Pascals. Every fitting, bend, change of section etc has an associated head loss coefficient, a sharp bend is 0.5 (depending on what you call sharp!), so in your case we have

velocity V=15.05

density ρ = 6.48 kg/m^3

g = 9.81 m/sec^2

head = (15.05^2*6.48)/(2*9.81) = 75 Pa

which is about 0.01 psi, which I wouldn’t get too worried about.

Quite so! The steam passage from boiler to steam chest is quite convoluted. Although my drawings are by LSM the cylinder castings are to the original Filby design, where the steam passages are a combination of drilled holes and slots machined into the outside of the thick (3/8" ) liners. The best I can do is ensure that the cross-sectional area remains fairly constant and try and reduce any sharp corners or edges. My gut feel is that heat loss is going to be more important than pressure drops due to the flow.

Andrew

Hello all,

I have only just come across this post, but hope I can shed a bit of light.

First, the theory, Imagine a graph of governor opening up the left and speed across to the right. To govern you must have a curve that falls from left to right. To get isochronous governing, you need a curve that is a vertical line at the desired speed. In practice the best we ever get is a very steep slope - even on electricity generation work. As Andrew has derived in his post of 15/7 you need to get the springs and masses right, otherwise you can get instability (hunting), when the curves described above on the opening / speed graph become a Z shape.

In practical terms, for a given mass of balls (bit like this post) you need the correct spring RATE. Changing pre load will change the set speed, but does nothing about stability or instability. You will also appreciate that to get some degree of governing with a modest speed variation is in theory achievable, but to get good governing you are trying to create that very steep curve, while avoiding creating a Z curve.

Everything that has been said about increasing forces by increasing rotational speed, and ball mass is correct and will give more actuating force.

The Filby design is dire, in that the governor is expected to move a cylindrical plug with 160 psi pushing it to one side - think if the stiction! On the 4" Burrell SCC, I managed to work in a scheme of drillings to achieve what Duncan has sketched above. I then very carefully made a wee bronze cage loctited into the block and a stainless bobbin,. After many years of further work, I was able to see if it would restrict speed. Under "no load", it didn't.

After 10 years of running the model, the governor drive pulley always has a load of oil on it - so I concluded that trying to drive a governor with a flat leather belt was probably a non starter.

Taking those two factors into account, my enthusiasm for working governors rather died. However, I have the world's only model of a Burrell Patent Dustproof governor - but without the internals completed. I then decided to build a 7" scale steam lorry, but that is another story.............

If you can do it, Andrew, I will be the first to applaud, but please don't get trapped down that avenue - I want to see your two engines in steam - governor or not!

All the Best,

Martin

Thanks for the reponse Martin. It's helped clarify some points and given me practical help.

I think I now understand the relationship between the balls and leaf springs. Initially the springs look complicated, but I think they can be broken down into simple cantilevers. Each spring is constrained by the ball and being clamped at the ends. So as the ball moves out the spring bends more towards the axis of rotation. But at some point the bend reverses as the spring is constrained at the outer end. At the point of reversal I think the bending moment and stresses are zero. So we can treat each half of the spring as two independent cantilever springs. So it should then be simple to do the calculations to come up with a thickess for the leaves, depending upon the material chosen.

One thing I'm not sure about is total movement of the control valve. If I've understood some of the posts on TT correctly the valve should be able to move from fully open to fully closed. At fully open you can get full power, if required. If something breaks on the governor then the valve needs to close to prevent unloaded run away. I think this is a facility not provided on my model governor, as the sleeve valve will be open with the balls at rest.

I'm not sure how much oooph the speed controlling spring needs to provide. It needs to resist the movement of the spindle, but presumably not by much. On the other hand it needs to be able to overcome any friction in the spindle so that when the governor slows down it can push the spindle upwards. Note: the spindle is pushed down as the balls move out via a ball acting as a thrust bearing, but there is nothing to pull the spindle back when the balls slow down, except the torsion spring. And of course steam pressure as designed.

My control theory is a bit rusty, alythough I am familar with the s-plane and the role of poles and zeros from filter theory. Maxwell showed that the response of the governor is dependent upon the roots of a second order polynomial. I'd guess that two complex conjugate poles would give a better frequency response than a single real pole. For stability the poles need to be on the left hand side of the imaginary jw axis. I'd wing the maths and say that an isochronous governor has the poles on the imaginary axis. I think that hunting is a different problem to stability, caused by friction in the case of a mechnical governor. In control theory a time delay can cause instability, due to a reduced phase margin, but I don't think this is the same as friction in a mechanical system.

Obviously I need to think a bit harder about the valve arrangement. I might even be able to eliminate the pulley offsets if I move the governor!

I'll try not to get bogged down. I'd like to get the engines running before I kick the bucket!

Andrew

Hi Andrew,

I agree with your proposal to analyse the leaf springs as 4 back to back cantilevers. To give you some more design flexibility, some of the original Pickerings had laminated leaves - I have seen up to 3. The earlier photo in this thread just about shows it. (I think!)

On the theory side, I think there are 2 cases to consider - steady state and time dependant. My description dealt with steady state - it is quite possible to end up with an inherently unstable governor if the change in Wr2 on the balls exceeds the change in force on the spring(s). Hence the attention needed to spring rate. Note no friction is considered in this analysis, but friction will make the situation worse.

It is also possible to get time dependant instability due to rapid changes in load, or periodic fluctuations in load coinciding with the natural response frequency of the governor system. I would suggest this is likely to be less of a problem in a steam engine model, where things happen relatively slowly. Remember the originals were built to cope with sawbenches and threshing machines - and quite a lot of skill in feeding both was required.

I also think there is an inherent problem with the sliding plug valve on the Filby design. It needs to move quite a lot to control, whereas the twin seat balanced valve is "fully open" at 1/4 of the seat diameter - I make that about 18% of the sliding plug travel (1/root 2 divided by 4) for a given passage. Having said that, unless the boiler pressure is way down, I very rarely have to open the regulator more than 1/4 travel, so it might be possible.

Have you made the cylinder blocks? If not, I will try and dig out what I did by way of wangling a caged valve into the design.

Best Wishes,

Martin

Stability, or otherwise is function of the time constant of the governor versus the rate of acceleration of the machine being controlled.

At C A V, the governor team were caused most concern by Diesel engines that had a high rate of acceleration. The most difficult could accelerate at 5,000 rpm/second. Conversely, a Governor with a very small time constant can cause problems. I've seen ones trying to react to, and control, torsional vibrations!

A full scale steam engine would accelerate much more slowly. (But probably still too quickly for peace of mind with a run away!) Models may be different because the pressures and areas ( = forces) will be smaller, but the masses needing to be accelerated will be smaller to compensate. So the problems, such as friction in the governor linkage causing instability will still be there.

As already said, Preload sets the speed, Spring Rate determines the slope of the governor curve, and if too steep will cause instability. Hunting is caused by too steep a governor run out curve..

Surging is likely to be caused by friction making the time constant of the Governor too long, (The standard BBC bus sound effect; a London Transport RT surging, can often be cured by adjusting the buffer stop on the injection pump to damp out excessive movement of the control rod)

As Scotty used to say, "Y'canna scale Physics"

Howard

Thanks for the replies, more things to think about!

I recall from discussions on TT that some full size governors had multiple leaves, usually three but sometimes five. Presumably this gave an additional variable to play with to 'tune' the governor if needed.

Ah, yes the smaller movement of the balanced valve makes sense now in terms of the control movements needed.

Martin: No I haven't machined my cylinder blocks yet. I'm itching to get on with them as most of the features such as cylinder and valve rod locations seem to agree with the drawings, for once! Even if I did get rid of the 1% tilt on the cylinder block. I would be most interested to see what you did in getting a balanced valve in place. Did it involve moving the governor? If so that may help with the pulley misalignment.

One thing seems odd about the governor control loop. The valve has one, and only one, position for each associated speed as the balls and valve position are tied together mechanically. This isn't normally the case where valve position can be moved independent of speed measurement. I assume that's why the Pickering governor causes a speed change as a result of load change. Whereas a governor which has independent valve movement can correct exactly for a speed change initially created by a load change.

Slightly to my surprise I've got my length of tungsten rod from China via Ebay. So I now need to do some trials to see how easy it is to machine.

Andrew

All mechanical governors have a speed change when the load varies, the difficult bit is to minimise it without inducing hunting. One of the best was the Lumb governor **LINK**

Even that had a speed change of ~3% from full load to no load. If anyone manages to make a working model of one I'll buy him/her a pint! (That is after it's been written up for ME)

Thanks for the link. That looks like an interesting book, but not cheap. Next time I'm in Cambridge I'll have a ferret in the CUP bookshop and see if I can look at a copy before deciding to purchase.

Andrew

Here is a sketch of how I worked a caged governor valve into my 4" Burrell SCC model. I don't have my original drawings, so have had to re-work this from scraps and memory. I can e-mail a .dxf file which will be easier to read - p.m. me with current e-mail address. The 3/8" cross drillings can have the ends plugged, but the valve chest cover gasket will do the job anyway.

I did find a sketch showing I thought about a valve with 45 deg. seats and slightly different seat diameters - but I obviously copped out of trying to make it seal! However, see my comments in an earlier post about this design not sealing sufficiently well either!

I hope it is reasonably clear.

Martin

Thanks Martin, I really appreciate you taking the time and trouble to put this together. It's a neat and simple solution. I now need to look harder at the cylinder block versus the drawings to see what space I have, as there appear to be some oddities. One example is top of the HP steam chest to top of the cylinder block. On the drawings this is shown as 1-15/32", but on the casting there is nearly 2". That seems a lot of metal to remove, and it seems strange that the casting is much bigger than it need be? If I make the dimension bigger than drawing that should give me a lot more metal to play with around the bottom of the regulator valve.

Andrew