Steam Engine Governors

I'm taking the notes on steam engine governors out of the 'WDIDT' thread, to avoid cluttering up the original thread with techie stuff.

There were several statements in the original flurry of replies saying that the balls didn't need to have a particularly high mass; I disagree.

Let's look at centripedal force causing a mass to move on a curved path. I prefer to use angular velocity w (rad/sec) so the equation is:

F = m r w²

I am building a 4" scale traction engine, so one third full size. Assuming that the governor is scaled correctly the radius will be scaled by a third. As pointed out by JasonB model engines tend to run faster than full size, let's say double. But the angular velocity is squared so we get a factor of four. So I make that:

F ~ 4m/3

But for a given density the mass the of the balls will be 1/27 that of full size. So that means that the force will be well down on full size, and out of proportion.

Roughly the best I can do is double the density, ie, double the mass, and I plan to make the balls slightly larger; 3/4" instead of 11/16".

Taking all the above factors into account I reckon I could end up with a force that is about 0.12 of full size.

Andrew

Andrew,

if the governor is using gravity then some fraction of the force m.g will be balancing the governor force m.r.w^2.

If the governor is using springs then the mass will no longer cancel out on both sides and your arguement above holds.

Cheers, Colin

Nothing wrong with your maths or reasoning, but what you can do is to make the governor go even faster by changing the gearing between governor and crankshaft.

as you wrote, force on balls is F = m r w^2. If you then speed it up by say 10% but don't allow the balls to fly out, the new force on the balls is F2 = m r (w*1.1)^2, so the excess force available to move the governor linkage is

F2 - F = 0.21 m r w^2. Bigger denser balls and going faster all help. The limit is aesthetics.

for spring controlled governors you need to make sure that the spring rate is high enough, otherwise they can be unstable, any increase in speed causing them to go full deflection. Think governor in hit and miss engine. Steam turbines have 2 governors, one progressive to work the control valve, the second unstable to trip the spring loaded stop valve in the event of over speed. As someone has said the control valve doesn't need to shut tight , the ones I worked on were double seated balanced poppet valves. I think Tubal Cain used butterfly valves on his models.

Edited By duncan webster on 15/07/2017 13:13:56

What matters, IMHO is the force available to correct the governor position.

This makes it all even more complex, as the displacement for any given error in speed will be much smaller, and that would suggest you really need a proportionately more sensitive mechanism. In particular 'stiction' in the valve is going to be a major obstacle for achieving the same degree of control as a full-size governor.

I don't speak from complete ignorance of the practicalities, I built enough bits to make about three non-functional governors before succeeding with this working one, in 1/12 scale.

I now in the other thread there were comments about the valve closing completely, I just settled for a loose fitting valve spindle so it just gives a significant throttling effect. That said I am not convinced it has any significant impact on engine speed.

I did mention a slight speed increase in the other thread as Duncan has also suggested which could be done without being too obvious to the casual onlooker. If I remember rightly you already have the crank pullies made so that would leave you with just a decrease in the governor pully to gain some speed but that may then give you issues with the amount of wrap around and risk slipping belts or excessive tension in the belt. As the speed is squared this would be worth looking into.

The other variable as I mentioned in the other thread is the springs both the flat springs that support the balls, making these thinner will allow the balls to throw out more. The same with the torsion spring and that can be reduced in dia and you may also be able to play with the levers that tension the spring.

Your biggest sticktion area will be that gland that seals the spindle into the top of the block, too tight and it will make it hard for the spingle to move up and down, too loose and it will leak. Fred has been having problems here on his Fowler.

It's a shame you did not mention your balls a couple of weeks ago as there was an engine running nicely on the belt driving a saw bench at Guildford I would have taken closer note of the set up.

The next stationary engine I plan to make did originally have a pickering type governor so I may make one too, though most of the photos that I have of it don't show the governor - no doubt there is more money to be made by Prestons if they sell it separately.

J

Edited By JasonB on 15/07/2017 13:38:25

I'm constructing a Pickering govermor, not a centrifugal Watts type. So the governor is spring controlled, and gravity doesn't play a part.

Andrew

Pic of a Pickering Governor FYI

Well, what the new forum ettiquette I thought it better not to; might have been misconstrued.

Andrew

Plenty to look at; the next items are stability and isochronism, tied with how F varies with r.

Also I don't see how any of these type of throttling governors control large changes in load. Speed I can see, simple control theory, but not large changes in load. Within limits an increase in load must result in a decrease of speed. Assuming that the governor is stable.

Andrew

According to the Pedia of Wick, this is the definitive analysis of how governors work:

www.jstor.org/stable/112510?seq=2#page_scan_tab_contents

You had better put your calculus hat on...

Neil

Yep, found the paper last night via a different route. I found it a bit difficult to follow due to the lack of diagrams. It wasn't always clear what system was being discussed. I wouldn't say it was definitive, but it was a major step forward. It introduced the concept of feedback determined by the roots of a polynomial for the first time. The values of those roots determines how the system reacts to an impulse and whether it will oscillate, with the oscillation increasing or decreasing. In control theory terms the roots are poles in the s-plane.

Andrew

Let's look at stability. There is the concept of a controlling force, being the radial force that tends to bring the balls back towards the axis of rotation. The force can be supplied by gravity or applied by springs.

Suppose the balls are disturbed and move out slightly while the speed remains constant. The radius of rotation of the ball has increased slightly so the centrifugal force will also increase slightly. What happens to the controlling force determines whether the governor is stable or not. If the controlling force increases, but proportionally less than the increase in radius then the small change in the centrifugal force will overcome the change in controlling force and tend to move the balls further out. The situation is unstable as a small disturbance has resulted in a tendency for the balls to move even further from equilibrium. Aka positive feedback. However, if the controlling force increases proportionally more than the radius then the balls will tend to return to thier previous position. Aka negative feedback.

In a Pickering governor there are two possible sources of controlling force, I think. First the torsion spring acting on the central spindle. And second the leaf springs on which the balls are mounted. So I surmise that if the combined force of both these springs is greater than the increase in centrifugal force for a given disturbance then the system will be stable. That knowledge should allow one to make some educated assumptions about the forces needing to be provided by the springs, and hence their characteristics.

Andrew

Edited By Andrew Johnston on 15/07/2017 16:44:29

I haven't quite got my head around the effect of changing load on throttling governors. But I don't think they respond well to changing load, as opposed to changing speed for other reasons.

As far as I can see for the Pickering governor there is only one position of the sleeve valve for each position of the balls, and hence speed. So if all is tickety-boo and the engine is humming along at a given speed with everything in equilibrium, what happens if there is an increase in the load on the engine? Presumably the engine will slow down slightly. The governor will then open the sleeve valve slightly, more steam will pass and the engine will try and pick up speed. But if it does the sleeve valve will move down slightly reducing steam supply and slowing the engine down again.

So it would seem that the basic centrifugal and spring loaded governors are fine for speed regulation at a relatively constant load but do not cope well with changes (especially large changes) in load without a consequent change in speed.

There are hints as to this in the literature but nothing I would consider definitive. But there are governors that work directly on the valve gear, altering cutoff, rather than throttling the steam supply. It seems logical that if there is an increase in load on an engine then to counteract that one would leave the inlet valve open for longer, allowing more steam at pressure to enter, before moving into the expansive phase.

Andrew

I understand that in the case of a rail locomotive, although there is an automatic governor (aka driver), once all is on the move at the required speed, the regulator (aka throttle) is kept wide open and the cut off used to control the speed as load varies. I would agree that the rotative governors are unlikely to cope with load variation because what is needed is a change of engine power at the required speed.

I see the flaw...

engine is humming along at a given speed with everything in equilibrium

What happens if there is an increase in the load on the engine? Presumably the engine will slow down slightly. - YES

The governor will then open the sleeve valve slightly, more steam will pass and the engine will try and pick up speed. - YES

But if it does the sleeve valve will move down slightly reducing steam supply and slowing the engine down again. - YES, BUT...

Because of the greater load it will (if set properly) stabilise at a lower speed but the difference will be considerably smaller than if the engine was ungoverned.

The knack must be to get the governor adjusted so there's very great non-linearity, with very large changes in steam admission for small changes in velocity very much targeted on the optimum speed. That would make it relatively easy to handle a large range of loads over a small range of speeds.

And following on from Kwil's observation, for most tasks the load will be fairly constant and a speed up off load is acceptable, as long as it is constrained within a safe maximum, because the governor will make sure that although there's an off-load speed increase, steam usage decreases.

I've got a booklet somewhere from a Stationary Steam Engine Group that mentions the need for a textile mill engine to govern both throttle and valve events in addition to having a giant flywheel. I can't remember if it was to manage load variation, or to improve economy, or both. I'll see if I can find it.

Dave

Tubal Cain's articles on Governors from ME in 1979 are in my album here

Rod

On a well designed simple governor, if you increase the load on the engine, the engine slows down a bit, the governor opens the steam valve to limit how much the engine slows down. If it opens the valve too much you will as Andrew suspects get an unstable system which hunts about the set speed. A simple governor will not give constant speed, the better it is the closer you get, but friction and damping in the linkage are your enemy

I think gravity does play some small part in a Pickering governor. The spring arms can be modelled as 2 pin jointed links with a spring pulling the balls to the centre, the spring being the bending stiffness of the arms. By the sounds of it there is also a torsion spring. Unless the balls are right under the spring arm anchor, gravity plays its part. Unless the governor spindle is horizontal of course.

Really clever governors, as made by the likes of Woodward, are hydraulically operated, the governor proper operates a hydraulic servo mechanism, so the operating force comes from the hydraulics, not the flyweights. Some mill engine governors had the governor engage a ratchet mechanism (like a mechanical oil pump but reversible), so if the engine was going too fast a pawl would engage with the closing ratchet and the engine would close its own valve very slowly, and if too slow it engaged the open ratchet. There was a speed range where neither ratchet was engaged. They really were clever chaps even without CAD, FE etc. Some mills had an engine driven clock. If it gained relative the the real clock, the operators got more money because the machines had been running faster and so they had to work harder, if it lost time the mill owner would have few words the the 'engine tenter'

What I still don't get is how you govern a turbine that is generating for the national grid, and so is forced to go at grid speed. How do you ensure it is doing it's bit? Something to do with phase angle

I would say you set the governor to give the correct loaded speed, eg on a saw bench you set it to give the desired blade speed when cutting x thickness of timber. So the opposite to Andrew:

So when sawing engine is running at the desired speed.

At the end of the cut there will be less load on the saw and therefore engine which will pick up speed

As it picks up speed the balls will travel faster and in so doing reduce the amount of steam bringing it back to idle

Push another bit of wood into the saw, engine speed dips for a second due to increased load, balls also drop and allow more steam through so getting back to desired running speed.

If you listen to and watch a full size or model doing belt work such as this you can hear the initial drop in speed before it picks up again during the cut and starts to sound like it is working , slight increase at the end then back to idle speed.

J

Edited By JasonB on 15/07/2017 18:46:54