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

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

Pic of a Pickering Governor FYI

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.

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

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

This video shows how the engines react to load change, speed does not seem to vary much between when the saw is cutting or when idle but the note of the engine certainly does change and so does what comes out of the chimney. When the video cuts to the right hand engine of the pair you can see the governor balls changing speed.