Posted by Martin Kyte on 13/07/2017 08:58:46:
Im sure Andrew will shortly dazzle us with the sums as it would seem to be well within his capabiliies especially after being scared off with the price of tungsten.
Bother, more mathematics to do; I'm never going to finish the traction engines at this rate.
There seems to be a dearth of information on how the Pickering governor actually works, and what is important. So to start with here is my qualitative explanation of how I think it works. We have three rotating balls on vertical leaf springs. As the governor speeds up the balls tend to fly out, but are constrained by the leaf springs. As the balls move out the leaf springs become bent and the ends move closer together. So far so good. The Pickering governor arranges that the leaf spring ends moving together cause a central spindle to move downwards. There seemed to be some confusion about the categorization of the Pickering governor in the literature, but as far as I can see it is a spring loaded governor. This is because there is an adjustable torsion spring resisting any downward movement of the central spindle. When these forces are in equilibrium the the sleeve valve operated by the governor should be in the correct position to let the engine run at the set speed.
Now the first question is what do the leaf springs actually do? If the downward force on the spindle caused by the balls moving outwards is countered by the torsion spring, why would we want the leaf springs to do anything at all in terms of resisting movement of the balls? So my WAG is that the leaf springs are essentially to hold the balls in place and act as flexible levers rather than as springs per se.
The force acting downwards on the spindle can be countered by adjusting the torsion spring, so do we want the forces to be large or small as they largely cancel anyway? I think larger is better within reason. Inevitably there is going to be some friction, static in particular, involved in moving the sleeve valve. I think the forces in the spindle need to be somewhat larger than the frictional forces, or the sleeve valve will not move proportionally. I'd see this as a sort of deadband, potentially leading to hunting, which rather defeats the object of the governor in the first place!
Mention of friction leads to another practical point. From what I can see of the full size Pickering governors they often came with attached valves, which were balanced, ie, the governor didn't need to work against the steam pressure. In the drawings I have this isn't the case. The sleeve valve is simply an inverted open can operating in a hole which crosses the steam path to the valve chest.
There are several possibilities; one the governor was never really intended to work, but just be for show, so it doesn't matter if the sleeve valve doesn't operate smoothly. There is nothing about finish or tolerances on either the sleeve valve or hole on the drawings. So is the hole intended to be leaky so that the sleeve valve sees roughly the same pressure top and bottom?
Or should I just drill a small hole in the top of the sleeve valve? 
That's enough pontification for the moment; the washing up calls!
Andrew
WAG = wild a** guess