I am currently building a Gauge One locomotive with slip eccentric valve gear. When I got to the stage of running it on air, it didn't seem to be working correctly. While it would turn over reasonably freely by hand, once air pressure was applied (but not enough to make it run) there seemed to be four distinct tight spots at roughly 90 degrees to each other. By the way this is a two cylinder engine, so there are four crank dead centres. More than 30psi and the engine would run, but as the pressure was reduced it ran in a more and more lumpy fashion before stopping at about 25psi. A careful measure of all the parts against the plans did not reveal any obvious fault. Further thought seemed to indicate that it might be a valve timing problem. A search on the internet and a look through all the relevant books in the club library failed to give any definite information. One thing that seemed to be said several times was to make the slot for the eccentric pin, then file a bit more to make it work properly. For my design, the eccentric angle EA was given as 120 degrees.
Fairly obviously from the diagram, the valve phase angle
2VP + EA = 360
VP = 180 - EA / 2
At one end of the slot, say the top in the diagram, the eccentric pin drives the valve gear for forward motion. At the other end the pin drives the valve gear for reverse motion. In the equivalent for Stephenson's valve gear, full forward gear is at the top of the slot, neutral gear is to the right and full reverse gear is at the bottom of the slot. Where the slip eccentric pin moves is in the no-go arc for Stephenson's valve gear.
Diagram A shows the situation for a simple valve with no lap. The eccentric is at 90 degrees to the crank. When the crank is at right dead centre, the valve is moving to the left and is just starting to open and admit steam to the right steam port as shown by the arrow next to the valve. If you imagine the crank has rotated 180 degrees the valve is in exactly the same position but moving to the right and ready to admit steam into the left steam port.
Diagram B shows the situation for a valve with lap. With the crank at right dead centre again, the valve phase angle VP needs to change so that the valve is just starting to open and admit steam to the cylinder at the same crank position as in diagram A. Notching up moves the valve phase clockwise (reducing VP) until it is in neutral gear when the valve is at the same angle as the crank. Continue moving the valve phase clockwise and you move into the reverse gear situation.
The length of the valve rod needs to be adjusted so that the left end of the valve is just opening when the crank is at left dead centre. This gives symmetry to each end of the valve gear. In fact once you have determined the VP and built it accordingly, the only adjustment needed is to the length of the valve rod so that there is equal port opening at each end of the valve.
For slip eccentric valve gear there can be no notching up as the eccentric pin has reached the end of the eccentric slot. Or rather any notching up is always to the same angle.
What seemed to be happening in my loco was that the valve was opening before the crank reached right dead centre, thus tending to slow the engine and create the apparent tight spots.
Having figured out the probable cause of the problem, it remained to find the correct angle for the eccentric.
V is the length of the valve
P is the distance between the outer edges of the steam ports
EO is the eccentric offset
E is the distance the eccentric displaces the valve at crank dead centre
It can be seen from the diagram that if we make
E = (V - P) / 2
then we will have a symmetrical situation for the valve once the crank turns 180 degrees.
To complete the maths
VP = 90 + sin(E / EO)
EA = 360 - 2VP
This only holds if the eccentric pin is very small. Additional allowance must be made for the diameter of the eccentric pin.
At full size the valve V was 13.3mm long and eccentric offset EO only 3.2mm so it was a bit too fiddly to deal with at that size. I therefore made a cardboard model of the valve and crank at ten times full size to prove to myself that the geometry was correct before I cut any metal. In my case EA needed to be increased from 120 degrees to 135 degrees. This included an allowance for the diameter of the eccentric pin. Having milled the increased angle of the slot into the eccentric I found that the engine would run smoothly down to less than 15psi and with no sign of the earlier lumpiness.