Section 2.1.2 The mechanics of the miniature steam engine

 

The basic engine

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Fig 8

Figure 8 shows a cross section of a simple slide valve engine. It was designed by Edgar T. Westbury and castings are sold by Reeves.

 

The engine is double-acting, that is, steam is admitted to both top and bottom of the piston. The piston is effectively integral with the piston rod that, in turn, is connected to a conventional crank and connecting rod. As the crankshaft rotates the piston goes up and down. In order to make this into a steam engine steam must be admitted, allowed to do work on the piston and then rejected to exhaust in a regular cycle. For this purpose the engine has a “D” valve that moves over the ends of the two steam ports to alternately open the ports to steam and then open them to exhaust. Almost without exception the valve is driven by an eccentric (which is just an oversize crank pin.) and a banjo. If the dimensions are correct and the eccentric properly placed relative to the crank the engine will run in one direction only and produce power. This very simple-looking device turns out to be anything but simple when one tries to adapt it to drive a model boat.

 

Desirable requirements of the marine engine

The first desirable requirement is that the engine should be self-starting. The simple engine cannot be self-starting because it can stop with its piston at one end of the stroke. The marine engine must have at least two cylinders.

 

Boats should be able to go both forwards and astern. The engine must either be reversible or if it can go in only one direction be fitted with some reversing mechanism.

 

The engine should use the steam expansively to minimise steam consumption.

 

The engine should not be unnecessarily heavy nor unnecessarily large.

 

 

Expansive use of steam

One might admit steam for the whole of the working stroke and exhaust for the whole of the exhaust stroke. This is what many model engines do. But, if the admission of steam is stopped somewhere near mid stroke, the steam can expand to do work during the rest of the stroke. This expansive work can be as much as 30% of the work done. We get this work for nothing compared with the full-admission engine. This is an attractive avenue if economic use of steam is to be achieved. In order to explore it I need to introduce the indicator diagram for the steam engine.

 

The basic indicator diagram for a steam engine

This diagram is what was taught in college when steam engines played a major role in transport. It is the best that we can think of if we plan to use steam. Such diagrams are called ideal indicator diagrams to distinguish them from real diagrams taken from an engine when running using some form of engine indicator.

 

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Fig 9
The first thing to notice is that we must work in absolute pressure. I have used a boiler pressure of 50 psi or 64.7 psia and, as the engine exhausts to atmosphere, it takes place at 14.7 psia. The volume of the steam includes the steam that fills the space between the piston and the cylinder head and the steam in the steam passages. This volume when the piston is on top dead centre is called the clearance volume. I have let it be 10% of the volume swept by the piston during one stroke ie the piston atea times the stroke.

 

In figure 9 I have drawn the ideal pressure variation in the cylinder during one cycle of events. It is shown to scale on the volume axis. During the portion of the stroke of the piston from B to C steam is admitted from the boiler until the inlet closes at C. This is the point of cut-off and, in this diagram I have let the cut off be 50% of the stroke. Once cut-off has taken place the steam is trapped and it expands as the piston continues its travel. The pressure drops continuously as shown in the curve CD. (Measurements have shown that this is the curve of .) At D the exhaust valve opens and the pressure suddenly drops. Then the piston reverses driving out the exhaust steam until the exhaust valve closes at A. At A the inlet valve also opens, the pressure rises suddenly and the cycle starts again. The cycle is closed and drawn in red.

 

The work done in the cycle is proportional to the area inside the cycle. The top line on the diagram is at boiler pressure the lower line at atmospheric pressure. The two end lines are at the ends of the stroke. These are all fixed so the engine cannot operate outside of it whatever cycle of events is chosen. Any practical diagram will lie within it. So why is this the best that we can do, that is, the ideal cycle? Simply because no one has ever been able to think of a better one. Once the cycle is in existence it can be explored to give us ideas for increasing the amount of work that can be extracted from a given quantity of steam.

 

This can be illustrated using Figure 9. The work done by the engine during one cycle if these events were to take place would be proportional to the area within the diagram. If the cut-off were to be at the end of the stroke the area would be proportional to 5,000. However in this diagram where the cut-off is at 50% the area is proportional to 4,118. For 60% of the steam used we get 82% of the work. This puts a magnitude to the potential for improvement. These calculations can be repeated for other points of cut-off to see what is possible. One might also see what effect the magnitude of the clearance volume has on the characteristics of the diagram.

 

In figure 10 I have calculated the variation of work done with cut-off for the cycle shown in figure 9.

 

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Fig 11
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Fig 10
Clearly and not surprisingly the work done per cycle falls as the cut-off is reduced. However figure 11 is a more significant relationship between the work done per cycle per unit volume of steam and cut-off. It increases dramatically as the cut-off is reduced until the effect of the clearance volume becomes important at very low cut-off.

 

Figure 11 also shows us that the clearance volume should be kept to a minimum. Of course there are other contrary trends in that a large clearance volume helps with the problem of condensate in the cylinders. In small engines there is a minimum clearance volume that is determined by the mechanical requirements of the engine.

 

We must now look to see why this ideal cycle is not achievable in practice.

 

The valve driven by an eccentric

 

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Fig 13
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Fig 12
The starting point must be the arrangement that is adopted on many model steam engines. This is the slide valve with a face width equal to the width of the steam port. I have shown it in Figure 12. In the position shown in, any movement of the valve downwards will open the cylinder to steam and any upward movement will open it to exhaust. Almost universally this valve is driven by an eccentric acting through the banjo to move the valve up and down as the crankshaft rotates. I have shown the relative positions of the crank and eccentric in Figure 13. I have added points A and B on the eccentric circle. When the eccentric is below AB the cylinder is open to steam. When the eccentric is above AB the cylinder is open to exhaust.. The positions of the crank corresponding to A and B are a and b. The valve will admit steam for 180° of crank rotation and be open to exhaust for the other 180°. The engine will work like a hydraulic motor. As we have seen this is not a good way to use steam. However the engine has one overwhelming advantage, water cannot be trapped in the cylinders. This alone justifies the use of full admission and full exhaust in the eyes of many steam modellers. They make the valve slightly wider than the port to prevent steam passing directly from boiler to exhaust. Its natural vehicle is the triple expansion engine where the steam is admitted to the high-pressure cylinder for the full stroke and then expanded into the intermediate-pressure and low-pressure cylinders. Such an engine must be turned back into a simple engine to start it and this is a major snag.

 

Valves with overlap

The eccentric is so simple a device that there is only one variable. The eccentric goes round and the valve rod goes up and down driving the valve no matter what we do. The only thing we can change is the throw.

 

The valve is another matter. The width of the valve faces can be changed to be wider than the port on which it operates. The extra width could be on one or both edges of the valve face. The valve is said to have overlap and these overlaps can be equal or unequal as the design requires. They are called the steam-side and the exhaust-side overlaps. In figure 14 I have drawn the wider valve with unequal overlaps in mid travel to show the overlaps on the steam and the exhaust sides. If this change were to be made to an engine with the eccentric set to lead by 90° the new travel of the eccentric is equal to the width of the steam port plus twice the greater overlap.

 

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Fig 14
In figure 14 I have shown the two overlaps on the eccentric diagram and the corresponding positions of the events in the steam cycle for the crank at 90° to the eccentric. Now steam is admitted from point A to point B. Exhaust takes place from point C to point D. When this is transferred to the crank diagram:-

     Inlet starts at a,

     Cut-off occurs at b,

     Release to exhaust is at c,

     Exhaust closes at d.

 

This diagram shows that steam will be admitted after the crank reaches top dead centre and will be cut off by an equal angle before bottom dead centre. Similarly release to exhaust takes place after bottom dead centre and the exhaust closes by an equal angle before top dead centre. It leads to the steam cycle show in figure 15

 

The valve just goes up and down opening and closing the two steam ports in a regular cycle.

 

Now figure 14 can be used to produce a cycle of events for a miniature engine.

 

 

 

 

 

 

 

Fig 15 shows the indicator diagram for an engine with unequal overlaps. To some scale the swept volume can have the same length as the piston travel. Then, on the pressure-volume plane we get the diagram ab12cd34a.

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Fig 15

a-b is admission of steam at boiler pressure

b-1 is the expansion after the steam is cut off

1-2 is the compression of the steam back up the same curve before it is released to exhaust at 2

2-c is the drop in pressure at the release to exhaust

c-d is the exhaust at atmospheric pressure (d is the point where the curve crosses the exhaust pressure line)

d-3 is compression of steam until the end of the stroke

3-4 is the expansion back down the same curve until the valve opens to admit steam at boiler pressure to the cylinder again.

 

I do not think that a steam engineer would consider using such a diagram yet it must be what goes on in lots of model engines. The engine will work and if you do not know what is happening in the cylinder there will be no problems except, possibly, the “compression” of water. I gather that model engineers accept this diagram and move their eccentrics to get what appears to be the best output from the engine. The steam engine is a very flexible device.

 

Clearly having no exhaust overlap would get rid of the condensed water problem and it may just be that this diagram then gives a route to expansive use of steam by using a large steam side overlap. Then admission of steam would be later and cut-off earlier. Then there would be an area of work under b2 that is due to expansion. There would also be an area of “negative” work in the small triangle between 4 and the exhaust line. The net result of these two is expansive work but the late opening to steam effectively increases the clearance volume enormously and this will off-set any gain from expansion when the work done per unit volume of steam is evaluated. I think that we must discard this idea and look elsewhere.

 

Giving the eccentric a lead

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Fig 16
There is another avenue to explore and that is to use the only change open to us, that is, to alter the angular relationship between the eccentric and the crank. Locomotive engineers used this and they called the angle in excess of 90° the lead.

 

In figure 16 I have drawn the circle representing a rotating crank from figure 14 in a new position where the valve opens to steam at top dead centre. It is an arbitrary decision but not an unreasonable one. Once this point is fixed the rest follow. It is now possible to draw the indicator diagram that matches this sequence of valve events.

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Fig 17

In figure 17 I have taken the crank diagram from figure 16 and turned it through 90° to give the stroke horizontally. The event points of the diagram have been projected down on to a pressure-volume graph.

 

At A the cylinder is opened to steam when the pressure immediately rises to boiler pressure. At B the valve closes the cylinder to steam, cut-off. The steam now expands to C where it is released to exhaust. Immediately the pressure drops to exhaust pressure at 1. The stroke is not yet finished so the cycle goes to 2 and then to D where the cylinder is closed to exhaust. The steam in the cylinder and the clearance volume is trapped so it will be compressed until the point A at the end of the stroke where the cycle will be completed with the opening to steam.

 

It is obviously a much better cycle if the object is to use the steam expansively. The cycle uses 72% of the steam used during full admission and gives 92% of the work.

 

Even though it was chosen arbitrarily with an eye to good sense the cycle obviously has potential for refinement. The big problem is the compression at the end of the exhaust stroke which would wreck the engine if it was water in the cylinder and not steam. This must be addressed.

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Fig 18

However there is one arrangement that we should look at before we leave this section and that is the valve with no exhaust side overlap because this arrangement cannot be locked with condensate.

 

Figure 18 shows the resulting cycle. The big changes are the early release to exhaust that we do not want and the later closing of the exhaust valve with much reduced compression that we do want.

 

We now get 84% of the work for full admission for a reduction in consumption to 74%. This is typical of the miniature steam engine and large ones, every change has

advantages and disadvantages.

 

 

 

 

Stephenson’s link motion.

I think that this motion grew out of a previous mechanism designed for reversing a steam engine. Two eccentrics were fitted, one for ahead one for astern and the two eccentric rods were joined by a short straight bar that drove the valve rod. One eccentric drove the valve, the other just moved the free end of the rod up and down. It evolved into the Stephenson’s link motion for reversing and for altering the travel of the valve. This is the last major parameter of the mechanism that can be altered and we must look to see what could be achieved using this facility.

 

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Fig 19
I have drawn layout of the Stephenson’s link motion in figure 19. There are two eccentrics mounted on the crankshaft. I have shown them at 120° before and after the crank because this is a typical practical value. The valve rod works up and down in the steam chest that contains the valve sliding over the ports. If the engine were to be unidirectional the eccentric could be joined to the valve rod by an eccentric rod and a pinned joint. As we are looking for a mechanism for a reversible engine we need a second eccentric and a means to alter the drive to the valve by switching the drive from one eccentric to the other. In the Stephenson’s gear the device for making the change is the quadrant or slotted link. The valve rod is now pinned through a block that slides in the link and the two eccentric rods are attached to lugs on the slotted link. All that is needed beyond this is a means of pushing the slotted link across so that the other eccentric rod becomes in line with the valve rod in order to go into reverse. A third lug on the slotted link is connected via two drag links (I have omitted one for clarity) to a lever on a shaft called the weigh shaft. Rotating this shaft permits the engine to be reversed.

 

However it must be obvious that the slotted link can be set in any position between the two extremes so there must be some relationship between the position of the slotted link and the travel of the valve. When I was designing my first engine I made a scale model of the mechanism and explore it practically. It was worth doing.

 

Before the scale model could be made I needed some leading dimensions. I have the drawings of the Marcher by Bertinat and these gave me some practical dimensions to start with. Reasoning that I could change them if the need arose, I made the model to 4 times scale and I learnt a lot. One surprise was that the radius of the quadrant could be chosen to give similar diagrams for both sides of the cylinder. I changed from the initial value of 1.5² radius to 1² and that was an over correction. In fact the radius is quite critical and I found that a good figure is 1.3125².

 

Figure 20 shows in four pictures  the mock-up of the link motion at the important points of its movement. In the model the red represents the upper and lower spools of a piston  valve; steam is admitted in the middle of the spool and exhaust is above and below the spool. The black lines represent the two ports. The model has two eccentrics with eccentric rods. These are linked by a quadrant with 9 holes. There were holes in the linking pins, one in the middle and three on each side to represent the ¼, ½, and ¾ positions of the quadrant. The drag link is represented by the “U” shaped link with suitably spaced holes in the back-board to set the quadrant position.

 

 

As I have said, the Stephenson’s gear is not quite symmetrical because the drag link affects the motion of the two ends of the quadrant in different ways. The forward direction of the engine would be when the drag link is over to the left so that the pin joining the eccentric rod and the quadrant is on the centre line of the gear.

 

All these pictures are for the gear in mid-travel between the end and the mid-position for the engine in forward gear. (Note the symmetry between the relative positions of the two spools.) It is much the same in all quadrant positions. I measured the cardinal points for the gear in all its five positions for what would be the forward direction of the engine. This gave the angles in the following table.

 

Quadrant position

end

3/4

1/2

1/4%

middle

Admission starts

356°

348°

337°

327°

315°

Point of cut-off

87°

75°

67°

55°

44°

Exhaust opens

170°

163°

155°

147°

135°

Exhaust closes

275°

260°

246°

234°

225°

It is interesting to see that, for the quadrant in the mid position the events occur at 45°, 135°, 225° and 315°, ie at every 90° from 45°. The engine would run in either direction at this setting of the motion.

 

These angles can be set out on a circle to show the crank position when the important events in the cycle take place. This circle can then be used to get a good idea of the indicator diagram simply by projecting down on to a pressure volume graph. The curves representing the expansions or compressions are all for . (The angle of the connecting rod will affect these diagrams a little but not enough to alter the facts that can be deduced from them.) When I first did this exercise I thought that a boiler pressure of 20 psig was adequate because it was used in my first steam-boat which was quite small. The cycles for four positions of the slotted link are shown in figures 21 a to 21 d. Somewhere between the fig 21 c and 21 d the diagram has no area and would produce no power.

 

 

However if the boiler pressure is increased to 50 psig the picture changes completely to that in figures 22 a to 22 d.

Now we have what looks like a very practical change in the area of the diagram. Unhappily it does not have the right characteristics for driving a boat. Boats require very little power to drive them slowly and the diagrams in figs 22 c and 22 d are a bit too big and control achieved by moving the slotted link by radio becomes too sensitive and the engine is likely to stop. It is much more predictable to use the Stephenson’s gear to reverse the engine between the two best running positions and control the speed by throttling the steam supply. At least the throttling valve can be profiled to give predictable low speed performance.

 

This has exhausted the mechanics of the simple steam engine. Now it is time to look at the practical aspects of designing a miniature engine.