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The drawing:

Analysis of the Duchess valve gear starts with the reconstruction of the gear from the official drawing.  In this case the dimension of the return crank is not given, but the associated pitch circle and angular setting provide the input. The front end of the radius rod is located from the cylinder centreline, and the weighshaft and expansion link trunnions are located both vertically and horizontally, though square to the frame line and not that of the 1:50 motion inclination.  Thus placed, the given expansion link cannot support the eccentric rod of 66.25″ without some adjustment to the 92.5o angle and length of the return crank.

Even when this adjustment is made at back dead centre a half revolution does not allow the expansion link to attain an identical position, causing the valve to move using the reverser with the crank on front dead centre.  The effect is to render reasonable valve events at the expense of equal leads, with back gear proving the better set of the two modes.  Since it is the practice of valve setters to adjust the eccentric rod length to attain primary equalisation any CAD analysis must allow a slight variation in this component, so mental account of this is taken – an angle of 92.5o produces an eccentric rod of 66.208″, with inferior lead equality.  The upper pins measurement of the combination lever is obscured but this figure can be gained on simulation to conform to the lap/lead geometry.

If we therefore allow the principle (no valve movement at dead centres), achieved in practice at valve setting by correcting the length of the eccentric rod, then the 92.5o return crank setting on the drawing has to be corrected first and the resultant CAD reappraisal fed into the simulation. All the simulated results must then bear in mind the alteration made.


Simulation proceeds initially with the stated eccentric rod and associated return crank, without any correcting influence of a reduced backset dimension, since this amounts to far more than production tolerances might incur in making the expansion links. The immediate results are not expected to be correct, since their sensitivity to valve setting is so critical and this is the next stage in simulation.  Initial valve setting in the simulator differs from that pertaining in practice because, effectively, the position of the cylinder in relation to the gear (or the relative length of valve spindle) is not made in the same way.

Regrettably, most locomotives have no means of adjusting the valve on its spindle, with a heavy reliance on manufacturing tolerances.  The initial aim, however, in both cases attempts to produce equality of leads, but in the case of simulation establishes the gear’s ability to support such equality.  This is important in gear design analysis and reveals directly what happens in reality when a valve setting exercise equalises leads at the valve heads when the gear design has no means of complying.  It must be understood that equalising leads at the valve when a gear cannot physically support this condition plays havoc with all other events.  All gears exhibit events very sensitive to very small changes in the valve setting. Since the leads display variations of power and economy for given cut offs any acceptable difference in lead from front to rear ports is probably ascertained more clearly by computer calculation for a specific locomotive.

Event symmetry:

The Duchess gear responds as frequently expected – attempts to gain better coincidence of the exhaust and cut off curves, in this case necessarily taking into account the reversal of events against a much shorter connecting rod in the rocker drive to the inner cylinder, results in lead asymmetry.  An equal lead of 0.25″ produces too much event inequality and the Duchess requires something like 0.178″ at the front port and 0.278″ at the rear in order to give events that satisfy forward running both for the outside cylinders and to pass on to the inside.  This leaves events portraying a typical LMS pattern, with a full gear cut off approaching 3% difference.  Note that the dimensioned return crank angle has been corrected – one must hope that the angle was corrected at manufacture – and that the lead discrepancy is fairly typical of Walschaerts’ designs.

The stated full gear cut off of 75% nominal is not obtainable at a 29o lifting arm angle. It barely stretches above 71%. The nominal figure is only 70%.  As so often happens, the reverse events are marginally better and one wonders why some design effort to shift the favour to forward at the expense of back gear seems not to have been applied to an express engine.  The age-old problems of layout associated with large-wheeled engines – finding a suitable place to accommodate the weighshaft and to produce a stiff enough mounting for the expansion link – have affected the Duchess, though with less trouble than her forebears, the Princess Royals.

Comparison is best made with the contemporary Class Five gear, which portrays marginally better events. The Duchess has ¼″ more lap, slightly greater depth-in-gear and 1″ greater return crank circle to give 6.98″ travel, whereas the Five manages 6.47″ travel. The net result is that the Class Five is comfortably within its design remit where the Duchess struggles to make its nominal parameters.

4 cylinders and two sets of gear:

The inside cylinder valves are operated by derivation from the outside gear. The designers therefore need to heed not only the event differences between the outside front and rear ports, but to derive matching horse-powers from the inside cylinder halves. Since the cranks are at 180o and the connecting rods of different length the solution is far from easy. 2.5% difference at the outside cylinders cannot inherently be reproduced at the inside by providing a straightforward 180o rocker to reverse the valve direction of travel, even if both connecting rods were the same length.

It is reported (No. 11 in the Wild Swan series) that a King Class arrangement was tried on the Derby valve gear machine and failed to show worthwhile advantage.  It is hard to believe that Swindon went to so much trouble to alleviate the problem on so many locomotives, and to improve on the Kings the advantage in equality obtained on the Castles. The inference is that the LMS misunderstood the principles involved. The advantages are less due to the cranking of the rocker than to careful evaluation of the rocker arm lengths and the length and juxtaposition of the short connecting link. The mechanism advances and retards the progress of the valve at the crucial points of event. Both the LMS and GWR engines sported valve travels of over 7″ (though the Duchess gear does not quite reach this according to the dimensions on the drawing) and the advantage gained by the Pearce device would indeed be reduced proportionately where a travel of less than 6″ only is required. It is fair to say that of the Big Four railways only Bulleid realised that the problems of increasing angularities with greater travels could be successfully ameliorated by gear miniaturisation. The immaculate event equality (when the erratic steam reverser could be persuaded to conform) of his Pacifics tells its own tale.

Inside out:

Ignoring for the moment the influence of the 180o rocker, but taking into account the different connecting rod lengths, when the outer crank reaches 50% outstroke its inside mate has arrived at 43.75% instroke.  With the outer crank on 50% instroke the inside has completed 56.25% of its outstroke. Such is the worst position for discrepancy, passed on to the valve gear if not attended to in design.

In addition, the valve excursions are reversed by the rocker and measured against a different connecting rod.  In full gear the cut offs are 72.3% and 69% outside, with 67.2% and 74.4% inside, a range of some 7%.  In the area of 50% cut off the results are 53% and 50.2% outside, with 47% and 56.5% inside, a range of 9.5%. Either of these would be considered unnecessarily unequal for a 2-cylinder design.

With a good gear the equality of cut offs will render exhaust events similar in pattern, yet even on the Castles at slow speed it was possible to notice double-beat exhausts either by chimney or by watching the firebed. Maybe this influenced the GW design office decision to attempt better detailed design in the King valve gear.

It seems odd that Derby should quietly dismiss Willie Pearce’s clever arrangement of the rocker to ameliorate the large range of cut off differences, especially when Beyer-Peacock took so much trouble in the matter of balancing these issues on their Garratts, but there are other factors affecting the drawing office decisions even without that of expense. Neither cut offs nor exhaust releases are the whole story. It should be noted that the port of longer cut off is frequently that of least port opening, serving as some amelioration, and that the turning moments are anything but constant.  Many things are contributory to the smooth running steam engine and the Duchesses proved equal to any task of the day.

The typical LMS pattern of events portrayed by the Duchess gear is evident and its deficiencies are heightened somewhat, no doubt from requiring a long valve travel. The rather simplistic reliance on the straightforward rocker feeding the inside cylinder gives credence to the testing of 46225 as late as 1958, resulting in new valve settings to correct quite disparate indicator diagrams for front and rear cylinder halves. The original test results confirm my scepticism of the drawn dimensions. A 1/16th″ back shift in the valves produced a great improvement rather too late to benefit the ageing Pacifics. The large range of mean effective pressures was reduced by over 50% but better attention at the design stage and a better understanding of the rocker arrangement could have rendered valve events worthy of the Duchess.  The palliative of new valve settings did not reach the whole Class at so late a stage of dieselisation. The figures in the table, at least for the outside cylinders, are perfectly reasonable, but since the analysis was fraught with anomalies it may be deduced from the Rugby test in original form that the actual events attained were much the poorer.  It may be that without any testing at the time of building nobody sought to question the abilities of a Duchess because so much power was available both on paper and in practice. The official test bulletin was not made public.