Before I set out on what is in many ways the meat of this exercise I think it only right to first give credit where its due. On the CLAG webs site you will find this link to a series of documents on “The Deflection of Beams” Of the four documents there, the third “Continuous Spring Beams” is of great significance in what follows and the fourth “Suggestions for the setting out of the vertical position of the fixed fulcrums on a CSB chassis” appears to be a strait rip off of what comes next. Ok, I may have got that last bit the wrong way round. You will find that, part from a certain cavalier disregard on my part for more than one place of decimals, there is little that follows that either Russ Elliot or Ted Scannell have not said before. In Russ’s case, in considerably more detail. I see my major roll here as no more than trying to demystify and popularise what has already been laid before us.
Before we set about out task, there are a few basic assumptions and dimensions etc which you need to have in mind, and even before that I think a quick word on tolerances is in order.
The main reason why I believe that CSBs are the bee’s knees is because, not only are they easy to install, but also I find the method is robust and insensitive to minor variations of measurements and/or construction tolerances. Which means any reasonably competent modeller can readily obtain a working result, with the good running characteristics you'd expect from an effective sprung chassis. Like fexi chassis before it, I think CSBs are implementable by kitchen table modelling technology. Yes I know anybody who has gone over Russ’s words in “Continuous Spring Beams” may have noticed he occasionally lapses in to numbers, who’s units are in millimetres, expressed to an accuracy of 3 decimal places. Do not be afraid. We will go over this topic big time when we have done our first simple example, and finally get to considering a general way of determining where fulcrum points should actually go. But, right now, I would like to suggest that even the man with no more than a steel rule and a scriber, who will struggle to set out and measure accurately anything not expressed in round half millimetres, should be able to get a good working result, even if his driving wheels centres aren’t exactly a scale 6’10” and 7’7” apart.
While contemplating the wheels, which ones are we going to include?
For the moment we will not be bothering ourselves with bogies and pony trucks. To be honest there is nothing I currently know about that lets you reliably include a bogie or pony truck into the fulcrum location calculations. Nor is there a simple or accepted way of attaching them to that single springy beam. In any event we will not be the first to treat them as cosmetic and allowed them to fend for themselves. As already stated, on the 04 2-8-0 the leading pony truck takes no part in the dynamics of the vehicle suspension. Yes there is an element of cop out here, and there are some loco’s for which this just will not do, e.g. most, if not all, 4-4-0’s. I would defend this approach on the basis that it is best to get to grips with the simple cases of our subject before moving on to more complicated situations. However it remains true that a viable approach is required for locos where a significant part of the body weight should be carried on a bogie, and I will eventually get to a worked example of a 4-4-2. Also note that I’m not excluding all carrying wheels. Any axle which is running in a simple bearing in the mainframe can be included readily, so there is nothing inherently different between a 2-2-2, a 2-4-0 or an 0-6-0.
Setting things out
One thing I think we can all agree on is that if you are gong to fit CSBs to a chassis, you really need to do it as an original fitting. Retro-fitting would be a pretty big ask. The implication here is this is something that gets done in the flat, either on an existing set of yet unassembled etched or milled frames, or even on the virgin metal. For the sake of argument, and because that’s what I did with the J10 tender chassis, my first example will be marked out on the virgin metal.
Consider the following diagram
What we are going to do is mark out the above diagram for a 3 axle chassis. Before you can start you need to know:-
( 1. ) The wheel base dimensions, w1-2, w2-3 and hence wb.
- From the prototype. Where the drawing office show them to be on the GA drawing.
- This is the distance from axel centre line to the spring centre line dictated by the hornblock/axle bearing design you use. If you are including wheels of different diameters (e.g. a 2-4-0) then for each wheel size, the sum of this dimension plus the wheel radius must be the same.
( 3. ) The designed static deflection of the spring, 0.5mm.
- This is the amount which you plan for your suspension to be depressed by the weight of the loco when standing at rest, with the wheels at the designed normal axle centre line. By convention, we design the suspension to have 1mm travel from unloaded to fully compressed, with the static deflection point/normal axle centre line half way. There is no real justification for this specific value, beyond the fact that nobody has yet made a case for using anything different.
- The most the axel will be free to move, under dynamic loads, above the normal axel centre line and before it hits the stops. The rest of the 1mm overall movement.
- I am well aware that working this out can be seen as a bit of a black art. In “Continuous Spring Beams” there is a link to a spreadsheet which will allow you to calculate your own. There are also a number of worked examples for regularly modelled prototypes, in which, you will be pleased to hear, Russ has not gone beyond 1 place of decimals. The robustness of the method means that, while the mathematical analysis which underlies all this allows great precision in defining the optimum configurations, the model will work just fine even if your marking out fails to capture the exact calculated dimensions. Later on I will also present an argument of my own which suggests rule of thumb approach to working this out that shouldn’t which gives workable answers without resorting to anything more technological than paper and pencil.
One final thing
While the CSB is normally installed above the axles as in the above diagram, mechanically you can just as easily install it below. In which case the fulcrum centre line is below the axle centre line by the axle to spring dimension plus the static deflection amount, and there needs to be somewhere down there to site the fulcrum points. Or being a smart arse you might consider building some of the classic 2-2-2s with the CSB above the carrying wheels and below the driving wheel, but at that point you are going to have to work it out for yourself.
Well that’s the theory, the next time we really will get to grips with the J10’s tender chassis.