This website summarizes the locomotive boiler finite element analysis (FEA) work undertaken over the last five years.
Launch 1 and 2 are small river launch boilers. Narrow Loco is a first attempt at modelling a much larger boiler. Wide Loco is a much more comprehensive analysis of a wide firebox boiler.
Each model variant of the model has it's own results page and menu entry at the top right of this web page. A full 3D web page display of the results is not practicable and so the information selected is a very small subset of that available in the model. Each results page has two switchable standardised views of the boiler and some graphs showing the maximum stress along selected stays. Both views can be animated to show (exaggerated 5 to 25 fold) how the boiler flexes under the applied thermal and pressure loads
The instructions on the images below work on most of the subsequent pages. The results web pages are large (~50MB) and will take some time to load on slower connections. A "spinner" will appear next to the page title while the background images are loading. Each page will be readable quite quickly but the animations will not work correctly until the page is fully loaded.
Each animation image is surrounded by controls as shown in the diagram below. These can display the results of the pressure and thermal loading separately or as a combined load
On lower resolution screens the legend is removed and the view and content controls move above the animation.
I became interested in this because there appeared to be very little published work on computer based analysis of locomotive boilers. Analytic approaches to pressure vessel design, specifically the use of Finite Element Analysis (FEA), were developed well after the “age of steam” was over. The last UK main line steam locomotive for British Rail was produced in 1960 and at that time computers were shrinking from the size of a room to the size of a large refrigerator. A state of the art computer in 1960 was 100,000 times slower than the lowliest of home PC’s today and cost about a million pounds in today’s money. FEA was in its infancy and was really only developed in the late 1960’s and the 1970’s.
Every analysis on this web site should be treated with a healthy dose of skepticism - please don't build a boiler just based on anything you see here!
A lot of the stress in any boiler is caused by differences in temperature and these are very difficult to model accurately. (I suspect the models built so far overestimate the tube temperatures and the consequential expansion.) Pressure loads are more straightforward to model but they do not necessarily generate the highest stresses. The design-by-rule standards use pressure based calculations almost exclusively while in service failures are often related to differential expansion induced fatigue.
Historically boilers were designed by rule.
Boiler Codes such as BS2790 and the ASME Power Boilers Code define a set of rules which will lead to a safe boiler design. The rules were developed through a combination of mathematical formula and are a distillation of the experience of what has worked satisfactorily for many years. However the most recent versions specifically exclude locomotive style boilers. It could be argued that this does not matter for heritage steam projects as the new boiler would be a copy of the original, which acts as an extensively tested prototype. To counter this, financial constraints or a move from riveted to welded construction drive continued development of locomotive boiler design.
Ideally an engineer should be able to calculate the stresses in each part of the boiler using mathematical equations. This is entirely possible for simple shapes. For example, the maximum hoop stress in a boiler barrel is calculated by multiplying the radius (half way between the inside radius and outside radius of the barrel) of the boiler by the internal pressure and dividing by the plate thickness. The design codes include simple equations, augmented with practical experience, for barrel stress, plate bending and stay loading. Unfortunately a locomotive boiler is much more complex than a simple cylinder and there are no mathematical equations that cover all the geometric shapes contained within it.
Modern computer aided engineering software can analyse a representation of a structure by breaking it down into discrete mathematical lego bricks. The software understands how the external forces affect the stresses in each brick (the general name used is finite element rather than brick) and how each element affects its neighbours. Modern cars, commercial airliners, mobile phones, oil refineries – the list is endless – will have been designed by analysis even if they are certified by design rule.