German Crown Sagging

M Austin · **Joined:** Sat Feb 05, 2005 1:05 am **Posts:** 488

Historically the Europeans used copper for the firebox. The firebox was square with flanged corners. The firebox crown sheet was FLAT. The traditional North American practice was to use the Radial Stayed crown sheet. The crown has a specific radius and the the crown stays are inserted equally spaced and perpendicular to the crown sheet (like a fan).

The Europeans started by replacing square copper fireboxes with square steel fireboxes. DEFLECTION CAUSED BY LOADS (PRESSURE OR THERMAL EXPANSION) IS A FUNCTION OF GEOMETRY. THE ONLY MATERIAL PROPERTY THAT AFFECTS DEFLECTION IS THE "MODULUS OF ELASTICITY", NOT THE STRENGTH.

Tross was challenged with a GEOMETRY problem. The modulus of elasticity of copper and steel are significantly different. The square firebox geometry made of copper was acceptable. The same geometry made of steel caused deflections that generated unacceptable loads and unacceptable service life.

Shrinkage of the boiler plates is a common theme in Tross' analysis. This occurs when the plate is heated and expands. An unrestrained metal plate when heated will expand from the geometric center of the plate in all directions. If the plate is restrained in a direction of movement, it will exert a force. The expansion force is proportional to the cross sectional area of the plate and the temperature. Another property of metal is that as the temperature goes up, the yield and tensile strengths go down.

Regarding the firebox crown sag, the firebox crown sheet is heated by the firebox combustion. The crown sheet is FLAT. It tries to expand sideways. Restrained by the corners, the expansion forces EXCEED the yield strength in the lateral direction. This causes a plastic yield. The plate becomes frozen in expanded condition. As the crown cools, it drags the restraining edges toward the center.

If an expansion cycle causes only a 0.001" set, after 1000 cycles the crown would be pulled in 1/2" on each side. This causes a flattening of the upper firebox corners.
There is a pressure component acting to cause the sag also. Boiler pressure acting on the area of the boiler shell between the top row of horizontal sidesheet staybolts and first edge of vertical crown stays tends to push the shell outward. This outward deflection force causes the upper boiler shell to deflect downward, aggravating the crown sag. Tross recognized this and concluded that the boiler crown (wrapper sheet or roof sheet in NA) needed to be increased in thickness by 20 to 23 mm. This is almost a 1" thickness increase. (Imagine a 1-1/2" thick wrapper.)

Crown Sag

Pressure deformation - downward force on firebox crown sheet by boiler pressure forcing wrapper outward
Heat expansion plastic - thermal force exerted sideways exceeding the yield strength of the metal
Heat contraction - cooling of the plate
Corner deflection - flattening of the upper firebox corners

From the paper "Tross New Knowledge Locomotive Rear Boiler" from Matt Janssen's website.

Crown Sagging is one component causing Tross' defined "arching" of the boiler backend. Firebox bulging seriously increases the crown sag, leading to the addition of mudring cross anchors (bars welded across the bottom of the firebox to restrain bulging.)

Robby Peartree · **Joined:** Wed Aug 25, 2004 11:16 am **Posts:** 767

So sag the crown sheet, bow the mud ring, and just how much defection does one have to take up at the furnace bearer?

Robby Peartree