5.4.1 Fir-tree roots
Fir-tree serrations may be in line with the axis of the machine, inclined to the axis, or curved, see Fig 1.88. Curved fir-tree roots follow the blade chord at the root section. The straight root, in line with the axis, is used for slightly-twisted end blades. Both the inclined and the curved fir-tree roots are used for highly-twisted blades to achieve a closer blade pitch at the inner steam path.
Optimum selection of the dimensions and number of serrations of the fir-tree root has been made possible by finite element calculations of stresses in the shaft and root. Because of unavoidable inaccuracies in manufacture, the pit between the supporting planks of the individual fir-tree tips varies. This is also taken into account in the calculations. Pull-out tests on fir-tree roots have confirmed their reliability. In view of their high strength and close packing capability, side entry fir-tree roots are generally used for fixing last stage LP blading.
In earlier turbine stages, fir-tree serrations are machined circumferentially in grooves in the rotor, and groups of blades are secured in the grooves by similarly-serrated side locking pieces cut from rolled strip. The blades of the first row of the HP turbine are axially attached to a short wheel disc on the rotor by straddle roots, which engage with corresponding shoulders machined circumferentially on the wheel rim. The straddle fixing therefore acts as an inverted fir-tree, the tree shape, usually with only one or two branches, being formed on the rotor disc.