Finite-element analysis of ring gear/casing spline contact

Abstract

The speed reduction from turbine to propeller is achieved in the Pratt and Whitney PT6 turbo propeller engines through a two-stage epicyclic gear train. In this arrangement, the ring gear is locked to the casing through external splines. The orbitting of the planet gears generate cyclic stresses in the teeth fillets of the ring gear and the casing. The sliding contact between the steel ring gear and the casing splines generates wear. A two-dimensional finite-element computer program was extended to iteratively solve the problem of load-dependent contact between the splines. Using this program, the nonuniform distribution of the reactive load and the relative sliding on the loaded splines are calculated for any planet gear load position. The analysis predicts that the relative sliding reduces through a change in the spline pressure angle from 20-30 deg. Spline wear is practically eliminated in field engine gearboxes through this design change. The cyclic variation of the fillet stresses are also determined due to the orbitting planet load using a detailed network and by imposing boundary displacements. Qualitative comparison of the stress prediction is made using instrumented test results. The paper demonstrates the analysis procedure using a typical ring gear and casing combination. Nomenclature D u= distance between nodes, / and / d = relative sliding between the splines /,/,/£ = probable contact node triplet FN = normal load on the spline F R = radial component of the planet load F e = tangential component of the planet load N = vector normal to line joining nodes / and / rpm = rotational speed of the planet carrier SHP = Shaft horse power of the engine S K = distance between / node and the projection of K node on line /-/ £//, Uj, U K = X displacements of nodes /, /, and K V/> Vj> VK = Y displacements of nodes /, /, and K A, Mue = direction cosines of the vector TV 8N 0 = shortest distance between K node and the line/-/ <t > = pressure angle of the splines