Building of a Mathematical Model for Solving the Elastic–Gas-Dynamic Task of the Gas Lubrication Theory for Petal Bearings

Petal gas bearings are widely used in industrial turbine installations. However, there practically no mathematical models that take into account the nonlinear dependence of elastic element deformations gas-dynamic bearing on pressure. It is very difficult to obtain a converged solution with given accuracy an acceptable time. On this basis, model motion petals package was proposed. The takes pressure deflections bearing, as well design features and its elements. A feature solving presented task joint two subtasks: lubrication elements bearing. problem contact areas not known advance. search for or formulation elasticity based Lagrange variational principle. Petals shape thin cylindrical shells. achieved by minimizing potential energy system deformed petal shells using first-order gradient method. gas-dynamics applying explicit finite-difference approximation To implement proposed model, numerical algorithm developed solve related tasks dynamics combining methods calculus, optimization, time scheme. order convergence corresponded 10−5. study demonstrated load-carrying capability increased 2–4 times increase number petals. results experimental studies allowed us estimate interval ascent speed rotor, which initial conditions modeling.