An in depth parametric evaluation of the effects of Coulomb friction in an axial spline joint on the stability of the rotor-bearing system was conducted through time transient integration of the equations of motion. Effects of: spin speed, friction coefficient, spline torque, external damping, imbalance and side load as well as asymmetric bearing stiffnesses were investigated.
A subsynchronous instability is present at the bending critical speed when the spin speed is above this critical. The limit cycle orbit is circular, is proportional to the product of the friction coefficient and spline torque (μT), is inversely proportional to the external damping and is independent of spin speed.
When imbalance is applied to the rotor, beating between the subsynchronous natural frequency and the synchronous (spin speed) frequency occurs. The subsynchronous component of the orbit is proportional to μT, while the synchronous component is proportional to the imbalance.
When a static side load is applied, the unstable node at the center of the orbitally-stable limit cycle grows into an elliptical orbitally-unstable limit cycle, separating stable - from unstable regions of the phase plane. Below a threshold value of side load, the transient motion approaches one of two asymptotic solutions depending on the initial conditions: the larger stable limit cycle or a point at the center of the smaller unstable limit cycle. Beyond the threshold value of side load the rotor-bearing system is stable and all motions decay to a point.
Asymmetry in the bearing stiffnesses reduces the size of the subsynchronous whirl orbit.