Influence of cross-coupling stiffness in tilting pad journal bearings for vertical machines

• Cross-coupling terms can be large in tilting pad bearings subjected to dynamic load.
• Influence from cross-coupling is dependent on the load in the bearing.
• Simplified and efficient bearing model allows for fast simulations.
• Dynamic load in a tilting pad bearing introduces higher frequency components in the response.

This paper evaluates how cross-coupling coefficients affects the dynamics of a vertical rotor with tilting pad journal bearings. For vertical machines, the bearing properties are dependent on the bearing load and direction. As a result, it generally requires that bearing properties are calculated at each time step using the governing fluid dynamic equations. This method gives a good representation of the bearing but computational time increases and can cause stability problems. In this study the bearing properties are instead modelled as a function of eccentricity and its direction. Hence, the bearing properties can be evaluated at each time step without solving Navier–Stokes or Reynold׳s equation. The main advantage of using this method is to decrease the computational time. The cross-coupling stiffness and damping coefficients are usually neglected since they are small compared to the radial stiffness and damping coefficients. In this paper, the simulated unbalanced response is compared to experimental results and it is seen that the cross-coupling stiffness for vertical machines can influence the dynamics. It is shown that the cross-coupling can be of the same order of magnitude as the radial stiffness component depending on the shaft angular position in the bearing. Including cross-coupling increases higher frequency components and the experiments show similar behaviour. Hence the cross-coupling stiffness and damping coefficients should be included when simulating vertical machines subjected to high loads or when the detailed dynamical behaviour is important to investigate.