Objective  The propulsion shafting system is an important part of a ship, and the bearing load directly affects its operating state and service life. In this paper, bearing load under hull deformation is studied using grey system theory.

  Method   First, according to the empirical formula of the relative displacement of each bearing caused by the deformation of the hull of a 57 000 DWT oil tanker, the relative displacement of each bearing is calculated and input into a finite element model, and the load value of each bearing is output. On this basis, grey relationship analysis of grey system theory is introduced to study the influence degree of stern bearing displacement on the load of each bearing, and the relative change of the load of each bearing caused by the displacement of the stern bearings is analyzed. A GM (1,1) prediction model is then established for the bearing load considering the bearing displacement conditions, and the hull deformation-fitting and prediction of each bearing load are made.

  Results  The results show that grey relationship analysis can effectively reflect the influence of hull deformation on bearing load. The GM (1,1) prediction model has high accuracy and prediction errors less than 6.0%, and the model test indexes can represent the accuracy of the prediction.

  Conclusion  Grey system theory is effective and practical in research on propulsion shaft load. It can accurately predict bearing load under bearing displacement, giving it certain reference value for research on bearing load under actual sailing conditions.