Finite difference method based calculation of gravity deformation curve for large span beam of gantry-type milling machine

To solve the problem that gravity deformation curve of cast-iron beam analyzed by Finite Element Method (FEM) simulation was inaccurate due to its neglect of material imperfection, a discrete calculation based on finite difference method was proposed. Supposed the flexural rigidity of beam was variable along the length, the continuous beam was discretized into segments and equivalent flexural rigidity was presented to characterize the inhomogeneity of material. Correction models of bending deformation and torsional deformation were constructed respectively to revise the results of FEM simulation based on equivalent flexural rigidity, which could be obtained by combining the discretization model and deformation data acquired in a simple self-weight load experiment. To accommodate the two proposed correction models, the bending deformation and torsional deformation of FEM simulation were separated by setting probes in the position of shear center. The experimental results showed that the proposed method could improve the G10 accuracy by comparing with FEM simulation.