In vertically oriented machines with tilting-pad journal bearings, there is no static load that allow to calculate the bearing properties around a determined static position. As a result, most of simulations are performed by solving Reynolds equation at each time-step which can result in long computational time. To avoid this concern, a simplified model is used that takes in account the variation of unbalance load depending on the pad configuration. This nonlinear model is used to simulate the dynamics of a hydropower turbine and compared with the Campbell diagram calculations used from hydropower industry standards. A comparison between the linear and nonlinear model is performed to evaluate how accurate the linear model is and until which limits it can be relevant. In case of qualitative discrepancies in the results in terms of natural frequencies and damping ratios, an improvement of the Campbell diagram calculation is proposed to obtain a more accurate linear model.