Model management, especially the selection of samples for model training and the infill sampling criterion, plays a significant role in the expensive many-objective optimization. Therefore, a number of good solutions will be selected from the database and used as samples to train surrogate models of objectives. The optimal non-dominated solutions of the surrogate models will be searched by the reference vector based evolutionary algorithm, among which two solutions will be selected for exact objective evaluation. The sampling criterion is proposed based on the mean value of the ranking on the approximation uncertainty (SaMVRAU). To evaluate the performance of the proposed method, a number of experiments are conducted on DTLZ and WFG many-objective optimization test problems, as well as two real-world applications. The experimental results show that the proposed method is efficient to solve expensive many-objective problems.