A design method of large-scale partial similar model test for cementing casing string system

When the cementing casing string system (CCSS) is subjected to a large-scale equal-scale model test, the huge aspect ratio of the system makes the wall thickness of the model casing string too thin to be manufactured. Therefore, this paper proposes a design method for model test with unequal scale of axial size and radial size of the CCSS. Firstly, the dynamic model of the CCSS is established and solved by the transfer matrix method (TMM), and the modal test is carried out and the results show that the numerical calculation error of the first five natural frequencies of the system is less than 4 %. Then, based on the dynamic model, the similarity laws of the complete similarity model and the partial similarity model of the CCSS are derived by equation analysis method, and the design process of the similarity model test is given. The advantages of the research are elaborated in details through examples. To verify the correctness of the similarity model’s similarity laws of the CCSS, similarity models with different parameters are designed, and the prediction errors of prototype response are analyzed based on numerical calculations. The results show that the maximum prediction error of the first eight natural frequencies of the prototype system is less than 3 %, and the response prediction results of the system are also accurate. Finally, considering uncertain factors of the partial similarity test, the similarity model test with the axial size of double scale is designed, and the results show that the maximum prediction error of the first three natural frequencies is 7.06 %, which meets the engineering requirements. This study can provide useful theoretical guidance for the large-scale model test design of the CCSS.