A Study of The Design Method and Similitude for A Small-Scale Test Drilling Rig (Part 1): An Application of The Geometrically Distorted Scaled Modeling Method

Drillstrings often vibrate severely and tend to twist off during hard rock drilling. Therefore, dynamic testing is crucial in the design of drilling systems. Designers tend to employ the most powerful analytical tools, using the most elaborate electronic computers, however, actual testing is required to the designed system function optimally. In cases of enormous drilling systems, complex dynamic tests are often performed on a smaller-scale replica of the system, referred to as the model, which is more convenient, cost-effective, and time-effective. This study, therefore, describes the establishment of similar conditions among structural systems, with the main objective of studying the similitude theory’s applicability in establishing the necessary similar conditions for designing scaled-down models to predict the drillstring’s vibration behavior. The scaling laws for all the relevant parameters regarding the scaled drillstring model, as well as the full-size drillstring system, were derived from the respective equations of motion. The scaling factors for all relevant parameters are determined using the theory of dimensional analysis. In addition, the geometry distorted similitude theory is revisited and employed to overcome the physical limitation and develop the necessary similar conditions for dynamic testing of the scaled drillstring. Meanwhile, the similitude relationship between the prototype and the model was validated with a case study using lumped segments bond graph modeling and simulation software.