The drilling industry is faced with many challenges, and the sudden failure of a drill string during drilling is one of major concern. Exploration of the causes for the failures reveals vibrations as the major cause. In order to test and analyze the vibration patterns of rotary drilling, a laboratory proto type of the process is set up. The mathematical model developed to analyze the vibration presents residual error. Robustness issues pertaining to model error and modelling error is discussed. Methods to counter the errors and minimize the vibrations are also discussed.