Analysis of the Influences of drilling fluid flow velocity inside and outside the drilling string on drilling string lateral vibration frequency

Drilling string lateral vibration is a severe damage, which is influenced by many complex factors. This paper makes a theoretical analysis of the drilling string lateral vibration frequency caused by drilling fluid flow velocity inside and outside the drilling string, which supplies some evidence for calculating rotation speed of rotary table and reduces the times of drill string resonance. The influence of drilling fluid flow velocity inside the drilling string on lateral vibration frequency is analyzed by Euler method. Besides, through the use of mechanical analysis method and the introduction of additional mass coefficient. A differential equation of drilling string lateral vibration with the consideration of drilling fluid flow velocity inside and outside the drilling string is built up, and a mathematical model of drilling string lateral vibration under the influence of drilling fluid flow velocity is obtained. Field applications indicate that this model is in agreement with the field condition.