Influence of sonic vibrator mass on the modal frequency of the drill string

Abstract

The sonic drill mainly utilizes a sonic vibrator to initiate standing wave resonance of the drill string to achieve high-speed drilling. However, the explicit function relation between the lumped mass and modal frequency could not be revealed. Precisely controlling the sonic vibrator frequency to maintain the standing wave resonance of the drill string is difficult. In this study, the one-dimensional wave theory is employed to establish the longitudinal vibration differential equations of the sonic drill string with vibrator mass. The modal frequency equation of the sonic drill string with an inertial boundary is obtained via the method of separation of variables. The explicit expression of the modal frequency with respect to the vibrator mass and system structure parameters is calculated by mathematical analysis. Moreover, the influence of the large vibrator mass on the dynamic characteristics of the drill string is revealed during drilling of a shallow hole. This can precisely track the vibration control frequency of the sonic drill during shallow hole drilling, while maintaining the standing wave resonance of the drill string coupled with the sonic vibrator. Thus the efficiency of sonic drilling is improved.