Method of determining drillstring bottom hole assembly vibrations

Lateral vibrations of drillstring bottom hole assemblies are confirmed by sensing longitudinal and torsional accelerations or displacements of the drillstring at or near its top end during rotation and determining the lateral critical speed and displacement of the drillstring from the mode shape of the bottom hole assembly which occurs during forward synchronous whirl and longitudinal shortening of the bottom hole assembly resulting from such whirl. Lateral motion of the bottom hole assembly, while drilling, is estimated based on longitudinal and torsional measurements at the top of the drillstring. Radial displacement of the bottom hole assembly due to impacting of the borehole wall imparts a torsional impulse which, together with considerable radial motion, is repeated each revolution. The lateral or radial motion causes a small axial motion to develop in the bottom hole assembly which results in an axial force on and axial shortening of the drillstring which varies once per revolution.