In this paper, we investigate the effect of a downhole passive regulator [anti-stall tool (AST)] on the dynamics of rotary drilling systems in interbedded formations. Drilling in interbedded formations can significantly affect the vibrational signature of these systems and the associated drilling performance. Hence, models to assess the impact of drilling in such formations are needed. Here, we construct a dynamic model of the drillstring system which incorporates the bit/rock interface laws for the transitional phase of bit motion between rock layers with distinct mechanical properties. In the model, the axial and torsional dynamics of the drillstring systems are coupled by these interface laws and cast in the form of discontinuous (state-dependent) delay differential equations. Next, we include the AST in the dynamic model to enable the assessment of the influence of this downhole tool on drilling performance, in particular in terms of rate-of-penetration (ROP) and drilling efficiency. Furthermore, we also investigate the mechanical specific energy (MSE) and steady-state power losses at the bit (due to frictional torque) for different operational conditions and rock layer thicknesses. The analysis reveals that an increased drilling efficiency and lower MSE are obtained by incorporating the downhole tool in the drillstring, resulting in a higher ROP and a lower frictional contact between the bit and rock in interbedded formations.

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