This paper formulates the generalized dynamics and stability of thread turning operations with custom multipoint inserts. The closed-loop chip regeneration mechanism is modeled by evaluating the effect of the current vibrations and the vibration marks left from the previous tooth. Using the developed chip discretization method, the dynamic cutting and process damping forces are obtained at each point along the cutting edge by projecting the three-dimensional (3D) vibrations of the tool and workpiece in the direction of local chip thickness. The equation of motion is derived in both physical and modal spaces, and stability is analyzed in frequency domain using Nyquist criterion. An iterative process optimization algorithm has been developed to maximize productivity while respecting machine tool's torque and power limits. Extension of the model to thin-walled workpieces along with the validating experiments on real-scale oil pipes is presented in Part II of this paper.

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