Cylindrical parts are widely used in the manufacturing industry, e.g., in making shafts. Such parts are typically machined on lathes by clamping the part on one end and removing material step by step using a cutting tool. The surface quality and dimensional accuracy of machined parts are critical as they directly affect the performance of end products. Structural flexibilities of a cylindrical part clamped on a lathe can lead to unstable vibrations known as chatter. Chatter causes poor surface finish on the part as well as damage to the tool and machine. Chatter can be avoided by proper selection of spindle speed and depth of cut, provided the structural flexibilities of the clamped part are known. However, as a part is machined, we observe changes in the structural dynamics of the part, which means the process parameters, such as spindle speed, must be updated at different stages during machining. This thesis presents a computationally efficient model to update the structural behavior of cylindrical parts during machining. These updated dynamics can then be used to calculate the stability lobe diagrams for each machining step, which leads to optimizing process parameters to maximize manufacturing efficiency. The proposed model is developed using the finite element (FE) method combined with deep learning techniques. First, a finite element model of the initial part is developed numerically, and the associated system matrices are generated and assembled. The removed volumes during the machining stages are then planned and segmented as substructures of the initial part. These substructures are dynamically decoupled from the workpiece by adding the opposite of their dynamics to the initial workpiece. This process updates the frequency response function (FRF) of the workpiece. A complete (full) order finite element model is implemented in the preliminary algorithm. Then, this model is reduced through model order reduction to improve the efficiency of the process by lowering the computational time. To reduce the order of the model, first, the master degrees of freedom (DOF) with the most contribution to the dynamics of the part are selected in an iterative procedure. Different methods are used to reflect the effect of the eliminated slave DOFs on the master DOFs. The FRF prediction results of the reduced order model are investigated. A deep learning-based framework is proposed to improve prediction efficiency. The developed algorithm in the first part of this study is used to generate a training dataset. A deep neural network is designed using hyperparameter tuning and then trained on the generated dataset. The performance of the trained neural network on an unseen set of workpieces is assessed. It is shown that the developed deep learning model can predict the structural dynamics of the part in less than 0.05s, making it suitable for online process monitoring and control applications.