Research

Machine Tool Vibration Theory and Applications for Machining, Additive Friction Stir Deposition and Hybrid Manufacturing

Machining - Advancing Machine Tool Chatter Theory and Applications

“Chatter is the most obscure and delicate of all problems facing the machinist, and in the case of castings and forgings of miscellaneous shapes probably no rules or formulas can be devised which will accurately guide the machinist in taking the maximum cuts and speeds possible without producing chatter”.

-Taylor, the pioneer of manufacturing engineering and industrial engineering, stated that in his 1906 ASME article.

Cutting Mechanics-based Machine Learning (CMML) : A physics-based machine learning method for model discovery, and that can integrate existing cutting mechanics to explore the unknown physics in experimental data for nonlinear cutting force model discovery. Feasibility on straight teeth and helical teeth milling systems has been verified and validated using time domain simulation. The metrology system has been built up, and experimental data has been acquired for nonlinear cutting force model discovery.

ChatterStabilizer: An accurate and scalable bifurcation and stability analysis framework, and that can generate stability maps fast from time domian for chatter suppression. ChatterStabilizer can use less than 3 minutes to generate accurate stability maps from time domain and outperform the well-renowned methods developed in the past sixty years, including average angle, zero order, multi-frequency, semi-discretization and traditional time domain simulation. ChatterStabilizer-GPU solver is in development to generate accurate stability maps from time domain in real-time (less than 10 seconds based on our preliminary results currently, coming soon).

Stability map for straight teeth milling tool. ChatterStabilizer generates accurate stability map in 2.2 seconds.

Stability map for helical teeth milling tool. ChatterStabilizer generates accurate stability map in 61 seconds.

M. Ma†, T. Shi* and T. Schmitz, “ChatterStabilizer-GPU: Real-Time Stability Map Generation from Time Domain for Chatter Suppression”, To be submitted to International Journal for Numerical Methods in Engineering in 2026.
T. Shi* and T. Schmitz, “ChatterStabilizer: An Accurate and Scalable Framework of Bifurcation and Stability Analysis for Advancing Machine Tool Chatter Theory and Applications”, Under review at ASME Journal of Manufacturing Science and Engineering, 2025.
M. Ma†, V. Wu†, J. Yi, H. Wang, B. Jared, T. Schmitz and T. Shi*, “An Interpretable Machine Learning based Predictive Control Method for Manufacturing Processes with Turning as A Case Study”, Under review at NAMRC 54, 2025.
A. Ren†, M. Ma†, V. Wu†, J. Karandikar, C. Tyler, C., T. Shi* and T. Schmitz, “A Cutting Mechanics-based Machine Learning Modeling Method to Discover Governing Equations of Machining Dynamics”, Manufacturing Letters, 44, 759-769, 2025, https://doi.org/10.1016/j.mfglet.2025.06.089.
M. Ma†, A. Ren†, C. Tyler, J. Karandikar, M. Gomez, T. Shi* and T. Schmitz, “Integration of Discrete-event Dynamics and Machining Dynamics for Machine Tool: Modeling, Analysis and Algorithms”, Manufacturing Letters, 35:321-332, 2023, https://doi.org/10.1016/j.mfglet.2023.08.096.

Additive Friction Stir Deposition - Pioneering AFSD Machine Tool Vibration Theory with Material Behaviors

AFSD Process

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The grand challenge of AFSD is that the process parameter selection is currently based on prior experience or trial and error, which significantly restricts the full potential of promising manufacturing capabilities by AFSD. We are pioneering the AFSD machine tool vibration theory integrating materials behaviors by mathematically describing the relations of AFSD machine, tools, processes and materials, and therefore establish the scienfitc laws for process parameters selection.

AFSD Machine Tool Vibration Theory in Progress: (1) Mathematically describe AFSD tool-materials engagement as second-order, coupled, nonlinear ordinary differential equations of motion with thermal effects including analytical or machine learning models of temperature distribution and deposition geometry for given material (e.g., Al6061); and (2) Perform bifurcation and stability analysis to derive the stability map of periodic motion with accurate temperature contour for process parameter selection. The design of experiments for verification and validation is in development.

AFSD Video.MOV

AFSD Machining Video.MP4

Vibration-based Materials Modeling in Progress: (1) Leverage machine tool vibration models as experimentally validated boundary conditions for materials behaviors; (2) Develop vibration-based CFD model first to accurately simulate the thermomechanical behaviors and microstructure evolution of materials; and (3) Extend structure-based bifurcation curve into AFSD stability map, as a milestone of AFSD machine-tool-process-materials convergence. The related models are ready to integrate experimentally validated AFSD machine tool vibration models.

T. Shi*, “A Theory of Machine Tool Vibration for Solid-State Additive Manufacturing”, In preparation.
V. Wu† et al., “ Investigation of Residual Stress Distribution for Additive Friction Stir Deposition by Numerical Modeling and Neutron Diffraction Analysis”, To be submitted to ASME Journal of Manufacturing Science and Engineering in 2026.
V. Wu†, M. Ma†, H. Li, B. Jared, T. Schmitz and T. Shi*, “A Machine Tool-informed Computational Fluid Dynamics Framework to Predict Temperature Evolution and Materials Flow for Additive Friction Stir Deposition”, To be submitted to ASME Journal of Manufacturing Science and Engineering in 2026.
V. Wu†, M. Ma†, J. Karandikar, C. Tyler, T. Shi* and T. Schmitz, “An Analytical Model Integrating Tool Kinematics and Material Flow for Spindle Torque Prediction in Additive Friction Stir Deposition”, Manufacturing Letters, 44, 1177-1186, 2025, https://doi.org/10.1016/j.mfglet.2025.06.137.
T. Shi*, H. Ma†, J. Wu†, C. Post†, E. Charles and T. Schmitz, “AFSD-Physics: Exploring the Governing Equations of Temperature Evolution during Additive Friction Stir Deposition by A Human-AI Teaming Approach”, Manufacturing Letters, 41, 1004-1015, 2024, https://doi.org/10.1016/j.mfglet.2024.09.125.
T. Shi*, J. Wu†, H. Ma†, E. Charles and T. Schmitz, “AFSD-Nets: A Physics-Informed Machine Learning Model for Predicting the Temperature Evolution during Additive Friction Stir Deposition”, ASME Journal of Manufacturing Science and Engineering, 146(8), 081003, 2024, https://doi.org/10.1115/1.4065178.

Additive Friction Stir Deposition-based Hybrid Manufacturing for a Sustainable Future

AFSD-based Hybrid Manufacturing. In collaboration with Dr. Tony Schmitz, we are working on the modeling efforts for AFSD-based hybrid manufacturing combined with metrology and machining to address casting and forging supply chain challenges for a sustainable future. We are using our established machine tool vibration theory and applications to achieve machine-tools-processes-materials convergence, from AFSD to machining.

AFSD_rib.mp4

machining.mp4

Robotics-based Hybrid Manufacturing: Wire Arc Additive Manufacturing (WAAM) and WAAM + Forging in Collaboration with NSF ERC-HAMMER

Residual Stress and Distortion. In collaboration with NSF ERC-HAMMER, we lead residual stress modeling efforts integrating microstructures to support the development of low-cost wire arc additive manufacturing (WAAM) and WAAM + Forging (WAAM-BAM) systems. In addition, integrated experiments and modeling efforts are in progress to improve the microstructure and residual stress under different process parameters, tool path planning, geometries and materials for WAAM and WAAM-BAM.

Systems Hybridization. In collaboration with NSF HAMMER ERC, we lead process modeling, control and machine learning efforts to contribute to the hardware and software developments for WAAM, WAAM-BAM and machining systems at UTK. We will contribute to center-wide engineered system hybridization of WAAM, WAAM-BAM and Machining, based on Agility Forge.

Low-cost CNC machine tool platform

Pneumatic actuator

Open-Source Controller

V. Wu†, et al., “Investigation of Residual Stress Distribution under Different Process Conditions and Materials for Wire Arc Additive Manufacturing by Numerical Modeling and Synchrotron X-ray at the Advanced Photon Source”, To be submitted to Journal of Materials Processing Technology in 2026.
M. Ma† et al., A White-Box Machine Learning Framework to Discover Analytical Geometry Models of Melt Pool and Bead from Experimental Data for Wire Arc Additive Manufacturing, To be submitted to Additive Manufacturing in 2026.
M. Ma†, V. Wu†, G. Zhang, B. Jared, T. Schmitz and T. Shi*, “ODEFinder: A Coupled Physics and Statistics based Machine Learning Method for Discovering Governing Equations of Dynamical Systems from Experimental Data”, To be submitted to Journal of Machine Learning for Modeling and Computing in 2026.
M. Ma†, V. Wu†, J. Yi, H. Wang, B. Jared, T. Schmitz and T. Shi*, “An Interpretable Machine Learning based Predictive Control Method for Manufacturing Processes with Turning as A Case Study”, Under review at NAMRC 54, 2025.
T. Shi* and T. Schmitz, “ChatterStabilizer: An Accurate and Scalable Framework of Bifurcation and Stability Analysis for Advancing Machine Tool Chatter Theory and Applications”, Under review at ASME Journal of Manufacturing Science and Engineering, 2025.
A. Ren†, M. Ma†, V. Wu†, J. Karandikar, C. Tyler, C., T. Shi* and T. Schmitz, “A Cutting Mechanics-based Machine Learning Modeling Method to Discover Governing Equations of Machining Dynamics”, Manufacturing Letters, 44, 759-769, 2025, https://doi.org/10.1016/j.mfglet.2025.06.089.

Large-Scale Wafer Inspection Optimization: Algorithmic Foundations and Framework

Optical, e-beam and atomic force microscope inspections are major wafer defect inspection techniques in semiconductor manufacturing. With the rapid technological development, defects in the wafers are becoming smaller and smaller to the nanometer level, most of which cannot be detected by optical inspection due to its low resolution. E-beam or atomic force microscope inspection is capable of detecting those smaller defects and much needed than ever to be used for in-line inspection to further improve the quality and yield of wafers. However, the high resolution brings extremely large-scale optimization challenge in wafer inspection making it suffers from very low throughput compared with optical inspection, and that significantly limits its in-line application.

We have mathematical described and defined the wafer inspection process as a fundamental computational geometry problem. We have developed a partition-shifting computing (PSC) framework for this problem to address the extremely large-scale optimization challenge in wafer inspection. The proposed PSC framework partitions the original problem into predefined amount of subproblems with the guarantee of strictly theoretical accuracy, which yields to a polynomial-time approximation scheme (PTAS) under certain conditions. The PSC framework will also achieve the high performance computing through its well-designed parallel computing mechanism and has the potential to be integrated into the state-of-the-art inspection techniques.

M. Qin, Z. Shi*, W. Chen, S. Gao and L. Shi, “Wafer Defect Inspection Optimization with Partial Coverage - A Numerical Approach”, IEEE Transactions on Automation Science and Engineering, 18(4), pp.1916-1927, 2020, 10.1109/TASE.2020.3024651.
Shi, Z.*, Qin, M., Chen, W., Gao, S. and Shi, L., 2019. Wafer Defect Inspection Optimization: Models, Analysis and Algorithms. Analysis and Algorithms (April 6, 2019), http://dx.doi.org/10.2139/ssrn.3371939.

Smart Shop, Factory and Supply Chain Management: AI-enabled Digital Twin Platform

Modern industry is stepping into a new era that heavily focuses on the interconnectivity through data and information. A holistic connected ecosystem for manufacturing firms needs to be created by marrying the physical production system with digitalization technology, cloud computing and artificial intelligence (AI). Enterprise system-wide integration of industrial software is also becoming more and more seamless and immediate. Those advanced technologies are significantly increasing the complexity and challenge of shop production systems management. The challenge derives not only from the scale of systems and customer demands, but also from the fact that a large amount of multi-source industrial data in production is not efficiently transferred to significant information for better decision making.

We have developed a AI-enabled digital twin platform, to address the design and operations challenge including efficiency, quality and cost for smart shop, factory and supply chain management. By utilizing simulation and sensing techniques, an AI-enabled control and optimization method has been developed as the solver engine. With system integration of industrial data and necessary components in production systems, the developed AI-enabled digital toolset can provide sustainable analytics and decision capabilities for modern shop and supply chain management.

H. Zhang, H. Xiao*, G. Kou and T. Shi, “Dynamic Simulation Budget Allocation for the Best and Worst Subsets Selection of Complex System Designs”, Under review at Naval Research Logistics, 2025.
M. Ma†, A. Ren†, C. Tyler, J. Karandikar, M. Gomez, T. Shi* and T. Schmitz, “Integration of Discrete-event Dynamics and Machining Dynamics for Machine Tool: Modeling, Analysis and Algorithms”, Manufacturing Letters, 35:321-332, 2023, https://doi.org/10.1016/j.mfglet.2023.08.096.
Y. Li, S. Gao* and T. Shi, “Asymptotic Optimality of Myopic Ranking and Selection Procedures”, Automatica, 151: 110896, 2023, https://doi.org/10.1016/j.automatica.2023.110896.
Z. Shi, Y. Peng*, L. Shi, C.H. Chen and M. Fu, “Dynamic Sampling Allocation under Finite Simulation Budget for Feasibility Determination”, INFORMS Journal on Computing, 34(1): 557-568, 2022, https://doi.org/10.1287/ijoc.2020.1057.
Z. Shi*, H. Ma†, M. Ren†, T. Wu and A.J. Yu, “A Learning-based Two-stage Optimization Method for Customer Order Scheduling”, Computers and Operations Research, 136:105488, 2021, https://doi.org/10.1016/j.cor.2021.105488.
F. Gao, S. Gao*, H. Xiao and Z. Shi, “Advancing Constrained Ranking and Selection with Regression in Partitioned Domains”, IEEE Transactions on Automation Science and Engineering, 16(1): 382 - 391, 2019, 10.1109/TASE.2018.2811809.
Z. Shi, S. Gao*, H. Xiao and W. Chen, “A Worst-Case Formulation for Constrained Ranking and Selection with Input Uncertainty”, Naval Research Logistics, 66(8): 648-662, 2019, https://doi.org/10.1002/nav.21871.
F. Gao, Z. Shi, S. Gao* and H. Xiao, “Efficient Simulation Budget Allocation for Subset Selection Using Regression Metamodels”, Automatica, 106: 192-200, 2019, https://doi.org/10.1016/j.automatica.2019.05.022.
Y. Peng, E. Huang, J. Xu, Z. Shi* and C.H. Chen, “A Coordinate Optimization Approach for Concurrent Design”, IEEE Transactions on Automatic Control, 64(7): 2913 - 2920, 2019, 10.1109/TAC.2018.2872196.
W. Wang, Z. Shi*, L. Shi and Q. Zhao, “Integrated Optimization on Flow Shop Production with Cutting Stock”, International Journal of Production Research, 57(19): 5996-6012, 2019, https://doi.org/10.1080/00207543.2018.1556823.
Z. Huang, Z. Shi* and L. Shi, “Minimizing Total Weighted Completion Time on Batch and Unary Processors with Incompatible Job Families”, International Journal of Production Research, 57(2): 567-581, 2018, https://doi.org/10.1080/00207543.2018.1470341.
Z. Shi*, Z. Huang and L. Shi, “Customer Order Scheduling on Batch Processing Machines with Incompatible Job Families”, International Journal of Production Research, 56(1-2): 795-808, 2018, https://doi.org/10.1080/00207543.2017.1401247.
Z. Shi*, S. Gao, J. Du, H. Ma and L. Shi, “Automatic Design of Dispatching Rules for Real-Time Optimization of Complex Production Systems”, Proceedings of the 2019 IEEE/SICE International Symposium on System Integrations, pp. 55-60, 2018, 10.1109/SII.2019.8700391.
L. Liu, Z. Shi and L. Shi*, “Minimization of Total Energy Consumption in an m-machine Flow Shop with an Exponential Time-Dependent Learning Effect”, Frontiers of Engineering Management, 5(4): 487-498, 2018, 10.15302/J-FEM-2018042.
Z. Shi, Z. Huang and L. Shi*, “Two-Stage Scheduling on Batch and Single Machines with Limited Waiting Time Constraint”, Frontiers of Engineering Management, 4(3): 368-374, 2017, 10.15302/J-FEM-2017034.
P. Liu, X. Zhang*, Z. Shi and Z. Huang, “Simulation Optimization for MRO Systems Operations”, Asia-Pacific Journal of Operational Research, 34(02): 1750003, 2017, https://doi.org/10.1142/S0217595917500038.
Z. Shi*, L. Wang, P. Liu and L. Shi, “Minimizing Completion Time for Order Scheduling: Formulation and Heuristic Algorithm”, IEEE Transactions on Automation Science and Engineering, 14(4): 1558-1569, 2017, 10.1109/TASE.2015.2456131.
Z. Huang, Z. Shi*, C. Zhang and L. Shi, “A Note on “Two New Approaches for a Two-stage Hybrid Flowshop Problem with a Single Batch Processing Machine under Waiting Time Constraint”, Computers & Industrial Engineering, 110: 590-593, 2017, https://doi.org/10.1016/j.cie.2017.04.010.
C. Zhang, Z. Shi*, Z. Huang, Y. Wu and L. Shi, “Flow Shop Scheduling with a Batch Processor and Limited Buffer”, International Journal of Production Research, 55(11): 3217-3233, 2017, https://doi.org/10.1080/00207543.2016.1268730.
Z. Shi, Z. Huang and L. Shi, “Two-stage Flow Shop with a Batch Processor and Limited Buffer”, Proceedings of the 2016 IEEE Conference on Automation Science and Engineering, pp. 395-400, 2016, 10.1109/COASE.2016.7743432.
Z. Shi, P. Liu, H. Gao and L. Shi, “Production Planning for a Class of Batch Processing Problem”, Proceedings of the 2015 IEEE Conference on Automation Science and Engineering, pp. 1188-1193, 2015, 10.1109/CoASE.2015.7294259.

Physics-based Machine Learning and Artificial Intelligence for Modeling and Optimization

Interpretable Machine Learning (Symbolic Regression) based on Genetic Programming: automatic design of high-quality tree-based dispatching or scheduling rules in an off-line learning manner by interpretable machine learning based on genetic programming.

Learned 5-layer tree-based dispatching rule. It is a mathematical function - A white-box function that could be understood by human.

Learned 17-layer tree-based dispatching rule. It is also a mathematical function - A black-box function that cannot be understood by human.

ODE-Finder as an interpretable machine learning solver to discover ODE-type governing equations from experimental data

Operator-based Machine Learning Framework to train reduced order models of PDE-type governing equations.

Human-AI Teaming Framework for Manufacturing Process Modeling:

combine known physics and human expertise with unknown physics in the experimental data to acquire the governing equations of manufacturing process by a human-artificial intelligence (AI) teaming modeling framework.

M. Ma†, V. Wu†, G. Zhang, B. Jared, T. Schmitz and T. Shi*, “ODEFinder: A Coupled Physics and Statistics based Machine Learning Method for Discovering Governing Equations of Dynamical Systems from Experimental Data”, To be submitted to Journal of Machine Learning for Modeling and Computing in 2026.
M. Ma†, V. Wu†, J. Yi, H. Wang, B. Jared, T. Schmitz and T. Shi*, “An Interpretable Machine Learning based Predictive Control Method for Manufacturing Processes with Turning as A Case Study”, Under review at NAMRC 54, 2025.
M. Shataraha, K. Liu, T. Shi, H. Li*, “Operator-based Machine Learning Framework for Generalizable Prediction of Unsteady Treatment Dynamics in Stormwater Infrastructure”, Under review at Journal of Environmental Engineering, 2025.
T. Shi, H. Ma†, H. Tran and G. Zhang*, “Compressive-Sensing-assisted Mixed Integer Optimization for Dynamical System Discovery with Highly Noisy Data”, Numerical Methods for Partial Differential Equations, 41(1):e23164, 2025, https://doi.org/10.1002/num.23164.
T. Shi*, H. Ma†, J. Wu†, C. Post†, E. Charles and T. Schmitz, “AFSD-Physics: Exploring the Governing Equations of Temperature Evolution during Additive Friction Stir Deposition by A Human-AI Teaming Approach”, Manufacturing Letters, 41, 1004-1015, 2024, https://doi.org/10.1016/j.mfglet.2024.09.125.
A. Ren†, M. Ma†, V. Wu†, J. Karandikar, C. Tyler, C., T. Shi* and T. Schmitz, “A Cutting Mechanics-based Machine Learning Modeling Method to Discover Governing Equations of Machining Dynamics”, Manufacturing Letters, 44, 759-769, 2025, https://doi.org/10.1016/j.mfglet.2025.06.089.
Z. Shi*, H. Ma†, M. Ren†, T. Wu and A.J. Yu, “A Learning-based Two-stage Optimization Method for Customer Order Scheduling”, Computers and Operations Research, 136:105488, 2021, https://doi.org/10.1016/j.cor.2021.105488.
H. Ma†, C. Zhang† and Z. Shi*, “A Simulation Optimization-Aided Learning Method for Design Automation of Scheduling Rules”, Proceedings of the 2022 IEEE Conference on Automation Science and Engineering, pp. 1992-1997, 2022, 10.1109/CASE49997.2022.9926615.
M. Qin, R. Wang, Z. Shi*, L. Liu, and L. Shi, “A Genetic Programming based Scheduling Approach for Hybrid Flow Shop with a Batch Processor and Waiting Time Constraint”, IEEE Transactions on Automation Science and Engineering, 8(1), pp.94-105, 2019, 10.1109/TASE.2019.2947398.
Z. Shi*, S. Gao, J. Du, H. Ma and L. Shi, “Automatic Design of Dispatching Rules for Real-Time Optimization of Complex Production Systems”, Proceedings of the 2019 IEEE/SICE International Symposium on System Integrations, pp. 55-60, 2018, 10.1109/SII.2019.8700391.
Z. Shi, L. Wang and L. Shi, “Approximation Method to Rank-One Binary Matrix Factorization”, Proceedings of the 2014 IEEE Conference on Automation Science and Engineering, pp. 800-805, 2014, 10.1109/CoASE.2014.6899417.

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