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Week #
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Lect./ Module
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Topic
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Description
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1-4
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Module 1 - Machining process modeling and analyses
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1
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1/1
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Course information;
Motivation; Intro. to mechanistic modeling
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Format, grading, philosophy, policies, goals, expectations. Introduction to machining terminology.
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2/1
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Intro. to mechanistic modeling
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Static and dynamic models of machining. Mathematical approach to machining process modeling
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3/1
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Intro. to orthogonal cutting
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Fundamental process geometry. Merchant’s theory. Velocity relations.
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2
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4/1
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Orthogonal cutting cont.
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Force circle diagrams.
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5/1
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Shear and strain. Specific energy and force prediction.
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Shear plane and rake face stress analysis. Power, machinability and cutting energy analysis.
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6/1
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Size effects
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Force modeling and understanding size effect in machining.
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3
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7/1
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The oblique cutting process. Modeling turning
operations
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Tool orientation, rake and flow angles. Chip ratio. Relation of 3D geometry to 2D orthogonal process. Force modeling.
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8/1
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Continue with modeling of turning operations.
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Equivalent lead angle and simplifying approximations. More complex distributed models. Mechanistic force modeling and summary of turning.
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9/1
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Introduction to milling process
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Differences between single point turning and multi-point milling processes.
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4
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10/1
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Milling process contd.
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Force transformations. Axial integrations.
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11/1
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Milling process contd.
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Analytical modeling of end milling process.
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12/1
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Milling process contd.
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Mechanistic identification of cutting constants.
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5-6
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Module 2 – Review of free and forced vibrations
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5
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13/2
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Review of basics of SDOF systems
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SDOF systems. FBDs. Formulation of EOM using different methods in different domains. Free vibrations.
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14/2
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SDOF systems contd.
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Damped free vibrations. Response to initial conditions.
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15/2
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SDOF systems contd.
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Forced vibrations. Steady state analysis. Different damping models.
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6
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16/2
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MDOF systems
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Modeling undamped free vibrations. EOMs for MDOF systems
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17/2
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MDOF systems
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Solution to eigenvalue problems for MDOF systems. Mode shape descriptions.
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18/2
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MDOF systems contd.
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Forced response analysis. Modeling machine tools as MDOF systems.
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7-8
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Module 3 – Analytical and experimental modal analyses
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7
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19/3
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Introduction to analytical modal analysis for MDOF
systems
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Modal transformations. Proportional systems. Special characteristics of modal domains – linearity; orthogonality.
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20/3
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Transfer function analysis.
Introduction to modal testing.
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Response function measurement techniques. Excitation of structures. Basics of measurements and digital signal processing (DSP).
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21/3
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Experimental modal analysis contd.
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DSP analysis contd. Working across multiple domains (time-frequency). FFT analysis. Construction of FRFs.
Preliminary checks of FRF data. Discussion on forms of FRFs
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8
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22/3
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Modal parameter extraction and derivation of mathematical models
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Extraction for SDOF/MDOF systems. Peak picking methods. Construction of modal models. Back transform from modal to physical models.
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23/3
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Modal testing of machine tools
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Considerations for modal testing of machine tools.
Instrumentation. Software tools. Post-processing results.
Constructing spatial models.
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24/3
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Modal testing of machine tools
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Tool point FRFs. Interpretation of dynamic stiffness. Modal parameter extraction.
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9-11
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Module 4 – Machining dynamics and regenerative chatter vibrations
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9
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25/4
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Forced vibration of cutting operations
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Forced vibration analysis during cutting.
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26/4
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Forced vibration of cutting operations
(turning/milling) contd.
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Tool and workpiece vibration analysis. Tooth passing frequency concepts.
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27/4
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Forced vibration of cutting operations
(turning/milling) contd.
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Frequency analysis of time domain cutting signals
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10
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28/4
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Feedback mechanisms and phase shifts
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Introduction to regenerative chatter. Wave generation.
Phase shifts. Block diagram level analysis of machining dynamics.
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29/4
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Machining stability and energy considerations
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Intro. to delay differential equations Review of definitions of stability. Causes and types of stability.
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30/4
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Regenerative chatter in turning
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Review Tlusty’s approach to stability diagrams. Construction of stability lobe diagrams for SDOF systems.
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11
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31/4
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Regenerative chatter in turning
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Introduce concepts of oriented FRFs.
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32/4
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Regenerative chatter in turning
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Turning stability of 2 DOF systems
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33/4
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Time-domain simulation
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Chip thickness, force and displacement calculation.
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12-13
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Module 5 – Process-machine interactions in milling
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12
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34/5
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Dynamic milling models
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Modeling of end milling dynamics.
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35/5
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Stability of milling operations
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Stability diagrams with Tlusty’s average tooth angle approach. Oriented FRF.
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36/5
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Stability of milling operations
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Linearization of process. Discussions about effect of milling mode and engagement
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13
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37/5
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Stability of milling operations contd.
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Stability diagrams with Fourier series approach. Linearization of process.
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38/5
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Stability of milling operations contd.
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Stability diagrams with Fourier series approach. Linearization of process.
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39/5
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Stability of milling operations
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Stability diagrams with Fourier series approach. Linearization of process.
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14
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40/5
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Advanced topics
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Discussion about advanced topics. Project consultations.
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