ME668A |
Machining Dynamics |
Credits: |
9 (3-0-0) |
Course Number:
ME 668A
Course Type:
Elective
Expected enrollment:
15-20 students
Prerequisites:
Instructors permission
Instructor(s):
Mohit Law
Course Overview:
Course covers modeling the mechanics and dynamics of machining operations, and their interactions with the machine tool system. Students will gain advanced knowledge of machining process modeling as well as vibration analysis of machine tools. Well-designed laboratory sessions will provide user-level familiarity with machine tool dynamics testing equipment and machining process monitoring equipment. Course will equip students to diagnose machining process related issues, and will motivate practical solutions for some industrial problems in the machine tool/cutting tool/automotive/aerospace industries.
Who Should Take This Course:
- PhD/M.Tech/M.S students interested in understanding machining processes and machine tool vibrations. Relevant to students interested in understanding the influence of undesirable vibrations in the metal cutting/machine tool industries.
- PhD/M.Tech/M.S interested in working in machine tool, cutting tool, or in their enduser industries such as the automotive and aerospace industries
- Advanced Bachelor’s degree students who have the above interests
Course Objectives:
- To teach basics of metal cutting mechanics of turning and milling operations
- To review fundamental concepts of free and forced vibrations
- To teach basics of modal analysis -analytical and experimental
- To teach chatter stability analysis of machine tools by introducing self-excited machine tool vibrations based on delay-differential equations
- To introduce advanced topics of high-performance (speed) machining
Course Outcomes:
- Understand basics of mechanistic modeling of metal cutting operations, and gain a qualitative understanding of the different parameters affecting cutting processes
- Gain a fundamental understanding of the interaction between the machining process and the vibration behavior of machine tools
- Gain user-level familiarity with machine tool dynamics testing equipment and machining process monitoring equipment
- Be able to plan and diagnose machining process related issues including becoming familiar with phenomena unique to high speed machining
Course Material:
Notes will be provided.
Reference Books:
- Manufacturing Automation by Y. Altintas;
- Machining Dynamics by T. Schmitz & K. Smith;
- Machine Tool Structures by Koenigsberger & Tlusty
Course outline:
1. Machining process modeling and analyses (12 lectures)
- Introduction to mechanistic modeling
- Orthogonal cutting mechanics (process geometry, chip characterization, stress and strain, force modeling)
- 3D oblique cutting mechanics
- The turning and milling processes
- Tool wear, tool life and cutting economics
2. Review of free and force vibration analysis (6 lectures)
- Single/multiple degree of freedom systems
- Review of matric algebra, Laplace solutions
- Review of system matrix development
3. Experimental Modal analyses (6 lectures)
- Introduction to modal analysis
- Orthogonality properties, and introduction to proportionally damped systems
- Modal data acquisition (digital signal processing, transducer considerations, structural testing conditions)
- Frequency response functions
- Modal parameter extraction
4. Machining dynamics and regenerative chatter vibrations in turning (9 lectures)
- Dynamic model for orthogonal cutting
- Single tooth, one-dimensional, linear time invariant models
- Feedback mechanisms and phase shifts
- Machining stability of turning
5. Process-machine interactions in milling (7 lectures)
- Stability solutions using traditional and frequency domain approaches
- Stability of milling processes
- Adv. topics – high speed machining
Course Schedule
| Week # | Lect./ Module | Topic | Description | |
| 1-4 | Module 1 - Machining process modeling and analyses | |||
| 1 | 1/1 | Course information; Motivation; Intro. to mechanistic modeling |
Format, grading, philosophy, policies, goals, expectations. Introduction to machining terminology. | |
| 2/1 | Intro. to mechanistic modeling | Static and dynamic models of machining. Mathematical approach to machining process modeling | ||
| 3/1 | Intro. to orthogonal cutting | Fundamental process geometry. Merchant’s theory. Velocity relations. | ||
| 2 | 4/1 | Orthogonal cutting cont. | Force circle diagrams. | |
| 5/1 | Shear and strain. Specific energy and force prediction. | Shear plane and rake face stress analysis. Power, machinability and cutting energy analysis. | ||
| 6/1 | Size effects | Force modeling and understanding size effect in machining. | ||
| 3 | 7/1 | The oblique cutting process. Modeling turning operations |
Tool orientation, rake and flow angles. Chip ratio. Relation of 3D geometry to 2D orthogonal process. Force modeling. | |
| 8/1 | Continue with modeling of turning operations. | Equivalent lead angle and simplifying approximations. More complex distributed models. Mechanistic force modeling and summary of turning. | ||
| 9/1 | Introduction to milling process | Differences between single point turning and multi-point milling processes. | ||
| 4 | 10/1 | Milling process contd. | Force transformations. Axial integrations. | |
| 11/1 | Milling process contd. | Analytical modeling of end milling process. | ||
| 12/1 | Milling process contd. | Mechanistic identification of cutting constants. | ||
| 5-6 | Module 2 – Review of free and forced vibrations | |||
| 5 | 13/2 | Review of basics of SDOF systems | SDOF systems. FBDs. Formulation of EOM using different methods in different domains. Free vibrations. | |
| 14/2 | SDOF systems contd. | Damped free vibrations. Response to initial conditions. | ||
| 15/2 | SDOF systems contd. | Forced vibrations. Steady state analysis. Different damping models. | ||
| 6 | 16/2 | MDOF systems | Modeling undamped free vibrations. EOMs for MDOF systems | |
| 17/2 | MDOF systems | Solution to eigenvalue problems for MDOF systems. Mode shape descriptions. | ||
| 18/2 | MDOF systems contd. | Forced response analysis. Modeling machine tools as MDOF systems. | ||
| 7-8 | Module 3 – Analytical and experimental modal analyses | |||
| 7 | 19/3 | Introduction to analytical modal analysis for MDOF systems |
Modal transformations. Proportional systems. Special characteristics of modal domains – linearity; orthogonality. | |
| 20/3 | Transfer function analysis. Introduction to modal testing. |
Response function measurement techniques. Excitation of structures. Basics of measurements and digital signal processing (DSP). | ||
| 21/3 | Experimental modal analysis contd. | DSP analysis contd. Working across multiple domains (time-frequency). FFT analysis. Construction of FRFs. Preliminary checks of FRF data. Discussion on forms of FRFs |
||
| 8 | 22/3 | Modal parameter extraction and derivation of mathematical models | Extraction for SDOF/MDOF systems. Peak picking methods. Construction of modal models. Back transform from modal to physical models. | |
| 23/3 | Modal testing of machine tools | Considerations for modal testing of machine tools. Instrumentation. Software tools. Post-processing results. Constructing spatial models. |
||
| 24/3 | Modal testing of machine tools | Tool point FRFs. Interpretation of dynamic stiffness. Modal parameter extraction. | ||
| 9-11 | Module 4 – Machining dynamics and regenerative chatter vibrations | |||
| 9 | 25/4 | Forced vibration of cutting operations | Forced vibration analysis during cutting. | |
| 26/4 | Forced vibration of cutting operations (turning/milling) contd. |
Tool and workpiece vibration analysis. Tooth passing frequency concepts. | ||
| 27/4 | Forced vibration of cutting operations (turning/milling) contd. |
Frequency analysis of time domain cutting signals | ||
| 10 | 28/4 | Feedback mechanisms and phase shifts | Introduction to regenerative chatter. Wave generation. Phase shifts. Block diagram level analysis of machining dynamics. |
|
| 29/4 | Machining stability and energy considerations | Intro. to delay differential equations Review of definitions of stability. Causes and types of stability. | ||
| 30/4 | Regenerative chatter in turning | Review Tlusty’s approach to stability diagrams. Construction of stability lobe diagrams for SDOF systems. | ||
| 11 | 31/4 | Regenerative chatter in turning | Introduce concepts of oriented FRFs. | |
| 32/4 | Regenerative chatter in turning | Turning stability of 2 DOF systems | ||
| 33/4 | Time-domain simulation | Chip thickness, force and displacement calculation. | ||
| 12-13 | Module 5 – Process-machine interactions in milling | |||
| 12 | 34/5 | Dynamic milling models | Modeling of end milling dynamics. | |
| 35/5 | Stability of milling operations | Stability diagrams with Tlusty’s average tooth angle approach. Oriented FRF. | ||
| 36/5 | Stability of milling operations | Linearization of process. Discussions about effect of milling mode and engagement | ||
| 13 | 37/5 | Stability of milling operations contd. | Stability diagrams with Fourier series approach. Linearization of process. | |
| 38/5 | Stability of milling operations contd. | Stability diagrams with Fourier series approach. Linearization of process. | ||
| 39/5 | Stability of milling operations | Stability diagrams with Fourier series approach. Linearization of process. | ||
| 14 | 40/5 | Advanced topics | Discussion about advanced topics. Project consultations. | |