me451 kinematics and dynamics of machine systems
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ME451 Kinematics and Dynamics
of Machine Systems
IntroductionSeptember 2, 2014
Dan NegrutUniversity of Wisconsin-Madison
Quote of the day: "The way to be happy is to like yourself and the way to like yourself is to do only things that make you proud.“ - Mark S. Lewis, professor, UT-Austin
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Overview, Today’s Lecture…
Discuss Syllabus Discuss schedule related issues Quick overview of what ME451 is about
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Instructor: Dan Negrut Polytechnic University of Bucharest, Romania
B.S. – Aerospace Engineering (1992)
University of Iowa Ph.D. – Mechanical Engineering (1998)
MSC.Software Product Development Engineer 1998-2005
University of Michigan Adjunct Assistant Professor, Dept. of Mathematics (2004)
Division of Mathematics and Computer Science, Argonne National Laboratory Visiting Scientist 2004-2005, 2006, 2010
University of Wisconsin-Madison, Joined in Nov. 2005 Research Focus: Computational Dynamics (Dynamics of Multi-body Systems) Established the Simulation-Based Engineering Lab (http://sbel.wisc.edu)
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ME451 – Fall 2014
Class time: 09:30AM – 10:45AM [ Tu & Th ] Room: 1153ME Contact:
Office 2035ME Phone 608 890-0914 E-Mail negrut@engr.wisc.edu
Other people involved with ME451 ADAMS-related questions: Justin Madsen (jcmadsen@wisc.edu) MATLAB-related questions: WoongJo Choi (wchoi26@wisc.edu) Assignment grader: Luning Fang (lfang9@wisc.edu)
Office Hours: Monday / Wednesday 2:30PM – 3:30PM Meeting outside office hours is fine, call or email to make sure I’m in
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Textbook
Edward J. HaugComputer Aided Kinematics and Dynamics of Mechanical Systems: Basic Methods(Allyn and Baker, 1989)
Book is out of print
Author provided PDF copy of the book, available for download at course website http://sbel.wisc.edu/Courses/ME451/2014/
On a couple of occasions, the material in the book will be supplemented with notes
We’ll cover Chapters 1 through 6 (a bit of 7 too)
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Course-Related Material
Handouts (slides and additional notes) will be printed out and provided before each lecture
Slides (pdf) as well as additional notes (pdf) for each lecture made available online at course website http://sbel.wisc.edu/Courses/ME451/2014/
I plan to also upload audio recording of each lecture in case you miss class or want to listen again to segments of a lecture
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Course-Related Material
Homework solutions will be posted at Learn@UW
Grades will be maintained online at Learn@UW
Syllabus available at http://sbel.wisc.edu/Courses/ME451/2014/ Updated as we go, will change to reflect current progress Shows topics we cover Homework assignments Exam dates and deadlines for projects
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Grading
Homework 40% Exams
Midterm 1 7.5% Midterm 2 7.5% Final 20%
Projects (Matlab) Project 1 7.5% Project 2 7.5% Final Project 10%
Total 100%
NOTE: Score related questions (homework/exams) must be raised withina week after the homework/exam is returned.
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Assignments
Pen and paper assignments Assigned every other lecture, almost always on Th Due one week later There will be about 9 HW assignments
Matlab/ADAMS assignments There will be about 9 Matlab and 6 ADAMS assignments
No late assignments accepted Two assignments with lowest scores will be dropped
Grading approach 50% - one random problem graded thoroughly 50% - for completing the other problems
Solutions will be posted on Learn@UW
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MATLAB and Simulink
MATLAB will be used extensively in ME451 It will be used to develop the basic simEngine2D MATLAB program which
will enable Kinematic and Dynamic Analysis of simple 2D mechanisms With the exception of the model data parser, it can be implemented using
standard MATLAB functionality
You are responsible for brushing up your MATLAB skills
Simulink might be used for ADAMS co-simulation
Matlab tutorial: September 16, Room TBA
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A Word on simEngine2D
A MATLAB program that you put together and by the end of the semester Should be capable of running basic 2D Kinematics and Dynamics analysis Each assignment adds a little bit to the core functionality of simEngine2D
You will: Setup a procedure to specify a model Implement various numerical solution sequences for different types of analysis Plot results of interest (positions, accelerations, reaction forces, etc.)
Link to past simEngine2D: [2010] http://sbel.wisc.edu/Courses/ME451/2010/SimEngine2D/index.htm [2011] http://sbel.wisc.edu/Courses/ME451/2011/SimEngine2D/index.htm Important: this year we change the format of the input files
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Projects
Two intermediate projects (using the simEngine2D) Kinematic analysis (assigned on October 21) Dynamic analysis (assigned on November 25) Each due one day before the each of the two midterm exams
Final Project, you’ll choose one of two options: ADAMS: you’ll choose the project topic, I decide if it’s good enough MATLAB:
Examples: use simEngine2D for analysis of a more complicated mechanism, or extend simEngine2D, etc.
Groups of two students for one project ok provided project has enough scope
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Exams
Two midterm exams, as indicated in syllabus Midterm 1: Tuesday, October 28 Midterm 2: Thursday, December 4 Review sessions: the evening before the exam, 6:30 pm (Room TBD)
Final Exam Tuesday, Dec. 16, at 2:45 PM Comprehensive Room: TBD (computer room) Requires you to use your simEngine2D to solve a simple problem
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Scores and Grades
Score Grade94-100 A87-93 AB80-86 B73-79 BC66-72 C55-65 D
Grading will not be done on a curve
Final score will be rounded to the nearest integer prior to having a letter assigned Example:
86.59 becomes AB 86.47 becomes B
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Quick Suggestions
Attend lecture if you find it useful If you attend, stay involved, pay attention, ask questions
Reading the textbook is good
Doing the homework is critical (and hard/time consuming)
Provide feedback Both during and at end of the semester I might be able to change small things that could make a difference in
the learning process
Scope of Kinematics and Dynamics
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Competencies gained, ME451
Ability to model a physical problem: Given a general mechanical system, understand how to generate in a systematic and
general fashion the equations that govern the time evolution of the mechanical system These equations are called the equations of motion (EOM)
Ability to solve a math problem (that is associated with dynamics) using computers Gain basic understanding of the techniques (called numerical methods) used to solve
the EOM We’ll rely on MATLAB to implement/illustrate some of the numerical methods used to
solve EOM
Ability to use commercial software to simulate and interpret the dynamics associated with complex mechanical system We’ll used the commercial package ADAMS, available at CAE
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Why/How Do Bodies Move?
Why? The configuration of a mechanism changes in time based on forces and/or motions applied to its components
Forces Internal (reaction forces) External, or applied forces (gravity, compliant forces, etc.)
Prescribed motion Somebody prescribes the motion of a component of the mechanical
system
How? They move in a way that obeys Newton’s second law However, there are additional conditions (constraints) that need to be
satisfied. These constraints come from the joints that connect the bodies (to be covered in detail later…)
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Putting it all together…
MECHANICAL SYSTEM =
BODIES + JOINTS + FORCES
THE SYSTEM CHANGES ITS CONFIGURATION IN TIME
WE WANT TO BE ABLE TO PREDICT & CHANGE/CONTROL
HOW SYSTEM EVOLVES
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Examples, Multibody Dynamics
Vehicle Suspension
Vehicle Simulation
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Examples, Multibody Dynamics
Powder, Additive Manufacturing (3D Printing)
Selective Laser Sintering (SLS) machine
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Courtesy of Professor Tim Osswald, Polymer Engineering Center, UW-Madison
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Powder Bed Roughness: Before and After Rollover
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“Studying the Effect of Powder Geometry on the Selective Laser Sintering Process,” H. Mazhar, J. Bollmann, E. Forti, A. Praeger, T. Osswald and D. Negrut, in SPE-ANTEC 2014
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Bulldozer Simulation
Vehicle: Total Mass: 7,300 kg 114 Parts 111 Kinematic
Constraints
Granular Material: 200,000 ellipsoids Cohesion = 500N Density 2000kg/m^3 ~0.7 million contacts
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Examples, Multibody Dynamics
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Examples of 2D Mechanisms
Windshield wiper mechanism[out of Haug’s book, available online]
Quick-return shaper mechanism[out of Haug’s book, available online]
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Nomenclature
Mechanical System, definition: A collection of rigid or deformable bodies that move in a fashion
consistent with mechanical joints that limit relative motions of pairs of bodies
Mechanical system, types of analysis Kinematic analysis Dynamic analysis Inverse Dynamic analysis Equilibrium analysis
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Kinematic Analysis
Concerns the motion of the system independent of the forces that produce the motion
Typically, the time history of one body in the system is prescribed
We are interested in how the rest of the bodies in the system move
Requires the solution linear and nonlinear systems of equations
Windshield wiper mechanism
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Dynamic Analysis
Concerns the motion of the system due to the action of applied forces/torques
Typically, a set of forces acting on the system is provided. Motions can also be specified on some bodies
We are interested in how each body in the mechanism moves
Requires the solution of a combined system of differential and algebraic equations (DAEs)
Cross Section of Engine
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Inverse Dynamic Analysis It is a hybrid between Kinematics and Dynamics
Basically, one wants to find the set of forces that lead to a certain desirable motion of the mechanism
Your bread and butter in Controls…
Windshield wiper mechanism Robotic Manipulator
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What is the Slant of This Course?
There are several ways to approach kinematics and dynamics of mechanical systems (that is, to find the time evolution of the mechanical system):
The ME240 way, on a case-by-case fashion Typically requires following a recipe, not always clear where it came from Typically works for small problems, not clear how to go beyond textbook cases
Use a graphical approach This was the methodology that used to be emphasized in ME451 (Prof. Uicker) Intuitive but doesn’t scale particularly well
Use a computational approach – this is the methodology emphasized in ME451 Leverages the power of the computer Relies on a unitary approach to analysis of any mechanical system
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Modeling & Simulation (1)
M&S applies to many (most?) disciplines: engineering, physics, chemistry, biology, economics, etc.
The goal is to figure out how “something” happens without having to actually (build it and) test it in real-life.
Modeling is the abstraction of reality while simulation is the execution of the model.
Computer M&S: Start with a physical phenomenon Use laws, principles, scientific theories to extract a mathematical model
(a set of equations that describe the salient features of the particular problem) Convert into a numerical model Implement into computer code Simulate, that is run the code Post-processing (data analysis, visualization, animation, …) Interpret results
“Essentially, all models are wrong, but some are useful.”George Box & Norman Draper
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Modeling & Simulation (2)
% Update position and velocity (using Newmark)q = q_prev + h*qd_prev + 0.5*h^2*((1-2*beta)*qdd_prev + 2*beta*qdd);qd = qd_prev + h*((1-gam)*qdd_prev + gam*qdd);
Geometrical Model
Mathematical Model
Numerical Model
Computer Implementation
Physical Reality
Post-processing
Simulation
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More on the Computational Perspective…
Everything that we do in ME451 is governed by Newton’s Second Law.
We pose the problem so that it is suited for solution using a computer:
1. Identify in a simple and general way the data that is needed to formulate the equations of motion.
2. Automatically solve the set of nonlinear equations of motion using appropriate numerical solution algorithms: e.g. Newton-Raphson, Newmark Numerical Integration Method, etc.
3. Provide post-processing support for analysis of results: e.g. plot time curves for quantities of interest, animate the mechanism, etc.
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Overview of the Class[Chapter numbers according to Haug’s book]
Chapter 1 – general considerations regarding the scope and goal of Kinematics and Dynamics (with a computational slant)
Chapter 2 – review of basic Linear Algebra and Calculus Linear Algebra: Focus on geometric vectors and matrix-vector operations Calculus: Focus on taking partial derivatives (a lot of this), handling time derivatives, chain rule (a lot of this too)
Chapter 3 – introduces the concept of kinematic constraint as the mathematical building block used to represent joints in mechanical systems This is the hardest part of the material covered Basically poses the Kinematics problem
Chapter 4 – quick discussion of the numerical algorithms used to solve Kinematics problem formulated in Chapter 3
Chapter 5 – applications (Kinematics) Only tangentially touching it; ADAMS assignments
Chapter 6 – formulation of the Dynamics problem: derivation of the equations of motion (EOM)
Chapter 7 – numerical methods for solving the Dynamics problem formulated in Chapter 6
Haug’s book is available online at the class website
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ADAMS Automatic Dynamic Analysis of Mechanical Systems
It says Dynamics in name, but it does a whole lot more Kinematics, Statics, Quasi-Statics, etc.
Philosophy behind software package Offer a pre-processor (ADAMS/View) for people to be able to generate
models Offer a solution engine (ADAMS/Solver) for people to be able to find the
time evolution of their models Offer a post-processor (ADAMS/PPT) for people to be able to animate
and plot results
It now has a variety of so-called vertical products, which all draw on the ADAMS/Solver, but address applications from a specific field: ADAMS/Car, ADAMS/Rail, ADAMS/Controls, ADAMS/Linear,
ADAMS/Hydraulics, ADAMS/Flex, ADAMS/Engine, etc.
ADAMS tutorial: October 9, Room TBA (given by Justin Madsen)
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