me451 kinematics and dynamics of machine...
TRANSCRIPT
ME451
Kinematics and Dynamics
of Machine Systems
IntroductionSeptember 4, 2013
Radu Serban
University of Wisconsin, Madison
2
Overview, Today’s Lecture…
Discuss Syllabus
Discuss schedule related issues
Quick overview of what ME451 is about
3
Instructor: Radu Serban
Bucharest Polytechnic Institute, Romania
B.S. – Aerospace Engineering (1992)
The University of Iowa
Ph.D. – Mechanical Engineering (1998)
University of California – Santa Barbara
Postgraduate Researcher (1998-2001)
Lawrence Livermore National Laboratory
Computational Scientist (2001-2008)
Xulu Entertainment
Senior Computational Scientist (2008-2012)
The University of Wisconsin – Madison, Joined in March 2013
Visiting Associate Researcher
Working with the Simulation-Based Engineering Lab - http://sbel.wisc.edu/
Senior Scientist in the Wisconsin Applied Computing Center - http://wacc.wisc.edu/
ME451 Logistics
5
The 411 on 451
Time 12:00PM – 1:15PM [ Mo, We, Fr ]
Room 1143ME
Contact
Office 2047ME
Phone 925 784-6158
E-Mail [email protected]
ADAMS-related questions: Justin Madsen ([email protected])
Course Webpage:
https://learnuw.wisc.edu – solution to HW problems and grades
http://sbel.wisc.edu/Courses/ME451/2013/ - for textbook, slides, notes, assignments
Forum Page:
http://sbel.wisc.edu/Forum/
Office Hours:
Tuesday / Thursday 2:00PM – 3:30PM
Stop by my office anytime in the afternoon if you have quick ME451 questions
6
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
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)
7
Course Material
Handouts (slides and any additional notes) will be printed out and provided
before each lecture
Slides (ppt and pdf) as well as additional notes (pdf) for each lecture made
available online at course website
http://sbel.wisc.edu/Courses/ME451/2013/
Homework solutions will be posted at Learn@UW
Grades will be maintained online at Learn@UW
Syllabus available at lab website
http://sbel.wisc.edu/Courses/ME451/2013/
Updated as we go, will change to reflect current progress
Topics we cover
Homework assignments and due dates
Exam dates
8
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 within
a week after the homework/exam is returned.
9
Assignments
Schedule
Homework assignments
Assigned every other lecture; due two lectures later
There will be about 9 HW assignments
Matlab/ADAMS assignments
Assigned once a week (Wed); due one week later
There will be about 9 Matlab and 6 ADAMS assignments
No late assignments accepted!
Grading approach
50% - one random problem graded thoroughly
50% - for completing the other problems
Solutions will be posted on Learn@UW
10
A Word on simEngine2D
A code that you put together and by the end of the semester should be
capable of running basic 2D Kinematics and Dynamics analysis
Each assignment will add a little bit to the core functionality of the simulation
engine
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
Note that this year we change the format of the input files!
11
MATLAB and Simulink
MATLAB will be used extensively for HW It will be used to develop the basic simEngine2D simulator which
will enable Kinematic and Dynamic Analysis of simple 2D mechanisms.
With the exception of the model data parser, it can be implemented using only standard Matlab functionality.
You are responsible for brushing up your MATLAB skills
Simulink might be used for ADAMS co-simulation
Matlab tutorial: September 13, Room 2261EH
12
Projects
Two intermediate projects (using the simEngine2D)
Kinematic analysis (assigned on October 10)
Dynamic analysis (assigned on November 20)
Due one week after assignment
Final Project, you’ll choose one of two options:
ADAMS: you’ll choose the project topic, I decide if it’s good enough
MATLAB: use simEngine2D for analysis of a more complicated
mechanism, extend simEngine2D, etc.
You are allowed to work in a group of two, provided there is enough
scope.
13
Exams
Two midterm exams, as indicated in syllabus
Midterm 1: Friday, October 11 (1143ME 12:00PM)
Midterm 2: Friday, November 1 (1143ME 12:00PM)
Review sessions the evening before the exam (Room/Time: TBD)
Final Exam
Saturday, Dec. 17, at 7:45 AM
Comprehensive
Room: TBD (computer room)
It will require you to use your simEngine2D to solve a simple
problem
14
Scores and Grades
Score Grade
94-100 A
87-93 AB
80-86 B
73-79 BC
66-72 C
55-65 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
15
Quick Suggestions
Be active, pay attention, ask questions
Reading the textbook is good
Doing the homework is critical
Provide feedback
Both during and at end of the semester
I can change small things that could make a difference in the learning process
Scope of Kinematics and
Dynamics
17
Goals of ME451
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)
Have a 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
Be able 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
18
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…)
19
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
20
Examples, Multibody Dynamics
Vehicle Suspension
Vehicle Simulation
21
Examples, Multibody Dynamics
22
Examples, Multibody Dynamics
23
Examples, Multibody Dynamics
24
Examples, Multibody Dynamics
25
Examples of 2D Mechanisms
Windshield wiper mechanism Quick-return shaper mechanism
26
Nomenclature
Mechanical System, definition:
A collection of interconnected rigid bodies that can move relative to one another, consistent with mechanical joints that limit relative motions of pairs of bodies
Why type of analysis can one speak of in conjunction with a mechanical system?
Kinematic analysis
Dynamic analysis
Inverse Dynamic analysis
Equilibrium analysis
27
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
28
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
29
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
30
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 this
course
Leverages the power of the computer
Relies on a unitary approach to analysis of any mechanical system
31
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
32
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
33
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.
34
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, will draw on the simulation facilities provided by the commercial package ADAMS Only tangentially touching it
Chapter 6 – states the dynamics problem
Chapter 7 – only tangentially touching it, in order to get an idea of how to solve the set of DAEs obtained in Chapter 6
Haug’s book is available online at the class website
35
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: September 16, Room 2261EH (given by Justin Madsen)
Questions? Comments?