ME451 Kinematics and Dynamics of Machine Systems

Transcription

1 ME451 Kinematics and Dynamics of Machine Systems Introduction September 4, 2013 Radu Serban University of Wisconsin, Madison

2 Overview, Today s Lecture 2 Discuss Syllabus Discuss schedule related issues Quick overview of what ME451 is about

3 Instructor: Radu Serban 3 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 ( ) Lawrence Livermore National Laboratory Computational Scientist ( ) Xulu Entertainment Senior Computational Scientist ( ) The University of Wisconsin Madison, Joined in March 2013 Visiting Associate Researcher Working with the Simulation-Based Engineering Lab - Senior Scientist in the Wisconsin Applied Computing Center -

4 ME451 Logistics

5 The 411 on Time 12:00PM 1:15PM [ Mo, We, Fr ] Room 1143ME Contact Office 2047ME Phone serban@engr.wisc.edu ADAMS-related questions: Justin Madsen (jcmadsen@wisc.edu) Course Webpage: solution to HW problems and grades - for textbook, slides, notes, assignments Forum Page: Office Hours: Tuesday / Thursday 2:00PM 3:30PM Stop by my office anytime in the afternoon if you have quick ME451 questions

6 Textbook 6 Edward J. Haug Computer 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 7 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 Homework solutions will be posted at Learn@UW Grades will be maintained online at Learn@UW Syllabus available at lab website Updated as we go, will change to reflect current progress Topics we cover Homework assignments and due dates Exam dates

8 Grading 8 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 9 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 10 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] [2011] Note that this year we change the format of the input files!

11 MATLAB and Simulink 11 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 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 13 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 14 Score Grade A AB B BC C 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: becomes AB becomes B

15 Quick Suggestions 15 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

16 Scope of Kinematics and Dynamics

17 Goals of ME 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? 18 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 19 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 20 Vehicle Suspension Vehicle Simulation

21 Examples, Multibody Dynamics 21

22 Examples, Multibody Dynamics 22

23 Examples, Multibody Dynamics 23

24 Examples, Multibody Dynamics 24

25 Examples of 2D Mechanisms 25 Windshield wiper mechanism Quick-return shaper mechanism

26 Nomenclature 26 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 27 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 28 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 29 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 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) 31 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) 32 Geometrical Model Mathematical Model Physical Reality Numerical Model Post-processing Computer Implementation % 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); Simulation

33 More on the Computational Perspective 33 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] 34 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 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)

36 Questions? Comments?