The single track model
|
|
- Dwain Fletcher
- 6 years ago
- Views:
Transcription
1 The single track model Dr. M. Gerdts Uniersität Bayreuth, SS 2003 Contents 1 Single track model Geometry Computation of slip angles Longitudinal tyre forces Lateral tyre forces Air resistance Equations of motion I Equations of motion II Constraints Parameters i
2 1 1 Single track model 1.1 Geometry l l h e SP α F Lx δ α ψ F Ly F s F u α h h F uh F sh Notation:, h elocity front/rear wheel δ steering angle elocity α, α h slip angle front/rear wheel β side slip angle ψ yaw angle F s, F sh lateral tyre forces F u, F uh longitudinal tyre forces l, l h distance from center of graity to front/rear wheel distance from center of graity to drag mount point e SP F Lx, F Ly air resistance in longitudinal and lateral direction m mass of car The steering angle δ is related to the steering wheel angle δ w by δ w = i L δ.
3 2 1 SINGLE TRACK MODEL 1.2 Computation of slip angles The slip angles are gien by ( ) l ψ sin β α = δ arctan, cos β ( ) lh ψ + sin β α h = arctan. cos β Explanation: Since the car body does not expand or shrink, the elocity components in the longitudinal direction of the car body hae to be equal: cos β = h cos α h = cos(δ α ). In the lateral direction the difference between the elocities is gien by the yaw angle elocity: h sin α h = l h ψ + sin β, sin(δ α ) = l ψ sin β. Combining these four equations yield the aboe formulas for the respectie slip angles. 1.3 Longitudinal tyre forces The car has rear wheel drie. The drier controls the braking force F B 0, the gear i {1, 2, 3, 4, 5} and the accelerator pedal position φ. The latter will result in the torque M wheel (φ, i) = i g (i) i t M mot (φ, i), where M mot (φ, i) = f 1 (φ) f 2 (w mot (i)) + (1 f 1 (φ))f 3 (w mot (i)) denotes the motor torque and w mot (i) = i g(i) i t R 1 1 S denotes the rotary frequency of the motor depending on the gear i and the longitudinal slip S. For conenience, the slip is neglected, e.g. S = 0. If the slip is not neglected, it is defined by 1, if R ϕ, R ϕ S = R ϕ 1, otherwise
4 1.3 Longitudinal tyre forces 3 ϕ denotes the rotary frequency of the wheel and is gien by the differential equation I R ϕ = F uh R. The functions f 1, f 2 and f 3 are gien by f 1 (φ) = 1 exp( 3φ), f 2 (w mot ) = w mot wmot, 2 f 3 (w mot ) = w mot. braking force: The braking force is distributed on the front and rear wheels by the formulas F B = 2 3 F B, F Bh = 1 3 F B such that F B + F Bh = F B holds. rolling resistance: The rolling resistance force at the front and rear wheel, respectiely, is gien by F R = f R () F z, F Rh = f R () F zh where f R () = f R0 + f R f R4 is the friction coefficient and F z = m l h g l + l h, F zh = m l g l + l h ( ) 4 ( in [km/h]), 100 denote the static tyre loads at the front and rear wheel, respectiely. longitudinal force front wheel: longitudinal force rear wheel: F u = F B F R. F uh = M wheel(φ, i) R F Bh F Rh
5 4 1 SINGLE TRACK MODEL 1.4 Lateral tyre forces The lateral tyre forces are functions of the respectie slip angles (and the tyre loads, which are constant in our model). A simple model is the AT-model (arcustangens-model): F s = c AT 1 arctan(c AT 2 α ), F sh = c AT 1 arctan(c AT 2 α h ). A famous model is the magic formula of Pacejka: F s = D sin (C arctan (B α E (B α arctan(b α )))), F sh = D h sin (C h arctan (B h α h E h (B h α h arctan(b h α h )))). The slope of F s at α = 0 is gien by B C D and similar for F sh. 1.5 Air resistance F Lx = 1 2 c w ρ A 2, F Ly = 1 2 c y ρ A 2 R Notation: c w ρ A c y R air drag coefficient air density effectie flow surface elocity lateral air drag coefficient lateral air elocity 1.6 Equations of motion I ẋ = cos(ψ β), ẏ = sin(ψ β), = 1 m [(F uh F Lx ) cos β + F u cos(δ + β) (F sh F Ly ) sin β F s sin(δ + β)], β = w z 1 m [(F uh F Lx ) sin β + F u sin(δ + β) + (F sh F Ly ) cos β + F s cos(δ + β)], ψ = w z, ẇ z = 1 I zz [F s l cos δ F sh l h F Ly e SP + F u l sin δ]
6 1.7 Equations of motion II Equations of motion II ẍ = 1 m [(F uh F Lx + F u cos δ F s sin δ) cos ψ (F sh F Ly + F u sin δ + F s cos δ) sin ψ] = 1 m [(F uh F Lx ) cos ψ + F u cos(δ + ψ) F s sin(δ + ψ) (F sh F Ly ) sin ψ] ÿ = 1 m [(F uh F Lx + F u cos δ F s sin δ) sin ψ + (F sh F Ly + F u sin δ + F s cos δ) cos ψ] = 1 m [(F uh F Lx ) sin ψ + F u sin(δ + ψ) + F s cos(δ + ψ) + (F sh F Ly ) cos ψ] ψ = 1 I zz [F s l cos δ F sh l h F Ly e SP + F u l sin δ] side slip angle: absolute elocity: (ẏ ) β = ψ arctan ẋ = ẋ 2 + ẏ Constraints The steering angle is restricted by δ [rad]. The steering angle elocity is restricted by δ 0.5 [rad/s]. The braking force F B is restricted by 0 F B [N]. The accelerator pedal position φ is restricted by 0 φ Parameters Car:
7 6 1 SINGLE TRACK MODEL m 1239 [kg] car mass g 9.81 [m/s 2 ] acceleration due to graity l [m] distance from center of graity to front wheel l h [m] distance from center of graity to rear wheel e SP 0.5 [m] distance from center of graity to drag mount point R [m] wheel radius I zz 1752 [kgm 2 ] moment of inertia i L 21.1 steering wheel transmission I R 1.5 moment of inertia of wheel Drag: c w 0.3 air drag coefficient ρ [N/m 2 ] air density A [m 2 ] effectie flow surface c y 0.3 lateral air drag coefficient Gear shift: i g (1) 3.91 first gear i g (2) second gear i g (3) 1.33 third gear i g (4) 1.0 fourth gear i g (5) fifth gear i t 3.91 motor torque transmission Tyre: AT-model c AT tyre coefficient AT-model c AT 1h tyre coefficient AT-model c AT tyre coefficient AT-model c AT 2h 30.0 tyre coefficient AT-model Tyre: Pacejka-model
8 1.9 Parameters 7 B tyre coefficient Pacejka-model (stiffness factor) C 1.3 tyre coefficient Pacejka-model (shape factor) D tyre coefficient Pacejka-model (peak alue) E 0.5 tyre coefficient Pacejka-model (curature factor) B h tyre coefficient Pacejka-model (stiffness factor) C h 1.3 tyre coefficient Pacejka-model (shape factor) D h tyre coefficient Pacejka-model (peak alue) E h 0.5 tyre coefficient Pacejka-model (curature factor) Rolling resistance: f R coefficient f R coefficient f R coefficient
Single-track models of an A-double heavy vehicle combination
Single-track models of an A-double heavy vehicle combination PETER NILSSON KRISTOFFER TAGESSON Department of Applied Mechanics Division of Vehicle Engineering and Autonomous Systems Vehicle Dynamics Group
More informationTutorial 1 - Drive fundamentals and DC motor characteristics
University of New South Wales School of Electrical Engineering & elecommunications ELEC4613 ELECRIC DRIVE SYSEMS utorial 1 - Drive fundamentals and DC motor characteristics 1. In the hoist drive system
More informationDetection of Critical Driving Situations using Phase Plane Method for Vehicle Lateral Dynamics Control by Rear Wheel Steering
Proceedings of the 7th World Congress The International Federation of Automatic Control Seoul, Korea, July 6-, 28 Detection of Critical Driing Situations using Phase Plane Method for Vehicle Lateral Dynamics
More informationDerivation of a Six Degrees-of-Freedom Ground-Vehicle Model for Automotive Applications
Derivation of a Six Degrees-of-Freedom Ground-Vehicle Model for Automotive Applications Berntorp, Karl Published: 2013-01-01 Document Version Publisher's PDF, also known as Version of record Link to publication
More informationSOLUTION di x = y2 dm. rdv. m = a 2 bdx. = 2 3 rpab2. I x = 1 2 rp L0. b 4 a1 - x2 a 2 b. = 4 15 rpab4. Thus, I x = 2 5 mb2. Ans.
17 4. Determine the moment of inertia of the semiellipsoid with respect to the x axis and express the result in terms of the mass m of the semiellipsoid. The material has a constant density r. y x y a
More informationSimple Car Dynamics. Outline. Claude Lacoursière HPC2N/VRlab, Umeå Universitet, Sweden, May 18, 2005
Simple Car Dynamics Claude Lacoursière HPC2N/VRlab, Umeå Universitet, Sweden, and CMLabs Simulations, Montréal, Canada May 18, 2005 Typeset by FoilTEX May 16th 2005 Outline basics of vehicle dynamics different
More informationUNIVERSITY OF BOLTON SCHOOL OF ENGINEERING
TW32 UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING BENG (HONS) AUTOMOTIVE PERFORMANCE ENGINEERING and BSC (HONS) MOTORSPORT TECHNOLOGY EXAMINATION SEMESTER 2-2015/2016 VEHICLE DYNAMICS AND ADVANCED ELECTRONICS
More informationMECH 3140 Final Project
MECH 3140 Final Project Final presentation will be held December 7-8. The presentation will be the only deliverable for the final project and should be approximately 20-25 minutes with an additional 10
More informationChapter 10 Single Track Models
Chapter Single Track Models Single track models allow a physically plausible description of the driving behavior of vehicles without major modeling and parameterization effort. Hence, in this chapter a
More informationPHYSICS (B) v 2 r. v r
PHYSICS 1. If Q be the amount of liquid (iscosity ) flowing per second through a capillary tube of radius r and length l under a pressure difference P, then which of the following relation is correct?
More informationProblems. 66 km/h B km/h 30 A. v A. 1.5 ft
Problems Problem 3.1 2700-lb automobile starts from rest and traels a quarter of a mile. ssume that the coefficient of static friction between the tires and the paement is 0.70, the automobile has frontwheel
More informationLow Complexity MPC Schemes for Integrated Vehicle Dynamics Control Problems
AVEC 8 Low Complexity MPC Schemes for Integrated Vehicle Dynamics Control Problems Paolo Falcone, a Francesco Borrelli, b H. Eric Tseng, Jahan Asgari, Davor Hrovat c a Department of Signals and Systems,
More informationProposal of Step Climbing of Wheeled Robot Using Slip Ratio Control
Proposal of Step Climbing of Wheeled Robot Using Slip Ratio Control Masaki Higashino, Hiroshi Fujimoto, Yoshiyasu Takase and Hiroshi Nakamura Department of Advanced Energy, The University of Tokyo 5--5
More informationThe University of Melbourne Engineering Mechanics
The University of Melbourne 436-291 Engineering Mechanics Tutorial Eleven Instantaneous Centre and General Motion Part A (Introductory) 1. (Problem 5/93 from Meriam and Kraige - Dynamics) For the instant
More informationINTI INTERNATIONAL UNIVERSITY FOUNDATION IN SCIENCE (CFSI) PHY1203: GENERAL PHYSICS 1 FINAL EXAMINATION: SEPTEMBER 2012 SESSION
INTI INTERNATIONAL UNIVERSITY FOUNDATION IN SCIENCE (CFSI) PHY1203: GENERAL PHYSICS 1 FINAL EXAMINATION: SEPTEMBER 2012 SESSION PHY1203(F)/Page 1 of 5 Instructions: This paper consists of FIVE (5) questions.
More informationStep Climbing Control of Wheeled Robot Based on Slip Ratio Taking Account of Work Load Shift by Anti-Dive Force of Suspensions and Accerelation
Step Climbing Control of Wheeled Robot Based on Slip Ratio Taking Account of Work Load Shift by Anti-Dive Force of Suspensions and Accerelation Masaki Higashino and Hiroshi Fujimoto The University of Tokyo
More informationCHAPTER 8: ROTATIONAL OF RIGID BODY PHYSICS. 1. Define Torque
7 1. Define Torque 2. State the conditions for equilibrium of rigid body (Hint: 2 conditions) 3. Define angular displacement 4. Define average angular velocity 5. Define instantaneous angular velocity
More informationSECTION A. 8 kn/m. C 3 m 3m
SECTION Question 1 150 m 40 kn 5 kn 8 kn/m C 3 m 3m D 50 ll dimensions in mm 15 15 Figure Q1(a) Figure Q1(b) The horizontal beam CD shown in Figure Q1(a) has a uniform cross-section as shown in Figure
More informationSimulation of the Stick-Slip Friction between Steering Shafts Using ADAMS/PRE
Simulation of the Stick-Slip Friction between Steering Shafts Using ADAMS/PRE Dexin Wang and Yuting Rui Research & Vehicle Technology Ford Motor Company ABSTRACT Cyclic stick-slip friction is a well-known
More informationJackknife stability of a tractor semi-trailer combination
TU/e Mechanical Engineering Masterproject 2006-2007 Jackknife stability of a tractor semi-trailer combination Author: J.W.L.H. Maas (0529865) Tutor: Prof. dr. H. Nijmeijer Eindhoven, 11 June 2007 Abstract
More informationSimulation of an articulated tractor-implement-trailer model under the influence of lateral disturbances
Simulation of an articulated tractor-implement-trailer model under the influence of lateral disturbances K. W. Siew, J. Katupitiya and R. Eaton and H.Pota Abstract This paper presents the derivation of
More informationControl of Mobile Robots Prof. Luca Bascetta
Control of Mobile Robots Prof. Luca Bascetta EXERCISE 1 1. Consider a wheel rolling without slipping on the horizontal plane, keeping the sagittal plane in the vertical direction. Write the expression
More informationRoad Vehicle Dynamics
Road Vehicle Dynamics Table of Contents: Foreword Preface Chapter 1 Introduction 1.1 General 1.2 Vehicle System Classification 1.3 Dynamic System 1.4 Classification of Dynamic System Models 1.5 Constraints,
More informationModeling and Validation of a Complex Vehicle Dynamics Model for Real-time Applications
Modeling and alidation of a Complex ehicle Dynamics Model for Real-time Applications Peter Riegl and Andreas Gaull Carissma, Ingolstadt Univ. of Applied Sciences, Esplanade 1, Ingolstadt, Germany peter.riegl@thi.de,
More informationTeam-Exercises for DGC 100 Modelica Course
Team-Exercises for DGC 100 Modelica Course Hubertus Tummescheit United Technologies Research Center, East Hartford, CT 06108. November 4, 2003 Abstract This document is a preliminary version and is going
More informationChapter 1: Kinematics of Particles
Chapter 1: Kinematics of Particles 1.1 INTRODUCTION Mechanics the state of rest of motion of bodies subjected to the action of forces Static equilibrium of a body that is either at rest or moes with constant
More informationHierarchical steering control for a front wheel drive automated car
Hierarchical steering control for a front wheel drive automated car Sándor Beregi, Dénes Takács, Chaozhe R. He, Sergei S. Avedisov, Gábor Orosz Department of Applied Mechanics, Budapest University of Technology
More information16.07 Dynamics Final Exam
Name:... Massachusetts Institute of Technology 16.07 Dynamics Final Exam Tuesday, December 20, 2005 Problem 1 (8) Problem 2 (8) Problem 3 (10) Problem 4 (10) Problem 5 (10) Problem 6 (10) Problem 7 (10)
More informationEstimation of Tire-Road Friction by Tire Rotational Vibration Model
53 Research Report Estimation of Tire-Road Friction by Tire Rotational Vibration Model Takaji Umeno Abstract Tire-road friction is the most important piece of information used by active safety systems.
More information1. Linear Motion. Table of Contents. 1.1 Linear Motion: Velocity Time Graphs (Multi Stage) 1.2 Linear Motion: Velocity Time Graphs (Up and Down)
. LINEAR MOTION www.mathspoints.ie. Linear Motion Table of Contents. Linear Motion: Velocity Time Graphs (Multi Stage). Linear Motion: Velocity Time Graphs (Up and Down).3 Linear Motion: Common Initial
More information1 MR SAMPLE EXAM 3 FALL 2013
SAMPLE EXAM 3 FALL 013 1. A merry-go-round rotates from rest with an angular acceleration of 1.56 rad/s. How long does it take to rotate through the first rev? A) s B) 4 s C) 6 s D) 8 s E) 10 s. A wheel,
More informationCONTROL DESIGN FOR AN OVERACTUATED WHEELED MOBILE ROBOT. Jeroen Ploeg John P.M. Vissers Henk Nijmeijer
CONTROL DESIGN FOR AN OVERACTUATED WHEELED MOBILE ROBOT Jeroen Ploeg John PM Vissers Henk Nijmeijer TNO Automotive, PO Box 756, 57 AT Helmond, The Netherlands, Phone: +31 ()492 566 536, E-mail: jeroenploeg@tnonl
More informationTime-Optimal Automobile Test Drives with Gear Shifts
Time-Optimal Control of Automobile Test Drives with Gear Shifts Christian Kirches Interdisciplinary Center for Scientific Computing (IWR) Ruprecht-Karls-University of Heidelberg, Germany joint work with
More informationThe basic principle to be used in mechanical systems to derive a mathematical model is Newton s law,
Chapter. DYNAMIC MODELING Understanding the nature of the process to be controlled is a central issue for a control engineer. Thus the engineer must construct a model of the process with whatever information
More informationOn my honor, I have neither given nor received unauthorized aid on this examination.
Instructor(s): Field/Furic PHYSICS DEPARTENT PHY 2053 Exam 1 October 5, 2011 Name (print, last first): Signature: On my honor, I hae neither gien nor receied unauthorized aid on this examination. YOUR
More informationPlane Motion of Rigid Bodies: Forces and Accelerations
Plane Motion of Rigid Bodies: Forces and Accelerations Reference: Beer, Ferdinand P. et al, Vector Mechanics for Engineers : Dynamics, 8 th Edition, Mc GrawHill Hibbeler R.C., Engineering Mechanics: Dynamics,
More informationENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 3 CENTRIPETAL FORCE
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D5 TUTORIAL CENTRIPETAL FORCE This tutorial examines the relationship between inertia and acceleration. On completion of this tutorial you should be able
More informationPhys101 Second Major-173 Zero Version Coordinator: Dr. M. Al-Kuhaili Thursday, August 02, 2018 Page: 1. = 159 kw
Coordinator: Dr. M. Al-Kuhaili Thursday, August 2, 218 Page: 1 Q1. A car, of mass 23 kg, reaches a speed of 29. m/s in 6.1 s starting from rest. What is the average power used by the engine during the
More informationMechatronics. MANE 4490 Fall 2002 Assignment # 1
Mechatronics MANE 4490 Fall 2002 Assignment # 1 1. For each of the physical models shown in Figure 1, derive the mathematical model (equation of motion). All displacements are measured from the static
More information5. Plane Kinetics of Rigid Bodies
5. Plane Kinetics of Rigid Bodies 5.1 Mass moments of inertia 5.2 General equations of motion 5.3 Translation 5.4 Fixed axis rotation 5.5 General plane motion 5.6 Work and energy relations 5.7 Impulse
More information2. Kinetic friction - The force that acts against an object s motion. - Occurs once static friction has been overcome and object is moving
Section 2.14: Friction Friction is needed to move. Without friction, a car would sit in one spot spinning its tires, and a person would not be able to step forward. However, the motion of an object along
More informationKinematics, Dynamics, and Vibrations FE Review Session. Dr. David Herrin March 27, 2012
Kinematics, Dynamics, and Vibrations FE Review Session Dr. David Herrin March 7, 0 Example A 0 g ball is released vertically from a height of 0 m. The ball strikes a horizontal surface and bounces back.
More informationQ2. A machine carries a 4.0 kg package from an initial position of d ˆ. = (2.0 m)j at t = 0 to a final position of d ˆ ˆ
Coordinator: Dr. S. Kunwar Monday, March 25, 2019 Page: 1 Q1. An object moves in a horizontal circle at constant speed. The work done by the centripetal force is zero because: A) the centripetal force
More informationElectric Vehicle Performance Power and Efficiency
Electric Vehicle Performance Power and Efficiency 1 Assignment a) Examine measurement guide and electric vehicle (EV) arrangement. b) Drive the route according to teacher s instruction and download measured
More informationProblem Set x Classical Mechanics, Fall 2016 Massachusetts Institute of Technology. 1. Moment of Inertia: Disc and Washer
8.01x Classical Mechanics, Fall 2016 Massachusetts Institute of Technology Problem Set 10 1. Moment of Inertia: Disc and Washer (a) A thin uniform disc of mass M and radius R is mounted on an axis passing
More informationFinal Exam April 30, 2013
Final Exam Instructions: You have 120 minutes to complete this exam. This is a closed-book, closed-notes exam. You are allowed to use a calculator during the exam. Usage of mobile phones and other electronic
More informationDesign a SSV. Small solar vehicle. Case SSV part 1
1 Design a SSV Small solar vehicle Case SSV part 1 2 Contents 1. The characteristics of the solar panel... 4 2. Optimal gear ratio... 10 3. Bisection method... 14 4. Sankey diagrams... 18 A) Sankey diagram
More informationChapter 6 Dynamics I: Motion Along a Line
Chapter 6 Dynamics I: Motion Along a Line Chapter Goal: To learn how to solve linear force-and-motion problems. Slide 6-2 Chapter 6 Preview Slide 6-3 Chapter 6 Preview Slide 6-4 Chapter 6 Preview Slide
More informationPhys101 Third Major-161 Zero Version Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1
Coordinator: Dr. Ayman S. El-Said Monday, December 19, 2016 Page: 1 Q1. A water molecule (H 2 O) consists of an oxygen (O) atom of mass 16m and two hydrogen (H) atoms, each of mass m, bound to it (see
More informationSOLUTION 8 7. To hold lever: a+ M O = 0; F B (0.15) - 5 = 0; F B = N. Require = N N B = N 0.3. Lever,
8 3. If the coefficient of static friction at is m s = 0.4 and the collar at is smooth so it only exerts a horizontal force on the pipe, determine the minimum distance x so that the bracket can support
More informationPhysics 107 HOMEWORK ASSIGNMENT #9b
Physics 07 HOMEWORK SSIGNMENT #9b Cutnell & Johnson, 7 th edition Chapter : Problems 5, 58, 66, 67, 00 5 Concept Simulation. reiews the concept that plays the central role in this problem. (a) The olume
More informationWe reserve the right to make changes in the course of technical development MAN Nutzfahrzeuge Aktiengesellschaft
Calculations GB We reserve the right to make changes in the course of technical development. 2000 MAN Nutzfahrzeuge Aktiengesellschaft Reprinting, reproduction or translation, even of excerpts, is not
More informationFinal Examination Thursday May Please initial the statement below to show that you have read it
EN40: Dynamics and Vibrations Final Examination Thursday May 0 010 Division of Engineering rown University NME: General Instructions No collaboration of any kind is permitted on this examination. You may
More informationis acting on a body of mass m = 3.0 kg and changes its velocity from an initial
PHYS 101 second major Exam Term 102 (Zero Version) Q1. A 15.0-kg block is pulled over a rough, horizontal surface by a constant force of 70.0 N acting at an angle of 20.0 above the horizontal. The block
More informationUNIVERSITY OF SASKATCHEWAN GE MECHANICS III FINAL EXAM APRIL 18, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS
UNIVERSITY OF SASKATCHEWAN GE 226.3 MECHANICS III FINAL EXAM APRIL 18, 2011 Professor A. Dolovich A CLOSED BOOK EXAMINATION TIME: 3 HOURS LAST NAME (printed): FIRST NAME (printed): STUDENT NUMBER: EXAMINATION
More informationInvestigation of Steering Feedback Control Strategies for Steer-by-Wire Concept
Master of Science Thesis in Electrical Engineering Department of Electrical Engineering, Linköping University, 2018 Investigation of Steering Feedback Control Strategies for Steer-by-Wire Concept Martin
More informationDrive train. Steering System. Figure 1 Vehicle modeled by subsystems
Proceedings of the XII International Symposium on Dynamic Problems of Mechanics (DINAME 7), P.S.Varoto and M.A.Trindade (editors), ABCM, Ilhabela, SP, Brazil, February 6 - March, 7 Wheel Dynamics Georg
More information[1] In your answer, you should use appropriate technical terms, spelled correctly.... A satellite. Fig. 4.1
1 (a) Define the following terms: couple... [1] torque of a couple. In your answer, you should use appropriate technical terms, spelled correctly.... [1] (b) Fig. 4.1 shows a satellite in space moving
More informationStatement: This paper will also be published during the 2017 AUTOREG conference.
Model Predictie Control for Autonomous Lateral Vehicle Guidance M. Sc. Jochen Prof. Dr.-Ing. Steffen Müller TU Berlin, Institute of Automotie Engineering Germany Statement: This paper will also be published
More informationMechanics II. Which of the following relations among the forces W, k, N, and F must be true?
Mechanics II 1. By applying a force F on a block, a person pulls a block along a rough surface at constant velocity v (see Figure below; directions, but not necessarily magnitudes, are indicated). Which
More informationLecture 6 Physics 106 Spring 2006
Lecture 6 Physics 106 Spring 2006 Angular Momentum Rolling Angular Momentum: Definition: Angular Momentum for rotation System of particles: Torque: l = r m v sinφ l = I ω [kg m 2 /s] http://web.njit.edu/~sirenko/
More informationState-Estimator Design for the KTH Research Concept Vehicle
DEGREE PROJECT IN VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2016 State-Estimator Design for the KTH Research Concept Vehicle FAN GAO KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING
More informationUNDERSTAND MOTION IN ONE AND TWO DIMENSIONS
SUBAREA I. COMPETENCY 1.0 UNDERSTAND MOTION IN ONE AND TWO DIMENSIONS MECHANICS Skill 1.1 Calculating displacement, aerage elocity, instantaneous elocity, and acceleration in a gien frame of reference
More informationAppendix W. Dynamic Models. W.2 4 Complex Mechanical Systems. Translational and Rotational Systems W.2.1
Appendix W Dynamic Models W.2 4 Complex Mechanical Systems W.2.1 Translational and Rotational Systems In some cases, mechanical systems contain both translational and rotational portions. The procedure
More informationSupplementary Problems
A Supplementary Problems These are practice questions: you do not need to hand in solutions. You can also study past exam papers. PH211 (now PHYS2006) was a new course in 1993, so you ll find some relevant
More informationChapter 10 Practice Test
Chapter 10 Practice Test 1. At t = 0, a wheel rotating about a fixed axis at a constant angular acceleration of 0.40 rad/s 2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad. What
More informationBench Test of Minimum Time Autonomous Driving for Electric Vehicle Based on Optimization of Velocity Profile Considering Energy Constraint
Bench Test of Minimum Time Autonomous Driving for Electric ehicle Based on Optimization of elocity Profile Considering Energy Constraint Yuta Ikezawa Hiroshi Fujimoto Daisuke Kawano Yuichi Goto Misaki
More informationVehicle Planar Motion Stability Study for Tyres Working in Extremely Nonlinear Region
1 Vol. 23, No. 2, 2010 DOI: 10.3901/CJME.2010.02.***, available online at www.cjmenet.com; www.cjmenet.com.cn Vehicle Planar Motion Stability Study for Tyres Working in Extremely Nonlinear Region LIU Li
More informationTerramechanics V MARYLAND U N I V E R S I T Y O F. Terramechanics V. ENAE 788X - Planetary Surface Robotics
Terramechanics V Note - I haven t posted the slides from Tuesday because there were a number of typos (and outright mistakes) that were (almost) all corrected on Thursday. This set of slides are the corrected
More informationPROBLEM Copyright McGraw-Hill Education. Permission required for reproduction or display. SOLUTION. ω = 29.6 rad/s. ω = = 36 3.
PROLEM 15.1 The brake drum is attached to a larger flywheel that is not shown. The motion of the brake drum is defined by the relation θ = 36t 1.6 t, where θ is expressed in radians and t in seconds. Determine
More informationMCE 366 System Dynamics, Spring Problem Set 2. Solutions to Set 2
MCE 366 System Dynamics, Spring 2012 Problem Set 2 Reading: Chapter 2, Sections 2.3 and 2.4, Chapter 3, Sections 3.1 and 3.2 Problems: 2.22, 2.24, 2.26, 2.31, 3.4(a, b, d), 3.5 Solutions to Set 2 2.22
More informationString tyre model for evaluating steering agility performance using tyre cornering force and lateral static characteristics
Vehicle System Dynamics International Journal of Vehicle Mechanics and Mobility ISSN: 0042-3114 (Print) 1744-5159 (Online) Journal homepage: http://www.tandfonline.com/loi/nvsd20 String tyre model for
More informationImproving EV Lateral Dynamics Control Using Infinity Norm Approach with Closed-form Solution
Improving EV Lateral Dynamics Control Using Infinity Norm Approach with Closed-form Solution Alexander Viehweider Dept. of Advanced Energy The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba, Japan
More information7.6 Journal Bearings
7.6 Journal Bearings 7.6 Journal Bearings Procedures and Strategies, page 1 of 2 Procedures and Strategies for Solving Problems Involving Frictional Forces on Journal Bearings For problems involving a
More information4) Vector = and vector = What is vector = +? A) B) C) D) E)
1) Suppose that an object is moving with constant nonzero acceleration. Which of the following is an accurate statement concerning its motion? A) In equal times its speed changes by equal amounts. B) In
More informationA. unchanged increased B. unchanged unchanged C. increased increased D. increased unchanged
IB PHYSICS Name: DEVIL PHYSICS Period: Date: BADDEST CLASS ON CAMPUS CHAPTER B TEST REVIEW. A rocket is fired ertically. At its highest point, it explodes. Which one of the following describes what happens
More informationModeling of Vehicle Dynamics using Matrix-Vector Oriented Calculation in Matlab.
CAINE 996, pp 5-2. ISCA, Orlando FL, Dec. 996 Modeling of Vehicle Dynamics using Matrix-Vector Oriented Calculation in Matlab. G. Edzko Smid, Ka C. Cheok and K. Kobayashi Department of Electrical and Systems
More informationNote on Posted Slides. Motion Is Relative
Note on Posted Slides These are the slides that I intended to show in class on Tue. Jan. 9, 2014. They contain important ideas and questions from your reading. Due to time constraints, I was probably not
More informationDept. of EEE, KUET, Sessional on EE 3202: Expt. # 1 2k15 Batch
Experiment No. 01 Name of the experiment Modeling of Physical systems and study of their open loop response Objectie (i) (ii) (iii) The objectie of this experiment is the modeling of physical systems and
More informationOn my honor, I have neither given nor received unauthorized aid on this examination.
Instructor(s): Field/inzler PHYSICS DEPATMENT PHY 2053 Final Exam April 27, 2013 Name (print, last first): Signature: On my honor, I have neither given nor received unauthorized aid on this examination.
More informationSelection Calculations For Motorized Actuators
Selection Calculations/ Selection Calculations For Linear Slides and Cylinders Select from the EZS Series, EZS Series for Cleanroom Use, EZC Series First determine your series, then select your model.
More informationName Student ID Score Last First. I = 2mR 2 /5 around the sphere s center of mass?
NOTE: ignore air resistance in all Questions. In all Questions choose the answer that is the closest!! Question I. (15 pts) Rotation 1. (5 pts) A bowling ball that has an 11 cm radius and a 7.2 kg mass
More informationMODELLING AND CONTROL OF A VEHICLE WITH SINGLE-WHEEL CHASSIS ACTUATORS. Ralf Orend
MODELLING AND CONTROL OF A VEHICLE WITH SINGLE-WHEEL CHASSIS ACTUATORS Ralf Orend Lehrstuhl für Regelungstechnik Universität Erlangen-Nürnberg Cauerstraße 7, 958 Erlangen, German ralf.orend@rt.eei.uni-erlangen.de
More informationSupplementary Information Microfluidic quadrupole and floating concentration gradient Mohammad A. Qasaimeh, Thomas Gervais, and David Juncker
Mohammad A. Qasaimeh, Thomas Gerais, and Daid Juncker Supplementary Figure S1 The microfluidic quadrupole (MQ is modeled as two source (Q inj and two drain (Q asp points arranged in the classical quardupolar
More informationEQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body
EQUATIONS OF MOTION: GENERAL PLANE MOTION (Section 17.5) Today s Objectives: Students will be able to analyze the planar kinetics of a rigid body undergoing general plane motion. APPLICATIONS As the soil
More informationAP Physics 1 Summer Assignment (2014)
Name: Date: AP Physics 1 Summer Assignment (2014) Instructions: 1. Read and study Chapter 2 Describing Motion: Kinematics in One Dimension. 2. Answer the questions below. 3. Submit your answers online
More informationPhysics 111. Lecture 23 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, Kinetic Energy of Rolling Object
Physics 111 Lecture 3 (Walker: 10.6, 11.1) Conservation of Energy in Rotation Torque March 30, 009 Lecture 3 1/4 Kinetic Energy of Rolling Object Total kinetic energy of a rolling object is the sum of
More informationVehicle Dynamics Control for Rollover Mitigation
ISSN 0280-5316 ISRN LUTFD2/TFRT--5746--SE Vehicle Dynamics Control for Rollover Mitigation Ola Palm Department of Automatic Control Lund Institute of Technology May 2005 Department of Automatic Control
More information(a) During the first part of the motion, the displacement is x 1 = 40 km and the time interval is t 1 (30 km / h) (80 km) 40 km/h. t. (2.
Chapter 3. Since the trip consists of two parts, let the displacements during first and second parts of the motion be x and x, and the corresponding time interals be t and t, respectiely. Now, because
More informationQuiz Number 4 PHYSICS April 17, 2009
Instructions Write your name, student ID and name of your TA instructor clearly on all sheets and fill your name and student ID on the bubble sheet. Solve all multiple choice questions. No penalty is given
More informationLast Time: Start Rotational Motion (now thru mid Nov) Basics: Angular Speed, Angular Acceleration
Last Time: Start Rotational Motion (now thru mid No) Basics: Angular Speed, Angular Acceleration Today: Reiew, Centripetal Acceleration, Newtonian Graitation i HW #6 due Tuesday, Oct 19, 11:59 p.m. Exam
More informationPhysics 106 Common Exam 2: March 5, 2004
Physics 106 Common Exam 2: March 5, 2004 Signature Name (Print): 4 Digit ID: Section: Instructions: nswer all questions. Questions 1 through 10 are multiple choice questions worth 5 points each. You may
More informationFirst Name: Last Name: Section: 1. March 26, 2008 Physics 207 EXAM 2
First Name: Last Name: Section: 1 March 26, 2008 Physics 207 EXAM 2 Please print your name and section number (or TA s name) clearly on all pages. Show all your work in the space immediately below each
More information(35+70) 35 g (m 1+m 2)a=m1g a = 35 a= =3.27 g 105
Coordinator: Dr. W. L-Basheer Monday, March 16, 2015 Page: 1 Q1. 70 N block and a 35 N block are connected by a massless inextendable string which is wrapped over a frictionless pulley as shown in Figure
More informationA study on wheel force measurement using strain gauge equipped wheels
A study on wheel force measurement using strain gauge equipped wheels PAVLOS MAVROMATIDIS a, ANDREAS KANARACHOS b Electrical Engineering Department a, Mechanical Engineering Department b Frederick University
More informationClosed-form Method to Evaluate Bike Braking Performance
Human Power ejournal, April 4, 13 Closed-form Method to Evaluate Bike Braking Performance Junghsen Lieh, PhD Professor, Mechanical & Materials Engineering Wright State University, Dayton Ohio 45435 USA
More informationPLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION
PLANAR KINETIC EQUATIONS OF MOTION: TRANSLATION Today s Objectives: Students will be able to: 1. Apply the three equations of motion for a rigid body in planar motion. 2. Analyze problems involving translational
More informationRigid Body Kinetics :: Virtual Work
Rigid Body Kinetics :: Virtual Work Work-energy relation for an infinitesimal displacement: du = dt + dv (du :: total work done by all active forces) For interconnected systems, differential change in
More informationChapter 6. Force and motion II
Chapter 6. Force and motion II Friction Static friction Sliding (Kinetic) friction Circular motion Physics, Page 1 Summary of last lecture Newton s First Law: The motion of an object does not change unless
More informationChapter 12: Rotation of Rigid Bodies. Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics
Chapter 1: Rotation of Rigid Bodies Center of Mass Moment of Inertia Torque Angular Momentum Rolling Statics Translational vs Rotational / / 1/ m x v dx dt a dv dt F ma p mv KE mv Work Fd P Fv / / 1/ I
More information