Intelligent vehicles and road transportation systems (ITS) Week 2 : - PDF document

ME400 Intelligent vehicles and road transportation systems (ITS) Week 2 : Vehicle dynamics and dynamical models Denis Gingras January 2015 1 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Course outline  Week 1 : Introduction to intelligent vehicles, context, applications and motivations  Week 2 : Vehicle dynamics and vehicle modeling  Week 3: Positioning and navigation systems and sensors (GPS, INS, odometer…)  Week4: Vehicle perception sensing and map building (lidar, radar, sonar, camera)  Week 5 : Multi-sensor data fusion techniques  Week 6 : Object detection, recognition and tracking (Midterm exam Week 1 to 5)  Week 7: Vehicle control and safe-by-wire basics  Week 7 : ADAS systems and safety applications  Week 8 : The connected vehicles: VANETS, DSRC, V2V, V2I and V2X  Week 9 : Multi-vehicular urban/highway scenarios and collaborative architectures  Week 10 : The future: toward autonomous vehicles and automated driving (Final exam) 2 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 1

Week 2 outline  Brainstorming and introduction  Forces acting on road vehicles  Resistance (Aerodynamic, rolling, grade)  Tractive Effort  Acceleration  Braking and stopping distance  State space model used in dynamical systems  Vehicular dynamics models  One wheel (point) model  Two-wheel model  Three-wheel and other full car models  Driving modes and IMM models 3 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Brainstorming Brainstorming Open questions and introductory discussion What is Vehicle Dynamics? 4 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 2

Brainstorming Brainstorming Open questions and introductory discussion How many dimensions are we dealing with in describing vehicular dynamics and what are the reference frames involved? 5 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 1 Brainstorming Brainstorming Open questions and introductory discussion What are the 3 main branches of classical mechanics used in vehicular dynamics ? 6 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 6 3

Brainstorming Brainstorming Open questions and introductory discussion What can we do with vehicle dynamics? Give some examples 7 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Brainstorming Brainstorming Open questions and introductory discussion Define force, torque, work and power in Newtonian mechanics and give their respective units. 8 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 4

Brainstorming Forces Brainstorming Open questions and introductory discussion What are the forces acting upon a vehicle ? 9 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Brainstorming Brainstorming Open questions and introductory discussion What are the three main types of motion we find typically in vehicle dynamics and what are the main vehicle subsystems influencing them? 10 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 5

Brainstorming Brainstorming Open questions and introductory discussion What are the main driving modes we encounter in vehicular dynamics ? 11 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Brainstorming Forces Brainstorming Open questions and introductory discussion What is resistance and what are the resistive forces? 12 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 6

Brainstorming Brainstorming Open questions and introductory discussion What is a model ? 13 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Brainstorming Brainstorming Open questions and introductory discussion What would be the system elements of a vehicle model in a schema block diagram ? 14 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 7

Brainstorming Brainstorming Open questions and introductory discussion What are the main concepts in rectilinear vehicle dynamics ? 15 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Forces acting on a vehicle Forces Distribution of forces  vehicle’s weight (resulting from gravitational force)  forces which act along the longitudinal axis of the vehicle, e.g. o motive force, o aerodynamic drag or rolling friction o braking force Forces which act laterally on the vehicle o steering force, o centrifugal force when cornering o Crosswinds The forces are transferred through o the chassis (e.g. wind), o the steering (steering force), o the engine and transmission (motive force), o the braking system (braking force). o braking system (braking force). 16 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 8

Forces acting upon a vehicle Forces Progression of Friction Coefficient under braking (longitudinally) – µ HF is friction coefficient – maximum between 10% and 40% brake slip, (depending on nature of road surface and tires) a): Rising slope of the curve is the “stable zone” - increase in brake slip increase in friction b): Falling slope is the “unstable zone” - increase in brake slip reduction in friction 17 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Forces: Turning forces Forces The different forces involved in the kinematics of a vehicle Turning Forces act on the entire vehicle  Example μ -split braking  Situation - wheels on one side of vehicle are on a slippery surface (e.g. black ice) - wheels on other side are on a road surface with normal grip (e.g. asphalt)  Result - vehicle will slew around vertical axis when the brakes are applied - rotation is caused by the yaw moment, which arises due to the different forces applied to the sides of the vehicle. 18 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 9

Forces acting upon a vehicle Forces Coefficient of friction µ – dependent on the nature of the road surface the condition of the tires the vehicle’s road speed the weather conditions – de fi nes frictional properties of material pairings between tire and road surface and the environmental conditions 19 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Forces Aerodynamic Resistance R a Composed of: Turbulent air flow around vehicle body (85%) 1. Friction of air over vehicle body (12%) 2. Vehicle component resistance, from radiators and air vents 3. (3%)   2 R C A V a D f 2   3 P C A V R a D f 2  ft lb  1 hp 550 sec Source: National Research Council of Canada 20 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 10

Forces Forces: rolling Resistance R rl Composed primarily of Resistance from tire deformation (  90%) 1. Tire penetration and surface compression (  4%) 2. Tire slippage and air circulation around wheel (  6%) 3. Wide range of factors affect total rolling resistance 4. Simplifying approximation: 5. rl  R f W  P f WV rl R rl rl   V   ft lb    f rl 0 . 01 1  1 hp 550  147  sec 21 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Forces Forces: grade Resistance R g Composed of  Gravitational force acting on the vehicle   R W sin g g θ g    sin tan For small angles, g g   R W tan R g g g  g  tan G θ g R g  W WG 22 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 11

Forces Forces: Vehicle Acceleration  Governing Equation     F R ma m  Mass Factor  (accounts for inertia of vehicle’s rotating parts)     2 1 . 04 0 . 0025 m 0 23 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Forces Forces: Available tractive effort The minimum of: Force generated by the engine, F e 1. Maximum value that is a function of the vehicle’s weight 2. distribution and road-tire interaction, F max    Available tractive effort min F e , F max 24 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 12

Forces Forces: tractive Effort Relationships 25 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Forces Forces: engine-generated tractive effort  Force F e = Engine generated tractive effort  0  M reaching wheels (lb)  F e d M e = Engine torque (ft-lb) e r ε 0 = Gear reduction ratio η d = Driveline efficiency r = Wheel radius (ft)  Power       ft lb torque ft lb engine rpm     hp  550  2  sec   sec  550   60  min  26 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 13

Forces Vehicle Speed vs. Engine Speed     2 rn 1 i  V e  0 V = velocity (ft/s) r = wheel radius (ft) n e = crankshaft rps i = driveline slippage ε 0 = gear reduction ratio 27 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Typical Torque-Power Curves Forces 28 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 14

Forces Forces: maximum tractive effort    l f h  Front Wheel Drive Vehicle  W r rl L  F  max h  1 L    l f h  Rear Wheel Drive Vehicle  f rl W L  F  max h  1 L  What about 4WD? 29 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 Forces Diagram θ g 30 23-nov.-14 D Gingras – ME470 IV course CalPoly Week 2 15