MECA0492 : Introduction to Vehicle Stability Control

Transcription

1 MECA0492 : Introduction to Vehicle Staility Control Pierre Duysinx Research Center in Sustainale Automotive Technologies of University of Liege Academic Year

2 Biliography T. Gillespie. «Fundamentals of vehicle Dynamics», 1992, Society of Automotive Engineers (SAE) W. Milliken & D. Milliken. «Race Car Vehicle Dynamics», 1995, Society of Automotive Engineers (SAE) R. Bosch. «Automotive Handook». 5 th edition Society of Automotive Engineers (SAE) J.Y. Wong. «Theory of Ground Vehicles». John Wiley & sons (2 nd edition) 2001 (3rd edition). M. Blundel & D. Harty. «The multiody Systems Approach to Vehicle Dynamics» Society of Automotive Engineers (SAE) G. Genta. «Motor vehicle dynamics: Modelling and Simulation». Series on Advances in Mathematics for Applied Sciences - Vol. 43. World Scientific

3 UNNDERSTANDING THE ESP Electronic Staility Program DESCRIPTION OF THE ESP SYSTEM AND ITS WORKING PRINCIPLES SIMPLE MODEL: 2-dof vehicle model Equations of the transient ehaviour (lateral equilirium) Extension of the model to include individual wheel rakings TOWARDS THE NUMERICAL SIMULATION : The automoile as mechatronic system Finite Element Multiody (SAMCEF-MECANO) Integration of control systems Sensors, control algorithms, actuators 3

4 FUNDAMETALS OF ESP Vitesse ang. des roues Accélération latérale Angle de raquage Accélération ang. de lacet Comportement sur-vireur: freinage à l avant Comportement sous-vireur: freinage à l arrière Calcul du comportement désiré du véhicule Décision si intervention de l ESP Calcul du comportement réel du véhicule ESP = (ABS+TCS)² Déviation entre le comportement désiré du véhicule et le comportement réel 4

5 INSTRUMENTATION OF ESP A micromechanical gyroscope (polysi surface micro machined MEMS) detects the rotations aout the vehicle vertical axis Miniaturized Sensors of the wheel rotation speed (ased Hall effect) A highly sensitive MEMS accelerometer (polysi surface micromachined MEMS) Record the lateral acceleration CAN us network Steering wheel rotation measured y a contact less sensor Source: Bosch 5

6 MODEL OF THE VEHICLE DYNAMICS MODEL OF THE VEHICLE: Assumptions: h Velocity Velocity Small slip and steering angles T f x,u,p F xf a F xf u V Vehicle is infinitely rigid in pitch q=0 and heave w=0 z,w,r y,v,q L r v M, J No roll p=0 2 dof model and r T r F xr F xr Bicycle model 6

7 MODEL OF THE VEHICLE DYNAMICS Newton-Euler equilirium equation in the non inertial reference frame of the vehicle ody e J x y = 0 e t J y z = 0 Velocity Model with 2 dof & r a F xf u V Equilirium equations in F y and M z : L r v M, J Operating forces Tyre forces Aerodynamic forces (can e neglected here) F xr 7

8 MODEL OF THE VEHICLE DYNAMICS The equilirium equations along F y and M z writes: Velocity Use small angles assumptions (linearized motion) a F xf u V Linearized equations of motion of the 2 dof model L r v M, J F xr 8

9 MODEL OF THE VEHICLE DYNAMICS Compatiility of slip angles and velocities: Velocity Use small angles assumption a F xf u V L r v M, J And so F xr 9

10 MODEL OF THE VEHICLE DYNAMICS Constitutive equations of the tyres Source: Gillespie (fig 6.2)

11 MODEL OF THE VEHICLE DYNAMICS Introducing the constitutive equations into the equilirium equations It comes Sustitute the slip angles value y their value in terms in the velocities from compatiility relations 11

12 MODEL OF THE VEHICLE DYNAMICS Standard form of motion equations for the vehicle dynamics h Velocity Velocity T f x,u,p F xf a F xf u V z,w,r y,v,q L r v M, J T r F xr F xr 12

13 ADAPTATION OF VEHICLE DYNAMICS MODEL TO ESP ESP system (Electronic Staility Program) : Apply individual raking forces in each wheel Develop a yaw torque aout the vertical axis h Equations of motion a Fr fg u V Fr fd L r M z v M, J Fr rg Fr rd 13

14 UNDERSTANDING THE ESP Brake a front wheel produces: An aligning torque A torque that tends to reduce the ody slip A lateral force that tends to deport the vehicle Brake a rear wheel produces a pure realigning torque a Fr f u V L r M z v M, J Fr r 14

15 UNDERSTANDING THE ESP For an understeer trajectory: The wheels of the front axle experience a larger side slip than rear wheels The front axle is deported towards the outer of the turn The ESP actuate the raking of the rear wheels, here the interior rear wheel to develop an aligning torque to come ack on the desired trajectory v M z M, J The rear axles tends to e deported to the outer of the turn The rear wheels have a higher side slip compared to the front wheels The ESP uses the raking of the front wheels, that is a raking on the outer Fr rg Fr rd front wheel in order to come ack on the ideal trajectory. 15 For an oversteer trajectory: L a Fr fg r u h V Fr fd

16 UNDERSTANDING THE ESP Understeer trajectory: The front wheels are sliding and the front axle is deported to the outer of the turn. The ESP actuates the rear wheel raking. Oversteer trajectory: The rear axle tends to slide towards the outer of the turn. The ESP systems reacts y raking the front wheel that is in the outer side of the turn. 16

17 NUMERICAL SIMULATION EXERCICE INTEGRATION OF MOTION EQUATIONS IN MATLAB-SIMULINK Phase I (t<0): V=30 m/s, R=100 m, M = 1000 Kg, J=1000 Kg/m 2, g=9.81 m/s², L=3 m, a==1.5, C f et C r = N/rad Phase II (t=0): Loss of friction on the front wheel: C f = N/rad Phase III (t>0): Find the raking torque ale to re-estalish the turn with the desired curvature. Check the feasiility of the raking torque (maximum friction under the raked wheels!) 17