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CHAPTER VI VEHICLE PLANAR DYNAMICS I II III IV V VEHICLE COORDINATE SYSTEM APPLIED NEWTON – EULER METHOD VEHICLE FORCE SYSTEM VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL VEHICLE LINEAR PLANAR DYNAMIC MODEL – EXAMPLE (HB120) I VEHICLE COORDINATE SYSTEM The vehicle force system (F, M) Vehicle body coordinate frame B(Cxyz) I VEHICLE COORDINATE SYSTEM Top view of a moving vehicle to show the yaw angle ψ between the x and X axes, the sideslip angle β between the velocity vector v and the x-axis, and the cruise angle β + ψ between with the velocity vector v and the X-axis Illustration of a moving vehicle, indicated by its body coordinate frame B in a global coordinate frame G II APPLIED NEWTON – EULER METHOD A rigid vehicle in a planar motion III VEHICLE FORCE SYSTEM The force system at the tire-print of tire number IV VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL A front-wheel-steering four-wheel vehicle and the forces in the xy-plane acting at the trire-prints A two-wheel model for a vehicle moving with no roll IV VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL Ignoring the aligning moments Mzi assume δ small IV VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL The global sideslip βi for the wheel i, is the angle between the wheel velocity vector vi and the vehicle body x-axis If the wheel number i has a steer angle δi then, its local sideslip angle αi, that generates a lateral force Fyw on the tire, is IV VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL Assuming small angles for global sideslips βf, β, and βr, the local sideslip angles for the front and rear wheels, αf and αr, may be approximated as: V VEHICLE LINEAR PLANAR DYNAMIC MODEL VI VEHICLE LINEAR PLANAR DYNAMIC MODEL – EXAMPLE (HB120) h l a1 a2 m Cαf No-load 1,63 6,150 3,840 2,310 13710 207730 Value Half-load 1,723 6,150 3,531 2,619 14910 238670 Full-load 1,815 6,150 3,818 2,332 16110 233010 m m m m kg N/rad Cαr Iz 278380 173918 278380 186975 292210 202808 N/rad kg.m2 Symbol Unit 0.2 rad  11.459deg t   (t )   t0 0 Turning radius R vs forward velocity vx (δ = 0.2(rad)) Lateral force Fy vs forward velocity vx (δ = 0.2(rad)) Critical velocity, vxc vs steering angle δ VI VEHICLE LINEAR PLANAR DYNAMIC MODEL – EXAMPLE (HB120) Lateral velocity vy(t) Turning radius R Angular acceleration r(t) Lateral force at the vehicle gravity center ... APPLIED NEWTON – EULER METHOD A rigid vehicle in a planar motion III VEHICLE FORCE SYSTEM The force system at the tire-print of tire number IV VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL A front-wheel-steering... for a vehicle moving with no roll IV VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL Ignoring the aligning moments Mzi assume δ small IV VEHICLE PLANAR DYNAMIC MODEL – 02-WHEELED MODEL The global... the front and rear wheels, αf and αr, may be approximated as: V VEHICLE LINEAR PLANAR DYNAMIC MODEL VI VEHICLE LINEAR PLANAR DYNAMIC MODEL – EXAMPLE (HB120) h l a1 a2 m Cαf No-load 1,63 6,150 3,840

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