Vehicle Dynamics and Control A - Appunti completi di tutto il corso

Name: Vehicle Dynamics and Control A - Appunti completi di tutto il corso
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Author: Polistudent

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Appunti di Vehicle Dynamics and Control A basati su appunti personali del publisher presi alle lezioni del prof. Cheli, dell’università degli Studi del Politecnico di Milano - …

Esame Vehicle Dynamics and Control A

Facoltà Ingegneria industriale

Dal corso del Prof. Cheli Federico

Università Politecnico di Milano

A.A. 2020-2021

114 pagine

6 download

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Estratto del documento

TIRES

F = F (x, k, δ, Fz, aniamment ...)

Tire models:

pure empirical
empirical method
simple physical
complex physical

LONGITUDINAL SLIPRATIO k = F

state of the system - evolution in the contact patch(k) = ΩR - V / V(F) = Fx

Fxmax

_dFx/_dk > 0 stable zone_dFx/_dk < 0 unstable zone_dFx/_{dk_kp} = k1 during return

Adhesion zone
Slippage zone

=> A Σ, B Σ

A => Force provided by elastic deformation τ = μqσB => Force provided by sliding friction τ = μdqσ

Brush model => reliability ↑, tire temp ↓, complexity ↓, material cost ↓

Tread made by elastic element several brushes, it is valid the Hook's law (∞ strain)
brushes cannot be deformed radially
neglect axial dimension
pressure distribution assumed parabolic (≠ Hertz that defines it as uni-elliptic) => no rolling resistance

TIRES

F = F (x, k, δ, Ft, alignment ...)

Tire models:

Pure empirical
Empirical formula
Semiempirical method
Simple physical
Brush model
Complex physical
FEM

Longitudinal slippage k -> Fx

k: state of the system -> evaluation in the contact patch

k <> 0 braking
k > 0 driving

dFx/dk > 0 stable zone

dFx/dk < 0 unstable zone

dFx/dk k = k1 driving wheel

Adhesion zone
Slippage zone

A -> Force provided by elastic deformation

B -> Force provided by sliding friction

Brush model

Predictability ↑, tire temp ↓, complexity ↓, numerical time ↓

Tread model by elastic element model brushes, it is valid the Hooke's law for main

Brushes cannot be deformed radially.
Neglected axial dimension.
Pressure distribution assumed parabolic, defines it as uni-elliptic -> no rolling resistance

biur is an elastic element (spring) with a failure CP.

it is considered isotopic -> new material along x and y

Σmax = μgτ = friction limit f(x) because f(x)

shear stress

qτ = Ax² + Bx + C + BCₛ @ x = ± a fτ = ø

-> f t = ∫_-a^ta qτ(x) dx -> 3 unknowns 3 conditions

):> qτ(x) = 3f_τ^a(a-(x/a)³/²)

pure rolling condition Vₓ = Ωl₂

V₀ = Ωl₂ linear rolling speed

Vₓ = Vx - Ωl₂ = Vx - Vr rolling speed -> Vl = Vx - Vₛx

Δt = a-x / Vl

u = -Vₛx Δt (deformation in εαυγοανακομισιαυ)

1 = -Vₛx (Ω-xₛ) proportional to x in the contact area

-> u = - Vₛx / Vₓ , u = (a-x) σₓ

planeless slip

-> ʎ = cp u -> D Fx = ∫_-a^a a(x) dx

= cp Vₓ ∫_-a^a (a-x) σₓ dx

= 2a² cp ʎ x cp = no friction limit considered,

kL ≈ 2a² cp

we can introduce the friction limit as μd = μs

Σ(x) = { cp (a-x) σₓ ʎ(x) < μs qτμs qτ(x) elsewhere

but in this way we -> have variation

So, to reproduce the experiment

tited we introduce μ_d < μ_s

=> T(x) = { cρ(a-x) σ_x if T(x) < μ_sq_z(x) μ_dq_z(x) elsewhere

NB σ_x = ^k/_k+1 -> k↑ => σ_y1

=> ⨁_{x_B}∫_-a^+aμ_dq_z(x) dx + cρ(a-x)_{x_B}∫_{x_B}σ_x dx

x_B from cρ(a-x_B)σ_x = μ_sq_z(x_B) => x_B

θ = ^2a²cρ/_{3μsf_z} x_B = 2aσ_x+

and free sliding condition if ^d/_dx(cρ(a-x)σ_x) = ^d/_dxμ_9t(x))_{l_a}

=> -cρ σⁱ x = -^{3f_i 2aσⁱμ_s}/_{μ a}

=> σ_x = ^3fⁱμ_s/2 σⁱ_x1/3

SIDE SLIP ANGLE ⊗ -> D [f₄]

β = {note of the wheel} evolved in the hub

⇒ α = arcβ( V_T/_{V_L})

V speed always tg to the trajectory

if V_T in this way => α = arcβ (+V_T/V_L)

otherwise if V_T some sign of ψ

we have α = arcβ (-V_T/V_L)

w(x) = (a - x) tgα block deformation

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