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

Appunto

Scarica

Estratto del documento

Tiresf = F (x, k, δ, Fz, alignment ...)

Tire models

Pure empirical
Empirical method
Simple physical
Complex physical

Longitudinal slipratio

Longitudinal slipratio k = F state of the system - evolution in the contact patch.

(k) = ΩR - V / V

(F) = FxFxmax

dFx/dk > 0 stable zone

dFx/dk dFx/dk_kp = k1 during return

Adhesion zone
Slippage zone

=> A Σ, B Σ

A => Force provided by elastic deformation τ = μqσ

B => 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 Hooke'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

Tiresf = 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

Elastic element and shear stress

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

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

Σmax = μg

τ = friction limit f(x) because f(x)

shear stress

qτ = Ax² + Bx + C + BC₇ @ 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

Pure rolling condition V_ₓ = Ωl₂

V₀ = Ωl₂ linear rolling speed

V_ₓ = Vx - Ωl₂ = Vx - Vr rolling speed -> Vl = Vx - V_ₛx

Δt = a-x / Vl

u = -V_ₛx Δt (deformation in εαυγοανακομισιαυ)

1 = -V_ₛx (Ω-x_ₛ) proportional to x in the contact area

-> u = - V_ₛx / V_ₓ, u = (a-x) σ_ₓ

planeless slip -> ʎ = cp u -> D Fx = ∫_-a^a a(x) dx

= cp V_ₓ ∫_-a^a (a-x) σ_ₓ dx

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

Friction limit

We can introduce the friction limit as μd = μs

Σ(x) = { cp (a-x) σ_ₓ ʎ(x) < μs qτ

μs qτ(x) elsewhere but in this way we -> have variation

So, to reproduce the experimenttited we introduce μ_d 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

=> ⨁_xB∫_-a^+aμ_dq_z(x) dx + cρ(a-x)_xB∫_xBσ_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))_la

=> -cρ σⁱ x = -^{3f_i 2aσⁱμ_s}/_{μ a}

=> σ_x = ^3fⁱμ_s/2 σⁱ_x1/3

Side slip angle

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

Anteprima

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