Analytical modelling of dump truck tire dynamic response to haul road surface excitations

ABSTRACT

Trucks experience excitations during haulage due to road roughness, generating dynamic loads. Current mine haul road design techniques assume static tire loads, ignoring dynamic forces. This paper presents mathematical models for estimating tire dynamic forces on haul roads. Models were solved in Simulink® and RStudio® to generate random road profile (class D) according to ISO 8608, and compute dynamic forces for 59/80R63 tire. Results show that road roughness significantly affects impact forces on roads, with tire dynamic forces (1638.67 kN) ~ 1.6 times static forces (~1025 kN) at rated tire payloads. The method presented gives realistic estimates of tire impact forces, which serves as useful input for haul road design.

KEYWORDS:

• Haul roads
• road surface roughness
• vertical velocity
• dynamic forces
• vehicle excitation

Nomenclature

The symbols and abbreviations used in the mathematical model are defined in this section.

DAF Dynamic amplification factor

IRI  International roughness index

PSD Power spectral density

CBR California bearing ratio

G(n) Displacement power spectral density

G(n₀) Reference displacement power spectral density

n  Wave number (also referred to as road unevenness frequency)

n₀  Reference wave number (n₀ = 0.1 cycle/m)

Z  Road surface elevations (tire vertical excitation)

N  Number of frequencies between lower and upper bound wave numbers

n_min Lower bound wave number

n_max Upper bound wave number

Δn  Wave number increment

ϕ  Random phase angle of road surface roughness

$\stackrel{\bullet }{\mathrm{Z}}$  Tire vertical velocity

$\stackrel{\bullet \bullet }{\mathrm{Z}}$  Tire vertical acceleration

Δt  Time interval between successive surface elevations

Z_t  Instantaneous road surface elevation (i.e. elevation at time t)

Z_t+Δt Road elevation at time t+ Δt

W_t  Total tire impact forces

g  Acceleration due to gravity (9.81 m/s²)

h  Dynamic tire sinkage

b  Tire width

d_w  Tire diameter

s  Soil deformation exponent

k_c  Cohesive modulus of soil deformation

k_ϕ  Frictional modulus of soil deformation

R_l  Tire-loaded rolling radius

R_f  Tire-free rolling radius

θ  Tire contact angles

$\mathrm{\partial }$f  Tire deflection

${\theta }_{\mathrm{\partial }\mathrm{f}}$  Tire deflection angle

R_Dyn Dynamic tire force (taken as total tire force)

R_Stat Static tire force

Acknowledgements

The authors are grateful to the Heavy Mining Machinery Research group under which the research is being funded. The inputs of Dr. Wedam Nyaaba, Prosper Ayawah and Charlotte Atiiru to the paper are greatly acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Robert Quenon Endowed Chair [N/A].