Modelling particle kinetic behaviour considering asperity contact: formulation and DEM simulations

Abstract

A model of formulating particle kinetic behaviour considering surface asperity is presented. The asperity was created by lining up on the surface a set of particles in varying distances. A moving particle was assigned a velocity to travel on the rugged surface where the particle trajectory and mechanical energy were gauged. The results were used to validate a discrete element framework which was developed and applied to examine the effect of surface asperity on the particle kinetic behaviour. Some interesting case studies were designed and simulated. The simulations suggested that the surface roughness influenced the energy dissipation caused in the particle–surface collisions. The research outcomes defined the inter-particle reaction from a micro-scale perspective and helped predict asperity-induced wear.

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Abbreviations

D t j :

Relative distance between the moving disc and base disc at time step t

E m :

System mechanical energy

E t :

Total energy

E k :

Kinetic energy

E β :

Dashpot energy loss

F d n , F d s :

Normal and dashpot force

F h n , F h s :

Nonlinear normal and shear contact force

g :

Gravity acceleration

k n :

Normal stiffness

L r :

Relative distance of the collision angle

m 1 , m 2 :

Mass of the bodies 1 and 2

m c :

Mass of the system

r :

Radius of the moving disc

r j :

Radius of base disc j

\(\bar{r}\) :

Average radius of the base disc

S γ,max :

Distance where the maximum collision angle occurs

S stop :

Total moving distance

t :

Time step

Δt :

Time step increment

Δt 0 :

Time step increment at bounce

v :

Velocity

v n :

Normal velocity before collision

v s :

Tangential velocity before collision

v n,r :

Normal velocity after collision

x t , y t :

Centre position of the moving disc at time step t

U :

Gravity potential

α n :

Restitution coefficient

β n :

Damping coefficient

γ :

Contact angle

γ c :

Collision angle

\(\bar{\gamma }^{c}\) :

Average collision angle

\(\dot{\delta }_{n}\) :

Relative normal translational velocity

ω :

Angular velocity

θ :

Rotation angle

η :

Disc gap coefficient

μ :

Mean of normal distribution

σ :

Standard deviation of normal distribution

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Acknowledgements

This study is performed under the supports provided by the Australian Research Council (Project No. DP140103004) and the University of Adelaide. Professional editor, Leticia Mooney, provided copyediting and proofreading services, according to the guidelines laid out in the university-endorsed national ‘Guidelines for editing research theses’.

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Correspondence to An Deng.

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Wang, C., Deng, A., Taheri, A. et al. Modelling particle kinetic behaviour considering asperity contact: formulation and DEM simulations. Granular Matter 21, 27 (2019). https://doi.org/10.1007/s10035-019-0879-5

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Keywords

  • Surface roughness
  • Collision
  • Contact mechanics
  • Energy dissipation