Oka Wear Model

The Oka or Impact Wear contact model extends any Base Model to give an estimation of erosion depth for Geometry surfaces due to particle impacts.

This model originates from the work by Oka and Yoshida (Oka and Yoshida, 2005). and is an erosion model that computes the volume of material removed from a surface due to high-velocity particle impacts according to equations 1-3.
V ω = g ( α ) E 90 m p MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvamaaBa aaleGabaGkgiabeM8a3bqabaGccqGH9aqpcaWGNbGaaiikaiabeg7a HjaacMcacaWGfbWaaSbaaSqaaiaaiMdacaaIWaaabeaakiaad2gada WgaaWcbaGaamiCaaqabaaaaa@4282@
g ( α ) = sin ( α ) n 1 ( 1 + H υ ( 1 sin ( α ) ) n 2 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zaiaacI cacqaHXoqycaGGPaGaeyypa0Jaci4CaiaacMgacaGGUbGaaiikaiab eg7aHjaacMcadaahaaWcbeqaaiaad6gadaWgaaadbaGaaGymaaqaba aaaOGaaiikaiaaigdacqGHRaWkcaWGibWaaSbaaSqaaiabew8a1bqa baGccaGGOaGaaGymaiabgkHiTiGacohacaGGPbGaaiOBaiaacIcacq aHXoqycaGGPaGaaiykamaaCaaaleqabaGaamOBamaaBaaameaacaaI Yaaabeaaaaaaaa@52B0@
E 90 = K ( α H υ ) k 1 b υ υ ' k 2 D D ' k 3 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaaI5aGaaGimaaqabaGccqGH9aqpcaWGlbGaaiikaiabeg7a HjaadIeadaWgaaWcbaGaeqyXduhabeaakiaacMcadaahaaWcbeqaai aadUgadaWgaaadbaGaaGymaaqabaWccaWGIbaaaOWaaeWaaeaadaWc aaqaaiabew8a1bqaaiabew8a1jaacEcaaaaacaGLOaGaayzkaaWaaW baaSqabeaacaWGRbWaaSbaaWqaaiaaikdaaeqaaaaakmaabmaabaWa aSaaaeaacaWGebaabaGaamiraiaacEcaaaaacaGLOaGaayzkaaWaaW baaSqabeaacaWGRbWaaSbaaWqaaiaaiodaaeqaaaaaaaa@50CC@
Where Vw is the removed volume, α is the particle impact angle, Hv is the Vicker’s hardness of the worn material, D is the particle diameter, v is the impact velocity, D' and v' are the corresponding reference values in Oka and Yoshida’s experiments (Oka and Yoshida, 2005), and n1, n2, k1, k2, k3, and b are empirical constants of arbitrary units.


The term (αHv)-b is lumped into a wear constant W of arbitrary units resulting in the following equation (the change in the sign of k1 is due to the definition of W).

E 90 = K W k 1 υ υ ' k 2 D D ' k 3 MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaaI5aGaaGimaaqabaGccqGH9aqpcaWGlbGaam4vamaaCaaa leqabaGaeyOeI0Iaam4AamaaBaaameaacaaIXaaabeaaaaGcdaqada qaamaalaaabaGaeqyXduhabaGaeqyXduNaai4jaaaaaiaawIcacaGL PaaadaahaaWcbeqaaiaadUgadaWgaaadbaGaaGOmaaqabaaaaOWaae WaaeaadaWcaaqaaiaadseaaeaacaWGebGaai4jaaaaaiaawIcacaGL PaaadaahaaWcbeqaaiaadUgadaWgaaadbaGaaG4maaqabaaaaaaa@4BE1@
The worn volume is converted into a uniform wear depth on Geometry elements according to equation 5.
D w = V w A MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleGabaGkgiaadEhaaeqaaOGaeyypa0ZaaSaaaeaacaWGwbWaaSba aSqaaiaadEhaaeqaaaGcbaGaamyqaaaaaaa@3C0E@

where Dw is the wear depth and A is the Geometry element area.



 The following table summarizes the values reported by Oka and Yoshida (Oka and Yoshida, 2005) that are taken for the empirical constants of the model.
Table 1. Values for the empirical model constants reported by Oka and Yoshida for SiO2 particles.
K n1 n2 k1 k2 k3 v' (ms-1) D' (μm)
65 0.71 Hv-0.94 2.4 Hv-0.94 -0.12 2.3 Hv0.038 0.19 104 326
The inputs of the model then reduce to the wear constant W and the Vicker’s hardness Hv of the worn material. The following table summarizes the values for some common metals reported by Oka and Yoshida (Oka and Yoshida, 2005).
Table 2. Values for the wear constant and Vicker’s hardness of some common materials as reported by Oka and Yoshida
Material W Hv (GPa)
Carbon Steel 3 0.54-1.18
Stainless Steel 10 1.770
Aluminium 1000 0.36
EDEM also provides the option to deform the Geometry according to the wear depth.


In the Oka Wear Model Parameter Values dialog box:
  1. Select the Enable Deformation check box to enable Geometry deformation.
  2. If you select Enable Deformation, you must specify the Scaling Factor which allows the deformation results to be linearly scaled as desired.