Model of non-interacted «concentration waves». The «third body» of the complex tribologic system CM1/LL,°/CM2 is presented by wear products of the composition materials CM1 and CM2 and the liquid lubricant (LL). In this case the volume concentration of the solid components is may be presented by next relation:
α = <α> – ∆α = <α> /(1 + αLL),
where <α> is the average concentration of the solid components without taking into consideration the volume share of the LL and the change of α is the following ∆α = <α> αll/(1 + αLL).
If the tribologic properties () of the compositional materials CMi (i = 1, 2) in CMi/°/CMi systems are may be calculated by next relations:
then the properties of these materials in system CM1/LL,°/CM2 are may be calculated by the following formulae:
where and Δδi ≅ 2αiΔαi(3αi - 2) are the relative value of the synergic effect and the change of its for surface of the i-composition (i = 1, 2) by friction, and ∆αi ≅ αiαLL/(1 + αLL) is the change of the volume concentration for according solid component.
It’s need to note, this additive model of non-interacted «concentration waves» are may be used for prediction of CM properties in any tribologic systems [1–4].
Model of interacted «concentration wave». The tribologic properties of the compositional materials CMi (i = 1, 2) in CMi/°/CMi systems are may be calculated by next relations:
where and are the sets of the properties values of the solid (with average concentration <αi>) and lubricant CMi components according to «standard scale», the symbol ° is denotes the «third body» (TB) without liquid lubricant (LL), δi – are the relative synergic effect for each system . The interacted «concentration waves» from each CMi are determine the composition of the TB. Then the additive model of the friction coefficient and the sum velocity of linear wear calculation may be presented by next formulae:
f = flub + (α – δ)(fsol – flub);
Ii = Ilub,i + (αi + δi)(Isol,i – Ilub,i),
– is the concentration of the solid components into TB volume.
The relative synergic effects are may be presented by following relations:
δi ≅ 2αi <α> (1 + αLL – <α>)/(1 + αLL)3 (for the velocity of linear wear) and
d ≅ 2 <α>2(1 + αLL – <α>)/(1 + αLL)3 (for the friction coefficient).
It’s need to note, this additive model of interacted «concentration waves» are may be used for prediction of CM tribologic properties in sоme systems [5–7].