[13]
In M-B fractal contact model, is the actual contact area considering of surface shape of contact bodies which introduces a the surface shape influence coefficienton the basis of the actual contact area of two rough plane[[] Chen Qi,Zhan Han,Huang Kang,Xu Shun. Research on Gears's Contact Stiffness Based on Fractal Theory. China Mechanical Engineering. 2010，21(9)：1014-1017． ]:
DOI: 10.1016/j.apsusc.2015.04.174
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[14]
(formula (15)) is the theoretical contact area of the contact body, andis the surface area sum of contact surfaces which is calculated by the specific contact object, Xh is integrated curvature coefficient.
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[15]
Actual contact area between rough surfaces and a rough plane exists the following relationship:
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[16]
The equation (16) into equation (12) can obtained the dimensionless contact stiffness of rough surfaces.Hertz contact stiffness is still calculated in accordance with the formula (9) and the integrated contact stiffness is computed according to equation (13). 4 Simulation validating In MATLAB, to establish the relationship between the contact stiffness and load, when the M-B contact deformation occurs, contact stiffness is calculated according to equation (12); when Hertz contact deformation occurs, the contact stiffness is calculated according to equation (9), the composite stiffness according to the formula (13). The two cylinders is taken as the object of study with parameters: the material for the 45 # steel, the modulus of elasticity E = 207GPa, Poisson's ratio v = 0.3, the density ρ = 7800kg/m3, the two cylinders of radii R1=100mm, R2=200mm, fractal dimension D, roughness parameters 10-14 <G* <10-10, γ = 1.5, L = 100mm, load F = 0~4000N. Load and stiffness curve about Hertz contact model, M-B contact model and parallel connection contact model is shown in Fig 8 and Fig 9. Fig 8 Rough cylinder contact(D=1.1,G*=10-10) Fig 9 Rough cylinder contact(D=1.2,G*=10-10) 5 Conclusion 1. Hertz contact model study the stress-strain state of the contact surface from a macro perspective which is the main factors of the contact stiffness; 2. M-B fractal contact model research on stress-strain state of contact surface asperities from the microscopic viewpoint which is the secondary effects of contact stiffness. 3. M-B fractal contact model plays an important role in the initial stages of contact which impose curve to render more obvious nonlinear; Hertz contact model determines the overall shape of stiffness curve. 4. After the parallel connection of Hertz contact model and the M-B contact model, the stiffness of the contact surface is declined. References
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