By L. Goryacheva
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Additional info for Contact Mechanics in Tribology
17) tends to the solution of Eq. 12) if n -> oo. Let us analyze the structure of Eq. 17). The integral term on the left side of Eq. 17) governs the influence of the real pressure distribution at the neighboring contact spots (r^ < An), on the pressure at the fixed contact spot with center (0,0) (local effect). The effect of the pressure distribution at the remaining contact spots which have centers ( n , ^ ) , r* > An, is taken into account by the second term in the right side of Eq. 17). This term describes the additional pressure pa(r) which arises within a contact spot (r < a) from the nominal pressure p — PN in the region Q1n (r > An).
N). If the approach of the bodies Do is unknown, and the load P is given, then in order to determine Do one should add to Eqs. 33) When we study the contact interaction of a system of smooth axially symmetric punches with the elastic half-space, the radius of each contact spot a* is the unknown value. We can find this value from the condition It follows from this relation and the equilibrium equation that —- = 0. Differentiation of Eq. 34) Eqs. 34) in conjunction with Eqs. 32) give the complete system of equations to determine the values of Z^, a\ and Pi for a system of punches, the shapes of which are described by a continuously differentiate function.
13). Different variants of the spatial arrangement of punches were considered. 1. The punches of the j-th layer are located at the same distance hj from the central punch of the system. e. the models were characterized by the same height distribution function. The results of the calculations have been described in details in the monograph by Goryacheva and Dobychin (1988). Fig. 45 (broken line). It must be L L L noted that the dependence is a piecewise-constant function for the model under consideration.
Contact Mechanics in Tribology by L. Goryacheva