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Advanced mechanics of materials (1993-John Willey) Episode 13

Tham khảo tài liệu 'advanced mechanics of materials (1993-john willey) episode 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 702 18 CONTACT STRESSES Also V Vi for a point in body 1 and V v2 for a point in body 2. We note that the stresses depend on the variables A B k k v15 v2 E19 E2 b and z. The first four variables depend only on the shape of the surfaces near the point of contact. Of these four A and B are found from Eqs. 18.15 and 18.16 and from Sec. 18.4 kf Ợ1 k2. Therefore one additional equation is needed for determining the value of k. This equation is B ụ k2 E kf K k A K k E k n The second group of four variables v15 v2 Elt and E2 depend only on the properties of the two bodies in contact and are found by tests of the materials. The variable b the semiminor axis of the area of contact depends on the eight variables previously listed but it is important to note that it also depends on the load p. The equation expressing this fact is b 73fe fe pA ka 18.22 V 2tĩ Values of the variable z which represent the distance of a point from the surface of contact may be chosen. Then the three principal stresses at any point on the z axis may be obtained. 18.6 METHOD OF COMPUTING CONTACT STRESSES Principal Stresses In Sec. 18.5 it is noted that the values of A and B must be computed first and that in Eq. 18.21 the ratio B A determines the value of k and k . It should be remembered that the values of A and B are related to the geometric shape and configuration of the two bodies. For example if two cylinders are crossed so that they are in point contact with their longitudinal axes perpendicular the value of B A 1 but if these cylinders are arranged so that their longitudinal axes are parallel line contact B A 00. With the values of the four quantities A B k and k known the terms in the brackets in Eqs. 18.18 18.19 and 18.20 can be evaluated for a selected value of Poisson s ratio V. Fortunately the value of V in these bracket terms has only a small influence on the final values of the stresses. Consequently we take a value of V ị to compute these terms. The actual values of vx and v2 of the .