Tham khảo tài liệu 'friction and lubrication in mechanical design episode 1 part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 30 Chapter 2 R R2 radii of cylinders positive when convex and negative when concave _ 1 1 Ee E E2 Eị E2 modulus of elasticity for the two materials Case 7 General Case of Contact Between Elastic Bodies with Continuous and Smooth Surfaces at the Contact Zone Analysis of this case by Hertz can be found in Refs 1 and 2. A diagrammatic representation of this problem is shown in Fig. and the contact area is expected to assume an ellipitcal shape. Assuming that R and R2 Rá are the principal radii of curvature at the point of contact for the two bodies respectively and ỳ is the angle between the planes of principle curvature for the two surfaces containing the curvatures 1 R and 1 R2 the curvature consants A and B can be calculated from I 1 1 .1 .1 A B 2 R Ri R2 . n I7 IV. 1 1V J1 1W1 A-B2 i-Ri R2-Ri 2 Rri0 Ri Ri These expressions can be used to calculate the contact parameter p from the relationship 31 The Contact Between Smooth Surfaces p Figure General case of contact. _ n B-A COSỚ -A B The semi-axes of the elliptical area are illtt P kỵ k2 ìlĩn P kỵ k2 where m n functions of the parameter Ớ as given in Fig. p total load 1 -J J-y2 k itE kỉ - E2 V v2 Poisson s ratios for the two materials E2 corresponding modulii of elasticity Case 8 Beams on Elastic Foundation The general equation describing the elastic curve of the beam is _ dy4 32 Chapter 2 where k foundation stiffness per unit length E modulus of elasticity of beam material 1 moment of inertia of the beam With the notation the general solution for beam deflection can be represented by y cos Px B sin fix e-ih C cos px D sin Px where A B c and D are integration constants which must be determined from boundary conditions. For relatively short beams with length smaller than Ỉ the beam can be considered rigid because the deflection from bending is negligible compared to the deflection of the foundation. In this case the deflection will be constant and is and the maximum bending moment PL .
