tailieunhanh - Engineering Tribology 2E Episode 8

Tham khảo tài liệu 'engineering tribology 2e episode 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Elastohydrodynamic Lubrication 291 It can be noted that for the spheres Rax Ray Ra and R x R y RB where Ra and Rb are the radii of the spheres A and B respectively. Substituting into equation gives 11 11 1 1 1 1 1 T77 - - - - 2I-7- -7- I R Rx Ry RA RB RA RB RA RB where 1 1 1 J_ Rx Ry Ra Rb it should be noted that in some publications the reduced radius for the contact between two spheres is defined as 1 1 1 R Ra Rb and consequently the formulae for the contact area dimension a and the maximum deflection 8 are presented in the slightly altered form 3WR 1 3 a I I t 2E w2 1 3 Ỗ l-W- Ie 2R7 EXAMPLE Find the contact parameters for two steel balls. The normal force is W 5 N the radii of the balls are RA 10 X 10-3 m and RB 15 X 10-3 m . The Young s modulus for both balls is E X 1011 Pa and the Poisson s ratio of steel is u . Reduced Radius of Curvature Since Rax Ray RA 10 X 10-3 m and Rbx Rby RB 15 X 10-3 m the reduced radii of curvature in the x and y directions are 111 1 1 R Rbx 10 X 103 15 X10-3 . x ax ux 111 1 1 Ry Ray Rby 10 X 10-3 15 X 10 3 . Rx 6 X 10-3 m Ry 6 X 10-3 m Note that 1 Rx 1 Ry . condition is satisfied circular contact and the reduced radius of curvature is 292 Engineering Tribology -1 -1 -1 R Rx Ry R 3 X 10-3 m Reduced Young s Modulus 1 E 1 p UA2 I 1 - UB2 n Ea Eb J 1 n 2 X 10 11 1 - X 10n E X 1011 Pa Contact Area Dimensions Maximum Shear Stress T .x 1Pmax Depth at which Maximum Shear Stress Occurs z a X X 10-5 MPa X 10-5 m Contact Between a Sphere and a Plane Surface The contact area between a sphere and a plane surface as shown in Figure is also circular. The contact parameters for this configuration can be calculated according to the formulae summarized in Table . The radii of curvature of a plane surface are infinite and symmetry of the sphere applies so that Rbx Rby and Rax Ray RA. The reduced radius of curvature according to is .