Radial force variation of rolling bearing

As shown in figure 62 is 1892, Bumq solved the radial stress distribution of the semi-infinite body, he USES several coordinates rather than rectangular. No shear stress boundary condition at the surface, the radial stress solution of 2 fcos6o TTR event from type) It can be seen that when r tend to zero, and will be infinite. Obviously this is impossible, because the surface material will result in serious yield or failure. Hertz's explanation is that will form a small area of contact instead of point or line contact, the load will be assigned to the z: the whole contact surface, so as to relieve the stress of infinity. Ht in the analysis put forward the following hypothesis: 1) All the deformation within the elastic range, there is no more than the proportional limit of material. 2) Load is perpendicular to the surface, ignoring the influence of shear stress on the surface of 3) Compared with the radius of curvature loaded object, the size of the contact area is small (4) Compared with the contact area of the foot す, radius of curvature of contact area is very large. X theory of elasticity problem of the solution is based on assuming that the stress function of the stress function must be individually or in combination with figure 6. 2 boussinesq analysis model of the full compatibility equations and boundary conditions. For semi-infinite elastic body stress distribution, Hertz USES the hypothesis is that Y = Y = ( 6. 17) Zs type b is arbitrary fixed-length, X, y, and Z is the parameters of the dimension is 1. A: au av r ax o au ( 618). Z we au, a type of c is arbitrary length, in order to make e, v/c, and w/e dimension is 1. U and V is arbitrary function of X and y, but want to meet U = 0. 6. 19) Y = 0 and the relationship between c and U ( 6. 20) Be these assumptions of intuition, part comes from experience, combining their relationship with the elastic ( Type ( 6. 7) , type ( 610). And az ( 612). To type ( 6. 14) ，得 a v ou az ava2Uっ Z az z: o Z a z az av au aray arar ( 6. 21 the av Z axa ayaz type ( - 2C) / b; U=( 1 - 2) WU( X,Y,) From the above formula, which can be determined by x plane for semi-infinite body stress and deformation of the interface, the: = 0 interface should satisfy r = T, 0, and o, is a limited value Hetz finally assumed that surface shape after deformation is a rotating ellipsoid, V can be expressed as the function: y Z V s + S1 + ( 6. 2) S type. Is one of the largest is the following equation root x2 + S1 + S2s8 ( 6. 23) And ( 6. 24) Here a and b is contact area projection ellipse semi-major axis and short half shaft. For the elliptical contact area, the stress of the geometric center of 30 O mab ( 6. 25 arbitrary length is defined as 30 c 6 c. 26) For the special case of x = 0 T (20 6 c奥g ( 628). Due to the assumption that the contact face for feet す object is very small, can be expressed as the distance between the contact body type,, and r, is the main curvature radius. 2r. 2r