§10.1 Contact Stress,Residual Stress and Stress Concentrations 387 2b P Moximum contoct pressure p (a)Contocting porollel cylinders (b)Pressure (stress)distribution Fig.10.3.(a)Contact of two parallel cylinders;(b)stress distribution for contacting parallel cylinders. and the maximum pressure or maximum compressive stress 2p P0=0c= xbL (10.7) The contact width can be related to the geometry of the contacting surfaces as follows:- P△ b=1.076 (10.8) 】 giving the maximum compressive stress as: P 0c=-p0=-0.5911 R R2 (10.9) LA (For a flat plate R2 is infinite,for a cylinder in a cylindrical bearing R2 is negative). Stress conditions at the surface on the load axis are then: 02=0e=一P0 0y=一p0 ox=-2vpo (along cylinder length) The maximum shear stress is: tmax=0.295p%s0.3p0 occurring at a depth beneath the surface of 0.786 b and on planes at 45 to the load axis. In cases such as gears,bearings,cams,etc.which (as will be discussed later)can be likened to the contact of parallel cylinders,this shear stress will reduce gradually to zero as the rolling load passes the point in question and rise again to its maximum value as the next$10.1 Contact Stress, Residual Stress and Stress Concentrations (01 Contacting parollel cylinders Maximum contact pressure P, (b) Pressure (stress) distribution 387 Fig. 10.3. (a) Contact of two parallel cylinders: (b) stress distribution for contacting parallel cylinders. and the maximum pressure or maximum compressive stress (10.7) The contact width can be related to the geometry of the contacting surfaces as follows:- (10.8) giving the maximum compressive stress as: 0, = -p~ = -0.591 (10.9) LA (For a flat plate R2 is infinite, for a cylinder in a cylindrical bearing R2 is negative). Stress conditions at the surface on the load axis are then: uy = -Po ax= -2vw (along cylinder length) The maximum shear stress is: occurring at a depth beneath the surface of 0.786 b and on planes at 45" to the load axis. In cases such as gears, bearings, cams, etc. which (as will be discussed later) can be likened to the contact of parallel cylinders, this shear stress will reduce gradually to zero as the rolling load passes the point in question and rise again to its maximum value as the next