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Bearing Design in Machinery Episode 1 Part 4

Tham khảo tài liệu 'bearing design in machinery episode 1 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | u u y the relation between the shear stress and the shear rate is described by the following equation t 1 dt m du 2-9 dt dy Here 1 is the relaxation time having units of time . The second term with the relaxation time describes the fluid stress-relaxation characteristic in addition to the viscous characteristics of Newtonian fluids. As an example In Newtonian fluid flow if the shear stress t is sinusoidal it will result in a sinusoidal shear rate in phase with the shear stress oscillations. However according to the Maxwell model there will be a phase lag between the shear stress t and the sinusoidal shear rate. Analysis of hydrodynamic lubrication with viscoelastic fluids is presented in Chapter 19. Problems 2-1a A hydrostatic circular pad comprises two parallel concentric disks as shown in Fig. 2-5. There is a thin clearance h0 between the disks. The upper disk is driven by an electric motor through a mechanical drive and has a rotation angular speed o. For the rotation power is required to overcome the viscous shear of fluid in the clearance. Derive the expressions for the torque T and the power Ef provided by the drive electric motor to overcome the friction due to viscous shear in the clearance. Consider only the viscous friction in the thin clearance h0 and neglect the friction in the circular recess of radius R0. For deriving the expression of the torque find the shear stresses and torque dT of a thin ring dr and integrate in the boundaries from R0 to R. For the power use the equation Ef To. Show that the results of the derivations are Tf 2mR4 6 - R o P2-1a 2 h0 R Ef 2m R4 6 - R o2 P2-1b 20 R 2-1b A hydrostatic circular pad as shown in Fig. 2-5 operates as a viscometer with a constant clearance of h0 200 mm between the disks. The disk radius is R 200 mm and the circular recess radius is R0 100 mm. The rotation speed of the upper disk is 600 RPM. The lower disk is mounted on a torque-measuring device which reads a torque of 250 N-m. Find the fluid viscosity in