tailieunhanh - Bearing Design in Machinery Episode 3 Part 11

Tham khảo tài liệu 'bearing design in machinery episode 3 part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | viscosity. Moreover it is possible to use higher viscosity oils without resorting to oil additives of long chain polymer molecules. An appropriate criterion for an improvement of the lubrication performance is the ratio between the friction force and the load capacity bearing friction coefficient . VISCOELASTIC FLUID MODELS1 For the analysis of viscoelastic fluids various models have been developed. The models are in the form of rheological equations also referred to as constitutive equations. An example is the Maxwell fluid equation Sec. . Multi-grade lubricants are predominantly viscous fluids with a small elastic effect. Therefore in hydrodynamic lubrication the viscosity has a dominant role in generating the pressure wave while the fluid elasticity has only a small second order effect. In such cases the flow of non-Newtonian viscoelastic fluids can be analyzed by using differential type constitutive equations. The main advantage of these equations is that the stress components are explicit functions of the strainrate components. In a similar way to Newtonian Navier-Stokes equations viscoelastic differential-type equations can be directly applied for solving the flow. Differential type equations were widely used in the theory of lubrication for bearings under steady and particularly unsteady conditions. Differential type constitutive equations are restricted to a class of flow problems where the Deborah number is low De 1. The ratio De is of the relaxation time of the fluid l to a characteristic time of the flow At De l At. Here At is the time for a significant change in the flow . in a sinusoidal flow At is the oscillation period. The early analytical work in hydrodynamics lubrication of viscoelastic fluids is based on the second-order fluid equation of Rivlin and Ericksen 1955 or on the equation of Oldroyd 1959 . These early equations are referred to as conventional differential-type rheological equations. Coleman and Noll 1960 showed that the .