大模数蜗杆铣刀专用机床设计计量器具的选择(任务书+CAD图纸+外文文献翻译) 第2页
In Eq. (5), α1 is the viscosity of the fluid. The second item on the right of the equation shows the effect of the viscosity to the normal stress. The third item shows the effect of the first normal stress difference. α2 is expressed as Eq. (6). λis relaxtion time and ηˆ is the differential viscosity[7].
The fourth item shows the effect of the second normal stress difference. It is commonly recognized that the second normal stress difference is far less than the first normal stress difference, the fourth item is omitted and the expression of the first normal stress difference is expressed as Eq. (7).
In the lubrication, the lubricant film thickness is far less than other dimensions. Compared with the dominating velocity u and velocity gradient yu∂∂, xv∂∂ and xay∂∂ are omitted in Eq. (7), the first normal stress difference is simplified to Eq. (8).
In Eq. (8), λ is the relaxation time, ω is the angular velocity of the following coordinate to the reference coordinate. ω is caused by the elasticity of non-Newtonian fluid and is considered as the natural frequency ωn of the viscoelastic micro unit . Thus, the first normal stress difference is specified as Eq. (9).
Generally, the definition of the first normal stress difference is
1γυ& is the function of the first normal stress difference, with Eq. (9) and (10), the )(1γυ& is expressed as Eq. (11).
3. Reynolds Equation including the First Normal Stress Difference
To analyze the effect of the normal stress in lubrication, a modified form of Reynolds equation that includes the first normal stress difference is firstly established under the condition of the steady laminar lubrication. In head-disk interface lubrication, the expression of the shear stress and the normal stress in the random coordinate system are shown as Eq. (12) after the conversion of the coordinates.
Eq. (12) is derived from the conversion of the coordinates, another equation showing the relation between the pressure and the stress is derived from the momentum equation shown as Eq. (13)
Under the real lubrication condition, Eq. (13) is simplified with some basic assumptions, and the momentum equation is changed to Eq. (14).
(1) The inertia force and the external force are not considered,
(2) The fluid can not be compressed,
(3) Compared with the principal flow
are omitted.
With Eq. (14) and Eq. (12), a modified Reynolds equation is derived and shown as Eq. (15). In Eq.(15), p is the pressure, U is the surface velocity, h is the thickness of the lubricant film, v is the velocity normal to the lubricant film. xyz are coordinates. The simplified slider geometry is shown as figure 2.
4. Numerical Results of Lubrication
In this section, numerical method is used to calculate the lubrication results. Based on the results, the effect of the first normal stress difference to the pressure profile and the load capacity is analyzed. The dimensionless equation used in calculation is shown as Eq. (16).
In Eq. (16), the dimensionless parameters are illustrated as follows.
上一页 [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] ... 下一页 >>
大模数蜗杆铣刀专用机床设计计量器具的选择(任务书+CAD图纸+外文文献翻译) 第2页下载如图片无法显示或论文不完整，请联系qq752018766
