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3页
To simplify the calculation, other factors such as temperature are considered as constant under the stable laminar lubrication, and the over relaxation method is used.
4.1 Numerical results in stable laminar lubrication
The first normal stress difference of non-Newtonian fluid will affect the pressure profile and the load capacity. The pressure of the intermediate cross-section at b/2 is shown in Fig. 3. 0p is the dimensionless pressure of the lubricant which is not affected by the first normal stress difference, 1p is the dimensionless pressure which is under the effect of the first normal stress difference. Corresponding load capacities are shown in Fig. 4. In Fig. 4, W1 is the dimensionless load capacity under the effect of the first normal stress difference, W2 is the dimensionless load capacity not considering the effect of the first normal stress difference. Wn is the dimensionless load capacity of Newtonian fluid.
Figure 3. Effect of the first normal stress difference to the pressure profile
Figure 4. Effect of the first normal stress difference to the load capacity
From the results shown in Fig. 3 and Fig. 4, the pressure and the load capacity of the lubricant increase under the effect of the normal stress. But the increment is not significant. So the effect of the normal stress can be omitted in lubrication calculation. In real lubrication, the effect of the first normal stress difference is to increase the load capacity, omitting the first normal stress difference is a safe design method.
From Fig. 4, we may also find that the variation of the load capacity is caused principally by the variation of the viscosity. For example, in Maxwell fluid lubrication, the differential viscosity is affected by the shearing rate greatly. The variation of the viscosity is the key factor to affect the lubrication effect, and the effect of the first normal stress difference is to increase the load capacity in small variation range.
The effect of the first normal stress difference is affected by two factors. One is the material dynamic property. From equation (11), the first normal stress difference is determined by the natural frequency and the relaxtion time of non-Newtonian fluid. Also, the differential viscosity is affected by the shearing rate.
The other factor is the normal velocity. In Eq. (16), the function of the first normal stress difference is constrained by the normal velocity v. Commonly in theoretical analysis, the normal velocity is considered small and is omitted compared with principal velocity .The normal velocity weakens the effect of the first normal stress difference. For example, under the parameters used in calculation, the value of the dimensionless first normal stress difference is -36, but the calculated normal velocity Uv is no more than 0.0021, so the effect of the second item on the right side of the Eq. (16) is far less than the geometric effect.
If the normal velocity is large enough, the effect of the first normal stress difference needs to be considered in the numerical calculation. The pressure profiles under different dimensionless normal velocities are shown in Fig. 5. With the increment of the normal velocity, the effect of the first normal stress difference to the pressure profile become more and more important. When the dimensionless normal stress is 1% of the surface velocity, that is 01.0=v, the increment of the pressure peak is about 5%.
Figure 5. Effect of the normal stress difference to the pressure profile
Normal velocity sometimess may be considered in the true magnetic head-disk interface lubrication. For example, in the head-disk contact dection experiment [8], the flying height of the slider changes. Also, it has been proved that the lubricant film thickness decreases under flying heads during drive operation[9,10]. The Reynolds equation needs to be modified to include the effect of normal velocity.
4.2 Effect of normal velocity
The normal veloctiy not only affects the effect of the first normal stress difference, but also causes extrusion effect [11]. With the item of the extrusion
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