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)
Normal Stress Effects in Slider-Disk Interface Lubrication with Non-Newtonian Fluid
Chen Haosheng1*, Li Jiang2, Chen Darong1, Wang Jiadao1
1. State Key Laboratory of Tribology, Tsinghua University, Beijing China 100084.
2. Department of mechanology, University of Science and Technology Beijing, China, 100083
Abstract
To analyze normal stress effects of non-Newtonian fluid in lubrication of the magnetic head-disk interface, a modified Reynolds equation including the effects of normal stress is established. The expression of the first normal stress difference in the equation is derived from the Rivlin-Ericksen second order flow equation and the fluid momentum equation. Lubrication results of the magnetic head-disk interface is calculated using the modified Reynolds equation. Under the condition of steady laminar lubrication, the pressure and the load capacity of non-Newtonian fluid is increased by the effect of the first normal stress difference, but the effect is constrained by the normal velocity and can be omitted in the calculation. When the slider flying height changes or the lubricant film thickness decreases, the normal velocity increases and the effect of the first normal stress difference need to be considered.
Keywords: non-Newtonian fluid, first normal stress difference, magnetic data storage systems
1. Introduction
As mentioned by De Bruyne and Bogy[1], a non-Newtonian lubricant is used for some magnetic recording system to avoid dry contact. It has been proved that a significant reduction of pressure buildup under the slider cover can be achieved by introducing non-Newtonian shear thinning lubricant at high shear rate. To specify the behavior of non-Newtonian fluid in the lubrication of the head-disk interface, Wang-Long Li[2] provides an average Reynolds equation and point out that the effect of the flow behavior index of the power-law fluid on load capacity is more significant than that of the surface roughness. The properties of non-Newtonian fluid are important factors in the lubrication of the magnetic head-disk interface.
Normal stress effect is a characteristic of non-Newtonian fluid. Some research results [3-5] have proved that the effects of the normal stress in some lubricants are obviously increased, and the first normal stress difference is far more than the second normal stress difference. The normal stress effect needs to be analyzed in the lubrication, and the method to calculate the first normal stress difference needs to be investigated. In this paper, the expression of the first normal stress difference of a kind of viscoelastic non-Newtonian fluid such as Maxwell fluid is derived and the lubrication equation which contains the effect of the normal stress is established. Numerical method is used to calculate the lubriation results of magnetic head-disk interface.
2. Expression of the First Normal Stress
The normal stress is derived from Rivilin-Ericksen [6] flow Eq. (1).
In Eq. (1), p is the pressure, ijτ is the tensor of the shear stress, ijγ& is the tensor of the shear rate, 1α is the fluid viscosity, 2α，3α are the second order coefficience of the viscoelastic fluid, tij/DDγ& is the material time derivative.
Equation (1) is applicable for random coordinate system. In this paper, the Cartisian coordinate system is adopted. The micro unit of non-Newtonian fluid in the coordinate systems is shown in Fig. 1. The (x, y, z) is the fixed coordinate system for the calculation, the (zyx′′′,,) is the reference coordinate system and the (1, 2, 3) is the following coordinate system fixed on the micro unit. ijω′ is defined as the angular velocity of the micro unit to the following coordinate system, ijω is defined as the angular velocity of the following coordinate system to the reference coordinate system. Then, the angular velocity of the micro unit is ijijijωωω+′=.
Figure 1. Maxwell micro unit in the coordinate systems
The following coordinate system (1, 2, 3) is a rigid Cartisian coordinate system. The origin of coordinate is fixed on the micro unit, and the coordinate moves and rotates as the unit moves and rotates. The direction of the following coordinate is always same to that of the tensor of the shear rate. With Prager’s theory, the material time derivative should be expressed by the Rivlin-Ericksen shearing rate and the Jaumann covariant derivative. In the following coordinate system, the new tensor dtdij/γ& is expressed by the partial derivative shown as Eq. (2) and can be used to random coordinate system. is the velocity on the direction .
When the lubricant is an ideal viscosity fluid, the direction of the principal axis of the following coordinate system is same to the axis of the principal stress tensor in the reference coordinate system, that means 0=ω and the first normal stress difference is zero.
Material time derivative in Eq. (2) is defined in the following coordinate system. If the material time derivative is in the reference coordinate, the angular of the micro unit to the following coordinate system should be added.
From the Eq. (4), the normal stress can be expressed as Eq. (5)：951
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] ... 下一页 >>