Stribeck curves

Fig. 3. Stribeck curve relating friction coefficient to absolute viscosity ]1, speed N in rpm, and unit loadp.

Due to the absence of a hydrodynamic effect, boundary film thickness is expected to be independent of speed of surface movement, as can be observed in the left part of the Stribeck curve. This is a significant criterion that distinguishes boundary lubrication from EHL and mixed lubrica-... 

The process of transition from hydrodynamic to boundary lubrication can be described qualitatively by plotting the measured friction coefficients against film thickness, which depends on the operational conditions, such as load, sliding velocity and lubricant viscosity. A typical diagram known as the "Stribeck Curve is schematically shown in Fig. 27, in which the friction coefficients are given as a function of, ... 

The Stribeck curve gives a general description for the transition of lubrication regime, but the quantitative information, such as the variations of real contact areas, the percentage of the load carried by contact, and changes in friction behavior, are not available due to lack of numerical tools for prediction. The deterministic ML model provides an opportunity to explore the entire process of transition from full-film EHL to boundary lubrication, as demonstrated by the examples presented in this section. 

FIGURE 4.1 The generic Stribeck curve and the three modes of contact envisaged during CMP (from Ref 6). 

FIGURE 4.4 Stribeck curves generated for different slurry flow rates (from Ref 10). 

FIGURE 4.7 Stribeck curves for polishing using different pad materials and groove patterns (from Ref 6). 

Analyses of Stribeck curves, Preston s coefficient, COF, and tribological mechanism indicator correlating with each other help to understand the polishing mechanisms. Such an analysis not only helps in the process development but also provides useful feedback to the pad development manufacturers. 

FIGURE 4.8 Stribeck curves for slurries with 13-nm abrasives (left) and 35-nm abrasives (right) (from Ref. 17). 

Dependent upon load, speed, viscosity, temperature and the nature of the lubricated surfaces in relative motion, differing degrees of separation of these surfaces occur. When significant oil film penetration occurs, frictional heating begins to cause wear, and then both friction and wear can be controlled by chemical/physical surface reactions. Within an engine a range of the above conditions operate. The influence of these conditions on friction can be seen from the Stribeck curve. Fig. 3.6. 

This dimensionless term is known as the hydrodynamic factor , where Fig. 8.2 represents the Stribeck curve in the log scale and shows that a compromise must be made with respect to lubricant viscosity, between the friction losses in the region of hydrodynamic (HD) lubrication, and bearing wear when passing through the regime of mixed friction. Both hydrodynamic and hydrostatic bearings operate with infinite service life below some critical value of load and above a critical value of speed assuming other modes of wear such as corrosion and erosion are not experienced. 

Stribeck Curve (1992) see l.M. Hutchings Tribology - Friction and Wear of Engineering Materials. Arnold (Butterworth-Heinemann), London. 

This can be rewritten in the more familiar form of the Stribeck curve as shown in Figure 4.2. 

Fig. 19 The "Stribeck curve" variation of the friction coefficient with the ratio of speed and load.

Figure 27. Schematic of a Stribeck curve and the four modes of lubrication.

Here, tj designates the viscosity of the lubricant, Vgi is the sliding velocity, and Fn is the normal force. The positions of the different lubrication regimes on the Stribeck curve are indicated in Figure 10.9. For hydrodynamic lubrication, the firiction coefficient can be described by the relation (10.16), where kf is a proportionality factor. 

It was shown that the friction force applied on the wafer was directly proportional to the downforce. In a dry pad condition without any slurry, the friction on the wafer was relatively constant with the wafer velocity. However, in the presence of polishing slurry on the pad, the friction force decreased with the wafer velocity (Figure 1.3). This phenomenon can be well explained by the Stribeck curve from tribology (Figure 1.4). 

The Stribeck curve explains the relationship between the coefficient of friction and the lubrication thickness with a certain constant called Hersey number. Hersey number is the multiplication of the viscosity of the lubricant and the velocity of the moving object divided by the pressure applied on the object. 

The Stribeck curve shows that the friction force applied on the moving surface decreases with the relative velocity of the moving object in the presence of lubrication. This is because the thickness of the lubrication film between two objects increases with the relative velocity. In the presence of the abrasive slurry, the friction between the wafer and the pad decreased with the wafer velocity. It is believed that this is caused by increased slurry thickness between the wafer and the pad from higher wafer velocity. 

Figure 11.21 Friction coefficient plotted as a function of fluid viscosity and shear velocity divided by load (Stribeck curve) with corresponding lubrication film thickness.

Figure 12.24 Qualitative sketch of a Stribeck curve. Drawn by the author.

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