rate and shear stress is defined as absolute or dynamic viscosity, τ:
(2.15)
The value of dynamic viscosity can be reported with different units: the SI system uses kg/(m s) (or Pa · s), but it is also common to find the dynamic viscosity expressed in poise, where 1 P corresponds to 1 g/(cm s) 1. One centipoise (cP) corresponds to 0.001 kg/(m s).
Sometimes, the viscosity can be expressed as ratio between absolute viscosity and density. This ratio is also referred to as kinematic viscosity:
(2.16)
The common unit for ν is the Stoke, where 1 Stoke corresponds to 1 cm2/s. At room temperature (300 K), the dynamic viscosity of the water is 0.89 cP, while typically hydraulic fluids have much higher viscosity, typically higher than 30 cP.
Usually, viscosity cannot be estimated well from theoretical relations, and experimental devices (viscometers) are commonly used to determine the value of viscosity of a given fluid.
2.6.1 Viscosity as a Function of Temperature
For liquids, it is very important to consider that viscosity is strongly affected by temperature. For many fluids, an empirical correlation of the form of Eq. (2.17) can be used:
where T is the absolute temperature (in K) and A, B, C are constants that can be determined once the value of viscosity at three different temperatures is known. For water, the values of these constants are [16]
(2.18)
For mineral oils, it is very common to use Walter's relation:
(2.19)
where ν is the kinematic viscosity in mm2/s, T is the temperature in K, and k, m, and a are constants dependent on the specific hydraulic fluid. For mineral oils
As reported in [17], some variants of Walter's relation have been developed to obtain a better match between numerical results and experimental data. Notwithstanding, the relation (2.20) is useful to understand the graphical dual‐logarithm representation, typically used to describe the dependence of the viscosity on temperature (Figure 2.7). In this plot, the viscosity variation with temperature appears to be linear (because of the logarithmic scale), but in reality there is an exponential decay as expressed by Eq. (2.17).
Figure 2.7 Viscosity of hydraulic fluids as a function of the temperature.
Table 2.5 ISO classes for hydraulic oils according to the viscosity grade.
| ISO code | υ40 ° C [mm2/s] | υmin (−10%) [mm2/s] | υmax (+10%) [mm2/s] |
|---|---|---|---|
| VG10 | 10 | 9.0 | 11.0 |
| VG22 | 22 | 19.8 | 24.2 |
| VG32 | 32 | 28.8 | 35.2 |
| VG46 | 46 | 41.4 | 50.6 |
| VG68 | 68 | 61.2 | 74.8 |
| VG100 | 100 | 90.0 | 110.0 |
The plot of Figure 2.7 reports curves for different fluids, identified by their viscosity grade (VG). This represents the ISO classification of hydraulic fluids based on the parameter VG. The VG of a hydraulic fluid is defined as the kinematic viscosity (in mm2/s) at 40 °C. According to the ISO standard, there are six classes of oils, which are reported in Table 2.5.
As mentioned at the beginning of this chapter, an ideal hydraulic fluid maintains its properties constants, even under high temperature or pressure variations. However, as it is clearly visible from Figure 2.7, the large variations of fluid viscosity with temperature are far from the desirable ideal trend. This aspect has large implications in practical applications of hydraulic control technology. This is particularly true for machinery operating outdoor, which are affected by the seasonal or daily temperature changes. The viscosity of the working fluid in hot summer days can differ by orders of magnitude compared with the values reached in cold winter days. A designer needs to be mindful of this temperature dependence when selecting the proper fluid for the hydraulic system. Often the oil has to be changed with the season. For example, manufacturers can recommend a VG46 for summer use and a VG32 for the winter.
In many cases, it is possible to use oil additives that limit the viscosity variation with temperature. To compare the behavior of different oils in this regard, a parameter called viscosity index (VI) was introduced in 1929 [18], and it is nowadays defined by engineering standards [19, 20]. A high value for the VI indicates a limited dependence of viscosity with temperature.
