Hydraulic Fluid Power. Andrea Vacca
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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. Vice versa, a low VI indicates a more pronounced variation of viscosity with temperature, as shown in Figure 2.8.
Figure 2.8 Qualitative representation of the viscosity index (VI).
Table 2.6 Typical values for the viscosity index.
Source: OelCheck [21].
| Oil type | Viscosity index |
|---|---|
| Mineral oil | 95–105 |
| Multi‐grade oil | 140–200 |
| Synthetic oils | 200–400 |
The VI was originally defined as a dimensionless value on a 0–100 scale, being 100 the best VI. Nowadays, thanks to the progress in the formulation of VI improvers, much higher values can be achieved as shown in Table 2.6.
2.6.2 Viscosity as a Function of Pressure
For liquids, the viscosity increases with pressure. While this effect can be negligible for limited pressure variations (<200 bar), it might be relevant for hydraulic systems working at high pressure (>200 bar). A formula that can be used to approximate the variation of fluid viscosity with pressure is given by
where μ0 is the dynamic viscosity at atmospheric pressure (at a given temperature), p is the fluid pressure (in bar), and b is a coefficient that depends on the fluid. For mineral‐based oils, b = 1.7 · 10−3 bar−1; for HFC oils, b = 3.5 · 10−4 bar−1; and for HFD oils b = 2.2 · 10−3 bar−1. Relation (2.21) is plotted in Figure