LITMIR.BIZ

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represents only one of the design requirements that has to be satisfied for the tanks. In fact, during the operation of the system, the volume of hydraulic fluid in the tank can significantly vary due to the presence of accumulators or differential cylinders. These elements store variable amounts of fluid: for this reason, the reservoir has to accommodate for such variation while also allowing for a sufficient air cushion. Therefore, the designer needs to ensure that the value provided by Eq. (2.35) is well above the maximum volume variation ΔV that can be observed during the operation of the system. Otherwise, the volume of the tank has to be increased accordingly.

      In case the tank is used as primary source of thermal conditioning of the fluid, to guarantee that the temperature of the working fluid remains stable during the operation of the hydraulic system, the volume of the tank needs also to allow a minimum heat exchange surface to the environment. An empirical formula, valid for parallelepiped‐shaped tanks, is the following [11]:

      (2.36)

      where c_p [kJ/kgK] is specific heat capacity (can be assumed to be 4.187 kJ/kgK), T_f is the temperature of the working fluid, T_amb is the ambient temperature, H [kJ] is the heat to dissipate, and c is a constant that, with the above units, is equal to 1.25.

2.9.2 Basic Design of a Tank

The basic design of a hydraulic reservoir consists of a parallelepiped made of steel sheets. Small tanks (usually below 70 l) can be made of metal alloy or plastic. In a simplified cross‐sectional view, the tank appears as shown in Figure 2.19. The suction duct and the discharge duct are usually placed at the opposite ends to increase the residence time of the working fluid inside the tank. Separator septs or baffles are used to prevent a straight flow path between the discharge and the suction pipe. In this way the fluid is forced to travel a longer path with reduced speed. In many cases, the septs force the fluid to flow vertically within the reservoir so that the release of the undissolved air is promoted by gravity. The discharge pipe is usually well below the free surface level of the fluid. This helps in preventing splashing of the fluid and whirls that would increase foam and entrained air. The pipes are often cut with angles greater than 45°. At the discharge pipe this further promotes a smooth entering of the fluid in the tank; but most importantly, at the suction pipe, it allows for a gradual acceleration of the fluid within the pipe, thus reducing the entrance losses.

      The figure also shows an air breather element, which should always be present to allow the air to enter or leave the tank as the level of the fluid varies to accommodate volume variations driven by accumulators or differential cylinders.

      Other accessories typically present in hydraulic reservoirs, not shown in Figure 2.19, include inspection ports, level indicators, filling inlet port and drainage or discharge caps, internal de‐aeration separators (which are used to promote air separation and reduce foam), and magnets to capture contamination. The bottom of the tank is usually concave so that the solid impurities that remain at the bottom of the tank can be periodically drained through the discharge caps.

Figure 2.19 Typical design of a hydraulic reservoir.

Problems

      1 2.1 A hydraulic cylinder is loaded such that the pressure in the piston chamber rises from 0 to 4000 psi (this chamber being blocked, for example, by a normally closed valve). Evaluate the motion Δx of the piston, in inches, as effect of oil compressibility. Assume no air entrapped in oil and Bliq = 2.2 · 105 psi (bulk modulus). The rod chamber is connected to atmosphere at null pressure. Neglect compressibility of the material of the cylinder.

      2 2.2 The cylinder in figure is loaded from 0 to 4000 psi keeping the bore port blocked. Evaluate the motion Δx of the piston from its initial position, in inches (in.), as effect of oil compressibility. Assume no air entrapped in oil and Bliq= 2.2 · 105 psi (bulk modulus). The rod chamber is connected to atmosphere at null pressure. Neglect the compressibility of the material of the cylinder.How much is the force F?

      3 2.3 A cylinder with a 3 in bore and an extension of 1.42 in from the retracted position is loaded from 0 bar to 5000 psi while keeping the bore port blocked (as in the previous problem figure). Evaluate the motion Δx of the piston, as effect of oil compressibility. Assume 5% air entrained in oil and Kliq = 2.2 105 psi. Neglect the compressibility of the material and of the cylinder walls. When evaluating the bulk modulus of the air, consider following two cases:Gradual (slow) process (isothermal)Fast process (adiabatic)

      4 2.4 Measurements are taken on the piston chamber of a cylinder with a bore diameter of 250 mm. The bore port is blocked, and the rod chamber is connected to atmosphere (as in the previous problem figure). When the stroke (from retracted position) is 225 mm, the pressure is 70 bar. When the stroke is reduced to 222 mm, the pressure is 140 bar.Determine the bulk modulus of the fluid.

Notes

      1 1 In the British units, the viscosity is expressed as (lbf · s)/ft.

      2 2 The polytrophic constant can be assumed as a function of the dynamic of the process. For a fast compression or expansion process, γ ≅ 1.4 (adiabatic); for a slow process, γ ≅ 1 (isothermal). Intermediate choices, such as γ = 1.2, are often made to describe a more general situation.

Chapter 3 Fundamental Equations

      The fundamental principles of fluid power are closely related to those of fluid mechanics: the basic relations used to analyze the operation of a fluid power system originate from the fundamental equations of fluid mechanics.

      The basic concepts of hydraulic systems are usually presented with the simplified assumption of stationary conditions. This allows deriving very simple equations for the working fluid, which are particularly suitable to describe the functioning of even complex system layout architectures. This chapter describes how these simplified equations are derived from the classic equations of fluid mechanics of general validity. Readers with basic knowledge of fluid mechanics will appreciate and understand the derivation of these basic equations used throughout this book.

      Knowledge of the tools used to perform a dynamic analysis is not necessary to understand the basic operation of a hydraulic circuit. This dynamic analysis becomes necessary when studying the system behavior during transients, for example, a sudden variation of the external load or the commutation of the system from one state to another (such as the sudden change in the commanded position of a hydraulic control valve). Some basic concepts pertaining to the dynamic behavior of hydraulic control systems during transients will be introduced in Chapter 5.

3.1 Pascal's Law

      Pascal's law states that the pressure is transmitted undiminished in a confined body of fluid at rest.

      The Pascal's law of fluid statics is the foundation of what is considered by most engineers the modern era of fluid power technology.

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