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Figure 4.1.: A basic hydraulic circuit with fixed-displacement pump, pressure relief valve, 4/3 solenoid valve and cylinder. NN EEE Hydraulic circuit static and dynamic analysis involves first developing the appropriate mathematical models for each component in the circuit and then using Pascal’s Law (pressure same at all points for fluid at rest) and conserva- tion of flow to connect the components into a set of equations that describes the complete system. For a static analysis, the set of equations will be alge- braic while a dynamic analysis a set of differential equations. For example, the circuit shown in Figure 4.1 could be modeled as a constant

Figure 4 1.: A basic hydraulic circuit with fixed-displacement pump, pressure relief valve, 4/3 solenoid valve and cylinder. NN EEE Hydraulic circuit static and dynamic analysis involves first developing the appropriate mathematical models for each component in the circuit and then using Pascal’s Law (pressure same at all points for fluid at rest) and conserva- tion of flow to connect the components into a set of equations that describes the complete system. For a static analysis, the set of equations will be alge- braic while a dynamic analysis a set of differential equations. For example, the circuit shown in Figure 4.1 could be modeled as a constant

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Table 1.1.: Element analogies in several domains.
Table 1.1.: Element analogies in several domains.
Table 2.1.: Conversions between pressure units Uilito, VU LY sae coisa Catt VE CALIMA ULI CULV ELI ad ian © auiimemanamei = Uilit. Pressure is an across type variable, which means that it is always measure with respect to a reference just like voltage in an electrical system. As show in Figure 2.1, one can talk about the pressure across a fluid power elemer such as a pump or a valve, which is the pressure differential from one sid to the other, but when describing the pressure at a point, for example th pressure of fluid at one point in a hose, it is always with respect to a referenc pressure. Reporting absolute pressure means that the pressure is measure with respect to a perfect vacuum. It is more common to measure and repo! gage pressure, the pressure relative to ambiant atmospheric pressure (0.1013 mPA, 14.7 psi at sea level). The distinction is critical when analyzing th dynamics of pneumatic systems because the ideal gas law that models th behavior of air is based on absolute pressure. eS ee a : ee ane i ne.
Table 2.1.: Conversions between pressure units Uilito, VU LY sae coisa Catt VE CALIMA ULI CULV ELI ad ian © auiimemanamei = Uilit. Pressure is an across type variable, which means that it is always measure with respect to a reference just like voltage in an electrical system. As show in Figure 2.1, one can talk about the pressure across a fluid power elemer such as a pump or a valve, which is the pressure differential from one sid to the other, but when describing the pressure at a point, for example th pressure of fluid at one point in a hose, it is always with respect to a referenc pressure. Reporting absolute pressure means that the pressure is measure with respect to a perfect vacuum. It is more common to measure and repo! gage pressure, the pressure relative to ambiant atmospheric pressure (0.1013 mPA, 14.7 psi at sea level). The distinction is critical when analyzing th dynamics of pneumatic systems because the ideal gas law that models th behavior of air is based on absolute pressure. eS ee a : ee ane i ne.
Figure 2.2.: Dial pressure gauge and electronic pressure transducer.
Figure 2.2.: Dial pressure gauge and electronic pressure transducer.
Table 2.2.: Conversions between volume flow rate units
Table 2.2.: Conversions between volume flow rate units
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Figure 2.3.: Types of flowmeters. Top row: turbine, digital paddle, variable area. Bot- tom row is a dual-rotar turbine flowmeter with a cutaway.
Figure 2.5.: The viscosity of hydraulic oils varies with temperature.
Figure 2.5.: The viscosity of hydraulic oils varies with temperature.
Figure 2.6.: Fluid bulk modulous. Liquids are nearly incompressible (left), except when there is trapped air, as shown on the right.
Figure 2.6.: Fluid bulk modulous. Liquids are nearly incompressible (left), except when there is trapped air, as shown on the right.
Figure 2.7.: Pascal’ Law. Fluid at rest has same pressure everywhere and acts at righ angles against the walls.
Figure 2.7.: Pascal’ Law. Fluid at rest has same pressure everywhere and acts at righ angles against the walls.
Figure 2.10.: Force in a cylinder acting at 60 psi. goes up with the square of the bore. Force can be increased two ways, raising the pressure or increasing the bore of the cylinder. Force is proportional to pressure but goes as the square of the bore, which means small increases in cylinder size results in large increases in force. For example, consider a small pneumatic cylinder with a 7/16 in. bore running at 60 psi. This cylinder can push with 9 lbs of force. But, as shown in Figure 2.10, force goes up as bore squared and a 4 in. bore cylinder at the same 60 psi can push with 754 lbs of force. Of course the extra force does not come free. A larger cylinder requires a ~aanainas en lana Attia 4a wenn La lASaA bhaw & eemal law Reelin aw Laem siivr!
Figure 2.10.: Force in a cylinder acting at 60 psi. goes up with the square of the bore. Force can be increased two ways, raising the pressure or increasing the bore of the cylinder. Force is proportional to pressure but goes as the square of the bore, which means small increases in cylinder size results in large increases in force. For example, consider a small pneumatic cylinder with a 7/16 in. bore running at 60 psi. This cylinder can push with 9 lbs of force. But, as shown in Figure 2.10, force goes up as bore squared and a 4 in. bore cylinder at the same 60 psi can push with 754 lbs of force. Of course the extra force does not come free. A larger cylinder requires a ~aanainas en lana Attia 4a wenn La lASaA bhaw & eemal law Reelin aw Laem siivr!
Figure 2.12.: Laminar and turbulent flow through a pipe.
Figure 2.12.: Laminar and turbulent flow through a pipe.
Figure 2.13.: Moody Diagram showing the experimental friction factor for pipes.
Figure 2.13.: Moody Diagram showing the experimental friction factor for pipes.
Solution: The Sun Hydraulics DAAA valve is a 2-position, 2-way cartridge valve. When the solenoid is energized the valve switches from blocking the flow to a fully open flow. The data sheet is at www.sunhydraulics.com. Some of the key valve specs are: Max flow = .25 gpm (1 L/m), Max pressure = 5000 psi (350 bar), Response time = 30 ms. The figure below shows a photo of the valve, the valve schematic and the experimental pressure vs. flow character- istics for the valve in its open position. These are cartridge valves, designed to screw into a manifold with the solenoid on top.
Solution: The Sun Hydraulics DAAA valve is a 2-position, 2-way cartridge valve. When the solenoid is energized the valve switches from blocking the flow to a fully open flow. The data sheet is at www.sunhydraulics.com. Some of the key valve specs are: Max flow = .25 gpm (1 L/m), Max pressure = 5000 psi (350 bar), Response time = 30 ms. The figure below shows a photo of the valve, the valve schematic and the experimental pressure vs. flow character- istics for the valve in its open position. These are cartridge valves, designed to screw into a manifold with the solenoid on top.
ylinders convert fluid power pressure and flow to mechanical translationa ower force and velocity (Fig. 3.1). Cylinders are linear actuators that cai ush and pull, and when mounted around a joint, for example, as is don 1 an ecavator, can actuate rotary motion. Cylinders come in single actin: oush only), single acting with spring return and double-acting (push-pull he rest of the section will focus on double acting cylinders, which are mos ommon in hydraulic applications. ! A cutaway illustration of a typical double-acting cylinder used for indus
ylinders convert fluid power pressure and flow to mechanical translationa ower force and velocity (Fig. 3.1). Cylinders are linear actuators that cai ush and pull, and when mounted around a joint, for example, as is don 1 an ecavator, can actuate rotary motion. Cylinders come in single actin: oush only), single acting with spring return and double-acting (push-pull he rest of the section will focus on double acting cylinders, which are mos ommon in hydraulic applications. ! A cutaway illustration of a typical double-acting cylinder used for indus
Figure 3.2.: Cut-away view of a welded body, industrial double-acting hydraulic cylinder. Source: Hyco International
Figure 3.2.: Cut-away view of a welded body, industrial double-acting hydraulic cylinder. Source: Hyco International
gure 3.5.: Pumps, motors and their schematic symbols. The difference between the two symbols is the direction that the triangle is pointing; out for pumps, in for motors
gure 3.5.: Pumps, motors and their schematic symbols. The difference between the two symbols is the direction that the triangle is pointing; out for pumps, in for motors
3.11.: (a) Pushbutton hydraulic 4/2 valve. In the nominal position, the cylin- der is held in the retracted postion because supply line P is connected to the rod side. When the button is pushed, the rod extends because supply line P is now connected to the cap side. When the button is released, the valve spring returns the valve to the nominal position, re- tracting the rod. (b) Solenoid 4/3 valve with center closed position and spring return to center. A computer can control extension and retraction of the cylinder by actuating the valve solenoids. (c) Same as b, but with a continuously variable proportional valve.
3.11.: (a) Pushbutton hydraulic 4/2 valve. In the nominal position, the cylin- der is held in the retracted postion because supply line P is connected to the rod side. When the button is pushed, the rod extends because supply line P is now connected to the cap side. When the button is released, the valve spring returns the valve to the nominal position, re- tracting the rod. (b) Solenoid 4/3 valve with center closed position and spring return to center. A computer can control extension and retraction of the cylinder by actuating the valve solenoids. (c) Same as b, but with a continuously variable proportional valve.
Figure 3.12.: Accumulator and ISO symbol. During use, hydraulic oil picks up contaminating particles from wear of slid- ing metallic surface that add to residual contaminants from the oil manufac- turing process, rust from metal and polymer particles from seal wear. These dirt particles are tiny grit that cause additional abrasive wear. Clumps of par- ticles can clog tiny clearances in precision valves and cylinders and can lead to corrosion.
Figure 3.12.: Accumulator and ISO symbol. During use, hydraulic oil picks up contaminating particles from wear of slid- ing metallic surface that add to residual contaminants from the oil manufac- turing process, rust from metal and polymer particles from seal wear. These dirt particles are tiny grit that cause additional abrasive wear. Clumps of par- ticles can clog tiny clearances in precision valves and cylinders and can lead to corrosion.
Figure 3.13.: Hydraulic filter and ISO symbol.
Figure 3.13.: Hydraulic filter and ISO symbol.
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