Mechanical Engineers Handbook 2011 Part 11 doc

top and bottom of spool 1. The force of spring 2 and the difference in area between the top side and the bottom side of spool 1 will quickly move the spool 1 down and close the outlet port. Figure 2.15 shows another version of the compound-type relief valve. This valve is referred to as a balanced-piston-type relief valve. The operating functions in Fig. 2.15a are basically the same as those in Fig. 2.14. The main difference is in the method of ¯ow. From the pilot valve 2, oil is returned to the reservoir. The pilot drain D is a hole or ori®ce passing through the main spool 1 directly into the outlet port. This feature requires fewer hydraulic lines, but it also allows outlet back pressure to adversely affect pilot operations. It is important that the outlet lines be unrestricted to ensure Figure 2.15 Version of the compound-type relief valve. (a) Valve shown closed. (b) Compound relief valve with remote venting valve in use. Valve shown open or vented. 2. Hydraulics 589 Fluid Dynamics minimum back pressure. Ori®ce B in Fig. 2.15a is placed differently, as is the pilot valve. The port V in Fig. 2.15 offers a new method of control for the compound-type unit. If port V is allowed to be open to the atmosphere or, by a simple valve, to the reservoir, the pressure on the top side of the main spool 1 will be relieved and the spool will immediately move upward and open. This practice is called venting and offers an auxiliary or additional method of instantly relieving the system pressure without altering or affecting the unvented operating setting of the valve. A simple direct-operating relief valve, manually operated, will handle venting functions and further increase the ¯exibility of this unit's operation. Figure 2.15b shows a typical arrange- ment that allows manually controlled venting andaor automatic system pressure operation. The vent valve is small since it is required to handle minor volumes. 2.6.7 COMPOUND-TYPE SEQUENCE VALVES Figures 2.16a and 2.16b show the revised compound relief valve. Figure 2.16a illustrates the unit designated as the Y type. Since the outlet chamber becomes the secondary port exposed to the system pressure when the valve opens, an external bleed line E (Fig. 2.16a) must be used. The pilot chamber is no longer opened at the center ori®ce D of spool 1. The ori®ce D is now used to ensure complete hydraulic balance of spool 1 when the unit is in its sequenced position. The operation of the valve in Fig. 2.16a starts when the system pressure at the inlet port passing through ori®ce A reaches the level required to unseat pilot piston 3. The pressure drop through ori®ce A causes a reduced pressure in chamber B and allows spool 1 to move upward and open, the outlet or secondary port. Oil passing through ori®ce D in the center of spool 1 is now opened to system pressure, and the effective areas on both Figure 2.16 Compound-type sequence valve. (a) Type Y sequence valve. (b) Type X sequence valve. 590 Fluid Dynamics Fluid Dynamics sides of valve 1 are equal. The continued ¯ow and pressure drop through ori®ce A maintains a lower pressure in chamber B, the valve remaining open. In the event that the inlet pressure decreases, pilot piston 3 closes, the pressure in chamber B rises, and the valve closes. The valve presented in Fig. 2.16a is dependent on the system pressure at the point of operation. Figure 2.16b shows another modi®cation of the basic compound unit. This model is identi®ed as the X type. For this type an open passage between the pilot chamber and the top of spool 1 is used. The ori®ce D through the center of spool 1 is eliminated. Operation of the X type is different from any type previously discussed. The purpose of this design is to ®ll the main circuit of a system with oil before ¯ow to the outlet or secondary circuit is allowed. As the main circuit becomes full, the pressure rises at the inlet of Fig.2.16b. The ¯ow through ori®ce A causes the opening of pilot 3, and, as a result, spool 1 opens. As the valve opens, the full area of the bottom spool 1 is exposed to system pressure. Since the small guide area of the top side spool 1 is opened to the pilot drain chamber, the spool 1 is hydraulically unbalanced because of the differential area. It is required that the system pressure be suf®cient to overcome the very light force of spring 2 to remain open. This X type does not close until the system pressure has decreased nearly to zero. This valve's main purpose is therefore limited to controlling the sequence of ¯ow as a hydraulic system is put into operation. 2.6.8 PRESSURE-REDUCING VALVES A low-pressure, low-volume ¯ow in addition to the main system high- pressure, high-volume ¯ow is required by some hydraulic systems. The extra pump can be eliminated by the use of a pressure-reducing valve to supply the small ¯ow at reduced pressure. Figure 2.17 shows an X -model pressure-reducing valve. The X -valve combines the features of the direct-operated valve type with those of the compound-type valve. This valve incorporates a pilot 1 to control the action of the main spool 3, thus being a compound valve. The pressure-actuated spool 3 seals because of its close ®t to the main body and because of a sliding action that opens and closes the outlet or reduced-pressure port. As system ¯ow begins, the inlet is supplied with oil at the main pressure-control-valve setting. The ¯ow to the outlet or reduced-pressure port is transmitted through ori®ce C , which is a narrow space between the reduced-diameter section of spool 3 and the main body. The ¯uid under pressure passes through chamber D and exerts a force on the bottom area of spool 3. A very small ori®ce E carries the pressurized oil through the center of spool 3 into chamber A. The areas of both ends of spool 3 are equal and under the same pressure so that a state of hydraulic balance exists. Spool 3 is thus held down by the force of spring 4. Since a reduced pressure at the outlet is desired, pilot 1 is adjusted to open at a pressure considerably lower than the pressure available at ori®ce C . The ori®ce E has a smaller area than chamber 2. Hydraulics 591 Fluid Dynamics D, and the ¯ow of the oil from E to F causes a pressure drop. The pressure in chamber F and on the top of spool 3 is lower than the pressure in chamber D or the pressure on the bottom of spool 3. Hydraulic unbalance occurs now; spring 4 is overcome and spool 3 is moved upward. As spool 3 moves upward, ori®ce C is reduced in size, opposing the ¯ow, and a pressure drop is created between the inlet and outlet ports. Port C will thus be consistently changed to increase or decrease the resistance to the ¯ow in order to maintain a constant reduced pressure at the outlet. As the ¯ow from the outlet port increases in response to an increased low-pressure ¯ow demand, the spool will move downward and open ori®ce C . As ¯ow is diminished, ori®ce C will be closed. The maximum pressure available at the outlet is the sum of the forces of spring 2 and spring 4. This valve has three critical situations. Ori®ce E is very small and it can be very easily plugged by minute foreign bodies. A constant ¯ow through ori®ce E to the drain port of the pilot valve is needed to maintain a constant dependable reduced pressure. Ori®ce F must remain completely open. The pilot drain must have a free, unrestricted, unshared line to the reservoir. The ®nal critical area of this valve is the close tolerance required between spool 3 and the bore of the main body. 2.7 Flow-Limiting Controls 2.7.1 CHECK VALVES The simple check valve limits the ¯ow to one direction. Figure 2.18a shows a simple check valve of the right-angle type in closed position, in which the ¯ow from outlet to inlet is not allowed. A round poppet A is placed in the inlet port by the force of spring B. System pressure at the inlet port acts on the bottom of poppet A, compressing spring B, and opening the valve to Figure 2.17 Pressure- reducing valve. (a) Valve shown static. (b) Valve shown operating. 592 Fluid Dynamics Fluid Dynamics allow the ¯ow from inlet to outlet. The ori®ce C in poppet A serves as a drain for chamber D. It also exposes the top side of the poppet to the prevailing pressure of the outlet side when it is closed and of the inlet side when it is open. The system pressure need only overcome the force of spring B to hold the valve open. The pressure drop through this valve, from inlet to outlet, is thus equal to the force of spring B when the valve is properly sized with respect to ¯ow volume. Figure 2.18b shows the valve in the opened position. There are situations in hydraulic circuit design when it is desirable to have the automatic single-¯ow feature of the simple check valve for only a portion of the time and at any given time to be able to allow ¯ow in either direction. This situation occurs in working with load-lifting devices. The normal single-¯ow characteristic allows the load to be lifted at any time and automatically held. It is also required that the ability to lower the load be included in the design. A pilot-operated check valve will adequately perform this function. Figure 2.19 illustrates a pilot-operated check valve. In Fig. 2.19a, the check valve has a portion constructed in a manner similar to the simple check valve in Fig. 2.18. A pilot piston D with a stem E and a pilot pressure port for external connection have been added. Figure 2.19b shows the valve when inlet pressure is high enough to overcome the force of spring B. Pilot pressure is still 0 lbain 2 , and thus the inlet pressure acts on the top side of piston D and holds the pilot stem E downward. The valve acts as the conventional check valve in Figs. 2.19a and 2.19b. Let us assume that we need to have the ¯ow from the outlet port to the inlet port. A load has been lifted by allowing ¯ow from inlet to outlet, and that it is now time to lower the load. The application of an independent external pressure to the pilot port will move piston D upward, allowing ¯ow from outlet to inlet, thus lowering the Figure 2.18 Simple check valve. Right- angle check valve shown (a) closed and (b) open. 2. Hydraulics 593 Fluid Dynamics load. To maintain the valve in an opened position, the following relation is required: P P  D B b Fs B  P C  D T or F P b Fs B  F i because P  A  F where P p is the pilot pressure, D B is the bottom area D, F SB is the spring B force, P i is the inlet pressure, D T is the top area D, F P is the pilot force, and F i is the inlet force. Also P is the pressure, A is the area, and F is the force. 2.7.2 PARTIAL-FLOW-LIMITING CONTROLS For a hydraulic cylinder, the speed in one direction can be controlled if a simple needle valve is located in the exhaust port of the cylinder. This is referred to as a meter-out application. The exhaust pressure of a hydraulic cylinder is relatively stable and, thus, it maintains a reasonably accurate ¯ow rate control with a simple needle valve. Figure 2.20a shows a simple needle- valve meter-out control. The unit depicted in Fig. 2.20 has the additional feature of allowing the ¯ow to pass through a check valve B in one direction, thus being unaffected by the adjustment of the metering valve A. The metered ¯ow direction of these valves is usually indicated by an arrow on the external surface of the unit. A ®ne adjustment thread on the stem of valve A provides a precise control of the ¯ow. An adjustment of A is minor while the valve is subjected to system pressure. Excessive looseness of the locknut for valve A and excessive turning of valve A may damage the small valve seal. If large adjustments are needed, they are best accomplished at 0 lbain 2 . Figure 2.19 Pilot-operated check valve shown (a) closed and (b) with pilot actuated to allow constant ¯ow or reverse ¯ow. 594 Fluid Dynamics Fluid Dynamics The ¯ow control illustrated in Fig. 2.20d is far superior to those shown in Figs. 2.20a to 2.20c. The unit shown in Fig. 2.20d is adjustable at any time, even while under maximum pressure. 2.8 Hydraulic Pumps Although many hydraulic pumps and motors appear to be interchangeable in that they operate on the same principles and have similar parts, they often have design differences that make their performances better as either motors or pumps. Moreover, some motors have no pump counterparts. In this chapter only positive-displacement pumps are considered (those pumps that deliver a particular volume of ¯uid with each revolution of the input drive shaft). This terminology is used to distinguish them from centrifugal pumps and turbines. 2.8.1 GEAR PUMPS The simplest type of these pumps is the gear pump, shown in Fig. 2.21, in which the ¯uid is captured in the spaces between the gear teeth and the housing as the gears rotate. Flow volume is controlled by controlling the speed of the drive gear. Although these pumps may be noisy unless well designed, they are simple and compact. 2.8.2 GEROTOR PUMPS Another version of the gear pump is the gerotor, whose cross section is presented schematically in Fig. 2.22. The internal gear has one fewer tooth Figure 2.20 Single-needle valve ¯ow control. (a) Metered ¯ow in both directions. (b) Check valve for reverse ¯ow. (c) Reverse ¯ow check valve shown open. (d) Valve constructed to allow adjustment while under pressure. 2. Hydraulics 595 Fluid Dynamics than the external gear, which causes its axis to rotate about the axis of the external gear. The geometry is such that on one side of the internal gear the space between the inner and outer gerotor increases for one-half of each rotation and on the other side it decreases for the remaining half of the rotation. It consists of three basic parts: the ring, the outer gerotor, and the inner gerotor. The number of the teeth varies, but the outer gerotor always has one more tooth than the inner gerotor. The ®gure shows the two kidney-shaped ports, namely, the suction port and discharge port. The axis around which the inner element rotates is offset by the amount e from the axis of the outer gerotor, which, driven by the inner gerotor, rotates within the ring. Figure 2.21 Gear pump. Figure 2.22 Gerotor pump. 596 Fluid Dynamics Fluid Dynamics 2.8.3 VANE PUMPS Figure 2.23a shows the sketch of a vane pump. The drive shaft center line is displaced from the housing center line, having uniformly spaced vanes mounted in radial slots so that the vanes can move radially inward and outward to always maintain contact with the housing. Fluid enters through port plates, shown in Fig. 2.23b, at each end of the housing. The advantages of vane pumps over gear pumps are that they can provide higher pressures and variable output without the need to control the speed of the prime mover (electric motor, diesel engine, etc). The design modi®cation required for a variable volume output from a pump having a circular interior cross section is that of mounting the housing between end plates so that the axis of the cylinder in which the vane rotates may be shifted relative to the axis of the rotor, as shown in Fig. 2.24. The maximum ¯ow is obtained when they are displaced by the maximum distance (Fig. 2.24a), and zero ¯ow is obtained when the axis of the rotor and the housing tend to coincide (Fig. 2.24b). Figure 2.23 Vane pump. (a) Cross section shown schematically. (b) Port plate with inlet port and outlet port. 2. Hydraulics 597 Fluid Dynamics 2.8.4 AXIAL PISTON PUMP An axial piston pump is shown in Fig. 2.25. The major components are the swashplate, the axial pistons with shoes, the cylinder barrel, the shoeplate, the shoeplate bias spring, and the port plate. The shoeplate and the shoe- plate bias spring hold the pistons against the swashplate, which is held stationary while the cylinder barrel is rotated by the prime mover. The cylinder, the shoeplate, and the bias spring rotate with the input shaft, thus forcing the pistons to move back and forth in their respective cylinders in the cylinder barrel. The input and output ¯ows are separated by the stationary port plate with its kidney-shaped ports. Output volume may be controlled by changing the angle of the swashplate. As angle a between the normal to the swashplate and the axis of the drive shaft in Fig. 2.26b goes to zero, the ¯ow volume decreases. If angle a increases (Fig. 2.26a), the volume also increases. Axial piston pumps with this feature are known as overcenter axial piston pumps. 2.8.5 PRESSURE-COMPENSATED AXIAL PISTON PUMPS For these pumps the angle a of the swashplate is controlled by a spring- loaded piston that senses the pressure at a selected point in the hydraulic system. As the pressure increases, the piston can decrease a in an effort to decrease the system pressure, as illustrated in Fig. 2.26b. Pressure compensa- tion is often used with overcenter axial piston pumps in hydrostatic transmis- sions to control the rotational speed and direction of hydraulic motors. 2.9 Hydraulic Motors Hydraulic motors differ from pumps because they can be designed to rotate in either direction, can have different seals to sustain high pressure at low rpm, or can have different bearings to withstand large transverse loads so Figure 2.24 Cross-sectional schematic variable vane pump (a) for maximum ¯ow, and (b) for minimum ¯ow. 598 Fluid Dynamics Fluid Dynamics [...]... terms of their ability to entrap these particles by means of a b value The symbol b is immediately followed by a number that denotes the diameter of the particles involved according to the relation Fluid Dynamics bd ˆ Number of particles of diameter d upstream from filter X Numbers of particles of diameter d downstream from the filter Most ¯uid ®lters are not rated for particles less than 3 mm; b may be... Flow Wiley & Sons, New York, 1977 10 W G Holzbock, Hydraulic Power and Equipment Industrial Press, New York, 1968 11 L S McNickle, Jr., Simpli®ed Hydraulics McGraw-Hill, New York, 1966 Fluid Dynamics 9 Control MIRCEA IVANESCU Department of Electrical Engineering, University of Craiova, Craiova 110 0, Romania Inside 1 Introduction 1.1 612 A Classic Example 2 Signals 614 3 Transfer Functions 3.1 3.2 613 616... return line, but with the risk of damaging the ®lter by forcing large particles through it A pilotoperated check valve may be used to bypass a clogged ®lter, but at the expense of circulating foreign matter that should have been ®ltered out Another alternative is to stop the system when the pressure across a ®lter exceeds a limiting value Particulate matter is described in terms of its largest dimension... coupling The schematic principle of operation of an Oldham coupling is presented in Fig 2.28 The main parts are the end plate 1, coupling plate 2, and block 3, which contains the pistons and the eccentric Fluid Dynamics Axial piston pump (a) Overcenter axial pump without drive shaft shown (b) Basic parts for axial piston pump 600 Figure 2.26 Fluid Dynamics Simpli®ed schematic of the operation of the... pf …2X17† where the value of n is given in Fig 2.30 and b is an experimentally measured factor given by b ˆ 1X24Y for bladder-type accumulators b ˆ 1X11Y for piston-type accumulators 2.12 Fluid Power Transmitted For calculating the power transmitted to a particular unit, it is necessary to know the functional formula for power, …2X18† where F is the force, and v is the velocity The force F can be written... Supplementary Zero 656 Effects of the Supplementary Pole 660 Effects of Supplementary Poles and Zeros 661 Design Example: Closed-Loop Control of a Robotic Arm 664 11 Design of Closed-Loop Control Systems by Frequential Methods 12 State Variable Models 669 672 611 612 Control Control 13 Nonlinear Systems 13.1 13.2 13.3 13.4 13.5 678 Nonlinear Models: Examples 678 Phase Plane Analysis 681 Stability of Nonlinear... Variable Structure Systems 700 A Appendix A.1 A.2 A.3 A.4 691 695 703 Differential Equations of Mechanical Systems The Laplace Transform 707 Mapping Contours in the s-Plane 707 The Signal Flow Diagram 712 703 References 714 T his chapter, ``Control,'' is an introduction to automation for technical students and engineers who will install, repair, or develop automatic systems in an industrial environment... 614 Control Control water level measured by a ¯oat that controls, by a mechanical system, the valve that, in turn, controls the water ¯ow out of the tank The plant is represented by the water tank, and the water ¯owing into the tank represents a disturbance of the system If the water level increases, the ¯oat moves up and, by a mechanical system representing the controller, initiates the opening of... …s† Y1 …s† ˆ X Xi …s† 1 ‡ Y1 …s† Á Y2 …s† …4X9† Relation (4.9) is particularly important because it represents the closed-loop transfer function (d) Complex connection: A complex structure can contain a number of variables under control This system can be described by a set of equations represented as Laplace transforms: X01 …s† ˆ Y11 …s† Á Xi1 …s† ‡ Y12 …s† Á Xi2 …s† ‡ Á Á Á ‡ Y1m …s† Á Xim …s† X02... 2 Hydraulics Figure 2.28 Front and side views of plates 1 and 2 and the block, which provides an Oldham coupling relation portion of the shaft Slot a is cut into plate 1 and accepts track A, which is part of plate 2 Track B is perpendicular to track A and is located on the opposite side of plate 2 from track A Slot b is cut into the block and accepts track B Thus, any displacement of the block relative . entrap these particles by means of a b value. The symbol b is immediately followed by a number that denotes the diameter of the particles involved according to the relation b d  Number of particles.  1X24Y for bladder-type accumulators b  1X11Y for piston-type accumulators 2.12 Fluid Power Transmitted For calculating the power transmitted to a particular unit, it is necessary to know the. principles and have similar parts, they often have design differences that make their performances better as either motors or pumps. Moreover, some motors have no pump counterparts. In this chapter