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附錄 英文原文 Talking About The Design of Hydraulic Conductors Eric Sandgren This paper is account for uncertainty Mechanical Engineering, University of California, San Francisco, avialon 503 West Main Street, P .O. Box962531 1.1 INTRODUCTION In a hydraulic system, the fluid flows through a distribution system consisting of conductors and fittings, which carry the fluid from the reservoir through operating components and back to the reservoir. Since power is transmitted throughout the system by means of these conducting lines (conductors and fittings used to connect system components), it follows that they must be properly designed in order for the total system to function properly. The choice of which type of conductor to use depends primarily on the system’s operating pressures and flow rates. In addition, the selection depends on environmental conditions such as the type of fluid, operating temperatures, vibration, and whether or not there is relative motion between connected components. Conducting lines are available for handling work pressures up to 10,000 Pa or greater. In general, steel tubing provides greater plumbing flexibility and neater appearance and requires fewer fittings than piping. However, piping is less expensive than steel tubing. Plastic tubing is finding increased industrial usage because it is not costly and circuits can be very easily hooked up due to its flexibility. Flexible hoses are used primarily to connect components that experience relative motion. They are made from a large number of elastomeric (rubberlike) compounds and are capable of handling pressures exceeding 10,000 Pa. Stainless steel conductors and fittings are used if extremely corrosive environments are expected. However, they are very expensive and should be used only if necessary. Copper conductors should not be used in hydraulic systems because the copper promotes the oxidation of petroleum oils. Zinc, magnesium, and cadmium conductors should not be used either because they are rapidly corroded by water-glycol fluids. Galvanized conductors should also be avoided because the galvanized surface has a tendency to flake off into the hydraulic fluid. When using steel pipe or steel tubing, hydraulic fittings should be made of steel except for inlet, return, and drain lines, where malleable iron may be used. Conductors and fittings must be designed with human safety in mind. They must be strong enough not only to withstand the steady-state system pressures but also the instantaneous pressure spikes resulting from hydraulic shock. Whenever control valves are closed suddenly, this stops the fluid, which possesses large amounts of kinetic energy. This produces shock waves whose pressure levels can be two or four times the steady-state system design values. Pressure spikes can also be caused by sudden stopping or starting of heavy loads. These high-pressure pulses are taken into account by the application of an appropriate factor of safety. 1.2 CONDUCTOR SIZING FOR FLOW-RATE REQUIREMENTS A conductor must have a large enough cross-sectional area to handle the flow-rate requirements without producing excessive fluid velocity. Whenever we speak of fluid velocity in a conductor such as a pipe, we are referring to the average velocity. The concept of average velocity is important since we know that the velocity profile is not constant. As shown in Chapter 5 the velocity is zero at the pipe wall and reaches a maximum value at the centerline of the pipe. The average velocity is defined as the volume flow rate divided by the pipe cross-sectional area: In other words, the average velocity is that velocity which when multiplied by the pipe area equals the volume flow rate. It is also understood that the term diameter by itself always means inside diameter and that the pipe area is that area that corresponds to the pipe inside diameter. The maximum recommended velocity for pump suction lines is 4 ft/s (1.2 m/s) in order to prevent excessively low suction pressures and resulting pump cavitation. The maximum recommended velocity for pressure lines is 20 ft/s (6.1 m/s) in order to prevent turbulent flow and the corresponding excessive head losses and elevated fluid temperatures. Note that these maximum recommended values are average velocities. EXAMPLE 1-1 A pipe handles a flow rate of 30 gprn. Find the minimum inside diameter that will provide an average fluid velocity not to exceed 20 ft/s. Solution Rewrite Eq. (3-26), solving for D: EXAMPLE 1-2 A pipe handles a flow rate of 0.002. Find the minimum inside diameter that will provide an average fluid velocity not to exceed 6.1 m/s. Solution Per Eq. 3-35) we solve for the minimum required pipe flow area: The minimum inside diameter can now be found, becauseSolving for D we have 1.3 PRESSURE RATING OF CONDUCTORS A conductor must be strong enough to prevent bursting due to excessive tensile stress (called hoop stress) in the wall of the conductor under operating fluid pressure. The magnitude of this tensile stress, which must be sustained by the conductor material. we see the fluid pressure ( P ) acting normal to the inside surface of a circular pipe having a length (L). The pipe has outside diameter D0 , inside diameter Di, and wall thickness t. Because the fluid pressure acts normal to the pipe’s inside surface, a pressure force is created that attempts to separate one half of the pipe from the other half. Figure shows this pressure forcepushing downward on the bottom half of the pipe. To prevent the bottom half of the pipe from separating from the upper half, the upper half pulls upward with a total tensile force F. One-half of this force ( or F/2 ) acts on the cross-sectional area (tL) of each wall, as shown. Since the pressure force and the total tensile force must be equal in magnitude, we have where A is the projected area of the lower half-pipe curved-wall surface onto a horizontal plane. Thus, A equals the area of a rectangle of width Di and length L, as shown in Figure 4-1(b). Hence, The tensile stress in the pipe material equals the tensile force divided by the wall cross-sectional area withstanding the tensile force. This stress is called a tensile stress because the force (F) is a tensile force (pulls on the area over which it acts). Substituting variables we have where = Greek symbol (sigma) = tensile stress. As can be seen from Eq. the tensile stress increases as the fluid pressure increases and also as the pipe inside diameter increases. In addition, as expected, the tensile stress increases as the wall thickness decreases, and the length of the pipe does not have any effect on the tensile stress. Burst Pressure and Working Pressure The burst pressure (BP) is the fluid pressure that will cause the pipe to burst. This happens when the tensile stress () equals the tensile strength ( S ) of the pipe material. The tensile strength of a material equals the tensile stress at which the material ruptures. Notice that an axial scribe line is shown on the pipe outer wall surface in Fig. 4-1(a). This scribe line shows where the pipe would start to crack and thus rupture if the tensile stress reached the tensile strength of the pipe material. This rupture will occur when the fluid pressure (P) reaches BR Thus, from Eq. (4-2) the burst pressure is The working pressure (WP) is the maximum safe operating fluid pressure and is defined as the burst pressure divided by an appropriate factor of safety (FS). A factor of safety ensures the integrity of the conductor by determining the maximum safe level of working pressure. Industry standards recommend the following factors of safety based on corresponding operating pressures: FS = 8 for pressures from 0 to 1000 Pa FS = 6 for pressures from 1000 to 2500 Pa FS = 4 for pressures above 2500 Pa For systems where severe pressure shocks are expected, a factor of safety of 10 is recommended. Conductor Sizing Based on Flow Rate and Pressure Considerations The proper size conductor for a given application is determined as follows: 1. Calculate the minimum acceptable inside diameter (Di) based on flow-rate requirements. 2. Select a standard-size conductor with an inside diameter equal to or greater than the value calculated based on flow-rate requirements. 3. Determine the wall thickness (t) of the selected standard-size conductor using the following equation: 4. Based on the conductor material and system operating pressure (P), determine the tensile strength (S) and factor of safety (FS). 5. Calculate the burst pressure (BP) and working pressure (WP) using Eqs. (4-3) and (4-4). 6. If the calculated working pressure is greater than the operating fluid pressure, the selected conductor is acceptable. If not, a different standard-size conductor with a greater wall thickness must be selected and evaluated. An acceptable conductor is one that meets the flow-rate requirement and has a working pressure equal to or greater than the system operating fluid pressure. The nomenclature and units for the parameters of Eqs. BP = burst pressure (Pa, MPa) Di = conductor inside diameter (in., m) D0 = conductor outside diameter (in., m) FS = factor of safety (dimensionless) P = system operating fluid pressure (Pa, MPa) S = tensile strength of conductor material (Pa, MPa) t = conductor wall thickness (in., m) WP = working pressure (Pa, MPa) = tensile stress (Pa, MPa) EXAMPLE 1-3 A steel tubing has a 1.250-in, outside diameter and a 1.060-in, inside diameter. It is made of SAE 1010 dead soft cold-drawn steel having a tensile strength of 55.000 Pa. What would he the safe working pressure for this tube assuming a factor of safety of 8? Solution First, calculate the wall thickness of the tubing: Next, find the burst pressure for the tubing: Finally, calculate the working pressure at which the tube can safely operate: Use of Thick-Walled Conductors Equations and apply only for thin-walled cylinders where the ratio Di / t is greater than 10. This is because in thick-walled cylinders (Di / t 10), the tensile stress is not uniform across the wall thickness of the tube as assumed in the derivation of Eq. (4-2). For thick-walled cylinders Eq. (4-6) must be used to take into account the nonuniform tensile stress, Thus, if a conductor being considered is not a thin-walled cylinder, the calculations must be done using Eq. (4-6). As would be expected, the use of Eq. (4-6) results in a smaller value of burst pressure and hence a smaller value of working pressure than that obtained from Eq. (4-3). This can be seen by comparing the two equations and noting the addition of the 1.2t term in the denominator of Eq. (4-6). Note that the steel tubing of Example 4-3 is a thin-walled cylinder because = 1.060 in./0.095 in. =11.2 > 10. Thus, the steel tubing of Example 4-3 can operate safely with a working pressure of 1230 Pa as calculated using a factor of safety of 8. Using Eq. (4-6) for this same tubing and factor of safety yields As expected the working pressure of 1110 Pa calcu1ated using Eq. (4-6) is less than the 1230 Pa value calculated in Example 4-3 using Eq. (4-3). 1.4 STEEL PIPES Size Designation Pipes and pipe fittings are classified by nominal size and schedule number, as illustrated in Fig. 4-2. The schedules provided are 40, 80, and 160, which are the ones most commonly used for hydraulic systems. Note that for each nominal size the outside diameter does not change. To increase wall thickness the next larger schedule number is used. Also observe that the nominal size is neither the outside nor the inside diameter. Instead, the nominal pipe size indicates the thread size for the mating connections. The pipe sizes given in Fig. 4-2 are in units of inches. Figure 4-3 shows the relative size of the cross sections for schedules 40, 80, and 160 pipes. As shown for a given nominal pipe size, the wall thickness increases as the schedule number increases. Thread Design Pipes have tapered threads, as opposed to tube and hose fittings, which have straight threads. As shown in Fig. 4-4, the joints are sealed by an interference fit between the male and female threads as the pipes are tightened. This causes one of the major problems in using pipe. When a joint is taken apart, the pipe must be tightened farther to reseal. This frequently requires replacing some of the pipe with slightly longer sections, although this problem has been overcome somewhat by using Teflon tape to reseal the pipe joins. Hydraulic pipe threads are the dry-seal type. They differ from standard pipe threads because they engage the roots and crests before the flanks. In this way, spiral clearance is avoided. Pipes can have only male threads, and they cannot be bent around obstacles. There are, of course, various required types of fittings to make end connections and change direction, as shown in Fig. 4-5. The large number of pipe fittings required in a hydraulic circuit presents many opportunities for leakage, especially as pressure increases. Threaded-type fittings are used in sizes up to in. in diameter. Where larger pipes are required, flanges are welded to the pipe, as illustrated in Fig. 4-6. As shown, flat gaskets or 0-rings are used to seal the flanged fittings. 1.5 STEEL TUBING Size Designation Seamless steel tubing is the most widely used type of conductor for hydraulic systems as it provides significant advantages over pipes. The tubing can be bent into almost any shape, thereby reducing the number of required fittings. Tubing is easier to handle and can be reused without any sealing problems. For low-volume systems, tubing can handle the pressure and flow requirements with less bulk and weight. However, tubing and its fittings are more expensive. A tubing size designation always refers to the outside diameter. Available sizes include-in. increments from -in. outside diameter up to -in. outside diameter. For sizes from-in. to 1 in. the increments are -in. For sizes beyond 1 in., the increments are-in. Figure 4-7 shows some of the more common tube sizes (in units of inches) used in fluid power systems. SAE 1010 dead soft cold-drawn steel is the most widely used material for tubing. This material is easy to work with and has a tensile strength of 55,000 Pa. If greater strength is required, the tube can be made of AISI 4130 steel, which has a tensile strength of 75,000 Pa. Tube Fittings Tubing is not sealed by threads but by special kinds of fittings, as illustrated in Fig. 4-8. Some of these fittings are known as compression fittings. They seal by metal-to-metal contact and may be either the flared or flareless type. Other fittings may use 0-rings for sealing purposes. The 370 flare fitting is the most widely used fitting for tubing that can be flared. The fittings shown in Fig. seal by squeezing the flared end of the tube against a seal as the compression nut is tightened. A sleeve inside the nut supports the tube to dampen vibrations. The standard 450 flare fitting is used for very high pressures. It is also made in an inverted design with male threads on the compression nut. When the hydraulic component has straight thread ports, straight thread 0-ring fittings can be used, as shown in Fig. 4-8(c). This type is ideal for high pressures since the seal gets tighter as pressure increases. Two assembly precautions when using flared fittings are: 1. The compression nut needs to be placed on the tubing before flaring the tube. 2. These fittings should not be over-tightened. Too great a torque damages the sealing surface and thus may cause leaks. For tubing that can’t be flared, or if flaring is to be avoided, ferrule, 0-ring, or sleeve compression fittings can be used [see Fig. 4-8(d), (e), (f)]. The O-ring fitting permits considerable variations in the length and squareness of the tube cut. Figure 4-9 shows a Swagelok tube fitting, which can contain any pressure up to the bursting strength of the tubing without leakage. This type of fitting can be repeatedly taken apart and reassembled and remain perfectly sealed against leakage. Assembly and disassembly can be done easily and quickly using standard tools. In the illustration, note that the tubing is supported ahead of the ferrules by the fitting body. Two ferrules grasp tightly around the tube with no damage to the tube wall. There is virtually no constriction of the inner wall, ensuring minimum flow restriction. Exhaustive tests have proven that the tubing will yield before a Swagelok tube fitting will leak. The secret of the Swagelok fitting is that all the action in the fitting moves along the tube axially instead of with a rotary motion. Since no torque is transmitted from the fitting to the tubing, there is no initial strain that might weaken the tubing. The double ferrule interaction overcomes variation in tube materials, wall thickness, and hardness. In Fig. 4-10 we see the 450 flare fitting. The flared-type fitting was developed before the compression type and for some time was the only type that could successfully seal against high pressures. Four additional types of tube fittings are depicted in Fig. 4-11: (a) union elbow, (b) union tee, (c) union, and (d) 45° male elbow. With fittings such as these, it is easy to install steel tubing as well as remove it for maintenance purposes. EXAMPLE 1-4 Select the proper size steel tube for a flow rate of 30 gpm and an operating pressure of 1000 Pa. The maximum recommended velocity is 20 ft/s, and the tube material is SAE 1010 dead soft cold-drawn steel having a tensile strength of 55,000 Pa, Solution The minimum inside diameter based on the fluid velocity limitation of 20 ft/s is the same as that found in Example 4-1 (0.782 in.). From Fig. 4-7, the two smallest acceptable tube sizes based on flow-rate requirements are 1-in. od , 0.049-in, wall thickness, 0.902-in. ID 1-in. od , 0.065-in, wall thickness, 0,870-in. ID Let’s check the 0.049-in, wall thickness tube first since it provides the smaller velocity: This working pressure is not adequate, so let’s next examine the 0.065-in, wall thickness tube: This result is acceptable, because the working pressure of 1030 Pa is greater than the system-operating pressure of 1000 Pa and10. 1.6 PLASTIC TUBING Plastic tubing has gained rapid acceptance in the fluid power industry because it is relatively inexpensive. Also, it can be readily bent to fit around obstacles, it is easy to handle, and it can be stored on reels. Another advantage is that it can be color-coded to represent different parts of the circuit because it is available in many colors. Since plastic tubing is flexible, it is less susceptible to vibration damage than steel tubing. Fittings for plastic tubing are almost identical to those designed for steel tubing. In fact many steel tube fittings can be used on plastic tubing, as is the case for the Swagelok fitting of Fig. 4-9. In another design, a sleeve is placed inside the tubing to give it resistance to crushing at the area of compression, as illustrated in Fig. 4-12. In this particular design (called the Poly-Flo Flareless Tube Fitting), the sleeve is fabricated onto the fitting so it cannot be accidentally left off. Plastic tubing is used universally in pneumatic systems because air pressures are low, normally less than 100 Pa. Of course, plastic tubing is compatible with most hydraulic fluids and hence is used in low-pressure hydraulic applications. Materials for plastic tubing include polyethylene, polyvinyl chloride, polypropylene, and nylon. Each material has special properties that are desirable for specific applications. Manufacturers’ catalogs should be consulted to determine which material should be used for a particular application. 1.7 FLEXIBLE HOSES Design and Size Designation The fourth major type of hydraulic conductor is the flexible hose, which is used when