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CHAPTER 60 HYDRAULIC SYSTEMS Hugh R. Martin University of Waterloo Waterloo, Ontario, Canada 60.1 HYDRAULIC FLUIDS 1831 60.8 SYSTEM CLASSIFICATIONS 1847 60.2 CONTAMINATIONCONTROL 1832 60.9 PUMP SETS AND ACCUMULATORS 1847 60.3 POSITIVEASPECTSOF CONTAMINATION HYDROSTATIC TRANSMISSIONS 1851 CONCEPT OF FEEDBACK CONTROL IN HYDRAULICS 1852 60.12 IMPROVEDMODEL 1854 60.13 ELECTROHYDRAULIC SYSTEMS—ANALOG 1856 ELECTROHYDRAULIC SYSTEMS—DIGITAL 1860 60.4 60.5 60.6 60.7 60.1 DESIGN EQUATIONSORIFICES AND VALVES 1833 1834 DESIGN EQUATIONS—PIPES AND FITTINGS 1835 HYDROSTATICPUMPSAND MOTORS 1838 STIFFNESS IN HYDRAULIC SYSTEMS 1843 60.10 60.11 60.14 HYDRAULIC FLUIDS One of the results of the study of fluid mechanics has been the development of the use of hydraulic oil, a so-called incompressible fluid, for performing useful work. Fluids have been used to transmit power for many centuries, the most available fluid being water. While water is cheap and usually readily available, it does have the distinct disadvantages of promoting rusting, of freezing to a solid, and of having relatively poor lubrication properties. Mineral oils have provided superior properties. Much of the success of modern hydraulic oils is due to the relative ease with which their properties can be altered by the use of additives, such as rust and foam inhibitors, without significantly changing fluid characteristics. Although hydraulic oil is used mainly to transmit fluid power, it must also 1) provide lubrication for moving parts, such as spool valves, 2) absorb and transfer heat generated within the system, and 3) remain stable, both in storage and in use, over a wide range of possible physical and chemical changes. It is estimated that 75% of all hydraulic equipment problems are directly related to the improper use of oil in the system. Contamination control in the system is a very important aspect of circuit design. In certain industries, such as mining and nuclear power, it is critically important to control the potential for fire hazards. Hence, fire-resistant fluids have been playing an ever-increasing role in these types of industry. The higher pressure levels in modern fluid power circuits have made fire hazards more serious when petroleum oil is used, since a fractured component or line will result in a fine mist of oil that can travel as far as 40 ft and is readily ignited. The term fire-resistant fluid Reprinted with permission from J. A. Schetz and A. E. Fuhs (eds.), Handbook of Fluid Dynamics and Fluid Machinery. © 1996 John Wiley & Sons, Inc. Mechanical Engineers' Handbook, 2nd ed., Edited by Myer Kutz. ISBN 0-471-13007-9 © 1998 John Wiley & Sons, Inc. (FRF) generally relates to those liquids that fall into two broad classes: a) those where water provides the fire resistance, and b) those where a fire retardant is inherent in the chemical structure.1"4 Fluids in the first group are water/glycol mixtures, water in oil emulsions (40-50% water), and oil in water emulsions (5-15% water). The second group are synthetic materials, in particular chlorinated hydrocarbons and phosphate esters. A disadvantage with water-based fluids is that they are limited to approximately 50-6O0C operating temperature because of evaporation. The high vapor pressure indicates this group is more prone to cavitation than mineral oils. Synthetic fluids such as the phosphate esters do not have this problem and also have far superior lubrication properties. Some typical characteristics of these various types of fluids are shown in Table 60.1. Of all the physical properties that can be listed for hydraulic fluids, the essential characteristics of immediate interest to a designer are 1) bulk modulus, to assess system rigidity and natural frequency, 2) viscosity, to assess pipe work and component pressure losses, 3) density, to measure flow and pressure drop calculations, and 4) lubricity, to determine threshold and control accuracy assessments. The first three items are discussed in separate sections, as they relate directly to circuit design. Lubricity, the final item, is difficult to define, as it is very much a qualitative judgment. Lubricity affects the performance of a system, since it is a major factor in determining the level of damping in the system, that is, viscous or velocity-dependent damping. It also affects the accuracy of operation of a system because of its influence on the other type of friction, coulomb friction, which is velocityindependent. Oil film strength is often referred to as the anti-wear value of a lubricant, which is the ability of the fluid to maintain a film between moving parts and thus prevent metal-to-metal contact. These characteristics are important for the moving parts in valves, cylinders, and pumps.5 60.2 CONTAMINATION CONTROL There is little doubt that component failure or damage due to fluid contamination is an area of major concern to both the designer and user of fluid power equipment. Sources of contamination in fluid power equipment are many. Although oil is refined and blended under relatively clean conditions, it does accumulate small particles of debris during storage and transportation. It is not unusual for hydraulic oil circulating in a well maintained hydraulic circuit to be cleaner than that from a newly purchased drum. New components and equipment invariably have a certain amount of debris left from the manufacturing process, in spite of rigorous post-production flushing of the unit. The contaminant level in a system can be increased internally due to local burning (oxidation) of oil to create sludges. This can be a result of running the oil temperature too high (normally 40-6O0C is recommended) or due to local cavitation in the fluid. The trend towards the use of higher system pressures in hydraulics generally results in narrower clearances between mating components. Under such design conditions, quite small particles in the range of 2-20 microns can block moving surfaces. Extensive work on contamination classification has been carried out by Fitch and his co-workers.6 To take a specific example, consider the piston pump shown in Fig. 60.1. Component parts of the pump are loaded towards each other by forces generated by the pressure, and this same pressure always tends to force oil through the adjacent clearance. The life of the pump is related to the rate at which a relatively small amount of material is being worn away from a few critical surfaces. It is logical to assume, therefore, if the fluid in a clearance is contaminated with particles, rapid degradation and eventual failure can occur. Although the geometric clearances are fixed, the actual clearances vary with eccentricity due to load and viscosity variations. Some typical clearances between moving parts are shown in Table 60.2. Contamination control is the job of filtration. System reliability and life are related not only to the contamination level but also to contaminant size ranges. To maintain contaminant levels at a magnitude compatible with component reliability requires both the correct filter specification and suitable placement in the circuit. Filters can be placed in the suction line, pressure line, return line, Table 60.1 Comparison of Some Hydraulic Fluids Property Density (38 C) Viscosity (38 C) (99C) Bulk modulus (38 C and 34.5 MPa) Vapor pressure Units 3 kg m~ In 2 S- 1 Nm~2 kPa (abs) FRF (Ester) Mineral Oil Water in Oil 1136.0 4.6 x 10~6 4.9 x 10~6 2.25 x 109 858.2 4.0 x 10~5 5.8 X IQ-6 1.38 x 109 980.0 0.15 x IQ-5 6 x 10~5 6 x 10-5 2.18 X 109 1.0 Fig. 60.1 Piston pump clearances. or in a partial flow mode. To use a broad approach of just inserting a filter with a very low rating is unsatisfactory from the aspects of both cost and high pressure loss. The optimization of choice can be approached using simple computer modeling, as described by Foord.7 Dirt in hydraulic systems consists of many different types of material, ranging in size from less than 1 micron to greater than 100 microns. Since most general industrial hydraulics operating below 14 MPa are able to tolerate particles up to 25 microns, a 25-micron-rated filter is satisfactory. Equipment operating at pressures in the 14-21 MPa range should have 10-15-micron-rated filters, while high pressure pumps and precision servo valves need 5 micron-rated filtration. A good practical reference for filter selection has been written by Spencer.8 The size distribution of particles is of course random, and, generally speaking, the smaller the size range the greater the number of particles per 100 ml of fluid. Filters are not capable of removing all the contaminants, but for example, a 10-micron filter is one capable of removing about 98% of all particles exceeding 10 microns of a standard contaminant in a given concentration of prepared solution. 60.3 POSITIVE ASPECTS OF CONTAMINATION Contamination buildup in a system can be used as a diagnostic tool. Regular sampling of the oil and examination of the particles can often give a clue to potential failure of components. In other words, this is a preventive maintenance tool. Many methods can be used for this type of examination, such as spectrochemical9 or Ferrographic10 methods. Sampling of the oil can be taken at any time and does not interfere with the operation of the equipment. Table 60.3 shows the normally expected contaminant levels in parts per million (ppm); levels rising above these values and particularly rates of change of levels are indicative of potential failures. Table 60.2 Typical Clearances in Pumps Component Spool to sleeve in valve Gear pump tip to casing Piston to bore Valve plate to body of pump Clearance Range (micron) 1-10 diametrical 0.5-5 5-40 0.5-5 Table 60.3 Material Iron Chromium Aluminum Copper Lead Tin Silver Nickel Silicon Sodium Some Typical Normal Contaminant Levels Source in System Max Level (ppm) Bearings, gears, or pipe rust. Pistons and valve wear. Alloyed with bearing steel Air cooler equipment Bronze or brass in bearings. Connectors. Oil temperature sensor bulb. Cooler core tubes. Usually alloyed with copper or tin. Bearing cage metal. Bearing cages and retainers Cooling tube solder Bearing steel alloy Seals; dust and sand from poor filter or air leak Possible coolant leak into hydraulic oil 20 4 10 30 20 15 3 4 9 50 The Ferrographic technique allows the separation of wear debris and contaminants from the fluid and allows arrangement as a transparent substrate for examination. When wear particles are precipitated magnetically, virtually all nonmagnetic debris is eliminated. The deposited particles deposit according to size and may be individually examined. By this method it is possible to differentiate cutting wear, rubbing wear, erosion, and scuffing by the size and geometry of the particles. However, the Ferrographic method is expensive compared to other methods of analysis.11 60.4 DESIGN EQUATIONS—ORIFICES AND VALVES The main controlling element in any hydraulic circuit is the orifice. The fluid equivalent of the electrical resistance, it can be fixed in size or can be variable, in the case of a spool valve. The orifice in its various configurations is also the main source of heat generation, resulting in the need for cooling techniques and a major source of noise. The orifice equation is developed from Bernoulli's energy balance approach, which results in the following relationship:12 e= CCCVA0 /2Cp11 - pvc) ~rm^^^ V V A11 / where Q = volume flow rate, m 3 /s A0 = orifice area, m2 A11 = upstream area, m2 pu = upstream static pressure, Pa pvc = static pressure at Vena contracta, Pa Cc = contraction coefficient Cv = velocity coefficient p — mass density of hydraulic fluid, kg/m 3 These parameters are shown in Fig. 60.2, together with the static pressure distribution on either side of a sharp-edged orifice. Experimental measurements show that the actual flow is about 60% of that given by Bernoulli's equation. Hence, the need for the contraction and velocity coefficients. This results in the practical form of Eq. (60.1) for typical industrial hydraulic oil Q = 3.12 X IQ-2A0Vp14 - / ^ m V 1 (60.2) The symbols have the same definition as those for Eq. (60.1). The adequacy of Eq. (60.2) is demonstrated in Table 60.4. In the case of a variable orifice, such as that found in a spool-type valve, the orifice area is a variable. In fact, it can be seen from Fig. 60.3 that the exposed area available for oil flow is part of a circle. If the orifice, in this case called a control orifice or port, is of radius r and the spool displacement from the closed position is jc, then the uncovered area is Vena contracta v Arbitrary downstream pressure tap position Cavitation effect Vena contracta Fig. 60.2 Static pressure distribution. A0 = [O- cos (0/2)] f yj (60.3) 6 = 2 COS^1 [1 - (xlr)} (60.4) The area displacement characteristic plotted in Fig. 60.3 shows the nonlinear nature of the curve. One of the significant differences between the theoretical valve and the practical valve is the lap. It is not economical to produce zero lapped valves, so that only at the center position is the flow through the valve zero. Normally, the valve is either overlapped or underlapped, as shown in Fig. 60.4. An overlapped valve saves fluid loss when the spool is central. This is fine for directional control valves, but it produces both accuracy and stability problems if the valve is a precision control valve within a closed-loop configuration. An underlapped valve gives much better control and stability, at the expense of a higher leakage rate (power loss). Many more details of valve design can be found in Martin and McCloy.12 60.5 DESIGN EQUATIONS—PIPES AND FITTINGS While orifices serve the important function of controlling flow in the system, pipes and fittings are necessary to transmit fluid power from the input (usually a pump) to the output (usually a ram or motor). It is important to minimize losses through these conductors as well as through other com- Table 60.4 Comparing Experimental Data to Predictions of Eq. (60.2) Supply Pressure = 13.78 MPa Valve overlap = ±0.0127 mm Valve Displacement (mm) Calculated Flow (ml /sec) +0.3810 +0.3048 +0.2540 +0.2032 +0.1270 +0.0508 +0.0254 Center -0.0254 -0.0508 -0.1270 -0.2032 -0.2540 -0.3048 -0.3810 104.140 56.088 40.180 20.172 4.920 1.968 O 1.968 4.920 20.172 40.180 56.088 Measured Flow (ml /sec) 79.540 59.860 45.264 24.272 6.560 0.820 O 0.820 4.264 20.992 41.000 58.384 76.588 104.14 Fig. 60.3 Effective exposed orifice area for a spool-type valve. Fig. 60.4 Characteristics of valve lap. ponents so that the maximum power is available for useful work at the circuit output. It is equally important to minimize component and piping cost. In some applications, it is also important to minimize weight and bulk size. Pipe sizes are specified by nominal diameters, and the wall thickness by schedule number. The three schedules (or wall thicknesses) used in hydraulic piping are 40, 80, and 160, corresponding to standard pipe, extra heavy, and a little less than double extra heavy. The metric system of units has helped to complicate things for the designer during this transition period, more details can be found in Martin and McCloy.12 In the selection of piping for hydraulic circuits, the following are suggested: • • • Suction lines to pumps should not carry fluid at velocities in excess of 1.5 m/sec in order to reduce the possibility of cavitation at the pump inlet. Delivery lines should not carry fluid at velocities in excess of 4.5 m/sec in order to prevent excessive shock loads in the pipework due to valve closure. Pressure loss due to friction in pipes should be limited to approximately 5% of the supply pressure and the recommendation also keeps heat generation to a reasonable level. Return lines should be of larger diameter than delivery lines to avoid back pressure buildup. For typical industrial hydraulic oil, we can write ^p = KJK1Q2 where A/? = pressure drop along a straight pipe (kPa) KL = loss coefficient = ft/ d f = friction factor e = pipe length (m) d = internal pipe diameter (m) K1 = see Table 60.5 (60.5) Table 60.5 Coefficients for Eqs. 60.5 and 60.6 Nominal Bore Old System S.I. System mm in. 8 10 15 20 25 32 40 50 1 X4 X8 1 X2 3 X4 1 I1X4 I1X2 2 3 K1 1.027 3.506 8.949 2.740 7.195 2.181 4.014 1.090 X X X x X X X X K1 K2 11 IQIQ- 11 IQ- 11 10-10 10-10 10~9 10~9 IQ-8 138 102 81 61 47 36 31 24 12.64 42.26 108.08 333.0 874.66 2620.49 4854.14 13180.81 Pipe Area m K2 10379.12 7663.28 6073.93 4584.95 3601.52 2737.68 2340.66 1823.64 6.64 12.27 19.60 34.30 55.57 96.76 13.13 21.65 in. 2 2 x X X X X X X X 5 10~ W-5 10-5 10~5 10~5 10-5 IQ-4 IQ-4 0.1041 0.1909 0.3039 0.5333 0.8643 1.496 2.036 3.355 Q = flow rate (m3/sec) The friction factor / has been shown experimentally to be a function of Reynolds number (Re) and of pipe roughness. The Reynolds number for industrial hydraulic calculations can be calculated from K2 RQ = -Q v (60.6) where the kinematic viscosity v has a typical value of 4.0 X 10~5 m 2 /s, and K2 can be found in Table 60.5. Given the flow through a section of straight pipe the procedure to calculate the pressure loss is simple. Using Eq. 60.6 and v given above calculate the Reynolds number. Using the Reynolds number to calculate the appropriate value for /, calculate a value for KL. Referring to Table 60.5 for K1, the pressure drop can be calculated using Eq. 60.5. Unfortunately, not all piping is in straight runs so when a bend occurs the loss of pressure will be greater. The effective bend loss can be estimated from Eq. 60.7 and Figs. 60.5 and 60.6. These results are from Ref. 13. A;? - (K + CK8)Q2IK1 (60.7) where c = correction factor for bend angle (Fig. 60.5) KB = resistance coefficient for 90° bends (Fig. 60.6) Further useful information about circuit design can be found in Keller.14 60.6 HYDROSTATIC PUMPS AND MOTORS The source of power in a hydraulic circuit is the result of hydrostatic flow under pressure with the energy being transmitted by static pressure. In another type of fluid power, termed hydrokinetic, the transmission of energy is related to the change in velocity of the hydraulic fluid. While hydrostatic systems use positive displacement pumps, hydrokinetic systems use centrifugal pumps.15 Positive displacement machines have been in existence for many years. The concept is simply a variable displacement volume which can take the form of a piston in a cylinder, gear teeth engaging, or the sweeping action of a vane with eccentric axis placement. All these configurations are positive displacement in the sense that for each revolution of the pump shaft, a nearly constant quantity of fluid is delivered. In addition, there is some form of valving which either takes the form of nonreturn valves or a porting arrangement on a valve plate. Examples of different types of pumps are shown in Figs. 60.7, 60.8, and 60.9. While torque and speed are the input variables to a pump, the output variables are pressure and flow. The product of these variables will give the input and output power. The difference between these values is a measure of the fluid and mechanical losses through the machine. These factors should be taken into account even for a simple analysis. The torque required to drive the pump at constant speed can be divided into five components: Tp = T1 + T0 + Tf + Tc where Tp = actual required input torque (Nm) T1 = ideal torque due to pressure differential and physical dimensions only (60.8) Fig. 60.5 Correction factor c. (Reproduced from AF Rocket Propulsion Lab., 1964.) Tv = resisting torque due to viscous shearing of the fluid between stationary and moving parts of the pump, that is, viscous friction Tf = resisting torque due to pressure and speed-dependent friction sources such as bearings and seals Tc = remaining dry friction effects due to rubbing The delivery from the pump can be expressed in a similar manner: QP = Qi -Q1-Qr where Qp Q1 Q1 Qr (60.9) = actual pump delivery (ml/sec) = ideal delivery of a pump due to geometric shape only — viscous leakage flow = loss in delivery due to inlet restriction16 If the pump is well designed and operating under its working specification, the loss represented by Qr should not occur. For a hydraulic motor, the procedure is reversed in the sense that flow and pressure are the input variables, and torque with angular velocity appears at the output. The corresponding equations are therefore Tp = T1 -T0-Tf-Tc (60.10) QP = Qi + a (60.11) Qr is not a factor in motor performance. Fig. 60.6 Correction factor K8 for pressure loss in pipe bends. The ideal positive-displacement machine displaces a given volume of fluid for every revolution of the input shaft. This value is given the name displacement of the pump or motor and is extensively used by manufacturers to label the pump size. Some typical characteristics for a hydraulic radial piston motor are shown in Fig. 60.10 and Table 60.6. If the pump or motor rotates at N rpm, then a = DpN where Dp = swept volume per revolution = nV V = swept volume per cylinder per revolution Fig. 60.7 Axial piston pump. (60.12)