1、SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirelyvoluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefro
2、m, is the sole responsibility of the user.”SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions.Copyright 1999 Society of Automotive Engineers, Inc.All rights reserved. Printed in U.S.
3、A.QUESTIONS REGARDING THIS DOCUMENT: (724) 772-8510 FAX: (724) 776-0243TO PLACE A DOCUMENT ORDER: (724) 776-4970 FAX: (724) 776-0790SAE WEB ADDRESS: http:/www.sae.org400 Commonwealth Drive, Warrendale, PA 15096-0001AEROSPACE INFORMATION REPORTAIR1087REV.BIssued 1969-01Reaffirmed 1994-02Revised 1999-
4、04Aircraft Accessory Drag Torque During Engine StartsFOREWORDChanges in this revision are format/editorial only.1. SCOPE:This SAE Aerospace Information Report (AIR) presents a discussion of drag torques of engine accessories operating at cold temperature. Various conditions of temperature, speed, an
5、d acceleration rates are reviewed showing the merits of each method and recommending a standard test method.1.1 Purpose:The purpose of this Aerospace Information Report is to present a brief discussion of the drag torques of aircraft accessories operating at cold temperatures, specifically -65 F. Th
6、e parameters affecting the magnitude of torque at various speeds and acceleration rates are reviewed. In conclusion, this report establishes the difference in accessory torque characteristics that are obtained by various test procedures and recognizes the need for a standard test method.2. REFERENCE
7、S:There are no referenced publications specified herein.SAE AIR1087 Revision B- 2 -3. MAIN ENGINE STARTING SYSTEM ANALYSIS:The presently accepted method for analyzing the starting system for gas turbine engines involves the generation, by the engine manufacturer, of an engine torque versus speed cur
8、ve at various temperatures with related light-off, minimum assist and idle speeds. Using this engine torque curve, engine inertia and starter output torque versus speed curve the basic starting system can be analyzed using the following equation:where,Tnet= net accelerating torque by the algebraic a
9、ddition of engine torque and starter outputtorque at a common shaft.IT= summation of engine and starter inertia reflected at a common shaft. = resultant rate of acceleration of a common shaft.By taking small increments of the net torque versus speed curve the average acceleration rate and time for e
10、ach increment can be used to determine total time to engine idle.In many cases this method of calculation provides the information necessary to complete the starting system analysis. If a more accurate analysis is required the effects of engine driven aircraft accessory gearbox loads can be included
11、. This is accomplished by determining the steady-state accessory torque versus speed and algebraically adding this torque magnitude to the engine torque curve and adding the accessory inertia to the total system inertia. This method is satisfactory for normal accessory loads and relatively large eng
12、ines. At temperatures below -40 F, and in particular-65 F, the loads from hydraulic devices and gearboxes can be increased many times because of the large increase in oil viscosity at these temperatures.The engine and accessory starting system analysis at -65 F is more involved because of increased
13、and transient torque loading due to large changes in oil viscosity in the engine, gearbox and hydraulic accessories. To make a detailed analysis of the -65 F system, special attention must be given to these loads before they can be added to the steady-state engine torque curve in the start calculati
14、on.TnetIT=SAE AIR1087 Revision B- 3 -4. COLD START DRAG TORQUE ANALYSIS FOR ACCESSORY LOADS:4.1 Basic Parameters:The torques required to rotate hydraulic devices and gearboxes during an engine acceleration are influenced by the following parameters:(1) Inertia (I) of the rotating massEquation 1: T =
15、 I (2) Windage of rotating parts in airEquation 2: T = K x function of speed ()(3) Pumping of fluidEquation 3: T = Displacement x pressure pressure head is also a function of the oil viscosity () and speed ().(4) Churning and shearing of the oilEquation 4: T = Geometrical constant x a function of sp
16、eed () and viscosity ().(5) FrictionEquation 5: T = a function of contact forces (F) and the coefficient of friction (f).Total loads from Items 1 (inertia) and 2 (windage) are easily determined by calculations and steady-state test measurements and impose no particular problems. On large engines the
17、 torques from Items 1 and 2 are small compared to total system torque during the engine start cycle and will not be considered in this study. The torque due to friction will not be considered as a separate item in this study.As noted in equation (3), the torque loads are a function of displacement a
18、nd pressure head. This displacement per revolution (D/rev.) can be considered a constant for a given fixed displacement unit during the start cycle which results in a flow rate proportional with speed (). The total hydraulic head is determined by system operating pressure and flow rate and decreases
19、 with increasing fluid viscosity (). Pumping pressure is normally a constant designed pressure, but at very cold conditions can be greatly increased. Special considerations would be necessary to determine the pumping torque of variable displacement hydraulic pumps which are pressure compensated and
20、destroked for low flow rates.SAE AIR1087 Revision B- 4 -4.1 (Continued):In equation (4), the torque loading is determined by the geometrical size of the unit which can be considered as a constant depicted as an area (A) in square inches, the speed of the individual components shearing the oil () in
21、feet per second, and the dynamic viscosity () in slugs per feet per second.The following illustrates how equations (3) and (4) can be generalized and combined by separating constants and variables which affect the system starting torque:(3) T = D/revolutions x pressureD/revolutions = constant (K1)P
22、= f (, )T = K1x f (, )(4) T = K2x f (, ) K2= Geometrical ConstantEquations (3) and (4) can be combined to yield:Equation (5) T = K3x f (, )Over normal operating temperature ranges, viscosity can be considered a constant and the steady-state torque would vary as a function of speed.4.2 Factors Affect
23、ing Fluid Viscosity:As seen on the graph of viscosity versus temperature (Figure 10) for a typical aerospace oil, the fluid viscosity changes approximately 50 to 1 between 0 F and -65 F. Correspondingly the resistance will vary considerably with small temperature changes in this range. This phenomen
24、on affects overall torque characteristics at low temperatures since local viscosity changes as a function of unit activity.After the initial revolution of a unit which has been cold soaked to -65 F, the fluid in contact with the bearings, gears, pistons, and other reciprocating and rotating parts in
25、 the unit is subjected to motion and shearing. The work (W) done on the fluid through shearing will in turn heat the oil adjacent to the moving surfaces. This causes a substantial change in local viscosity and therefore a change of work input for the next increment of time.During a cold start cycle,
26、 the oil temperature within a unit at any time after initial start will vary significantly within the unit itself. A rapid temperature rise would be noted adjacent to the moving surfaces which are imparting the most work to the oil, in contrast to a slow temperature rise in a relatively stagnant sum
27、p area.SAE AIR1087 Revision B- 5 -4.3 Effect of Work on Fluid Temperature:It is assumed that any work absorbed by an accessory above its normal steady-state output energy is transferred into heating of its internal fluid.Therefore:Dynamic viscosity () is a function of its temperature (Te)Equation (6
28、): = f (Te)The fluid temperature (Te) is a function of the work (W) imparted to the fluid by moving parts.Equation (7): Te= f (W)Work is equal to a force times distance and in this caseEquation (8) = W = T x Where, T = torque (to overcome viscous friction) = revolutions or radiansIt can be generaliz
29、ed that the fluid temperature or viscosity at any time (t) after start initiation is dependent upon the summation of the torque transmitted to the unit times the number of revolutions to time (t).In Figure 1 below, the transmitted torque is plotted against revolutions ().FIGURE 1. Typical Torque Ver
30、sus RevolutionsSAE AIR1087 Revision B- 6 -4.4 Acceleration Rate Varies the Work Accomplished:Assume an accessory is accelerated at two different uniform rates 1, and 2from zero to a speed 1, and there is no change in the fluid temperature, the torque versus speed curve is as shown in Figure 2. For t
31、his same accessory, torque versus revolutions is shown in Figure 3 where the areas shown as A1and A2represent the total work done on the unit where A1 A2and W1 W2.It is noted that with different amounts of work done on the oil, the temperature of the oil at speed 1for the acceleration with 1is highe
32、r than with 2.As an example, assume:1= 10 radians/second22= 20 radians/second21= 50 radians/secondfrom, = x tt1= 5 secondst2= 2.5 secondssubstituting = 1/2 x t21= 125 radians2= 62.5 radiansAs shown in Figure 3, the area under the respective curves would be A1= 2A2.Therefore, the work accomplished wi
33、th 1would be twice the work accomplished with 2. If this generalized example is carried a step further, and it is assumed that the accessory temperature is uniform at -65 F, and W1raises the oil temperature 20 F and W2raises it 10 F it can be seen from Figure 10 that the viscosity 1= .06 and 2= .12
34、W1= 2W21= 1/2 2It can now be stated that if all the work is transferred into heating up the oil, the torque at speed 1for run (1) is not equal to the torque for run (2) as originally stated.slugsfeet second-slugsfeet second-SAE AIR1087 Revision B- 7 -FIGURE 2 - Torque Versus SpeedFIGURE 3 - Torque V
35、ersus Revolutions for Two Acceleration RatesSAE AIR1087 Revision B- 8 -4.4 (Continued):But, T1 T2Cold start test results of hydraulic or lubricated accessories have shown that the change in fluid viscosity is a dominant factor in determining the shape of the accessory torque versus speed curve durin
36、g the accelerated start such that the slope of the curve is not as shown in Figure 2, but more as shown below in Figure 4.This curve shape shows that decreasing fluid viscosity has a greater effect on the absolute torque than increasing speed.The change in torque required by bearings and other compo
37、nents that operate with an interference or tight fit at -65 F condition and loosen as temperature increases also affects the cold start in a manner similar to oil viscosity changes.FIGURE 4 - Torque Versus SpeedSAE AIR1087 Revision B- 9 -4.5 Generalized Cold Start Torque Equations for Accessories:Eq
38、uation (5) noted in Section 4.1 combined the pumping and shearing drag torques into one equation and grouped the independent constants.Equation (5) T = K3x f (, )This equation is not very useful because it is very difficult to determine or measure fluid temperature at the critical moving surfaces du
39、ring the start cycle. Therefore, it is necessary to reflect the viscosity variable as a measurable function. Equations (6), (7) and (8) showed how viscosity is a function of work (W) or (T x ).Equation (9) = f (T x )From this it can be stated that the torque at any time or speed during the start cyc
40、le is a function of the speed and of the work done on the fluid up to the speed in question.Equation (10) T = K x f , f (T x )5. TEST METHODS FOR DETERMINING DRAG TORQUE:5.1 Steady-State Torque and Polar Moment of Inertia:The component to be tested is conditioned in the required environment and then
41、 driven to a predetermined speed. The torque required to drive the component is then measured while the acceleration rate is zero. From a series of points derived in this manner, a steady-state curve of torque versus speed is obtained. The polar moment of inertia of the component is determined throu
42、gh testing or calculations. The accessory drag torque is then added to the engine drag curve and the inertia is added to the system inertia.This method is greatly influenced by the lapse of time between data point measurements. For instance, on a -65 F test the hydraulic and lubricating fluids are v
43、ery viscous, but warm up rapidly as work is being done on them. Once the constant speed data point is reached (acceleration = 0) the torque continues to decrease with time as the fluids become less viscous. The problem of an accurate reading is influenced by:1. The torque measurement is made after t
44、oo much work is put into the component producing too low a value.2. The torque measurement is made before enough work is put into the component which produces too high a value. This is possible when actual engine acceleration rates are lower than used on the test.This test method is considered accep
45、table at moderate temperatures where the change in oil viscosity is not large.SAE AIR1087 Revision B- 10 -5.2 Uniform Acceleration Rate:The component is accelerated at a fixed rate during which time the accessory torque is continually monitored. This test method is satisfactory for applications wher
46、e the engine drag is large compared to the accessories. However, on a small engine, a more accurate method of determining accessory drag may be desired.The polar moment of inertia of the system can be determined, and an adjustment made in the torque to account for acceleration of the masses. This wo
47、uld provide a steady-state torque versus speed curve for that specific acceleration rate. However, a different acceleration rate would mean a different level of energy being put into the fluid resulting in a different range of change of fluid viscosity which directly affects the torque absorption of
48、 the accessory.5.3 Variable Acceleration Rate:Measure torque absorption of an accessory using a variable acceleration rate to more closely simulate actual engine conditions. This is an improvement over the other two methods as it more closely simulates actual operational start conditions.It is neces
49、sary in this approach to determine the approximate engine acceleration profile. This acceleration profile would then be segmented into constant acceleration rates between predetermined speeds. An example of this is shown in Figure 11, which also dramatizes the difference between variable rate acceleration and constant rate acceleration.An undesirable factor in this test method is each change in temperature or start
