Appendix 1 Appendix 1. Tables and Figures Table 1-1. Example Transport Airplane Operating Spectrum.
No. Condition GW Yaw deg.
Bank deg.
Flaps deg.
Load g's RPM % Torque % V KCAS Time Event sec.
Events per 70k hrs Stress cycles per 70k hrs Stress cycles per Flight Typical Flight 1 Taxi no crosswind 1 0 0 0 1 70 GI 0 100 35000 4.90E+07 466.66667 2 Taxi 15kt crwind 1 0 0 0 1 70 GI 0 100 35000 4.90E+07 466.66667 3 Taxi 25kt crwind 1 0 0 0 1 70 GI 0 100 35000 4.90E+07 466.66667 4 TO roll 1 0 0 15 1 100 100 0-100 40 105000 8.40E+07 800 5 TO rotation 1 0 0 15 1 100 100 110 2 105000 4.20E+06 40 6 Climb A 1 0 0 15 1 100 100 110 30 105000 6.30E+07 600 7 Climb B 1 0 0 15 1 100 100 130 40 105000 8.40E+07 800 8 Climb Spectrum Contained in spectrum data below 10 Cruise Spectrum Contained in spectrum data below 13 Descent Spec. Contained in spectrum data below 15 Approach Spec. Contained in spectrum data below 17 Reverse max 1 0 0 20 1 100 70 120 10 35000 7.00E+06 66.666667 18 Reverse 1/2 1 0 0 20 1 100 35 120 10 35000 7.00E+06 66.666667 Vertical Maneuver Spectrum 19 Vertical Maneuver 2 0 0 0 2.6 100 70 180 15 5.6 1.68E+03 0.016 20 Vertical Maneuver 2 0 0 0 2.2 100 70 180 18 47 1.69E+04 0.1611429 21 Vertical Maneuver 2 0 0 0 1.8 100 70 180 22 576 2.53E+05 2.4137143 22 Vertical Maneuver 2 0 0 0 1.4 100 70 180 25 23838 1.19E+07 113.51429 23 Vertical Maneuver 2 0 0 0 1 100 70 180 30 122354 7.34E+07 699.16571 24 Vertical Maneuver 2 0 0 0 -1.4 100 70 180 25 23838 1.19E+07 113.51429 25 Vertical Maneuver 2 0 0 0 -1.8 100 70 180 22 576 2.53E+05 2.4137143 26 Vertical Maneuver 2 0 0 0 -2.2 100 70 180 18 47 1.69E+04 0.1611429 27 Vertical Maneuver 2 0 0 0 -2.8 100 70 180 15 5.6 1.68E+03 0.016 28 Vertical Maneuver 2 0 0 0 2.6 80 70 200 15 5.6 1.34E+03 0.0128 29 Vertical Maneuver 2 0 0 0 2.2 80 70 200 18 47 1.35E+04 0.1289143 30 Vertical Maneuver 2 0 0 0 1.8 80 70 200 22 576 2.03E+05 1.9309714 31 Vertical Maneuver 2 0 0 0 1.4 80 70 200 25 23838 9.54E+06 90.811429 etc.
Lateral Gust - Yaw Spectrum 72 Lateral Gust - Yaw 2 9.12 0 0 1 100 70 180 0.5 34 3.40E+02 0.0032381 73 Lateral Gust - Yaw 2 7.45 0 0 1 100 70 180 0.5 364 3.64E+03 0.0346667 74 Lateral Gust - Yaw 2 5.23 0 0 1 100 70 180 0.5 7324 7.32E+04 0.6975238 75 Lateral Gust - Yaw 2 3.12 0 0 1 100 70 180 0. 5 56398 5.64E+05 5.3712381 76 Lateral Gust - Yaw 2 0 0 0 1 100 70 180 0. 5 345626 3.46E+06 32.916762 77 Lateral Gust - Yaw 2 -3.12 0 0 1 100 70 180 0.5 56398 5.64E+05 5.3712381 78 Lateral Gust - Yaw 2 -5.23 0 0 1 100 70 180 0.5 7324 7.32E+04 0.6975238 79 Lateral Gust - Yaw 2 -7.45 0 0 1 100 70 180 0.5 364 3.64E+03 0.0346667 80 Lateral Gust - Yaw 2 -9.12 0 0 1 100 70 180 0.5 34 3.40E+02 0.0032381 etc.
Vertical Gusts etc.
Extreme Maneuvers 213 Limit Yaw 1 32 0 0 1 100 100 170 3.3 1 6.60E+01 0.0006286 214 Limit Pull out 1 0 0 0 3 100 100 150 3.2 1 6.40E+01 0.0006095 215 Rudder kick 1 21 0 0 1 100 100 150 2.3 4 1.84E+02 0.0017524 etc.
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Appendix 1 Figure 1-1 Establishment of an RPM Restriction for a Cross Wind Condition 0
0.2
0.4
0.6
0.8 1
1.2
1.4 Relative Stress Level Measured Stress Stress adjusted for downward frequency shift Stress adjusted for upward frequency shift RPM avoidance band without accounting for variabilty RPM avoidance band with accounting for variabilty Endurance LImit
0 200 400 600 800 1000 1200 1400 1600 Rotational Speed - RPM Figure 1-2 First Blade Mode Propeller Critical Speed Variability 0 20 40 60 80 100 120 Frequency - Hz 950 RPM Accounting for:
Maximum paint and thickness 1050 RPM Accounting for:
Wear to minimum dimensions Nominal Blade 1000 RPM Predicted Blade Frequencies 1P 4P 3P 2P 0 200 400 600 800 1000 1200 1400 1600 Rotational Speed - RPM A1-2
Appendix 1 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0
0.2
0.4
0.6
0.8 1
1.2
1.4
1.6 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 Relative Stress G-A-G Ground-Air-Ground Takeoff Climb Cruise Descent Taxi To gate Reverse Max Tension Max Compression Time Minutes Cyclic stress Mean stress Taxi To runway Figure 1-3
SIMPLE FLIGHT PROFILE Note: The vibratory stress cycles shown for each flight phase (take-off, climb, cruise, etc.) are for illustration purposes. The frequency of vibratory stress is generally 15hz or greater and therefore thousands of vibratory stress cycles may exist in each flight phase.
Figure 1-4
COMPOSITE FLAW GROWTH RATE 1000 Growth Rate - % of growth rate at limit load 100 10 1 1 10 100 1000 Alternating Moment - % of limit load A1-3
Appendix 2 Appendix 2. Propeller Vibration Background Information
1. Introduction. Propeller vibration, as it applies to propeller certification, refers to the dynamic loading that a propeller is subject to during operation on an airplane. The loads include a combination of cyclic or vibratory loads and steady or zero frequency loads. The loads can be defined in terms of stress in pounds per square inch (psi), moment in inch-pounds (in-lbs), microstrain in µin/in, or any other appropriate engineering unit. The loads are either induced mechanically, aerodynamically, or through a combination of both, and can vary greatly in both amplitude and frequency throughout the intended operating envelope of the airplane. Propeller vibration evaluation quantifies the dynamic loads that a propeller is subjected to during operation on an airplane. The evaluation ensures the loads will remain within predetermined limits and establishes appropriate operating limitations and restrictions, when needed, to ensure continued safe operation of the propeller.
2. Airplane Configuration . The type of vibration loading the propeller receives depends on the engine and the airplane configuration. The two major categories of engines are reciprocating and turbine. The three major airplane configurations are single engine tractor, wing-mounted multi-engine tractor, and pusher airplanes. The various combinations of engine category and airplane configuration result in unique sources of propeller excitation. Reciprocating engines generate mechanical excitation; wing-mounted multi-engine tractor configurations and pusher configurations can contribute additional aerodynamic excitation to the propeller. The propeller vibratory load evaluation should be tailored to the type of engine and category of airplane.
3. Airplane Operation. The intended operation of the airplane should also influence the propeller vibratory load evaluation. Types of operation include: commuter, transport, utility, acrobatic, amphibious, firefighting, agricultural, and others. The type of operation has a major influence on the loading environment and the utilization rate. Propeller test data from one type of airplane may not provide adequate substantiation for use of the same propeller on an airplane with a different loading environment and utilization rate.
4. Propeller Excitation Sources. Propellers operate in an environment that has a complex combination of vibratory and steady loads. The loads arise from many sources and depend on both the airplane installation and the type of engine. Each propeller is evaluated to determine if it has acceptable strength and dynamic characteristics to operate in the complex load environment on the airplane. Since there are many sources of excitation, it is best not to over generalize or over simplify the testing that will be required. Each installation should be evaluated to determine the extent of testing and evaluation required.
a. Mechanical Excitation Forces. The mechanical excitation forces of propellers are primarily associated with reciprocating engine installations. The reciprocating engine introduces to the propeller a whole series of vibrational impulses generated by the engine rotating system.
The frequencies of these impulses are generally in multiples of the engine rpm and produce a combination of both forced and resonant frequency propeller loading. The firing impulses from normal four cycle reciprocating engines will excite the propeller at two impulses per revolution for a four-cylinder engine; three per revolution for a six-cylinder engine; four per revolution for A2-1
Appendix 2 an eight-cylinder engine; and so forth. In some instances, the engine impulses may be at fractional orders of the rotational speed. These firing impulses comprise only one component of the excitation forces generated by the engine rotating system.
(1) The crankshaft in a reciprocating engine, like any flexible body, has a series of natural frequencies in both torsion and bending. These natural frequencies are excited by engine power impulses and by inertia forces from the engine rotating system. The free end of the crankshaft, to which the propeller is attached on direct drive engines or indirectly attached through a gearbox on geared engines, vibrates due to the various mechanical inputs. The propeller, which is attached to the free end of the crankshaft or gearbox output shaft, has a high level of inertia and acts as a flywheel that rotates with a minimum of angular acceleration and responds to the various mechanical inputs from the engine with varying frequencies and amplitudes of vibratory loads.
(2) Each propeller model has unique natural frequencies for each of the modes of vibration. When a natural frequency of the propeller in any one mode coincides with a frequency of the engine rotating system, resonance occurs (critical speed) and the propeller load amplitudes increase to a peak value. Most modern reciprocating airplane engines are equipped with some form of mechanical damping to reduce the amplitude of specific frequencies.
Pendulum type dampers installed on the crankshaft and tuned to specific frequencies are the most common, with some engines using other methods such as flexible couplings to reduce reciprocating engine frequency output amplitudes. For more information on engine vibration, refer to paragraph 4c, titled “Mechanical Vibrations,” in the body of this AC.
(3) Reciprocating engines generally have a few dominant excitation forces, with multiples of those excitations that become less severe with increasing harmonics. The excitation frequencies can be plotted on a critical speed diagram with the blade natural frequencies to identify rotational speeds of potential high response and the cause of the high response as shown in figure 2-1 in this Appendix. When there are significant critical speeds, placards or other operating restrictions may be required.
(4) Other factors should be considered when evaluating reciprocating engines. Many reciprocating engine crankshafts use pendulum dampers to reduce crankshaft vibration at specific frequencies, which consequently lowers the excitation forces transmitted to the propeller. Over time, if not properly maintained, the effectiveness of the dampers may be reduced at the targeted frequencies. If this occurs, the propeller, as well as the crankshaft, may experience unacceptable stress levels. For engines with dampers, the continued airworthiness program for the airplane should account for the effectiveness of the damper with wear. One cylinder not operating is generally detectable on small reciprocating engine airplanes. However, in large multi-cylinder engines, detecting one cylinder not operating may not be possible, even by the torquemeter reading. However, one cylinder not operating/firing can have a major effect on propeller vibration stresses under particular conditions; the continued airworthiness program for the airplane should account for this.
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Appendix 2
(5) The frequency of turbine engine mechanical excitations is in general too high to contribute to the excitation of the propeller.
b. Aerodynamic excitation forces. The aerodynamic excitation forces of propellers are typically associated with turbine engine installations because the mechanical vibrations are lower in amplitude. Aerodynamic excitation is the primary exciting force on turbine engine installations. However, aerodynamic excitation can also be a major contributing factor to the propeller loads on reciprocating engine installations.
(1) A propeller is an open rotor and is subjected to a non-uniform inflow that results in aerodynamic excitation. The major contributor in flight is angular inflow into the propeller. The propeller thrust axis is generally not aligned with the direction of flight of the airplane; it is usually pointed at some combination of up, down, left, or right a few degrees. When the flow into the propeller is at an angle relative to the thrust axis, the local blade angle of attack changes as a sinusoid with each revolution of the propeller. This causes a 1P sinusoidal loading of the propeller. The magnitude of the 1P loads is directly related to the inflow angle and the dynamic pressure. The inflow angle and dynamic pressure changes with airspeed, flap setting, gross weight, and maneuvers. The 1P aerodynamic excitation of the propeller is a forced loading and is not associated with any of the propeller critical speeds.
(2) The aerodynamic effects are generally greater on wing mounted multi-engine airplanes because the wing upwash magnifies the flow angularity, and the installation creates more opportunities to angle the propeller installation up and down (tilt) and left and right (toe in or toe out). Other factors such as the proximity of the propeller to the fuselage may contribute to the flight 1P loads.
(3) Experience has shown that propeller resonant frequencies are not excited by 1P loading, although the 1P loading may be magnified by the proximity of the first mode natural frequency to the 1P frequency. In flight excitation forces at orders greater than 1P are caused by disturbances to the airflow into the propeller disc, such as the flow around the airplane. Pusher installations and swept wing installations may cause 2P, 3P, 4P, and other harmonic excitations of both major and minor axis modes due to the disturbances to the airflow into the propeller disc.
These higher order excitations may become dominant if there is a critical speed in the propeller operating range.
(4) One of the worst operating environments for a propeller is on the ground when the airplane is not moving and the wind is blowing from the side to behind the propeller disc. This type of operation is known as ground cross-wind operation. Under this type of condition, the flow into the propeller is constantly changing and many excitation orders occur: 1P, 2P, 3P, 4P, etc. The amplitude of the excitation forces tends to decrease with increasing order, but the high number of excitation frequencies increases the likelihood of a critical speed in the propeller operating range. When a critical speed is found in the propeller operating range, a placard or other operating restriction may be required to prevent high propeller loads. The ground cross- A2-3
Appendix 2 winds may range from mild, under 10 knots, to severe, over 30 knots. The higher the crosswind, the higher the loading.
c. Gyroscopic loads. In addition to aerodynamic 1P loads, a propeller may be subjected to gyroscopic 1P loads due to maneuvers that force the propeller out of its normal plane of rotation and can significantly increase the propeller vibratory loads. This is of particular significance on acrobatic airplanes equipped with either turbine or reciprocating engines. The rapid pitch and yaw changes of the rotating propeller during aerobatic maneuvers result in 1P aerodynamic loads that are further amplified by the out of plane gyroscopic 1P loads.
d. Propeller flutter. Propeller blade flutter is indicated by a self-excited vibration and can generate extremely high propeller load amplitudes in the blade tip area and in the pitch change mechanism. Blade flutter is most likely to occur during high power static operation or during landing, when flat or reverse pitch blade angles are selected at high forward speeds. The susceptibility of a propeller blade to flutter can be influenced by surface wind speed and relative direction of the propeller to the wind; atmospheric conditions such as temperature and relative humidity; and airspeed when flat or reverse pitch blade angles are selected. The load amplitudes may change dramatically with minor changes in operating conditions. In addition to generating potentially fatigue damaging stresses in the propeller blades and pitch change components, flutter may at times be identified by a high frequency airframe vibration and significant change in propeller noise levels. Although some installations have been approved with operating restrictions that prevent the occurrence of blade flutter, it is usually desirable to redesign the propeller blade when a susceptibility to flutter has been demonstrated.
5. Propeller Response. Propeller response to the various excitation forces depends on the propeller natural resonant frequencies, blade strength, and damping. The propeller response is magnified when the excitation frequency is at or near a natural resonant frequency of the propeller blades. These resonant frequencies are generally classified as flatwise (minor axis), edgewise (major axis), and torsional, and can be excited as either symmetrical or unsymmetrical (whirl) modes, symmetrical modes, and reactionless modes of vibration. Figure 2-2 and table 2- 1 of this Appendix illustrate these modes of vibration.
a. General. Due to the complex loading and geometry of propellers, multiple areas of the propeller are subjected to varying amplitudes and frequencies of loads. The propeller blade load areas are typically identified as tip area, mid-blade area, and blade shank/retention area. These loads are usually evaluated against allowable fatigue limits unique for those specific areas of the blades. In addition, the propeller hub and other load bearing components in the propeller pitch change system may require evaluation against specific fatigue limits for those components. The type of propeller response in these various load-bearing areas is greatly influenced by the type of excitation force. Propeller response to mechanical excitation force from reciprocating engines is typically characterized by maximum minor axis vibratory loads in the blade tip area and major axis loads in the blade shank area. Propeller response to aerodynamic excitation is typically characterized by minor axis vibratory loads on the mid-blade and blade shank areas. More complex response combinations will occur when mechanical and aerodynamic loads combine.
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Appendix 2
b. Reactionless mode. Propellers with four or more blades will also have a resonant frequency known as the reactionless mode of vibration. The primary characteristic of this mode is a 2P or 3P frequency, depending on the number of blades, with all loads canceled in the hub.
This mode of vibration is excited primarily on the ground when surface winds are from behind the propeller disc (cross-wind) and can generate high loads in the mid-blade and blade shank/retention area. Most installations with these characteristics are subject to operating restrictions to prevent continuous operation within the rpm range in which these modes can be excited.
c. Centrifugal stiffening. The natural frequencies of the minor axis change with the effects of rotational speed and blade angle due to changes in centrifugal stiffening. Major axis and torsional frequencies are not affected as much by changes in blade angle and centrifugal stiffening. The blade frequencies and excitation frequencies can be shown graphically on a critical speed diagram, which provides a method to assess rotational speeds at which the vibratory loads may be magnified. Critical speeds should be calculated before vibration testing and verified during the test. For a general discussion of response magnification at and near natural frequencies, refer to paragraph 4c of this AC titled “Mechanical Vibrations.”
d. Flight response . In flight, the propeller response is dominated by engine mechanical excitation forces on reciprocating engine installations and by 1P aerodynamic excitation forces on turbine engine installations. The 1P aerodynamic excitation is always present, but the propeller response to the 1P aerodynamic excitation may be masked by a higher reciprocating engine excitation.
e. Ground Air Ground (GAG) Cycle. Propellers also experience a maximum and minimum load cycle during each flight, commonly called the GAG cycle. This maximum and minimum load with each flight is due to the combination of:
(1) Centrifugal loads varying from zero to maximum;
(2) Steady bending loads varying from full forward thrust to maximum reverse thrust ;
and
(3) Maximum and minimum vibratory bending loads.
A2-5
Appendix 2 Table 2-1. Types of Propeller Modes
Number of Blades P order 3 4 5 6 8 10 1 W W W W W W 2 W R R R R R 3 S W R R R R 4 W S W R R R 5 W W S W R R 6 S R W S R R 7 W W R W W R 8 W S R R S R W - Whirl or unsymmetrical S - Symmetrical (all blades in phase) R - Reactionless (blade reactions cancel at hub) Figure 2-1 Sample Critical Speed Diagram for Engine Excitations 0 50 100 150 200 250 300 350 0 200 400 600 80010001200140016001800 Frequency 1E 9E 1 1/2E 4 1/2 E Engine Orders Blade Frequencies Critical Speeds Rotational Speed A2-6
Appendix 2 Figure 2-2 Aircraft Propeller Interaction Engine Whirl mode Shaft orbits Blades move together Engine Symmetrical Mode No shaft motion Engine Reactionless mode A2-7
Appendix 3 Appendix 3. Propeller Vibration Evaluation Test Conditions
1. Introduction. This appendix list s the typical propeller vibration test conditions for part 23 installations with reciprocating and turbine engines. These lists provide guidance for developing the specific test points for a test plan. Tests for propellers on airplanes designed for operating outside the standard normal and utility category type of operations should evaluate the specific maneuver envelope associated with the installation. This applies to agricultural airplanes, aerobatic airplanes, short takeoff and landing airplanes, or to any other special mission type of installation.
2. Test Conditions For Reciprocating Engine Installations .
a. General comments.
(1) The intended operating envelope and maneuver spectrum should be evaluated for each installation and test conditions added, deleted, or changed to fully evaluate propeller loads.
(2) Applicants may need to revise their test conditions as data is reviewed during the test.
(3) Multi-engine installations may require testing on more than one engine, depending on airplane configuration and previous test experience.
(4) Testing may be required to verify repair allowances such as reduced diameters, reduced thickness, and for composite blades, significant shell repairs.
(5) The maximum governing rpm should be set to a minimum of 103% of maximum rated rpm.
(6) Maximum power should be the maximum manifold pressure permitted at the rpm and altitude of the test point.
(7) These test conditions are based on conventional reciprocating airplane engines with separate throttles and propeller controls that use a conventional constant speed propeller.
Installations that deviate from this standard will require modifications to the test conditions to fully evaluate propeller vibration characteristics.
(8) Multi-engine airplanes should be tested in flight at high and low gross weights.
b. Test conditions. Tests under 2b(1) apply to all propellers: tests under 2b(2) apply only to propellers with four or more blades.
(1) Ground testing with the airplane static into the wind.
(a) Increase the rpm from idle to maximum in increments.
A3-1
Appendix 3
(b) Accelerate and decelerate between idle and maximum rpm.
(c) Conduct normal engine and propeller preflight functional checks.
(d) Maintain maximum power and reduce rpm from maximum to minimum governing rpm.
(e) Decrease blade angle to maximum reverse.
(2) Ground testing with the airplane static in a 45° cross-tail wind of not less than 15 knots for propellers with four or more blades.
(a) Repeat 2b.(1)(a).
(b) Repeat 2b.(1)(b).
(c) Record wind velocity at beginning and end of test.
(3) Flight Testing.
(a) Take-off rotation and initial climb with maximum power. Consider all possible flap positions. Test at high and low gross weights.
(b) Maintain climb airspeed and maximum power and reduce rpm from maximum to minimum climb rpm in increments. Test at high and low gross weights.
(c) Maintain level flight and maximum power and reduce from maximum to minimum governing rpm in increments. Conduct this test at low altitude (at or below approximately 5000 ft. sea level (SL)) and at approximately 10,000 ft. SL. Consider testing at higher altitudes for turbocharged installations. Test at high and low gross weights.
(d) Repeat 2b.(3)(c) as necessary at reduced manifold pressure settings.
(e) Increase the airspeed with the throttle closed to achieve maximum rpm, then begin a continuous reduction in airspeed to the minimum airspeed prior to stall. Record the resulting rpm reduction.
(f) Reduce power to idle for multi-engine installations on the engine without the instrumented propeller and record data with maximum power and rpm during single engine climb and level flight.
(g) Record propeller feather/unfeather and/or engine shutdown/restart for multiengine installations and functional checks over the full range of rpm and power, as applicable.
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