equivalent level of safety finding can be made for the remaining requirements based on the previously approved data.
b. Procedures.
(1) Section 27.923(a) requires the rotor drive system and rotor control mechanism to be in a serviceable condition at the end of the test. Verification of this requirement requires a complete disassembly and examination of the entire rotor drive system and rotor control mechanism. The disassembly itself should be closely monitored for evidence of adequate breakaway torque on all bolted fasteners. Samples of lubrication from oil sumps and filters should be retained for spectrographic analysis, and seals should be examined for possible damage due to test requirements. Care should be taken to differentiate between seal damage and bearing damage due to disassembly procedures so that the direct results of the test may be properly considered. Close visual observation of each tooth on each gear is necessary to affirm proper load/contact patterns and absence of excessive surface stress or scrubbing motions. Bearings should be examined to verify that ball or roller paths are within limits, bearing cages are undamaged, and bearing balls or rollers and their races are free from pitting. Any evidence of bearing races turning or spinning in respective housing or bores probably indicates design or fit deficiencies. The applicant should have available wear limits data which include items such as distance across pins and tooth profile limits for gears. Many of these items require special, close tolerance inspection equipment and trained inspectors to determine compliance. In some instances, bearings, clutches, oil pumps, etc., should be returned to the original manufacturer for a finding of serviceability. Localized overheating usually exhibited by discolorations is an indication of an unsatisfactory condition. Should any of the items discussed above or other defects appear such that the component is unserviceable, a redesign which includes recognizable improvements should be required before authorizing a retest. To simply "try again" in hopes of success should not be accepted.
(2) Section 27.923(a) also prohibits intervening disassembly which might affect test results. Generally, this simply means no disassembly whatsoever. However, some very limited disassembly can usually be conducted provided care is used to ensure that items such as critical fastener torques or gear backlash controls are not disturbed.
(3) Section 27.923(b) requires that each rotor drive system and control mechanism be tested for not less than 100 hours. This endurance test is intended to demonstrate a minimum level of reliability and proper functioning of this system. The test should be conducted on the rotorcraft to provide the most realistic test environment. Exceptions can be made only if a ground or flight test facility is used that closely simulates the support and vibration conditions existing on the actual rotorcraft.
The rotor system installed on the ground test article should be the same as that used on the flight test vehicle. If significant productivity changes are made after completion of the tests, retesting may be required.
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(4) In § 27.923(c), (d), (e), and (f), the runs should be made with the proper torques, rotor speeds, and control positions specified by each paragraph. The controls discussed in each paragraph are the flight controls; i.e., cyclic and directional controls for rotorcraft with tail rotor and single main rotor. The collective control is normally used to set power and is not involved in the control cycling described in § 27.923(h). During control cycling the controls may be cycled from stop to stop, or a limited travel may be accepted if the travel produces the maximum fore and aft, left and right, and yaw thrust components of the rotors as measured in flight for a particular flight condition. One method of determining the required control displacement is to measure main rotor mast bending in level forward flight at maximum continuous power (or the power associated with the maximum rearward flight speed to be expected) for the aft control displacement limit. Using the same mast bending instrumentation with the rotorcraft in the ground tie-down situation and with collective control set for maximum continuous power, displace the cyclic fore and aft to obtain the same mast bending as measured in flight.
Similar measurements and control displacements may be used for sideward thrust components. Yaw control displacement should consider maneuver requirements in conjunction with sideward flight. Critical gross weight and center of gravity should be used to establish test conditions. Vertical thrust may be used during the takeoff run and the runs at 2 ½-minute power. OEI runs should be conducted with the cyclic set for maximum forward thrust for the 30-minute power run and at maximum vertical thrust for the 2 ½-minute power run. For these runs and any run that does not specity the position for the yaw control, that control should be set to react main rotor torque.
(5) Section 27.923(e) prescribes the takeoff portion of the endurance test. This is a 10-hour test that must be run at not less than the maximum torque and the maximum RPM to be approved for takeoff. For this test the main and auxiliary rotor controls should be in the normal position for vertical ascent. If the applicant elects (for a multiengine rotorcraft) to perform the 2 ½-minute OEI power test, a series of three 2 ½-minute repetitive runs should be conducted during the course of the 10-hour test.
For these tests, main and auxiliary rotor controls should be in the position for vertical ascent, and power settings for the operating engine should provide red line torque (or manifold pressure) and RPM for the 2 ½-minute OEI power rating. The nonoperating engine may be allowed to operate at idle or may be shut down.
(6) The torque and speed requirements in § 27.923(e) for the optional 2 ½-minute OEl tests should be interpreted as described above for the takeoff runs. If the test is conducted during warm ambient conditions, excessive engine gas temperatures may be required to achieve the torque and speed conditions required by this part of the test. Minor adjustments in the run schedule may be allowed to take advantage of cooler nighttime ambient temperatures. Addition of water/alcohol systems to increase engine hot-day power may be appropriate in some instances. Liquid nitrogen spray into engine inlets has also been used to depress inlet temperatures sufficiently to obtain test conditions.
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АС 27-1A 7/30/97
(7) The requirement in § 27.923(g) for declutching the engine may be difficult to achieve if engine decelerations and rotor system decelerations rates are similar. In some cases, the engine fuel control deceleration schedule may be adjusted to achieve clutch disengagement; otherwise, an engine shift brake mechanism may be needed.
(8) Tests described in § 27.923(h) should be conducted under the conditions of maximum continuous power and RPM as described in § 27.923(c).
(9) Section 27.923(1) requires 200 clutch engagements. This test is prescribed to establish a level of reliability of clutch components installed as a part of the rotor drive system of rotorcraft. The clutch tests apply to all clutches installed to comply with § 27.917(b), and each such clutch must be tested. A rotor brake is not required for certification, although a brake of some type may be installed temporarily to facilitate conducting the clutch testing required by this section. Clutch disengagement is also required by this section; thus, malfunction of the disengagement feature would be a basis for discontinuance. Some rotorcraft configurations (those with single-spool turbine engines or reciprocating engines) include an additional clutch to decouple the engine from the drive system to facilitate engine starting. These clutches should also be exercised at least 200 times during this test.
(10) Section 27.9230) sets forth the optional tests to be conducted if a 30-minute OEI rating is requested. Flight control positions should be set for level flight or climb, whichever produces the maximum forward thrust component, and the antitorque system control should be set to react the maximum rotor torque. The torque and rotational speed values should be the maximum for which approval is requested.
c. Additional Test Considerations.
(1) Pressure Lubricated Gearboxes. The endurance test hardware can be adjusted/modified to sustain high-limit oil temperature and low-limit oil pressure to provide a basis for approval of the values listed as limits. A minimum of 20 hours at maximum continuous torque and maximum continuous rotational speed should be involved in the test. Other parameters such as minimum oil temperature and maximum oil pressure may more appropriately be evaluated by bench test. The significant points here are effects of extremely high oil pressure (due to the high viscosity of cold oil) on any positive displacement oil pump, on filters for possible collapse, on oil coolers for possible rupture due to internal pressure, seals, bypass valves, and most important, adequate lubrication of gears, bearings, etc., under conditions of minimal oil flow.
Normally, an operational restriction against exceeding idle power/speed conditions until significant warm-up occurs is prescribed. Individual component qualification tests may provide data to meet some of these aspects.
(2) Asymmetric Power Inputs. The existing endurance test schedule does not necessarily provide for any asymmetric power inputs from multiengine drive system arrangements. For this situation, the drive system should at least be subjectively 536 Par 423
evaluated for possible hazards or excessive loads to be expected from asymmetric torque inputs. If required, additional testing should be considered.
(3) Accessory Drives. Normally, all accessory drives on a gearbox will be loaded during the endurance test. Electrical load banks or other suitable methods may be used to ensure that the generator drives are loaded and thus properly qualified.
Hydraulic pumps may be loaded by resetting hydraulic system relief valves to maintain limit pressure (load) continuously. If this condition is excessively severe, a method of load cycling may be appropriate. Note that accessory loads reduce the power available to the main rotor. Also, tail rotor loads are, insofar as the transmission is concerned, another large accessory. Care should be taken to ensure that in-flight unloading of these accessory drives, including the tail rotor, does not subject the main gearbox to loads significantly beyond those qualified by endurance tests.
(4) Gearbox Oil Tanks. Normally, gearbox oil is contained in an integral cast sump which, for other reasons, has sufficient strength to obviate the need for pressure tests. However, a subjective evaluation should be made to ensure that detail design features such as sight gauges, filler caps, etc., offer adequate strength.
423A. § 27.923 (Amendment 27-23) ROTOR DRIVE SYSTEM AND CONTROL MECHANISM TESTS.
a. Explanation. Amendment 27-23 revised § 27.923(c) to remove the references to "engine power" to avoid confusion. Previous wording could have been interpreted to mean tests prescribed by this section should be conducted at powers corresponding to engine ratings established under Part 33, rather than rotorcraft powers which may be lower than those established under Part 33, but selected by the applicant as a limit on their product. Section 27.923(d) was revised to remove the references to "engine power" and to clarify the test requirements for 30-minute and continuous OEI powers.
Previously, §§ 27.923(e) and I), as they relate to the 2 ½-minute and 30-minute power ratings, respectively, provided for only minimal testing of the capability of the rotor drive system to sustain these powers. Amendment 27-23 amended these sections to extend the testing to adequately assure valid qualification tests. These changes ensure the integrity of the rotor drive system so that it will safely sustain the higher stresses expected with actual, repeated use of these power ratings. A new § 27.923(k) was added that provides a qualification test schedule for the new, optional, continuous OEI rating.
b. Procedures. The policy material pertaining to this section remains in effect with the following additions:
(1) Section 27.923 requires a minimum of 100 hours of endurance testing.
(i) For single engine rotorcraft and others that will not have OEI ratings, the 100-hour test is comprised of 60 hours at not less than maximum continuous power, Par 423 537
30 hours at not less than 75 percent maximum continuous power, and 10 hours at not less than takeoff power.
(ii) For multiengine rotorcraft for which OEl ratings are requested, the test is comprised of 60 hours at not less than maximum continuous power, 25 hours at not less than 75 percent maximum continuous power, 10 hours at not less than takeoff power, and 5 hours at simulated OEI power conditions.
(2) The endurance time, cited in Paragraph b(1) above, excludes the time required to adjust power or to stabilize operating conditions. Extension of the total test time beyond 100 hours (or extension of any test run segment beyond the minimum) will occur if qualification for the 2 ½-minute, 30-minute, or continuous OEl optional ratings is proposed by the applicant for rotorcraft equipped with two or more engines.
(3) The requirements in § 27.923(f) stipulate that the endurance tests conducted at maximum continuous and 75 percent maximum continuous power should be conducted in intervals of not less than 30 minutes. These tests may be conducted on the ground or in flight. The takeoff power endurance test described in § 27.923(e) should be conducted in intervals of not less than 5 minutes.
(4) The new § 27.923(k) sets forth the tests to be conducted if a continuous OEl rating is requested. Flight control positions should be set for level flight or climb, whichever produces the maximum forward thrust component. The anti-torque system control should be set to react the maximum rotor torque. The torque and rotational speed values should be the maximum for which approval is requested.
423B. § 27.923 (Amendment 27-29) ROTOR DRIVE SYSTEM AND CONTROL MECHANISM TESTS.
a. Explanation. Amendment 27-29 added § 27.923(e)(2) that defines qualification tests for 30-second/2-minute OE ratings. This new paragraph also allows for the 30-second/2-minute OE portion of the endurance test to be accomplished on a representative bench test facility using the drive system components which can be adversely affected by these tests.
b. Procedures.
(1) For accomplishment of the endurance test for 30-second/2-minute OEl, Paragraph 27.923(e)(2) requires that 10 applications of 30-second/2-minute OEl power be demonstrated for each power section during the 10 hour takeoff power segment of Paragraph 27.923(e). Each 30-second/2-minute OEl application should be conducted immediately following a 5 minute stabilized takeoff power run. Following the 5 minute takeoff power run, one engine must simulate a power failure and each engine providing power after the failure must apply the maximum torque and maximum speed for use with 30-second OE power. This power level should be maintained for at least 538 Par 423A
30-seconds. The 30-second OEI power should then be followed by an application of the maximum torque and maximum speed for 2-minute OE power for at least 2 minutes. Paragraph 27.923(e)(2) also requires that one of the 30-second/2-minute OEI segments for each engine be accomplished from the flight idle condition.
(2) Additionally, due to the damage inflicted on the engines and the ensuing cost caused by operating the engine at these powers, the 30-second/2-minute portion of the endurance test can be accomplished on a bench test found to be representative of the rotorcraft. The representative bench test rig should have the ability to generate the torques, speeds, vibration frequency, and acceleration rate generated by the rotorcraft. The power should have the same method/path of application as that used on the rotorcraft. The test rig should be configured with the same components used for conducting the endurance test on the rotorcraft except that the test components not affected by asymmetric power application may not have to be installed (i.e., if a combining gearbox is used it may not be necessary to have the main transmission installed on the bench test rig).
(3) The takeoff portion of the endurance test should be accomplished on the rotorcraft. When conducting the bench test for 30-second/2-minute OEl it is not necessary to repeat the takeoff portion of the endurance test; however, the simulated power failure and application of 30-second/2-minute OEI power by the remaining engine(s) should be accomplished after the input power has stabilized at takeoff power.
424. § 27.927 (Amendment 27-12) ADDITIONAL TESTS.
a. Section 27.927 (a):
(1) Explanation. This paragraph is the authority to require any special tests or investigations to establish that the rotor drive system is safe.
(2) Procedures. The certification engineer should review the design of the rotor drive system and its installation and intended operation for features or conditions that may not be adequately qualified in the tests prescribed by this part and, if necessary, additional qualification test programs should be developed and accomplished to ensure safe operation of the rotor drive system. Items of interest would include poorly defined load paths associated with redundant design features, flight deflections of structure and of mounting arrangements, and special or unusual operating procedures which may be anticipated or proposed by the applicant.
b. Section 27,927 (b):
(1) Explanation. This paragraph prescribes testing to quality the rotor drive system for the power excursions to be expected with governor-controlled engines wherein the power from the engine(s) changes automatically to maintain rotor speed at preselected values. At high collective flight control displacements, the normal rotor Par 423B 539
speed droop will result in the governor-controlled engine(s) automatically accelerating to maximum fuel flow or to any other power, speed, temperature, or torque limiting device, regardless of crew action or artificially established limitations reflected by instrument markings. This high power condition can occur typically during a normal landing when the crew applies high collective to cushion ground contact or, for multiengine rotorcraft, during any flight regime when an engine fails and the corresponding loss of power results in drooping the rotor speed. Special tests are prescribed by this section to provide assurance that the rotor drive system can safely sustain these conditions. The tests of this section should be conducted without intervening disassembly, and all rotor drive system components should be in serviceable condition after the test. It is permissible but not required that these tests be performed on the same specimen of the rotor drive system used to show compliance with § 27.923.
(2) Procedures. Testing as prescribed by this section should be conducted on a ground-test rotorcraft conformed to the type design suggested for the endurance test of § 27.923. In most cases, testing to comply with § 27.927(b)(1) is accomplished as a continuation of the test of § 27.923 using the same test vehicle. For this test, the main rotor control (cyclic/collective) may be set to simulate vertical lift. The auxiliary rotor control (antitorque) may be set or adjusted to react main rotor torque. Rotation speed should be maximum normal for the test condition; i.e., all engines operating as for takeoff. Using the collective control, obtain torque as required to meet either § 27.927(b)(1)(i) or (ii). This will normally be 110 percent of takeoff torque or a lower value as limited by an approved, reliable device to simultaneously limit torque on all engines. If individual torque limiters are provided for each engine, rigging tolerances should be at maximum allowed mismatch for the type design. For the one-engine-inoperative (OEI) test of § 27.927 (b)(2), rotor RPM droop, if any, may be allowed as would occur in service. Since this OEl test requires the remaining engine(s) to produce power not usually available under normal atmospheric conditions, supplemental power augmentation may be needed such as inlet air refrigeration, ramming, or overfueling the engine. Alternatively, bench testing with a transmission test rig may be appropriate providing close simulation of the drive system torsionals, shaft/coupling, misalignment, etc., is achieved. Overtesting (excessive torque) to compensate for inadequacies in the bench test may be negotiated with the FAA/AUTHORITY approval office. Note that compliance with § 27.903(b) requires that the remaining engine(s) be capable of safe, continued operations under the high power conditions of this test. This may require the engine manufacturer to conduct special testing or to produce suitable evidence that the stresses (and gas temperatures) associated with these governor-induced high power excursions do not compromise the airworthiness of the remaining engines or their capability to produce topping power automatically during the initial moments of flight after an engine failure.
c. Section 27.927(c):
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(1) Explanation. This paragraph prescribes a test which is intended to demonstrate that in the event of a pressure failure of any pressurized lubrication system used on the rotor drive system, no failure or malfunction will occur in the rotor drive system that will impair the capability of the crew to execute an emergency descent and landing. The lubrication system failure modes of interest usually are limited to failure of external lines, fittings, valves, coolers, etc., of pressure lubricated transmissions.
(2) Procedures. Conventionally, a bench test (transmission test rig) is used to demonstrate compliance with this rule. Since this is essentially a test of the capability of the residual oil in the transmission to provide limited lubrication, a critical entry condition for the test would be the critical eligible lubricant preheated to the transmission oil temperature limit. With the transmission operating at maximum normal speed, with lubricant as described above, with nominal cruise torque applied (reacted as appropriate at main mast and tail rotor output quills), and with a vertical load at the mast equal to gross weight of the rotorcraft at 1g, disconnect or cause to leak an external oil plumbing device. Upon illumination of the low oil pressure warning (required by § 27.1305), reduce engine input torque to zero to simulate autorotation, and continue rotation for 15 minutes. Apply input torque to simulate a minimum power landing for approximately 15 seconds to complete the test. Successful demonstration may involve limited damage to the transmission provided it is determined that the autorotative capabilities of the rotorcraft were not significantly impaired.
424A. § 27.927 (Amendment 27-23) ADDITIONAL TESTS.
a. Explanation. Amendment 27-23 changed § 27.927 by adding a requirement that the rotor drive system overtorque tests prescribed by § 27.927(b)(3) be conducted at the maximum rotational speed intended for the power condition of the test. The previous rule only specified the torque to be applied to the rotor drive system during the overtorque test.
b. Procedures. The changes to this section did not change the suggested method of compliance.
425. § 27.931 SHAFTING CRITICAL SPEEDS.
a. Explanation.
(1) At certain speeds, rotating shafts tend to vibrate violently in a transverse direction. These speeds are variously known as "critical speeds," "whirling speeds," or "whipping speeds." The vibration results from the unbalance of the rotating system and can be shown to reach destructive values with only minimal unbalance. The nature of this phenomena is that as shaft rotational speed increases, residual unbalance in the shaft gives rise to centrifugal forces. These forces cause the shaft to rotate in a bent or bowed configuration with the centrifugal force induced bending loads being balanced by coriolis and elastic forces in the shaft. As shaft rotational speed increases, the Par 424 541
АС 27-1А 7/30/97 centrifugal forces increase to the point at which they exceed the elastic forces in the shaft, and divergence occurs. This point in the speed range is called the critical speed.
At shaft speeds above the critical speed, a 180° phase change occurs, the shaft's mass center moves toward the center of rotation, and the amplitude of vibration diminishes with further increases in shaft speed.
(2) A design option would be to operate the shafting subcritical; i.e., below the first critical speed, with adequate margins between critical speed and the maximum allowable speed, including transients. However, another option, that of supercritical shaft operation; i.e., operating above the first or even higher critical speeds with adequate margins between any critical speed for the normal operating speed range may be permitted. This latter option requires some form of system damping to permit safe transition through the critical speed range and to avoid excessive nonsyncronous vibrations or instability when transitioning through the critical speed.
(3) A review of typical design practices and drive system arrangements discloses several types of shaft support and loading:
Main rotor/mast/transmission assemblies rigidly mounted to the airtrame.
(її) Main rotor/mast/transmission assemblies compliantly mounted to the airframe.
(iil) Main rotor supported through a bearing arrangement by a rigid nonrotating structure with a coaxial torque shaft driving the rotor.
(iv) Cross-shafting, interconnect shafting, tail rotor drive shafting which are generally supported by gearboxes at each end and by hanger bearings and couplings at intervals along the tail rotor drive shaft.
(v) Engine to transmission shafting which, for compliant pylons, incorporates a flexible or geared coupling, to accommodate the misalignment and chucking.
(vi) Tail rotor/mast/gearbox supported on the tailboom or near the upper extremity of a vertical fin.
(4) With regard to compliant pylon mountings, recent developments in vibration control have led to rotor isolation wherein the fuselage is isolated from the rotor and transmission, resulting in improved vibration and system reliability. Rotor isolation systems typically entail the installation of isolation devices at the transmission-airframe interface. The crux of rotor isolation is providing adequate, low-frequency isolation without excessive relative displacement or loss of mechanical stability. Rotor isolation affects shaft critical speeds in the tollowing ways:
542 Par 425
First, the transmission mounting configuration, system stiffness, and tuning requirements may result in different fore-and-aft and lateral natural frequencies, imposing additional analytical requirements. For compliant mounting, the response while transitioning through the fundamental or rocking modes is generally controlled by dampers or elastomeric elements.
(ii) Second, the relatively high displacements permitted by the isolation system, depending on configuration, may result in variations in shaft misalignment and length thus adding further complexity to the analytical prediction of critical speeds.
b. Procedures.
(1) Subcritical Shafting Designs. Three basic methods of qualification may be considered, with the required margins relative to the degree of assurance provided.
The margins are shown for guidance only.
Analytical.
(A) Simplistic model (s) as shown in Figures 425-1 and 425-2;
35-percent margin shown above maximum operating speed.
(B) Detailed model, taking into account significant variations in shaft stiffness, mass distribution, cone adapters, support bearing stiffnesses, support structure; 20-percent margin shown above maximum operating speed.
(ii) Analytical supported by tests. Analysis supported by shake test (rotating or nonrotating) or by bench test, where appropriate adjustments are made for differences between the bench and the aircraft; 15-percent margin shown above maximum operating speed.
(iii) Whirl test on the aircraft (A) For all cases, it should be shown that, under maximum permissible unbalance and at the maximum operating speed, the shafting and support structure has acceptable clearance and does not have excessive vibration.
(B) For compliant pylon mountings, damping of the rigid body rocking modes, which are often transitioned during runup to normal speed (and which are not critical flexing modes), may be verified by analyses, laboratory tests, or ground runup with the rotor at maximum permissible unbalance. Damping on the order of 5 percent equivalent viscous damping is generally acceptable.
(C) For tail rotor masts, the analysis should include fixed system structural response including tailboom, fixed control surfaces, and vertical fin. The Par 425 543
frequency analysis will then contain both fixed system and rotating system modes. An energy analysis can then be used to identify whether the modes are predominantly fixed system or rotating system modes. Systems with up to 35-percent energy in the rotating system have been operated in the field without significant problems. For this type of shafting installation, it is advisable to avoid fixed system modes at multiples of shaft speed, particularly where highly nonisotropic mountings exist.
(2) Supercritical Shafting Design. Another facet occasionally encountered with shafting is the concept of normally operating at speeds above the critical speed, commonly referred to as "supercritical operation." To function properly, suitable dampers must be installed to enable the shaft to pass safely through the lower critical speed up to the operating speed, and speed controls should be devised to avoid any tendency to operate continuously at any critical speed. Accurate balancing of the rotating components will also decrease the energy to be dissipated into the damping device during transition thereby increasing its serviceability and reliability. Note that damper design and locations become more complex as selected operating speed increases through the third or fourth critical frequency. Multiple node points will exist where dampers will not be effective. Production specimen testing at high speed/high torque conditions should include checks for shaft straightness until experience verifies that shaft deflecting is not significant. For systems utilizing squeeze film dampers at the support bearings, variations in oil pressure, flow restrictions, and the effects of bearing preload should be evaluated. The effects of shaft and unbalance and the proximity of the damper to bottoming under maximum unbalance should be evaluated.
(3) If the shafting configuration of the rotorcraft includes universal joints or misalignment couplings, a velocity differential will exist across the joint which creates sinusoidal torques and bending moments at both shafts at multiples of the rotation speed. To avoid amplification of these torques and bending moments, the design should preclude coincidence of critical speeds and multiples of normal speeds.
(4) Order 8110.9, Handbook on Vibration Substantiation and Fatigue Evaluation of Helicopters and Other Power Transmission Systems, also addresses this subject. This document is distributed to section level and above in all Regional Aircraft Certification Offices.
544 Par 425
Wer = M + 0.23m Wer = first critical speed, RAD/SEC = shaft spring rate, LB/IN = 3EI/L 3 E = modulus of elasticity = moment on inertia M = mass of weight, LB-SECZ/IN m = mass of shaft, LB-SEC /IN FIGURE 425-1. CANTILEVERED SHAFT, FIRST CRITICAL SPEED D/SEC Wer = a E I u L4 Wer = first critical speed-RAD/SEC = mass per unit length E = Young's modulus L = length between supports = inertia of shaft a = a numerical constant: for first critical speed, a = (pi) = 9.87 The numerical constant (a) for higher critical whirl modes or other shaft support systems may be derived from standard texts on this subject.
FIGURE 425-2. SHAFT BETWEEN SUPPORT BEARINGS, FIRST CRITICAL SPEED Par 425 545