ACTIVE CONTROL OF GEARBOX VIBRATION Brian Rebbechi Carl Howard Colin Hansen Airframes and Engines Division Aeronautical and Maritime Research Laboratory Melbourne, Victoria Australia Department of Mechanical Engineering University of Adelaide Adelaide, South Australia Australia Department of Mechanical Engineering University of Adelaide Adelaide, South Australia Australia ABSTRACT Active vibration control was successfully applied to the meshing of gear teeth inside a gearbox to reduce the vibration at the mounting points of a gearbox and the radiated sound pressure level. Magnetostrictive actuators inside the gearbox were used to move the shaft on which the input pinion was mounted, which in turn modifies the kinematic meshing behaviour of the gear teeth. An adaptive feedforward controller was used to determine the correct amplitude and phase of the force the actuators applied to the shaft to minimize the vibration at the feet of the gearbox housing. The vibration was attenuated by 20-28dB at the 1x, 5-10dB at 2x and 0-2dB at 3x gear mesh frequencies, by simultaneously minimizing the first 3 harmonics of the gear mesh frequency. INTRODUCTION In the field of transmission design, it may be advantageous to reduce the vibration transmission into the support structure. Designers often use helical or herringbone shaped gear teeth in gearboxes because they result in lower vibration levels compared to spur shaped gear teeth. Once the gear tooth shape and the manufacturing process and precision has been chosen, the resulting vibration that the gearbox exhibits is accepted as inherent and it is then left to a vibration engineer to select suitable isolators to reduce the vibration transmitted into the support structure. However even with well designed isolators there will always be some residual vibration that is transmitted into the support structure. If the source of the vibration in the gearbox can be reduced, then there will be less residual vibration in the support structure. There are essentially three mechanisms responsible for the generation of noise and vibration by gear teeth. If the transmitted force between the teeth varies in amplitude, direction or position, then the gears will vibrate and will generate noise. These mechanism occur when there is friction between the teeth, poor surface finish on the mating parts, an imperfection in the tooth profile or a transmission error, which is the relative displacement between the gear teeth [1]. This paper describes an experimental gearbox that can reduce the transmission error and the
Transcript
ACTIVE CONTROL OF GEARBOX VIBRATION
Brian Rebbechi Carl Howard Colin HansenAirframes and Engines
DivisionAeronautical and Maritime
Research LaboratoryMelbourne, Victoria
Australia
Department of MechanicalEngineering
University of AdelaideAdelaide, South Australia
Australia
Department of MechanicalEngineering
University of AdelaideAdelaide, South Australia
Australia
ABSTRACT
Active vibration control was successfully applied to the meshing of gear teeth inside a gearboxto reduce the vibration at the mounting points of a gearbox and the radiated sound pressurelevel. Magnetostrictive actuators inside the gearbox were used to move the shaft on which theinput pinion was mounted, which in turn modifies the kinematic meshing behaviour of the gearteeth. An adaptive feedforward controller was used to determine the correct amplitude and phaseof the force the actuators applied to the shaft to minimize the vibration at the feet of the gearboxhousing. The vibration was attenuated by 20-28dB at the 1x, 5-10dB at 2x and 0-2dB at 3x gearmesh frequencies, by simultaneously minimizing the first 3 harmonics of the gear meshfrequency.
INTRODUCTION
In the field of transmission design, it may be advantageous to reduce the vibration transmissioninto the support structure. Designers often use helical or herringbone shaped gear teeth ingearboxes because they result in lower vibration levels compared to spur shaped gear teeth.Once the gear tooth shape and the manufacturing process and precision has been chosen, theresulting vibration that the gearbox exhibits is accepted as inherent and it is then left to avibration engineer to select suitable isolators to reduce the vibration transmitted into the supportstructure. However even with well designed isolators there will always be some residualvibration that is transmitted into the support structure. If the source of the vibration in thegearbox can be reduced, then there will be less residual vibration in the support structure.
There are essentially three mechanisms responsible for the generation of noise and vibration bygear teeth. If the transmitted force between the teeth varies in amplitude, direction or position,then the gears will vibrate and will generate noise. These mechanism occur when there isfriction between the teeth, poor surface finish on the mating parts, an imperfection in the toothprofile or a transmission error, which is the relative displacement between the gear teeth [1].This paper describes an experimental gearbox that can reduce the transmission error and the
resulting vibration using active vibration control. Actuators inside the gearbox are used to movegears relative to each other to minimize the vibration transmitted through the shaft supportbearings to the gearbox housing.
A review of the literature did not reveal that this application has been considered previously.Previous researchers [2] have used piezo-electric pushers attached to a rotating shaft to reducethe unbalanced vibration in a rotor using feedback control to increase the damping at theresonance frequency of the system.
Previous research into reducing the noise from gears has mainly focused on the tooth shape andirregularities of the tooth profile. Little research has been conducted into using active vibrationcontrol applied to the meshing of gear teeth. A great deal of research has been conducted intothe use of gearbox vibration isolators to minimize the noise and vibration transmitted byhelicopter gearboxes into the cabin [2-6]. A helicopter’s gearbox usually sits directly above thepassengers’ heads and is the source of high levels of noise and vibration. The gearbox is usuallyattached to the fuselage using support struts that are designed to take large mechanical loads.The struts also provide a structural vibration transmission path between the gearbox generatedvibration that couples with the helicopter’s fuselage. The vibration that is transmitted along thestruts comes from the low frequency vibration of the helicopters main rotor and the highfrequency vibration from the gear vibration in the main rotor gearbox. The low frequencyvibration excites the support struts along the longitudinal axis and the high frequency vibrationtends to excite the strut flexurally [7]. Brennan [8] suggested the use of a thin rubber isolatorbetween the gearbox and the fuselage. The thin rubber isolator has a high longitudinal stiffnesscompared to flexural stiffness and hence is able to provide the support for the large longitudinalmechanical load. The isolator can effectively isolate the high frequency flexural vibrations in thesupport strut, but is unable to isolate the longitudinal vibration. The longitudinal vibration alongthe support struts is dominant across the entire frequency range and is the most significantmechanism for noise generation in the fuselage [7-9]. An active vibration isolation system couldbe used to reduce the longitudinal vibration along the support strut. The system would need tobe incorporated in parallel to the existing struts so that the system is fail-safe and the largemechanical load is still supported by the conventional struts. This type of system has beendemonstrated in the Eurocopter [10], and used hydraulic actuators fitted inside each of the strutsto generate a counteracting force to reduce the longitudinal vibration along the strut.
APPARATUS
A schematic of the experimental gearbox is shown in Figure 1. A 30kW synchronous electricmotor drives the input shaft of the gearbox and the output shaft is connected to a dynamometer.Inside the gearbox, spur gears are attached to the input and output shafts, which have 27 and 49teeth respectively. A double row bearing is mounted on the input shaft next to the input pinionand is acted upon by 4 magnetostrictive actuators. Two actuators are aligned with the normal tothe contact point of the meshing gears. Another pair of actuators is perpendicularly mounted tothe first pair, as shown in Figure 2. Each pair of actuators is electrically connected 180° out ofphase so that one actuator is pushing while the other is pulling. Only results obtained using theactuators mounted along the horizontal axis are reported here. The actuators mounted along the
vertical axis had a much smaller effect, presumably due to the small influence that they have ontransmission error.
The experimental rig is shown in Figure 3. A gear with 27 teeth was attached to the output shaftof the gearbox and a proximity probe with conditioning electronics was used to obtain asinusoidal tachometer signal at the gear mesh frequency. A frequency multiplier was used togenerate a sinusoidal signal at 2x and 3x the gear mesh frequency. The particular multiplier thatwas used was not capable of accurately tracking the 4x and 5x gear mesh frequencies. For futurework it is intended to use a different gear with 108 teeth to generate the reference signal for the1x - 4x gear mesh frequencies. The conditioning electronics will be modified so that the 108toothed gear can be used to generate the 1x gear mesh frequency by dividing the number ofpulses by 4. Generating the reference signal for the 1x – 4x gear mesh frequencies by dividingthe frequency of the tachometer signal will be more accurate than multiplying the 1x gear meshfrequency.
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M otor
D yno
G earboxH ousing
M agnetostric tiveA ctuatorD rive G ear
D riven G ear
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Figure 1: Schematic of the equipment setup.
C ontro lA ctua to rs
Foot of gearboxhousing
Figure 2: Side view of the gearbox
Figure 3: The experimental rig
Slight errors occur in the triggering from the square wave signal from the tachometer and theseerrors are amplified when the 1x gear mesh frequency is multiplied to generate a signal at the 4xgear mesh frequency. When the 108 tooth gear is used, the 1x gear mesh frequency will begenerated by dividing the frequency of the tachometer signal by 4, and hence the errorsassociated with the triggering from the square wave signal become smaller.
A Causal Systems feedforward adaptive vibration controller was used to minimize the vibrationat an accelerometer attached to the foot of the gearbox casing. The controller uses a floatingpoint SHARC digital signal processor and has 10 input channels and 10 output channels. Agraphical user interface that runs on a Windows based computer is used to interface with theSHARC controller.
The sinusoidal tachometer signal was used by the controller as a reference signal and wasdigitally filtered to produce a control signal that was supplied to the power amplifiers that wereconnected to the control actuators. The adaptive controller adjusted the weights of the FiniteImpulse Response digital filter until the error signal was minimized, which in this case was theacceleration at one of the feet of the gearbox housing or the sound pressure level at 1m from thegearbox.
RESULTS
Figure 4 shows the vibration levels at the foot of the gearbox housing without active control.The figure shows that the acceleration levels at 1x, 2x, 3x and 4x gear mesh frequencies areclearly distinguishable from the broad-band vibration levels.
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Figure 4: Power spectral density of the vibration at the foot of the gearbox when theactive vibration control system was turned off.
The adaptive controller was used to minimize the vibration at the feet of the gearbox, as shownin Figure 1, at the 1x, 2x and 3x gear mesh frequencies for varying levels of power transmissionand the results are shown in Figure 5. The figure also shows the reduction in Sound PressureLevel (SPL) at 1m from the gearbox when the vibration was minimized. The results show thatactive control was able to reduce the vibration level of the 1x gear mesh frequency by 20dB forall power levels. Although not shown in this figure, the vibration at the 1x gear mesh frequencywas reduced to the level of the broad band vibration spectrum. The corresponding reduction insound pressure level at the 1x gear mesh frequency was between 5-10dB which can be describedas “clearly noticeable” [7].
An active control experiment was conducted to minimize the SPL at a distance of 1m from theside of the gearbox at the 1x and 2x gear mesh frequencies for various power transmission levelsand the results are shown in Figure 6. The 3x gear mesh frequency was not controlled in thisexperiment due to difficulties with the convergence of the controller, however the vibration andSPL levels are shown in the figure for comparison with the previous results. The figure showsthat at the 1x gear mesh frequency there was a reduction in the SPL of about 20dB which couldbe described as “much quieter” [7]. It is interesting to note that for the 5kW to 6kW powerlevels, the vibration level at the 2x GMF was greater for active control by minimization of soundpressure than when the control system was turned off. In this experiment, there was a globalreduction in the SPL because the source of noise generation was being actively controlled.Further measurements are required to quantify these findings.
Figure 5: Active control of the vibration at the feet of the gearbox of the 1x, 2x and 3xgear mesh frequency for varying transmission power levels.
As shown in Figure 4, the SPL and vibration levels at the 4x and 5x gear mesh frequencies weresignificant and should be targeted for reduction by the active control system. At this stage, asuitable reference signal at the 4x or 5x gear mesh frequency could not be generated and will beinvestigated in the future.
Figure 7 shows that when the vibration was minimized at a single frequency, then the vibrationat the feet of the gearbox could be reduced by about 20dB. Minimization of the vibration at thefundamental frequency and the harmonics resulted in less attenuation than achieved byminimizing the vibration at a single frequency. Further work will be conducted to ensure that thesame amount of vibration attenuation is achieved for minimizing the vibration at a singlefrequency or minimizing all of the harmonics of interest simultaneously.
Figure 6: Active control of the SPL at the 1x and 2x gear mesh frequency for varying levelsof power transmission.
CONCLUSIONS AND FUTURE WORK
The experimental results showed that it is possible to reduce substantially the vibration of thegearbox at the 1x, 2x and 3x gear mesh frequencies and the radiated sound at the 1x gear meshfrequency by about 20dB by actively controlling the gear transmission error. The tonal vibrationwas reduced to the level of the broad band spectrum. Further investigations will be conducted tominimize simultaneously the vibration at the 1x to 5x gear mesh frequencies using an adaptivecontroller. Experimental difficulties were found in accurately generating a reference signal thatwas correlated with the shaft speed. Future work will be conducted using a toothed gear attachedto the driving shaft that has the same number of teeth as the 4x gear mesh frequency. Additionalinvestigations need to be conducted to ensure that the same amount of vibration attenuation isachieved when controlling the vibration at a single frequency or controlling the vibration at theharmonics. The actuators along the vertical and horizontal axes will be used simultaneouslytogether with effort weighting to avoid overdriving one set of actuators or the other. Soundpressure level measurements will be taken at several locations around the room to quantify theglobal reduction in the SPL when active control is used to minimize the vibration or SPL.
Minimizing Vibration or SPLat 1x 2x or 3x GMF
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Figure 7: Minimizing the vibration or SPL at a single frequency.
REFERENCES
1. J.D. Smith, Gears and their vibration, (Marcel Dekker Inc., New York, 1983)
2. “Piezoelectric pushers for active vibration control of rotating machinery,” A.B. Palazzolo,R.R. Lin, R.M. Alexander, A.F. Kascak, J. Montage, Journal of Vibration, Acoustics, Stress,and Reliability in Design, 111, July p298-305 (1989).
3. “Helicopter interior noise reduction by active gearbox struts,” W. Gembler, H. Schweitzer,R. Maier, M. Pucher, in Annual Forum Proceedings - American Helicopter Society, 1, May20-22 AHS p 216-229 (1998).
4. “Active isolation of multiple structural waves on a helicopter gearbox support strut,” T.J.Sutton, S.J. Elliott, M.J. Brennan, K.H. Heron, D.A.C. Jessop, Journal of Sound andVibration, 205(1), 81-101 (1997).
5. “Test results of AVR (Active Vibration Reduction) system”, Kawaguchi Hitoshi, BandohShunichi, Niwa Yoshiyuki, in Annual Forum Proceedings - American Helicopter Society, 1,Jun 4-6, American Helicopter Soc, p 123-136 (1996).
6. “Helicopter active noise control system,” C.A. Yoerkie Jr., W.A. Welsh, T.W. Sheehy,United States Patent 5,310,137 (1992).
7. “Active vibration control systems,” A.E. Staple, B.A. MacDonald, United States Patent5,219,143 (1992).
8. “Mechanisms of noise transmission through helicopter gearbox support struts,” M.J.Brennan, R.J. Pinnington, S.J. Elliot, Journal of Vibration and Acoustics, 116 (4), October,p548-554 (1994).
9. “Noise propagation through helicopter gearbox support struts – An experimental study,”M.J. Brennan, S.J. Elliot, K.H. Heron, Journal of Vibration and Acoustics, 120 (3), July,p695-704 (1998).
10. “Terminal source power for predicting structureborne sound transmission from a maingearbox to a helicopter fuselage,” M. Ohlrich, Inter Noise 95, p 555-558 (1995).
11. “The development and testing of an active control system for the EH101 helicopter,” A.E.Staple, D.M. Wells, 16th European rotorcraft Forum, 3, p6.1.1-6.1.11 (1990).
