AGMA 13FTM19-2013 Gear Resonance Analysis and Experimental Verification Using Rapid Prototyped Gears.pdf
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1、13FTM19 AGMA Technical Paper Gear Resonance Analysis and Experimental Verification Using Rapid Prototyped Gears By S.R. Davidson and J.D. Hayes, The Boeing Company - Philadelphia 2 13FTM19 Gear Resonance Analysis and Experimental Verification Using Rapid Prototyped Gears Scott R. Davidson and Jeffre
2、y D. Hayes, The Boeing Company - Philadelphia The statements and opinions contained herein are those of the author and should not be construed as an official action or opinion of the American Gear Manufacturers Association. Abstract Determination of gear resonance frequencies is necessary in the des
3、ign of light weight aerospace gears. Resonant frequencies and mode shapes calculated are then identified as damaging or non-damaging and compared to the gears mesh frequencies to determine if gear tooth bending stresses will be amplified in a particular operating speed range. Finite Element Analysis
4、 (FEA) is well suited to determining gear resonant frequencies and modes. In order to verify the analysis quickly, rough gear geometry is fabricated and tested using accelerometers and a calibrated hammer in a modal excitation test. In past efforts, rough geometry fabricated was a simplified version
5、 of the final part minus gear teeth or other features. To reduce the time of fabrication and to increase the accuracy of the prototype part, modern rapid prototyping manufacturing techniques may hold promise in approaching the realism of the actual part with material properties that are similar to m
6、aterial properties of gear steels. This paper studies gear resonance modal excitation testing of two stage idler spur gear rapid prototyped parts, using two different rapid prototyping techniques and compares results to the final production part and FEA model. Damaging and non-damaging modes and nom
7、enclature will be reviewed as well as the testing method. Copyright 2013 American Gear Manufacturers Association 1001 N. Fairfax Street, Suite 500 Alexandria, Virginia 22314 September 2013 ISBN: 978-1-61481-076-6 3 13FTM19 Gear Resonance Analysis and Experimental Verification Using Rapid Prototyped
8、Gears Scott R. Davidson and Jeffrey D. Hayes, The Boeing Company - Philadelphia Introduction Weight reduction is of great importance in the design of gearing for aerospace applications. Natural resonance responses of the gear head and shaft change in frequency and amplitude as weight is reduced for
9、aerospace gears. Care should be taken to understand the gear resonance modes and compare the modes with operating speeds. Modes should be evaluated and characterized by their impact on amplifying gear tooth root bending stresses. If not addressed, damaging modes could magnify fatigue bending stresse
10、s and cause tooth bending failures of the gear. Once determined, damaging modes can be shifted or gear damping techniques applied to the design. Finite Element Analysis (FEA) is used to determine gear resonance frequencies which are compared to the usage of the aerospace gear. Due to the costs and t
11、ime involved in the design and build of an aerospace gearbox, tests to reduce risk are used to build confidence in the design and analysis techniques before the final product reaches an aircraft. In main power drive applications for helicopters as well as aircraft mounted accessory drives, gear reso
12、nance response tests, known as rap tests, are conducted to determine by test, the frequencies and shapes of gear resonance modes. Due to the long lead time involved in manufacturing light weight, carburized steel gears, rap tests are sometimes conducted on non-carburized test parts that approximate
13、the final shape of the completed gear design. In aerospace, our internal culture is one of demonstration of an acceptable design by test. We step through the gates shown in Figure 1 for a gear design as it relates to gear resonance. The focus of this paper is to reduce the time of step 3 validation
14、of the FEA result and not on the overall method used. Tests help to mitigate a potential cost and scheduling debacle if damaging modes are not predicted correctly before the transmission enters test or service. All cost effective opportunities to reduce risk along the development process of aerospac
15、e gearing should be taken advantage of, particularly those which can happen early in the development phase. A test was conducted to evaluate rapid prototyping techniques available on the market. A two stage idler gear was fabricated by using two different rapid prototyping techniques. The two rapid-
16、prototype test specimens as well as the production part were rap tested to experimentally determine resonant frequencies and mode shapes. FEA results were compared to the experimental test results as well. The test gave us a chance to “try-out” rapid prototyped metal parts, now known as additive man
17、ufacturing and attempt to reduce a portion of our risk reduction test time. This paper summarizes the testing conducted, FEA result predictions, and compares rapid-prototype gears to production gear resonance results. The modal excitation test, whether done on the production part late in the program
18、 or on rapid-prototyping parts early in program verify that the FEA analysis has been done correctly and reduce overall program risk. Background Aerospace gears are designed to be as light as possible to transmit speed and torque from one location to another. Understanding loads and environment help
19、 to define a solution which minimizes weight and space required. Gear resonance excitation is a phenomenon where natural frequencies of the gear and shaft are excited by operating speeds. Depending upon the mode shape of the natural frequency, tooth root bending stresses can be amplified beyond inte
20、nded design limits. If not accounted for during the design, unknown elevated bending stresses can lead to crack initiation in the gear tooth root and subsequent failure of torque and speed transmission. 1. Gear/Gearshaft Design2. FEAModify to shift frequencies3. Risk ReductionRap approximate test pa
21、rt to validate FEA step4. Rap Test Final Aircraft Part5. XMSN TestFigure 1. Gear/gear shaft development for resonance 4 13FTM19 Analysis of gear resonance in the design stage consists of using FEA software to mesh three dimensional computer aided geometry and analyzing the geometry under different b
22、oundary conditions. Traditionally modal analysis of gears is done using a free-free boundary condition. The main advantage to free-free analysis is the convenient comparison with experimental test results which are collected by suspending the test gear on elastic strings. The most damaging vibration
23、 modes of interest involve vibration of the gear in diametral modes which are largely unaffected by bearing support boundary conditions. Shaft modes which lie on or near gear mesh frequencies can be further investigated by performing frequency analysis of a finite element model with boundary conditi
24、ons simulating bearing supports. In order to verify analysis of the gear geometry, testing can be conducted before the final part is fabricated on a test gear that is similar in geometry, stiffness and density. In past efforts, rough test gear geometry fabricated was a simplified version of the fina
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