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
25、l part minus gear teeth or other features (Reference 1). Part fabrication was simplified to reduce the time needed and traded for accuracy of predicting the final part gear resonance frequency and mode shapes. The goal of the rap test is to cost effectively validate the FEA results with a focus on n
26、ot all the modes, but the ones that we believe amplify bending stress. With the evolution of computing power and FEA packages, increasingly complex parts with denser meshes can be analyzed that more closely match testing of final part geometries. On the manufacturing front, advancements in five axis
27、 machining and rapid prototyping, or additive manufacturing, hold promise for more accurate test gear geometries without sacrificing the fabrication time. Test specimen design and analysis A two stage spur gear design with an integral shaft was chosen for the test which is used in an aircraft transm
28、ission design. A cross section of the idler gear is shown in Figure 2. Basic parameters of the two gears are listed in Table 1. Figure 2. Cross section of Idler 4/5 Table 1. Test gear description Idler 4 Idler 5 Diametral pitch 1/inch 10 10 Number of teeth 44 63 Pitch diameter inches 4.400 6.300 Fac
29、e width inch 0.600 0.600 NOTE: Gear teeth and bearing races are carburized and ground. 5 13FTM19 For the resonance test, two rapid prototyping processes were employed for the manufacturing of test gears. One test gear was made using Direct Metal Laser Sintering (DMLS) technology, see Figure 3. DMLS
30、is an additive manufacturing process where metal powder is deposited on a surface and made solid by the use of a laser. Layers were deposited in 0.001 inch increments until the entire part was created. Part size is limited to the dimensions of the machine; in this case the volume was limited to 9 in
31、ch x 9 inch x 8 inch. A second test gear was made of 1018 steel using a 5 axis Computer Numerical Controlled (CNC) milling operation, see Figure 4. The computer aided design file was provided as a template for the milling machine. The gear teeth were cut by electric discharge machining (EDM). Figure
32、 5 shows the as-received test gear. The actual aircraft gear application is a carburized and hardened gear made of Pyrowear 53 gear steel. The part was manufactured using conventional turning, hobbing, and grinding processes. Figure 5 shows a picture of the aircraft gear used for the test. Gear mate
33、rials for the test were chosen to closely match the density of the final part configuration. Table 2 compares material properties for the two test gears and the actual aircraft part. Figure 3. Direct metal laser sintering test part Figure 4. Five (5) axis CNC milled test part 6 13FTM19 Figure 5. Act
34、ual aircraft gear Table 2. Gear material properties Test gear 1 Test gear 2 Aircraft gear Manufacturing process DMLS 5 axis CNC Conventional Material Maraging steel 1018 steel Pyrowear 53 steel Modulus 23.5-29.5 Msi 29.0 Msi 29.0 Msi Density 0.289-0.293 lb/in3 0.284 lb/in3 0.283 lb/in3 Part weight 5
35、.9127 lbs 5.9859 lbs 5.9013 lbs An FEA analysis of the gear was performed using ABAQUS. The solid geometry was taken directly from a Computer Aided Design (CAD) model created in CATIA and imported into ABAQUS. The CAD model contained gear and spline teeth that were modeled as involute teeth. After t
36、he gear geometry was imported, a detailed mesh using 10-node quadratic tetrahedron elements (C3D10) was constructed, as shown in Figure 6. Figure 6. Finite element mesh of gear 7 13FTM19 A frequency analysis solution was run using the Lanczos eigensolver method. Modes in the frequency range of 10 Hz
37、 to 20,000 Hz were extracted. Six rigid body modes, three rigid and three rotational, at zero frequency were ignored. Only the lower frequency mode of the orthogonal modes was processed. At this point, we need to address how to describe each shape. Shapes can act individually or respond together at
38、a particular frequency. Reference 2 provides guidance for classification of different mode shapes into three categories of increasing concern. Below summarizes the three categories presented in 2: Insignificant modes modes that are unlikely to magnify gear bending stress Complex modes modes that cou
39、ld be significant Simple modes modes that will magnify gear bending stress Presented in Table 3 are descriptions and classifications of some of the modes noted during the test. Test A gear rap test was performed of each test gear configuration. The test setup consisted of suspending the test gear by
40、 a rubber cord. The gear was inspected by striking with an instrumented hammer at a prescribed location and then recording the response using an accelerometer mounted on the part. This mimics an unsupported gear configuration where the part is free from mounting constraints known as a free-free rap
41、test. A picture of the test setup is shown below in Figure 7. A special instrumented hammer was used to apply a force to the part. The accelerometer measured the magnitude of the load applied and acted as a trigger for the time measurement of the response. An accelerometer to measure the response wa
42、s chosen based on the size of the part. The response accelerometer was moved between various predetermined positions while the hammer impacted the same location and direction. The accelerometer was mounted on the web to measure axial response and then the test was repeated mounting the accelerometer
43、 on the gear tooth topland to measure radial response. A data analysis package was used to align the different responses and to provide a visual representation of the measured results. The goal of the test is to determine the frequency at which mode shapes occur. Not all mode shapes will be sought d
44、uring the test. Figure 7. Idler 4/5 gear in test setup 8 13FTM19 Table 3. Mode shapes Name Description Figure Category 2DR Diametral mode about 2 nodal lines C WB Web rocking where gear 4 and gear 5 are rocking out of phase A SR/2WB Shaft rocking in phase with web rocking with two nodal lines B UMB
45、Umbrella mode with both gears in phase A 3DR Third diametral mode C SR/WB Higher order coupled shaft rocking and web B 9 13FTM19 Results Table 4 summarizes mode shapes and frequencies measured for the two rapid prototyping gear parts, the production aircraft part and the FEA results. The subject idl
46、er gear has two gears on a common shaft. The larger gear is labeled gear 5 and the smaller is labeled gear 4. The first column in Table 4 describes which gear was active in the modal response for that frequency. When both gears were involved to a significant degree in the mode shape the “gear” is la
47、beled 4/5. The second column in Table 4 describes the mode shape. The first mode shape as represented in the test laboratory software is shown in Figure 8. Discussion of results Results showed correlation between the FEA approach, the DMLS test gear and the 5-axis CNC gear. The natural frequencies p
48、redicted by the FEA method were within 1% of the frequencies measured on the aircraft part. The 5-axis CNC part produced responses with an average error of 2% greater than the aircraft part. The DMLS gear produced responses that were on average 9% lower than the production part. The lowest and highe
49、st deviations of the DMLS part from the aircraft part were 8.28% and 10.29% respectively. Although this was not as accurate as the other methods from the absolute frequency stand point, the DMLS gear natural frequencies were consistently lower than the production gear by roughly 9%. This is due to either a lower modulus of the DMLS maraging steel, a higher density or a combination of both. In natural frequency analysis, the ratio of the elastic modulus to the density of the material is a key parameter. nEf (1) Table 4. Summary of mode shapes and frequencies me
