1、12FTM16AGMA Technical PaperGear DesignOptimization for LowContact Temperature ofa High-Speed,Non-lubricated SpurGear PairBy C.H. Wink and N.S. Mantri,Eaton Corporation VehicleGroupGear Design Optimization for Low Contact Temperature of aHigh-Speed, Non-lubricated Spur Gear PairCarlos H. Wink and Nan
2、dkishor S. Mantri, Eaton Corporation Vehicle GroupThe statements and opinions contained herein are those of the author and should not be construed as anofficial action or opinion of the American Gear Manufacturers Association.AbstractThis paper presents a gear design optimization approach that was a
3、pplied to reduce both tooth contacttemperatureandnoiseexcitationofahigh-speedspurgearpairrunningwithoutlubricant. Theoptimumgeardesign search was done using the RMC (Run Many Cases) program from The Ohio State University. Over480 thousand possible gear designs were considered, which were narrowed do
4、wn to the31 best candidatesbased on low contact temperature and low transmission error. The best gear design was selectedconsidering,also,itsmanufacturability. Theselectedoptimumgeardesignwascomparedtoanexistinggearset using LDP (Load Distribution Program) from The Ohio State University. Tooth conta
5、ct temperature wascalculated for both designs using dry a steel-on-steel coefficient of friction. Predicted contact temperaturecorrelated well with results observed on dynamometer tests with the existing gear set. Predictions with theoptimized design showed a 48% contact temperature reduction and a
6、79% noise excitation reduction. Thelow contact temperature of the optimized design will significantly contribute to preventing tooth surfacedamage under no lubricant operating conditions.Copyright 2012American Gear Manufacturers Association1001 N. Fairfax Street, Suite 500Alexandria, Virginia 22314O
7、ctober 2012ISBN: 978-1-61481-047-63 12FTM16Gear Design Optimization for Low Contact Temperature of a High-Speed,Non-lubricated Spur Gear PairCarlos H. Wink and Nandkishor S. Mantri, Eaton Corporation Vehicle GroupIntroductionEliminating lubricant in geared systems is both cost saving and environment
8、ally sound, but poses sometechnical challenges. Metal-to-metal contact of tooth surfaces sliding and rolling against each other undercontactpressurecauseshightoothtemperature,whichmayresultinmaterialmicrostructurechanges. Toothsurfaces can severely wear away, and even deform plastically. Tooth slidi
9、ng velocity and contact pressurecan be reduced by changing the gear design. However, such design changes may adversely affect geardynamics and noise that are critical parameters of high speed gears. This paper presents a gear designoptimization approach that was applied to reduce both tooth contact
10、temperature and noise excitation of ahigh-speed spur gear pair running without lubricant. After defining upper and lower boundaries of the maindesign parameters, and the problem constraints, an exhaustive search within the feasible design region wasdone using the RMC (Run Many Cases) program from Th
11、e Ohio State University 1. Over 480 thousandspossible gear designs were considered, which were narrowed down to 31 optimum candidates based on lowtooth contact temperature and low transmission error. Each one of those designs was critically analyzed interms of manufacturability. The selected optimum
12、 gear design was compared to an existing gear set usingLDP (Load Distribution Program) from The Ohio State University 2, which was also used to optimize mi-cro-geometry modification of profile and lead. Tooth contact temperature was calculatedby LDPfor boththeexistingdesignandtheoptimumdesign,andwit
13、hadrysteel-on-steelcoefficientoffriction. Agoodcorrelationbetween predicted tooth contact temperature of the existing gear set and test results was observed. A 48%reduction of tooth contact temperature and a 79% reduction of transmission error were achieved with theoptimized gear design. The low con
14、tact temperature of the optimized design can significantly contribute topreventing tooth surface damage under no lubricant operating conditions.Tooth contact temperatureConjugateactionofgearteethinmeshconsistsprimarilyofslidingandrollingmotions. Atthepitchlineslidingvelocityiszero. However,slidingve
15、locityincreaseswhentheconjugatedteethcontactlinetravelsawayfromthe pitch line in both directions. Contact pressure of gear teeth in mesh also changes along the line of action3. Heat is generated by sliding friction of teeth surfaces. The temperature distribution is proportional to thedistributionofc
16、ontactpressureandslidingvelocity. Theinstantaneous(orflash)temperatureoftoothcontactalong the line of action is calculated by Bloks contacttemperature theory4. The contacttemperature isthesum of maximum flash temperature along the line of action and the tooth temperature, which is thetemperature of
17、the tooth surface before it enters the contact zone 4.The maximum contact temperature is obtained by equation 1.(1)Bmax= M+ flmaxwhereMis tooth temperature, C;fl maxis maximum flash temperature along the line-of-action, which is calculated by Bloks equation.fli= 31.62 K mmiXiwnbHi0.5vr1i vr2iBM1vr1i
18、0.5+ BM2vr2i0.5(2)4 12FTM16whereK is 0.80, a numerical factor for the Hertzian distribution of frictional heat over the instantaneouscontact band width;mmiis mean coefficient of friction;Xiis load sharing factor;wnis normal unit load, N/mm;Xiis semi-width of the Hertzian contact band, mm;BM1is therm
19、al contact coefficients of the pinion, and given byBM=10- 3(MMCM)0.5BM2is thermal contact coefficients of the gear, and given byBM=10- 3(MMCM)0.5Mis heat conductivity, W/(m.K)Mis material density in kg/m3CMis specific heat per unit of mass in J/(kg.K).vr1iis rolling tangential velocities in m/s of t
20、he pinion;vr2iis rolling tangential velocities in m/s of the gear;i is a subscript of line-of-action points.Gear dynamics and noiseTransmission error is widely accepted in the gear community as one of the major excitation sources of noiseand vibration of geared systems 3 5.Transmission error (TE) ca
21、n be described as irregularities of the motion transmitted by gear pairs caused bydeviations from the ideal tooth contact, which arise from tooth topological modifications, manufacturingdeviations, shaft deflections, tooth deflections and mesh stiffness variation along the line of action. Relativeac
22、celerationsbetweenthegearscausedbytransmissionerrorresultinvibrationofgearmassesanddynamictooth forces 6.Transmission error may be expressed as a linear displacement along the line of actions by equation 3.TE = Rb2z2z11(3)whereTE is transmission error, mm,Rbis gear base radius1, 2are the angular rot
23、ation of pinion (input) and output gear, respectively,z1, z2are the number of teeth of pinion (input) and output gear, respectively.The dynamic response of the geared system to transmission error excitation is influenced by the mass andstiffness of gears, shaft, and other major internal components,
24、and damping characteristics 6.Gear design optimization approachThechallengeisamulti-objectiveoptimizationtominimizetoothcontacttemperature,andtransmissionerror,subject to maximum contact and tooth root stresses below allowable stresses values, and also subject toconstraintsrelatedtopackagingsize,suc
25、hasmountingcenterdistance,andmaximumfacewidth,andmanu-facturability such as undercut condition, minimum topland, and root clearance. There are many designvariables to be determined as part of the problem solution. These variables refer to the gear geometricalparameters, such as module, pressure angl
26、e, addendum modifications, and outside diameter.5 12FTM16One convenient and robust approach to solve this optimization challenge is to combine the gear designknowledgeandcomputationalpowerofmoderncomputerstocompletely sweepthe feasibledesign regiontofind the optimum design.UsingtheRMC(RunMany Cases)
27、program developedby TheOhio StateUniversity 1,thousands ofpoten-tialgeardesigncandidatesarequicklygeneratedandanalyzedbasedonthegeardesignersinputs. Thegearset that best meets the objective functions and constraints can be identified using range reduction methodsthat select design candidates within
28、defined ranges and parameter prioritization 7.Application exampleAn existing spur gear set of an automotive timing gear application that runs at high speed was tested withoutlubrication. Results of this exploratory test were used to create a baseline for comparison with the optimizeddesign.Thegearsw
29、eremadeofSAE4100(Cr-Mo)seriessteelandinductionhardenedto56to61HRCsurfacehard-ness. Tooth flanks were ground to achieve AGMA grade A4 8. The gear samples were submitted to adynamometer cycle of rotational speeds up to 16,000 rpm (pitch line velocity up to36.3 m/s), and light loads(up to 0.86 Nm/mm of
30、 face width). The outlet air temperature recorded during the test was 150C.Figure 1 shows the baseline gear set after over 100 hours of test.Thedrivesideoftheteethofbothgearswasseverelyworn,andmaterialplasticallyflowed outtoward thetwofaces(seeFigure 2). The amountof wearmeasured ontooth profileof t
31、hedriver gear,which isshown ontheleft side of Figure 1 and Figure 2, was 0.130 mm, and the driven gear was 0.115mm.Figure 1. Baseline gear set after testFigure 2. Base gear teeth after test6 12FTM16Both gears were metallurgically analyzed. Microhardness measured results on the gear teeth indicated t
32、hatthe gears were exposed to a temperature range of 450 and 510C, which was estimated using the materialtempering curve.In parallel with the metallurgical analysis, the tooth contact temperature was calculated using LDP program.Table 1 shows the temperature parameters that were used for the calculat
33、ion.The results of tooth contact temperature is shown in Figure 3 for the baseline gear set, which is close to thelowerlimitestimatedfromthemetallurgicalanalysis. Inadditiontothetoothcontacttemperaturepredictionatnominaldesigncondition,arobustnessanalysiswasalsoperformedoverdeviationsandtolerancessp
34、ecifiedon the gear drawings. The results are shown in Figure 4.Table 1. Temperature calculation parametersParameter ValueCoefficient of friction 0.5Inlet bulk temperature 150CThermal conductivity 48 W/(m K)Density 7860 kg/m3Specific heat 544 J/(kg K)Figure 3. Predicted tooth contact temperature of b
35、aseline gear setFigure 4. Robustness analysis of baseline gear set7 12FTM16The robustness analysis results indicate that the tooth contact temperature prediction for the baseline gearset falls in range of 411 to 543C with average of 475C and standard deviation of 23.78C. Therefore, anexcellent corre
36、lation was established for the baseline gear set.Then,theboundaryconditionswereestablishedfortheoptimumdesignsearchinRMC,alongwithupperandlowerlimitsforthedesignparameters. Table 2showsthevaluesthatwereusedonthisstudy. Thelastcolumnin Table 2 is the number of points between the lower and upper limit
37、s. Center distance and gear face widthwere kept the same as the current design. Gear ratio is 1.0.A total of 483,372 good gear design candidates were generated under those conditions. They are shown inFigure 5.RMC uses a modified equation to calculate tooth contact temperature that is different from
38、 equation 1 and 2.Thus RMC results were used as directional values only.The Range Reduction Method in RMC was used to eliminate candidates with bending and contact stressesthatexceedtheallowablestressesfortheapplication,eventhoughthecontacttemperatureandtransmissionerror were acceptable. The 31 cand
39、idates that met the given restrictions are displayed in Figure 6. Thedifferences among them in terms of tooth contact temperature and transmission errors are small. The pointidentified with a star was the one selected as the best design because of its manufacturability.The best design geometry was t
40、hen transferred into LDP to confirm the calculation results, optimizemicro-geometry modifications, and do robustness analysis. Micro-geometry modifications were definedusing LDP 3D Microgeometry Analysis module as 2 to 6mm profile crown, and 0 to 4mm lead crown.Table 2. Variable limits for optimizat
41、ionDesign parameter Value LevelsNumber of teeth 10 - 60 51Pressure angle, degrees 12.5 - 25 20Tool dedendum coefficient 1-1.2 10Hob shift level - - 10Backlash coefficient 0.048 - -Minimum topland coefficient 0.20 - -Minimum root clearance 0.15 - -Minimum SAP roll angle, degrees 4 - -Figure 5. RMC tr
42、ansmission error versus tooth contact temperature results8 12FTM16Figure 6. RMC best results(The star identifies the selected design.)Table 3 shows a comparison of the current design and the optimized design for low contact temperature andtransmission error (PPTE).The robustness analysis also showed
43、 that the optimized design is less sensitive to manufacturing deviationsthan the current design. Predicted tooth contact temperature ranges from 233 to 262C with a standarddeviationof6.16Ccomparedtothe411to543Cwithastandarddeviationof23.78C forthe currentdesign.Gear samples have been made for valida
44、tion testing, Figure 7. Two heat treatment processes have beenconsidered: induction hardening (current process), and nitriding, which may provide additional wear resist-ance because of high surface hardness and white nitrided layer. In this case the gears are finished beforenitriding.Table 3. Result
45、s before and after optimizationParameter Current gear set Optimized gear setNumber of teeth 41 57Module, mm 1.06 0.75Pressure angle, degrees 14.5 18Contact ratio 2.24 2.15Slide to roll ratio 1.32 0.63Contact stress, MPa 797 752Tooth root stress, MPa 131 198PPTE, mm 0.59 0.12Contact temperature, C 44
46、7 232Figure 7. Gear samples of optimized design9 12FTM16The gear samples of the optimized design will be tested with the same dynamometer cycle used for thecurrent gear endurance testing, and results will be compared to the current gear set test results.DiscussionsA good correlation between the pred
47、icted tooth contact temperature using LDP and the temperatureestimated from micro-hardness and material tempering curve was obtained to an existing gear set that wastested at high speed and without lubrication. The gear design was, then, optimized using RMC and LDPprograms. The best gear design for
48、low contact temperature and low transmission error was selected frommore than 480 thousand designs. A 48% reduction of tooth contact temperature and a 79% reduction oftransmissionerrorwereachievedwiththe optimizedgear design,which isalso morerobust tomanufacturingdeviationsthanthecurrentdesign. Them
49、ainreasonforthereductionincontacttemperatureoftheoptimizeddesign was the slip-to-roll ratio reduction, which was proportional to the reduction in temperature. The lowcontact temperature of the optimized design can significantly contribute to prevent tooth surface damageunder no lubricant operating condition, which will be confirmed through dynamometer endurance testing.AcknowledgmentsThe authors thank Eaton Corporations Vehicle Group for support to develop this p
