ROMAC齿轮与齿轮传动系统分析PPT文档格式.pptx

1、,Talk 25Analysis of Gears and Geared Systems,Jason Kaplan Paul Allaire Tim Dimond Brad Nichols Amir Younan,Table of Contents,IntroductionObjectivesMotivationModeling of gear mesh stiffnessExternal Parallel Shaft-StagesSpur gearsHelical gearsPlanetary StagesApplicationsSteam-Turbine/Generator Gearbox

2、NREL Wind Turbine GearboxConclusions/Future work,07/26/2011,2,ROMAC Objectives,Geared systems are quite important to many rotating machinesNo major ROMAC geared systems code currentlyNew major advance in ROMAC codesBlake Stringer developed 12x12 generalized gear stiffness matrix in 2006Needs to be m

3、erged with MatlabRotor code combined lateral,torsional,axial motionsNow expanded into planetary gears and other new modeling of geared system componentsMany new applications,07/26/2011,3,From the gearboxes in the cars to the Jet engines.Also in the helicopter specially in the rotor shat and its tran

4、smission system.The focus of our talk today in the Models of these gears stiffness,PW-1000G Geared Turbofan,Jet Engine in Aircraft,Introduction（Gear Application）,4,AH-64D Apache Lon0g7b/2o6w/2011,Automotive gearbox,OH-58D Kiowa Warrior,Motivation,Gearing exists in a large variety of different rotati

5、ng machines where speed and torque conversion is necessaryGear mesh stiffness has significant effects on the mode shapes and critical speeds for the coupled low and high speed shaftsStatic transmission error and other geometric imperfections may produce significant excitation forcesFailure to proper

6、ly model gear mesh stiffness and excitation sources would hinder the ability to predict machine vibration levels,07/26/2011,5,The first is the rotordynamic where the gear is look at as a connection between two point.In these models,the forces of the gear is modeled in a stiffness matrix to connect b

7、etween two nodes.On a smaller level,the contact between the surface of the gear in mesh are affected with the EHL which takes place.EHL contribute to the stiffness between the teeth due to the elastic deformation of the teeth as well as the compressibility of the oil.The third part is the tooth comp

8、liance as seen as a contiliver.Those three stiffness are the three major contributor to build a full gear stiffness.We will be focusing on the Rotordynamic and EHL stiffness,Introduction（Main Idea）,EHL Stiffness Models,Tooth Compliance Models,Rotor Dynamics Models,Full Gear Stiffness model,07/26/201

9、1,6,The stiffness matrix is function of the dimension of the gear as well as the orientation angles of the force.Also this matrix is function of the stiffness coefficient which is multiplied by the matrix.In the same time,the EHL analysis focus on the pressure distribution of the lubricant and the e

10、lastic deformation which takes place between the teeth.As seen in the right diagram.The elasticity of the surface as well as the compressibility of the lubricant affects the stiffness of gear.Here,it came the idea of merging the work done on the gear dynamic with the EHL lubrication to come up with

11、a general model for the stiffness,Introduction（Our Focus）,07/26/2011,7,x,y,K,r2,r1,2,O2,O1,1,1 Rotordynamic Analysis,（Stringer,2008）,Spur Gears vs.Helical Gears,Forces and moments act in xy-plane only（2-D space）Function of pressure angle（an）only3-DOF model（x,y,qz）,Forces and moments in 3-D spaceFunc

12、tion of pressure angle（an）and helical angle（b）6-DOF model（x,y,z,qx,qy qz）,07/26/2011,8,General 12-DOF Mesh Stiffness Matrix,Constructed by using direct method along line-of-action.,Matrix is a function of axis orientation（j）,pressure angle（an）,helical angle（b）,gear and pinion pitch radii（ri and rj）,

13、and average gear mesh stiffness（Kg）.,x,y,K,rj,ri,j,Oj,Oi,i,i,07/26/2011,9,j,Why 12 Degrees-of-Freedom?#,12-DOF models sparse in literatureApplicable to spur gears（3 DOFs）and helical gears（6 DOFs）If modeling a spur gear mesh,helical angle will be set to zero,and the extra DOFs reduce to zeroNumber of

14、 DOFs are generally reduced by convenient choice of axes.Convenient choices are not always available（i.e.,rotorcraft transmission）,12 DOF model necessary,x,y,K,rj,ri,j,Oj,Oi,i,07/26/2011,10,Average gear mesh stiffness,（Spotts,1985）Formula applies for single-tooth-to-tooth contact where,b=face widthE

15、1=Elastic modulus of pinionE2=Elastic modulus of gear,Image From Wikipedia,07/26/2011,11,Average gear mesh stiffness,Factor of 1.3 added to account for the average number of teeth in contact（Stringer,2008）Now automatically included in codeActual stiffness is time-varying as number of contact pairs c

16、hanges,TradeI,07/26/2011,12,Force/Moment Displacement Relationship,x,Nodes i and j contain the DOF solutions for the coupled shafts at the locations of the gear and pinion.All elements of Kmesh are then added into the global stiffness matrix such that the DOFs at nodes i and j match the DOFs at the nodal locations of the gears on the shaft.y,K,rj,ri,j,Oj,Oi,i,i,07/26/2011,13,j,General 12-DOF Mesh Stiffness Matrix,07/26/2011,14,Planetary Stage Modeling,Sunn PlanetsCarrierAnnulus,Kahraman,1994,rj i