AGMA-07FTM18-2007.pdf
《AGMA-07FTM18-2007.pdf》由会员分享,可在线阅读,更多相关《AGMA-07FTM18-2007.pdf(12页珍藏版)》请在三一文库上搜索。
1、07FTM18 Bevel Gear Model by: T. Krenzer TECHNICAL PAPER American Gear Manufacturers Association Bevel Gear Model Ted Krenzer 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 Associatio
2、n. Abstract The paper presents a method for developing an accurate generic bevel gear model including both the face milling and face hobbing processes. Starting with gear blank geometry, gear and pinion basic generator machine settings are calculated. The contact pattern and rolling quality are spec
3、ified and held to the second order in terms of pattern length, contact bias and motion error. Based on the setup, a grid of tooth points are foundincludingthetoothflank,filletand,ifitexists,theundercutarea.Itisproposedasthemodelforthenext generationofbevelgearstrengthcalculationsinthattheprocedurepr
4、oducestruebevelgeargeometry,uses blank design parameters as input and is vendor independent except for cutter diameter. Copyright 2007 American Gear Manufacturers Association 500 Montgomery Street, Suite 350 Alexandria, Virginia, 22314 October, 2007 ISBN: 978-1-55589-922-6 1 Bevel Gear Model Ted Kre
5、nzer For over a hundred years bevel gear tooth strength has been approximated using virtual spur gears. The calculation has adequately served the gear in- dustry. However with new high speed computers, strength estimatesshould bebased ona morereal- istic model.Recognizing the need for improved bevel
6、 and hypoid strength calculations, finite ele- ment and boundary element strength programs based on bevel gear geometry have been develo- ped. Most notable is Dr. Lowell Wilcoxs finite ele- ments stress TCA (tooth contact analysis). Inputto these programs is the actual machine settings and cutter sp
7、ecifications as defined by vender calcula- tions. This is an excellent check on the strength of designed sets. However the engineer must com- plete the entire design process and depend on vendersoftwareforinputdatabeforeatruestrength analysis can be made. In this paper a generic bevel gear tooth mod
8、el that canbethenextgenerationgeartoothstrengthmod- el is developed. Input is basic gear design parame- ters. Thereforecalculations canbe madeat thebe- ginning of design process.Output is basic generator machine settings that can be used to cal- culate a grid of pinionand gearpoints includingfillet
9、and undercutpoints sothat finiteelement orbound- aryelementaswellasconventionalanalysis canbe applied. The only vender input required is cutter di- ameter, blade edge radius and number of blade groups. Eitherthefacemilling(FM)orfacehobbing (FH) generating method can be used. Thesettingsproducespecif
10、iedtoothsurfacestothe second order. Procedures for calculating toothsur- facepointsaswellasfilletpointsareincluded. Sep- arate pinion setups for the drive and coast sides, rather than completing setups, are calculated. This is partly done so as not to provide generation meth- ods that compete with v
11、ender calculations. Due to length constraints not all formulas can be included. A complete set of formulas can be found in the authors book titled The Bevel Gear. Basic generator The basic generator is configured with a machine base that carries a generating head and a work head mounted on its horiz
12、ontal face with the offset perpendicular to the horizontal face. The generating head has a cradle that carries the face mill cutter whose axis is offset from the cradle axis by an adjustable radial distance, S, set at an angle, q, from the horizontal direction. The cutter, which has a radius, rcP,an
13、d a pressure angle, b, can have its axis tilted by an angle, i, relative to the cradle axis. The direction of the cutter tilt angle is referenced relative to a perpendicular to the radial distance by the swivel angle, j. The cutter phase angle, G, about the cutter axis (not shown) is from the direct
14、ion of tilt to the contact point. The work head holds the work in a spindle with its axis the in horizontal plane. The work head is ro- tated by the angle, m, about the offset line that in- tersects thecradle axis. Thework isadjusted adis- tance, Xp, along its axis and a distance, Em, in the offset
15、direction. The work head also is adjusted a distance, XB, along the cradle axis. A timed roll relationship between the cradle and work, Ra,is set.For face hobbing an additional timed roll relationship between the cutter and the workisadded. The basicgenerator configurationis shown in Figure 1. Figur
16、e 1. Basic generator configuration 2 Generating processes With face milling, the generator is setup so that the cutter produces the desired spiral and pressure angles and the cutter blade tips follow the root line. Cutter blades rotate through the work piece, pro- ducing a slot as the generator and
17、work rotate togethertogeneratethetoothsurface. Thecutteris withdrawn, the work piece is indexed and cycle is repeated. See Figure 2. Figure 2. Face milling cradle/cutter setup With face hobbing, the generator is setup to follow the root line and produce the desired spiral and pressure angles taking
18、into account the continuous indexing motion.Cutter blades are arranged in groups with the work indexing one tooth as each blade group passes through the cut. The indexing motion is superimposed onthe generatingprocess. All teeth are formed in a continuous cycle.The lengthwise tooth form is a kinemat
19、ic curve.See Figure 3. Figure 3. Face hobbing cradle/cutter setup Generator vector model Thecoordinatesystemisdefinedwiththeivectorin the machine horizontal plane pointing to the right. Thejvectorisalongthemachineverticalaxispoint- ingup. Thekvectorpointsoutinthedirectionofthe cradle axis. Figures 4
20、 and 5 show a vector setup of the generating machine as defined below. Unit vector along the cradle axis g = (0, 0, 1) Unit vector in the offset direction e = (0, 1, 0) Unit vector along the pinion axis p = cosm, 0, sin m Vector from machine center to cutter center S = S (cosq, sin q,0) Unit vector
21、along the cutter axis c = ( sinisinj, sinicosj, cosi) Cutter radial unit vector r = ( cos i sinj, cosi cosj, sini) Unit vector along the cutting element t =sinb isinj, sinb icos j,cosb i Figure 4. View looking along cradle axis Figure 5. View looking down on generator 3 Assuming some distance s alon
22、g the cutting ele- ment t from the tip of thecutter toa pointon thecut- tingelement,thepositionvectorAfromthemachine center to the point is A = S + rcpr st The position vector R from the crossing point to the point is R = A + Eme + Xpp XBg Input data Gear design: PinionGear Number of teethnN Pitch a
23、ngles Mean cone distanceA Spiral angle Pressure angle (drive/coast)1/2 Face widthF Mean dedendumbPbG Dedendum anglesPG Clearancec Mean gear slot widthWG BacklashBL Cutter specifications: Cutter radiusrc Number of blade groups (FH)nb Cutter edge radiusrePreG Contact parameters (drive/coast): Pattern
24、length factorBd/Bc Contact bias angled/c Motion errorGd/Gc Anyone unfamiliar with the above terms is referred to ANSI/AGMA 2005-D03, Design Manual for Bevel Gears. Control factors A portion of a gear tooth painted with marking com- poundiswipedcleanasagearisrolledwithitsmate under light load. The pa
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- AGMA 07 FTM18 2007
链接地址:https://www.31doc.com/p-3732679.html