1、摆线泵泵站设计计算说明书1.前言摆线泵是一种内啮合齿轮泵，具有结构紧凑，容积效率高，工作平稳等特点，在动力机械、机床、和许多轻工业机械中被广泛应用。参阅相关的论文，目前很少有能直接用于摆线泵理论排量精确计算的数学模型，所论述的外转子非啮合区齿廓以锐角转折，不便于制造。为此，根据啮合传动原理，导出摆线泵的齿廓坐标计算的数学公式，并得出了理论排量计算的数学公式，便于从事摆线泵设计和制造的同行直接引用。2.设计原始参数直流电机转速为 8000r/min,行星齿轮转动比 6.0,中心距 a=2.2,油压 8Mpa。3 摆线泵泵站的结构概述摆线泵是一种为输送液质流体而提供中、低压力的装置，它与渐开线齿轮
2、泵比较，在相同的结构尺寸条件下具有流量大的优点。图 1 中绘出摆线泵的三个构件，在座圈上切制了容纳摆线啮合副的圆柱形凹坑，钻出进液孔和出液孔，并且还制出两个圆弧形构槽，作为进液区和出液区。进液孔和出液孔分别与阀板连通。另有一个端盖将摆线啮合副密封（图中未画出） 。在端盖上有，供驱动轴通过并与摆线齿轮键销联接。 出 油 孔进 油 孔 座 圈 摆 线 齿 轮圆 弧 齿 圈内 啮 合 中 心 距图 1 摆线泵的主要构件电动机的转速经一级渐开线行星齿轮机构减速后，使摆线齿轮的驱动轴低速回转，带动摆线泵运转。图 2 中绘出摆线泵的啮合过程，其中摆线齿轮的齿数为 8，分齿角为 45，图示的每步转角 9；圆
3、弧齿圈的齿数为9，在摆线齿轮的推动下，每步对应回转角 8（注：实际运行是连续回转，而不是步进回转） 。当摆线齿轮的转角为 45 时，完成一对轮齿的啮合传动全过程。从图 2 中可以看出：在水平中心线的上方，摆线齿轮与内齿圈之间的齿间空腔逐渐增大，产生负压，因而能经由管道从储液箱吸入油液或其它液态工质；在水平中心线的下方，齿间空腔逐渐减小，从而使已存贮在齿间空腔内的液态工质的压力增大并输出。液态工质的工作压力由后续的液压系统中的溢流阀或调压阀控制。图 2 摆线泵的啮合过程摆线泵的总体结构如图 3 所示，电动机经一级渐开线行星减速机构降速驱动摆线泵的摆线啮合副工作，摆线泵上附有低压液体进液管、溢流阀
4、和高压液体出口接头等相关配件。图 3 摆线泵站的总体结构4 电动机主要参数选择直流电机转速为 8000r/min5 渐开线行星减速传动机构设计渐开线行星齿轮传动设计时必须满足以下 4 项准则要求：1)传动比条件在选配中心齿轮和内齿圈的齿数时，必须满足传动比求。2)同中心距条件即行星齿轮与内齿圈的中心距和行星齿轮与中心齿轮的中心距必须相等。3)多个行星齿轮均匀分布条件即必须保障多个行星齿轮能够被均匀安装在行星架上，并能与内齿圈和中心齿轮正确啮合。4)不邻接条件行星齿轮数量在三个以上时，必须防止相邻的行星齿轮不干涉。5.1 齿数、模数和行星齿轮数目确定(1) 为满足准则 1）,渐开线行星减速机构的
5、传动比按下式计算311Hzi（1）根据输入和输出转速的要求，即可按式设计确定中心齿轮 1 和齿圈 3 的齿数，即 =12(6-1)=60 31()Hzi（2）行星齿轮 2 可按下式计算确定=(60-12)/2=24 31z5.2 变位传动设计计算求得的 值若非整数，应取邻近的整数。为满足准则 2）的要求，可分两种2z情况处理：如按上式求得的 值是整数，则必然满足准则 2）的要求，齿轮2z可以采用标准齿轮，也可以采用变位齿轮；如 值是经圆整后整数，则必须2z采用变位齿轮才能满足准则 2）的要求。5.3 齿轮几何尺寸计算1） 确定模数和齿数根据结构尺寸要求，初选齿轮的模数 m。根据传动比和设置行星
6、齿轮的数量，按式（2）和（4）计算确定齿数 z1、 z3，然后按式（3）计算行星齿轮 2 的齿数 z2。确定齿数 z1、z 2、 、z 3 的过程是一个反复分析比较的过程，力求获得一组优化的数据。齿形标准参数为刀具角 =20、齿顶高系数 ha* =1.0、顶隙系数c*=0.25。2） 变位齿轮传动设计和主要几何尺寸计算计算中心距: 两对齿轮的标准中心距为=0.5(12+24) =18 1212()amz=0.5(60-24)=18 33根据同中心距条件，取 123a3）计算啮合角=34.401779 1212cosar()=34.401779 2323rs()4）计算变位系数=1.178226
7、912121()tanzxivin=-0.7854832323()tii式中渐开线函数按下式计算=0.03872881212taniv=0.014904=0.0387292323taiv角度值以弧度计。根据求得的 和 值，可适当分配 、 、 。1()x32()x1x23在确定各变位系数值时，必须顾及不发生根切的条件和齿顶不变尖条件5.4 齿轮齿廓的渐开线坐标计算及齿形绘制绘中心齿轮 1 的齿廓数据5.63815572471545,05.75008134290669,0.01503337220067825.86188875235798,0.04297290480667495.9734589636
8、1471,0.07976763684788636.08467220523171,0.124060300378546.1954080010376,0.1751054778250596.305545248013,0.2324225988258336.41496229474006,0.2956726142378936.52353702038017,0.3646013811034196.63114691413643,0.4390095661846586.73766915515729,0.5187350108272596.84298069283727,0.60364164873626.946958327
9、47058,0.6936121631718167.04947879121315,0.788542915567917.1504188293083,0.8883403238268837.24965528153119,0.992918203832047.34706516380699,1.102195772738217.44252574995746,1.216096120002887.53591465353061,1.33454501716114绘行星齿轮 2 的齿廓数据11.2763114494309,011.4001953361241,0.012317041873717411.5240392431
10、066,0.035045305514674511.647803037881,0.064761189571203211.7714464284603,0.10028611933527311.8949289713092,0.1409593072526412.0182100793241,0.18634756512058112.1412490298504,0.23614152537409112.2640049727352,0.29010771220971812.3864369384149,0.34806291067470812.5085038460359,0.40985905874358512.6301
11、645116067,0.47537369652381712.7513776561805,0.5445035999650712.8721019140672,0.61716035691866612.9922958410725,0.69326718785482813.1119179227637,0.77275659679539713.2309265827596,0.85556859475817513.3492801910448,0.9416493292463613.4669370723055,1.0309500087245绘内齿轮 3 的齿廓数据29.7764055171656,0.36614264
12、040734329.9225206064648,0.4191987757158130.0685088430429,0.4747891800634330.2143593751647,0.53284027583126130.3600613350851,0.59328744487037630.5056038395319,0.65607343251223830.65097599019,0.72114711589516130.796166874187,0.78846253657179930.9411655645785,0.8579781289671331.0859611208359,0.92965609
13、670548731.2305425893335,1.0034619024280131.3748990038378,1.0793638459934731.5190193859964,1.1573327124120731.662892745829,1.2373414754459631.8065080822183,1.3193650461205431.949854383402,1.4033800578196332.0929206274655,1.4893646814443932.2356957828354,1.5772984654775432.3781688087738,1.667162196833
14、175.5 行星传动啮合状态检验采用多个行星齿轮能提高传动机构的负荷能力，但必须满足上述准则 3）和准则 4） 。设行星齿轮的数量为 ，根据准则 3）的要求，必须按下式校核计n算，并调整 、 和 值。3z12=(60+12)/3=24 为整数 3zk根据准则 4）的要求，必须满足条件式*122()sin(azzh（5）(12+24)sin(/3)=31.167 281）避免产生根切。要求选定的变位系数不小于齿轮不产生根切最小变位系数。2）避免齿顶变尖。要求选定的变位系数不能太大，过大的变位量会导致齿轮的齿顶厚度缩小为零值甚至为负值，这是不允许的。3）各齿轮的变位系数值按无侧隙啮合方程式计算确定
15、。4）绘制啮合状态图为了检查设计计算的正确性，应用 excel 软件计算渐开线齿廓坐标，再应用 auto cad 平台绘制齿轮截面图，并将齿轮截面图安装成行星星传动机构的啮合状态图。在啮合状态图中齿廓不得相交，也不能存在间隙。 渐开线齿廓的坐标计算渐开线方程为 cosbkkrtan基圆半径为，1cos2brmz在基圆上渐开线的压力角为 0，从基圆开始计算渐开线的直角坐标值为csinkkxry值从 0开始，按取定的计算步长，逐次计算出渐开线齿廓的坐标值。k应用 auto cad 平台绘制齿轮啮合状态图。6 摆线泵设计计算6.1 摆线泵的结构参数设定齿数：圆弧齿圈齿数 Z2=9,摆线齿轮齿数 Z1
16、=8、圆弧齿圈的齿面圆弧半径 R=22、齿面圆弧中心的分布圆半径 R=3.8、圆弧齿圈和摆线齿轮的啮合中心距（即偏心距）e=2.26.2 摆线齿轮齿廓坐标计算 绘摆线齿轮的齿廓数据16,7.35089072945172E-1616.0357106774063,0.5218730013113716.1360998539109,1.0121547484420716.2840784658746,1.4480184428295716.4590906695013,1.8191087959856416.6430838831946,2.1257343922557816.8232215868005,2.374
17、5859084711616.9918732195284,2.5748315779644917.1453747404737,2.7356691652784417.2826380951163,2.8651867914663917.4040560660934,2.9700334179820317.510770065953,3.0554826779918817.6042275464505,3.125642008395417.6859347513672,3.1836859389852517.7573297082895,3.2320647159048417.8197248578449,3.27267449
18、47539617.8742879999238,3.3069900489377817.922043141355,3.3361658941145217.9638808135438,3.361112503136318.0005721509342,3.382553520058818.0327837328553,3.4010687237204818.0610917121872,3.417126386121218.085994587031,3.4311077561365818.0973064486072,3.4374198558636818.1079244135602,3.4433256893522518
19、.1272564817092,3.454038911888418.1443175787661,3.4634630127632718.159393004926,3.4717789714719418.1727325105912,3.4791398174117518.1845553148839,3.4856758644934718.19505434779,3.4914988521381718.2043998394807,3.4967052415167218.2127423621058,3.5013788551435118.2202154128194,3.5055930028875318.226937
20、6123469,3.5094122038694818.2330145810718,3.5128935885160818.2385405442192,3.516088046031618.2435997090346,3.5190411681195318.2482674496465,3.5217940287739618.252611329328,3.5243838315060518.2566919849415,3.5268444488430218.2605638942674,3.5292068738704418.2642760435505,3.5314995996337518.26787250980
21、58,3.5337489391127518.2713929701136,3.5359792960367918.2748731482173,3.5382133948700418.2783452071386,3.5404724767538418.2818380951969,3.5427764669588218.2853778517063,3.5451441184086718.2889878776953,3.5475931350377918.2926891762108,3.5501402780973818.2965005661137,3.5528014579976518.300438872715,3
22、.555591813843818.3045190981369,3.5585257824710318.3087545738825,3.5616171584935718.3131570977626,3.564879146643818.3177370570383,3.5683244074789718.3225035393949,3.5719650973685618.3274644331507,3.5758129035378118.3326265179255,3.579879074828418.3379955468374,3.5841744487406118.3435763211648,3.58870
23、94752406518.349372758294,3.5934942377482618.355387953673,3.5985384716620318.3616242374086,3.6038515807308418.3680832260635,3.6094426515381418.3747658701514,3.6153204663302618.3816724977653,3.621493514389718.3888028547291,3.627970002128118.3961561416149,3.6347578620516518.4037310479346,3.641864760732
24、0718.4115257837775,3.6492981059001418.4195381091368,3.6570650527641818.4277653611444,3.6651725096435818.4362044794063,3.6736271429967618.4448520296148,3.682435381913618.4537042255918,3.6916034221341518.4627569499057,3.7011372296484318.4720057731866,3.7110425439259618.481445972254,3.7213248808179718.
25、4910725471596,3.7319895351708618.5008802372376,3.7430415831848818.5108635362456,3.7544858845486718.521016706672,3.7663270843767718.5313337932792,3.778569614974518.5418086359424,3.7912176974519218.5524348818429,3.8042753432065618.5632059970642,3.8177463552923918.5741152776404,3.8316343296906918.58515
26、58600958,3.8459426564972618.5963207315174,3.8606745210384418.6076027391924,3.8758329049277418.6189945998447,3.8914205870732518.6304889084989,3.907440144645318.6420781469974,3.923893954012918.6537546921971,3.9407841916564918.6655108238652,3.9581128350640218.6773387322974,3.9758816636166718.6892305256
27、739,3.9940922594697818.701178237173,4.0127460084342318.7131738318568,4.0318441008629218.7252092133423,4.0513875325464818.7372762302732,4.0713771056222418.7493666826025,4.0918134294996818.7614723276975,4.1126969218056818.7735848862785,4.1340278093523118.7856960481983,4.1558061291298318.7977974780729,
28、4.1780317293270518.8098808207702,4.2007042703813118.8219377067648,4.2238232260598818.8339597573643,4.2473878845743818.8459385898141,4.2713973497300218.857865822286,4.2958505421106118.8697330787556,4.320746200300918.8815319937736,4.346082882147118.8932542171343,4.371858966056618.9048914184467,4.39807
29、26523376918.9164352916105,4.4247219645800518.9278775592012,4.4518047510764418.9392099767668,4.479318686286418.9504243370391,4.507261272342118.9615124740621,4.5356298405968518.9724662672399,4.5644215532165318.9832776453063,4.5936334048140818.9939385902174,4.6232622241272119.0044411409699,4.6533046757
30、394719.014777397346,4.6837572618445219.0249395235868,4.7146163240538119.0349197519946,4.7458780452473119.0447103864673,4.7775384514673219.054303805963,4.8095934138551719.0636924678987,4.8420386506304119.0728689114824,4.8748697291124619.0818257609787,4.9080820677841819.0905557289112,4.941670938397151
31、9.0990516191989,4.9756314681182519.1073063302303,5.0099586417170519.1153128578732,5.0446473037936219.1230642984222,5.0796921610463419.1305538514839,5.1150877845789819.1377748227992,5.1508286122467719.1447206270043,5.1869089510407719.1513847903296,5.2233229795098619.1577609532376,5.2600647502199619.1
32、638428729989,5.297128192249619.1696244262067,5.3345071137213719.1750996112312,5.3721952043684519.1802625506113,5.4101860381355519.1851074933867,5.4484730758135519.1896288173679,5.4870496677071419.193821031345,5.5259090563345519.1976787772362,5.5650443791588119.2011968321746,5.6044486713495619.204370
33、1105332,5.6441148685747219.2071936658898,5.6840358098210719.2096626929293,5.7242042402431519.2117725292856,5.7646128140392519.2135186573208,5.8052540973540319.2148967058439,5.8461205712065519.2159024517667,5.8872046344430519.216531821699,5.9284986067134919.2167808934806,5.9699947314708619.2166458976
34、521,6.0116851789925519.2161232188634,6.0535620494225619.2152093972196,6.0956173758338919.2139011295654,6.137843127309919.2121952707058,6.180231212043919.2100888345657,6.2227734804558219.2075789952857,6.2654617283251319.2046630882561,6.3082876999388519.2013386110881,6.3512430912538619.1976032245212,6
35、.3943195530723319.1934547532697,6.4375086942293919.1888911868041,6.4808020847919419.1839106800717,6.5241912592676419.1785115541527,6.5676677198230119.1726922968543,6.6112229395096619.1664515632412,6.6548483654975819.1597881761043,6.6985354223144919.1527011263649,6.7422755150901719.1451895734178,6.78
36、60600328047119.1372528454099,6.8298803515397919.1288904394574,6.8737278377316519.1201020217999,6.9175938514250519.1108874278912,6.9614697495268619.101246662429,7.0053468890584219.0911798993208,7.0492166304055819.0806874815885,7.0930703405652619.0697699212107,7.1368993963876319.0584278989026,7.180695
37、1878127819.0466622638345,7.2244491211007719.0344740332889,7.2681526220541619.0218643922555,7.3117971392317919.0088346929656,7.3553741471528718.9953864543652,7.3988751494903618.9815213615275,7.4422916822524718.9672412650049,7.4856153169513318.9525481801206,7.5288376637577818.9374442862005,7.5719503746412318.9219319257455,7.614945146493518.9060136035438,7.6578137242357518.8896919857255,7.7005479039073118.8729698987569,7.7431395357354718.8558503283781,7.7855805271852718.8471424632302,7.8067420202478318.8383364184814,7.827862845988136.3 摆线齿轮齿形绘制、圆弧齿圈的齿形绘制
