高阶变性正弦类非圆齿轮节曲线建模及仿真

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Mar.2013机 床 与 液 压Hydromechatronics Engineering Vo1.41 No.6DOI：10.3969/j.issn.1001～3881.2013.06.023Modeling and Simulation about Sinusoidal Non.circular GearPitch Curve of the High Order and Denatured Featurexu Gaohuan ，CHEN JiannenZhejiang Water Conservancy and Hydropower Colege，Hangzhou 310018，China；2.Zhejiang Sci-Tech University，Hangzhou 310018，ChinaAbstract：The eliptical gear pair transmission has sound characteristics， with which the non.circu。

1ar planetary gear mechanism has played a unique role in the new hydraulic motor. Sinusoidalnon。circular gear also has the characteristics of the closure and smooth of the eliptical gear. Inorder to get the best performance，a mathematical model for the sinusoidal non.circular gear pitchcurve with the high order and the deformed feature， as wel as the simulate examples.is estab。

Key words：high order deformed， sinusoidal，non-circular gearNon-circular gear hydraulic motors will gradualyreplace the drive piston hydraulic motor because of itscharacteristics of simple structure，strong anti-pollu-tion，non-hydraulic pulse，no trapped oil，the stabil-ify of the output torque and the long lifecycle[1]。

The core institution of the non.circular gear hydraulicmotor is composed of non-circular gear planetary gearmechanism.The main components are the non.circu。

1ar sun gear，the cylindrical planetary gear and thenon-circular gear(motor housing).The design ofnon-circular pitch curve is one of the key technolo-gies. The general line is the high-order ellipticalpitch curve or the multi-arc curve.You can also useother curves which have the engagement requirements[1]。

circular gear pair，which also has the excellent char。

acteristics of high order elliptic curve，and its basicforms.But the paper was lack of the discussion of thecombination of design， and it did not create themathematical mode1.On this basis，we propose thatthe sinusoidal non.circular gear pitch curve with theReceived：2012-11-28XU Gaohuan.E-mail：6787135### qq.cornhigh order and deformed feature is characterized bvcontinuity and smoothness.More adjustable parame。

ters are easier to optimize the hydraulic performanceof the motor.This paper mainly studies on the designand mathematical model of the sinusoidal non-circulargear pitch curve with the high order and the deformedfeature，and also performs the simulation with a trueexample.These works provide a theoretical basis forthe design of new low speed high torque hydraulicm otor。

1.The basic principles of sinusoidal gearpairThe main feature of the sinusoida1 gear is thatthe angle of driving wheel and the driven have the re。

1ationship of the sinusoidal function2]. On theplane xO1Y，the relationship just folows this equa。

tion：YAsin( ) (1)On the plane 1 O2 2， the angle of drivingwheel and the driven have the relationship with，Y，and they are just satisfied with these equations：1XcosO-ysin0 (2)2xsinOycos0 (3)here，0 represents the angle between O2 tpI and OI，Hydromechatronics Engineeringin the equation(1)，A is the amplitude of Y in thexO1Yplane，and bcos( )。

In order to comply with the gear meshing law：① non-circular gear pitch curve is dosed，② Thecircumference meets the relationship of l ， (m isthe modulus and z is the number of teeth)。

al non-circular gear pitch curve、 th thehigh order and deformed featureThe high·-level order of non-circular gear is saidthat the pitch curve in a rotation cycle finished theorder cycle of sinusoidal transformation，and the de·formed pitch curve， said non-circular gear pitchcurve with a number of diferent sections of the orderferm i3-4].The high order and deformed sinusoidalnon-circular gear pitch curve constitute nl and n2pitch curve，which meets the engagement require-ments of that the pitch curve is continuous，and thecircumference is integer muhiple of the modulus andthe number of teeth3].In order to achieve thesegoals，this research studies on the curve equation，the circumference and the transmission ratio fuBe。

tion，and gives the angular velocity and angular ac-celeration equations。

1)Rotation relationship，the angle and thetransmission ratio functionIn the high order and deform ed sinusoidal non-circular gear pair，angle l， 2 and ，Y follow thepiecewise function expression：YAIsinb1 x-2Tk)， 2kT≤ ≤2m T2kT ，YAzsin(b2 x-2豫)c2)，2m6 弛 ≤ ≤2T妣 、here，T-/ 'Cnl 2， bis the ref0瑚ed c。efj。

The relation between the driving wheel angleand the driven wheel angle： XCOS(0)-ysin(0) xsin coshere，0 is the angle between O2 1 and O1The transmission ratio function：2)Pitch curve equation2kT≤ ≤2m6 2kT(5)2mbT2kT≤ ≤2T2kT(6)a × Z21r2 ： a - rIhere a is the wheelbase3)Pitch curve perimeterld(cos(0)-A1b1 sin(0)cos(bl( -2kT))2kT≤ ≤2m6T2kTld(ccos(O)-A2b2sin(O)cos(b2( -2k2m6 2kT≤ ≤2T2kTana c ，2mbT2kT 212kTZ(7)(8)dr1 ) )，溉 (9)fd /z d (10)2kl 2mb72k4)Driven wheel angular velocity and angularacceleration driven wheel angular velocity：2sin(0)Abcos(bx)COS(0) (11)angular acceleration2-Ab sin(bx)COS(0) (12)here A and b are taken in different ranges of A1，b1and A2，b2。

3.Examples and simulationTo study the high order and deform ed sinusoidalnon-circular gear pair characteristics more easily，Matlab20 1 l b was selected for the simulation plat-form ，and the program was written to simulate thegear pair as follows。

1 1 is taken as the independent variable.De-pending on nl and n2，discreted to 360 equal partsin area 0～2Txnl or 0～2T×n2。

2)Calculate the parameters of Y， 1， 2，i12，and store them in the array。

3)According to the gear teeth and the mode au-tomaticaly，adjust the wheelbase。

4)Calculate the high order and deformed sinu-soidal non-circular gear pair pitch curve coordinatesinto the appropriate aray。

5)Establish a GUI interface，cal the high orderand deformed sinusoidal non-circular gear pair pitchcurve function， plot output coresponding curvethrough matlab library function。

Example：for the high order and deform ed sinu-soidal non-circular gear pair，the input parameter is- - ～～～～XU Gaohuan，et al：Modeling and Simulation about Sinusoidal Non-circular GearPitch Curve of the High Order and Denatured Feature 117m 3，a120 mm，mb0.5，nl5，n23，ypi/38。

Fig.1 is the high order and deformed sinusoidalnon-circular gear pair pitch curve simulation graph-ics.Fig.2 is 1， 2，i12 The relationship between thecharacteristic values of simulation graphics50日0口 . 50. 1O0xdataFig.1 The high order and deformed sinusoidal non-circulargear pair pitch curve simulation graphics口 窭O2 3 4 5 6 7/radThe curve ofdriving wheel angle andhe driven wheel angle/radThe curve of driving wheel angle andthe driven wheel speedReferences：4.Conclusions1、 The mathematical model of the h Jgh order and de·formed sinusoidal non-circular gear pair in line with the gearcombination principle， and the Matlab graphical simulationCOnfirln the correctness of the design method。

2)Based on the adjustment of the high order and de-formed sinusoidal non-circular gear pair by parameters Z，m，a，mb，nl，n2 and ，a variety of sinusoidal noncireular gearpitch curve can be designed，which extends the range of op-tions。

3)Adjusting the parameters can change the hish orderand deform ed sinusoidal non-circular gear pair bump in con-sidering the processing problems，you can control its concave。

4、The design methods and the properties of the high 0pder and deform ed sinusoidal non.circular gear can be used i13。

the follow.up of new hydraulic motors and vane pump drivemechanism，and provide a theoretical basis。

2.22.0l 81.61.40 l 2 3 4 5 6 7/radThe relationship between driving wheel angle and drive ratio0 1 2 3 4 5 6 7/radThe curve ofdriving wheel angle andthe driven wheel acce1erationFig.2 l， 2，i12 The relationship between the characteristic values of simulation graphics[1] LI Lei，DU Changlong，YANG Shanguo.The Developmentof Hydraulic Motor with Non-circular Planetary Gear andIts Application in Coal-mining Machinery[J].CHINESEHYDRAULICS＆ PNEUMATICS.2007。9：16-18。

[2] ZHANG Rui，ZAO Fengxia，wu Xutang.Study on theDesign Method of a New.style Sinusoidal NoncircularGearJ].MACHINE DESIGN&RESEARCH，2010，26(4)：71-74。

5 O 5 O 5 O 5 O 1 l O O 1 l 2 O O O O O O O - -(il18 Hydromechatronics EngineeringWU Xutang，WANG Haigui.Non-circular Gear and Non-uniform Drive[M].Beijing：Mechanical Industry Press，1996：105-106。

GAO Hong.LU Xingsheng.Design and Graphic Simula-高阶变性正弦类非圆齿轮节曲线建模及仿真徐高欢h，陈建能1.浙江水利水电专科学校，杭州 310018；2.浙江理工大学 ，杭州 310018tion about Pitch-line of Denatured Ellipse Gead J].CHI-NA MECHANICAL ENGINEERING，2003，10(14)：1645- 164 8。

摘要：椭圆齿轮副传动特性优 良，由它组成的非圆行星齿轮机构在新型液压马达中起到了独特的作用。正弦非圆齿轮也具有椭圆齿轮的封闭、光滑的特性。为获得最佳性能，建立了新型的高阶变性正弦类非圆齿轮节曲线数学模型，并通过算例进行动态仿真。

关键词：高阶变性；正弦类；非圆齿轮中图分类号：TH13Yilin Hydraulic GroupHarbin General Hydraulic Machinery W orks Co.，Ltd。

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