新型摩擦式限滑差速器壳体有限元分析

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Jun.2013机 床 与 液 压Hydromechatronics Engineering V0l41 No.12DOI：10.3969/j.issn.1001-3881.2013.12.022Finite Element Analysis for a New Friction-basedLimited-slip Diferential HousingHUANG Xia，DING Jun，QIAO HuiliChongqing University of Technology，Chongqing 400054，China1.IntroductionAbstract：A friction。based limited。slip diferentialjs used to ensure that the wheels on both sidesof the drive axle move at diferent rotational speeds.The diferential automaticaly changes thedistribution of torqMe between the drive wheels depending on road conditions to improve the pas-sage capaci of a vehicle。Based on the new friction-based limited-slip diferential of impoReddrive axle of heavy vehicles.a finite element analysis of structure strength has been conductedon diferential housing for various work cases.The results indicate that the structural strength andstifness of the diferential housing meet the requirements of vehicle driving kinematics.These re-suits also provide a theoretical basis for an improved design and structural optimization of difer·ential housing。

Key words：Friction-based；Limited-slip diferential；FEM；Structural strengthA differential is an important component of adrive axle of a vehicle and ensures that wheels onboth sides of the drive axle move at different rotation。

al speeds to meet the requirements of vehicle tractionkinematics.At present，the torque of a widely usedsymmetric style bevel gear differential is evenly dis-tributed because of its less frictional torque.W heelslip has a significant impact on the passage capacityof vehicles traveling on a road with low friction coeffi。

cient or unequal friction coefficients. Friction-basedlimited-slip differential has been widely used to im。

prove the automatic adjustment of torque alocationproblems between driving wheels[1].In this work，considering the new friction.based limited.slip differ。

ential of drive axle imports of heavy vehicles.theReceived：2013-05-O9Supported by Science and Technology Project Affiliated to theEducation Department of Chongqing Municipality(KJ120801)。

HUANG Xia.E-mail：huangxia### cqut.edu.elcurrent study analyzed the structural strength of a dif-ferential housing based on the finite element methodunder different conditions to improve the design of thedifferential housing of vehicle drive axles。

2.Structure and working principle of the newfriction·based limited-slip diferentialFig.1 shows the structure of the new friction-based limited-slip differentia1.The diferential hous-ing is designed using a bisection method centered onthe sphere.The left housing 1 and the right housing 6of the differential are integrally formed with bolt con-nections。

Both ends of the housing assembly are supportedin the middle axle housing by a tapered roler bear-ing.Four pieces of planetary gear 3 without an en-closed cross axle 4 match the sphere in the housingvia a spherical gasket 7 at the back.A friction platesystem is placed between the half axle gear 2 and thesurface of the differential housing.which is composedof a thick friction plate 5，ten driving friction platesarranged at regular intervals，and eight driven frictionHUANG Xia，et al：Finite Element Analysis for a New Friction-basedLimited-slip Differential Housing l07plates.The four outer teeth of the driving frictionplate match the four tooth spaces along the axis dis-tributed in the differential housing.The driven fric-tion plate with a spline bore matches the externalsplines of the half axle gear。

1.The left housing of diferential，2.Half axle gear；3.Planeta-ry gear，4.Cross axle，5.Thick friction plate，6.The fighthousing of diferential，7.Sphereical gasket，8.Driving anddriven friction platesFig.1 A new friction-based limited-slip differentialTwo half axles have the same speed with torquedistributed equally on left and right axles when vehi-cles are used for straight driving. The ax ial forcesgenerated by the planetary and the half-axle gearsmesh with one another，thereby forcing the half axleat both ends，the thick friction plates，the drivingfriction plate，and the driven friction plate to tightlypress together and to produce frictional torque.Thistorque can be distributed on the half axle in twoways：① via the cross axle，the planetary gear，andthe half-axle gear.② via the active friction and driv-en the friction plates。

The rotation of the planetary gear produces a dif-ferential with unequal rotating speeds of the left andfight half-axle gears when the vehicle makes a run orone side of the wheel spins on a slippery road sur-face. With this speed difference，the driving anddriven friction plates produce frictional torque at thetime of the slip.The direction of the frictional torqueand the direction at which the half axle quicklyturned are oriented in opposite directions. By con-trast，the direction of the frictional torque is orientedin the same direction as the direction of a slow.turn。

ing half axle.The value is proportional to the torqueand the number of friction plate transmitted by thedifferential mechanism.This case is similar to a partof torque transmitted from the quick-turning side tothe slow-turning side. Thus，the torque transmitedby the slow-turning half axle is increased to improvethe passage capacity of a vehicle[2-4]。

3.Finite element analysis for diferentialhousing3.1.Establishment of the finite element model ofa diferential housingThe FEM model for differential housing used asa discrete model of the original structure has a signif-cant influence on the validity and accuracy of FEA。

A three.dimensional model of the differential housingis established using CATIA.and which is importedinto HyperMesh software to complete the modelmesh，the material property definitions，and the loadas wel as the displacement boundary condition pre-scription，while solving and postprocess are comple-ted in ABAQUS software.Due to the accuracy andeficiency.the element type used for FEM model isC3D4 in ABAQUS software.It is a four.node lineartetrahedral element。 with each node having threetranslational degrees of freedom，that iS，the transla。

tional degrees of freedom at ，Y，and z directions。

Fig.2 shows the mesh configuration for the differenti-al housing with 331.915 elements and a t0tal of78，557 nodes.The material used is QT5O0 with elas。

tic modulus is 173 GPa，Poissons ratio is 0.3，andyield limit is 3 10 MPa。

Fig.2 FEM model for diferential housingFor the displacement boundary condition con。

straints.it follows as described.Based on the geome。

try configuration of differential assemblies in the driveaxle housing，the translational DOF along Y and z di-rection are constrained at the nodes located on theouter ring on both ends of the diferential housing as。

tion is also constrained at the nodes on the surface inthe right end of the housing.With regard to the nodeslocated at the cross axle hole of differential housing。

the multiple points constraints(MPC)are firstly em-ployed to constrain all DOF of nodes at the hole to theHUANG Xia，et al：Finite Element Analysis for a New Friction-basedLimited-slip Differential Housing 1 09Tab.2 The calculated force in clockwise rotation for driving gearFig.3 shows the VonMises stress distribiation fordifferential housing for six different cases. It showsthat，when driving gear rotates anticlockwise in mainreducer，the maximum stress value is 229 MPa，which is located near the small hole at the inner endof the fight differential housing，as illustrated in Fig。

3(a).When the right side wheel slips，the torque isapplied at the inner right end of the housing，ilustra-ted as Fig.3(b)，and the Von-Mises stress atains235 MPa at the same location，slightly higher thancase 1. However，for case 3，as shown in Fig.3(c)，the location occurring the maximum Von.Misesstress value shifts to the left end of the housing，reac-hing to 25 1 MPa， much smaller than the thresholdvalue when yielding happens.As the driving gear ro-tares clockwise in the main reducer，in comparison tothe values its opposite case，that is，in anticlockwiseway，the max imum Von-Mises stress increases to 24 1MPa，ilustrated as Fig.3 (d)， higher than229MPa，still nears the small hole at the inner end ofthe right diferential housing.For case 2 and case 3when clockwise， similar condition happens. Themaximum stress values for case 2 and case 3 attain257 MPa and 272 MPa，as shown in Fig.3(e)andFig.3(f)，respectively.Likewise，the location atthe limiting stress value remains as they are。

4.ConclusionsTh e structures and the working principles of fric-tion-based limited.slip diferential were studied andthe finite element analyses for the strength of housingwere conducted in this work.The results indicate thatthe structural strength of the diferential housing issufficient to satisfy the requirements of vehicle drivingkinematics.which also provide a theoretical basis foran improved design and structural optimization of dif-ferential housing。

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基于对角递归神经网络的在线自整定解耦控制算法陶 平 ，肖 超1.重庆第二中级人民法院 数据处理中心，重庆 404020；2.重庆大学 自动化学院，重庆 40004摘要：为了解决控制系统中-个回路参数变化导致其他回路的运行参数改变，提出了-种基于DRNN的在线自整定解耦控制算法。以某被控对象温湿度控制为例构建了数学模型，分析了系统变量之间的耦合关系，设计了解耦网络～存在耦合关系的多变量控制系统变换为独立的单变量控制 系统，以消除相关控制通道之间的影响。基于所提 出的对角递归神经网络解耦算法进行 了系统仿真实验。系统仿真响应显示：经过解耦后的温湿控制2个通道相互之间影响很小.实现 了耦合变量的解耦。仿真研究结果表明：提出的解耦控制算法是可行与合理的。

关键词：自整定解耦PID控制器；对角递归神经网络；参数整定策略；温湿度解耦中图分类号：TP273(Continued on 109 page)新型摩擦式限滑差速器壳体有限元分析黄 霞 ，丁 军，乔慧丽重庆理T大学 ，重庆 400054 摘要：摩擦式限滑差速器用于保证驱动桥两侧车轮在行程不等时能以不同转速旋转，并根据路面情况自动改变驱动轮间转矩的分配，提高汽车的通过能力。基于载重汽车某进口驱动桥新型摩擦式限滑差速器，对其壳体在不同工况下进行结构强度的有限元分析。分析结果表明：该差速器壳体的结构强度符合要求。为差速器壳体的改进设计和结构优化提供了-定的理论依据。

关键词：摩擦式；限滑差速器；有限元；结构强度中图分类号：TH12