齿式离合器接合过程动态特性的仿真研究

大功率低速离合器接合过程动态特性仿真傅顺军;马永明;易小冬;徐昕【期刊名称】《舰船科学技术》【年(卷),期】2010(032)008【摘要】为得到大功率低速离合器轮齿在轴向接合过程中的动态冲击载荷,进而为强度分析提供依据,首先以存在转速差和轴向相对运动的内啮合齿轮副作为研究模型,采用系统动力学分析软件ADAMS分析了轮齿接合过程的动态特性,给出了完整接合过程的动态扭矩、轴向力和转速等关键参数,结果显示存在转速差和轴向相对运动的齿轮副在接合过程中产生较大的轴向力和扭矩冲击值,并且轮齿转速差、接合速度和轴向推力等参数对冲击载荷具有较大影响;以存在锁止角的锁销和摩擦片联动为主要研究对象,分析了锁销及摩擦片接合过程的动态特性,给出了完整接合过程的动态扭矩、轴向力和转速等关键参数,结果显示锁销及摩擦片在该联动过程中产生较大的轴向力和扭矩冲击值.该结果可为相关离合器的设计提供依据.【总页数】5页(P162-166)【作者】傅顺军;马永明;易小冬;徐昕【作者单位】中国船舶重工集团公司第七○四研究所,上海,200031;中国船舶重工集团公司第七○四研究所,上海,200031;中国船舶重工集团公司第七○四研究所,上海,200031;中国船舶重工集团公司第七○四研究所,上海,200031【正文语种】中文【中图分类】TH132.4【相关文献】1.齿式离合器接合过程动态特性的仿真研究 [J], 傅顺军;马永明;徐昕2.基于动摩擦系数的微型车离合器起步接合过程动力学仿真 [J], 李礼夫;孙利昌3.湿式离合器接合过程油膜厚度和转矩仿真 [J], 杨夏;曹雪梅;穆亮圣4.湿式离合器接合过程中瞬态温度场的仿真 [J], 胡宏伟;王泽湘;张志刚;王哲5.面向离合器接合过程的比例电磁阀动态特性模型与设计 [J], 李晓祥; 王安麟; 樊旭灿; 李晓田因版权原因，仅展示原文概要，查看原文内容请购买。

Dynamic simulation of spur gear with tooth root crack propagating along tooth width and crack depthZaigang Chen,Yimin Shao ⇑State Key Laboratory of Mechanical Transmission,Chongqing University,Chongqing 400030,Chinaa r t i c l e i n f o Article history:Received 11April 2011Received in revised form 26June 2011Accepted 8July 2011Available online 22July 2011Keywords:Tooth crack PropagationGear mesh stiffness Sidebandsa b s t r a c tGear tooth crack will cause changes in vibration characteristics of gear system,based on which,operating condition of the gear system is always monitored to prevent a presence of serious damage.However,it is also a unsolved puzzle to establish the relationship between tooth crack propagation and vibration features during gear operating process.In this study,an analytical model is proposed to investigate the effect of gear tooth crack on the gear mesh stiffness.Both the tooth crack propagations along tooth width and crack depth are incorporated in this model to simulate gear tooth root crack,especially when it is at very early stage.With this analytical formulation,the mesh stiffness of a spur gear pair with different crack length and depth can be obtained.Afterwards,the effects of gear tooth root crack size on the gear dynamics are simulated and the corresponding changes in sta-tistical indicators –RMS and kurtosis are investigated.The results show that both RMS and kurtosis increase with the growth of tooth crack size for propagation whatever along tooth width and crack length.Frequency spectrum analysis is also carried out to examine the effects of tooth crack.The results show that sidebands caused by the tooth crack are more sensitive than the mesh frequency and its harmonics.The developed analytical model can predict the change of gear mesh stiffness with presence of a gear tooth crack and the cor-responding dynamic responses could supply some guidance to the gear condition monitor-ing and fault diagnosis,especially for the gear tooth crack at early stage.Ó2011Elsevier Ltd.All rights reserved.0.IntroductionGearboxes are the most important mechanisms in industrial machinery,automotive applications,and our daily lives to transmit power and produce high rotational speed changes and/or change the direction of motion.And due to their growing applications,gearbox health monitoring and early fault detection have been under intensive investigation [1,2].As is known,gear tooth failure can cause removal and/or plastic deformations on the contacting tooth surfaces or even presence of fatigue crack.And the severity of tooth damage is usually assessed by the reduction of the stiffness [3,4].There has been a lot of work carried out to investigate gear tooth stiffness with and/or without tooth faults.Finite element models (FEA)[4–8]and analytical methods are the widely used approaches to fulfill the stiffness modeling and calculation.However,FEA models for the tooth stiffness calculation need mesh refinements and are computationally expensive.On the other hand,analytical methods show good results with less computation time compared with FEA models [4,9,10].Gear mesh stiffness without defects was computed analytically by Weber [9],Cornell [10],while a digitization approach was used by Kasuba and Evans [11].Yang and Lin [12]used the so-called potential energy method to calculate the total mesh stiffness of a gear pair versus gear rotational position.And their model was further refined by Tian [13]and Wu et al.[1]by 1350-6307/$-see front matter Ó2011Elsevier Ltd.All rights reserved.doi:10.1016/j.engfailanal.2011.07.006⇑Corresponding author.Tel.:+86(0)2365112520;fax:+86(0)2365106195.E-mail address:ymshao@ (Y.Shao).2150Z.Chen,Y.Shao/Engineering Failure Analysis18(2011)2149–2164taking the shear mesh stiffness into consideration.But,they did not take thefillet-foundation deflections into account yet.All the former research papers on the analytically modeling of gear tooth crack assumed that the tooth crack was through the whole tooth width with a constant crack depth.In this paper,the crack propagating along tooth width and crack depth is modeled and its influences on gear mesh stiffness and dynamic responses are investigated.Lewicki[14–16]did many works on the tooth crack propagation path and gained some useful conclusions.He noted that crack propagation paths depend on the backup ratio which is defined as the ratio of rim thickness to tooth height and it tends to be smooth,continuous,and rather straight with only a slight curvature.For the gear with high backup ratio,gear tooth root crack would propagate through the tooth along tooth width.While for those with low backup ratio,the crack would go through the rim.The initial crack angle is also a determinative factor for the propagation.In the case of low initial crack angle,the propagation is through the rim even with high backup ratio.In this paper,the crack along its depth direction is also assumed to be straight but with a non-uniform distribution along tooth width,which is more realistic and different from those proposed by Wu et al.[1]and Chaari et al.[4].This model makes it possible to check the effectiveness of algorithms in fault diagnosis and condition monitoring,especially for the crack at early stage.The earliest review papers on the numerical modeling of spur gear dynamics are made byÖzgüven and Houser in1988 [17]and by Parey and Tandon in2003[18].But,there are few reviews on the gear tooth defects.Randall[19,20]reported the advantages of simulating faults in machine such as producing sufficient representative signals to train automated fault rec-ognition algorithms,generating signals for faults with different sizes and locations in order to test and compare diagnostic algorithms and being very helpful in gaining a physical understanding of the complex(often nonlinear)interactions.In his work,gear tooth crack and spall were involved.Chaari et al.[3]stated that dynamic responses of the transmission is closely related to the time varying gear mesh stiffness,and higher vibration and acoustic emission level is noticed when the mesh stiffness is reduced due to some gear tooth faults.Modelling of the gear transmission failure would help to analyze the change in dynamic characteristics which can be a suitable tool for maintenance teams to diagnose such failures.Li et al.[21]developed an embedded modelling approach for identifying gear meshing stiffness from measured gear angular dis-placement or transmission error and then using an embedded–dynamic–fracture model to predict gear fatigue crack prop-agation[22].Endo et al.[23,24]presented a technique to differentially diagnose two types of localized gear tooth faults:a spall and a crack in the gear toothfillet region by simulation and experiment.These researches may provide useful informa-tion for fault detection.Vibration-based time domain,frequency domain,and time–frequency domain analyses are the most powerful tools available for fault detection of rotating machinery[1].Traditional techniques based on statistical measure-ments and vibration spectrum analysis are applied to analyze the effects of tooth crack on the gear vibrations in this paper.Based on the discussions above,the published papers on the gear tooth root crack are always under the assumption that the crack is through the whole tooth width with the same depth.In reality,the crack is not always through the whole tooth width but from an initial position where a stress concentration is observed.In the present paper,the tooth crack propagating along tooth width is formulated and an example is also simulated and analyzed.The main objective of this paper is to develop an analytical model of mesh stiffness for spur gear pair to predict the tooth root crack which propagates along both tooth width and crack depth.Thus,it can make up the shortage of previous research that they are limited to the assumption that the tooth crack is through the whole tooth width with a constant depth.And the developed model is validated by comparisons with FEA results in Ref.[4].With the developed model,the effects of gear tooth root crack with different length and depth on the mesh stiffness are investigated.After obtaining the gear mesh stiffness with tooth root crack,a six-degree-of-freedom spur gear system is established to investigate the influence of gear tooth root crack on its dynamic responses.The statistical indicators—RMS and kurtosis,which are widely used in fault diagnosis and condi-tion monitoring,are applied to expose the influence of gear tooth crack.Analysis of the dynamic responses in time–and frequency-domain are also carried out so that the effects of tooth crack on the gear dynamic characteristics are obtained quantitatively.Thus,the developed analytical model can be used to assess the impact of gear tooth crack with different sizes on the gear mesh stiffness and the corresponding dynamic responses,which is useful in the gear condition monitoring and fault diagnosis,especially for the gear tooth crack at early stage.This paper is organized as follows:reviews on gear tooth fault in the published papers and other documentations are gi-ven in introduction.Thefirst segment introduces Wu et al.[1]tooth crack model and extend it to include the effect offillet-foundation deformation,based on which,the crack model to simulate the propagation along tooth width is also developed in this part.And the investigations on the effects of gear tooth root crack on gear mesh stiffness are carried on in the second part.Then,after incorporating the gear mesh stiffness with different sizes into gear dynamic model,the effects of the gear tooth root crack on dynamic responses of gear system are analyzed in the third section which is followed by conclusions.1.Modeling of gear mesh stiffness with a crack at tooth rootFor the analytical studies on the tooth crack of spur gears,there has been many works published.Nearly all of them as-sumed the crack is through the tooth width with a constant crack depth.Few work focus their attentions on the gear tooth propagating along tooth width,namely the crack depth varies along tooth width.A gear mesh stiffness calculation model with consideration of tooth crack propagating along tooth width is proposed in Section1.2which is based on the existing analytical model and method reviewed in Section1.1which assumes the tooth crack was though the tooth width with a con-stant depth.1.1.Mesh stiffness calculation with crack through tooth widthDeflections of a spur gear tooth can be determined by considering it as a non-uniform cantilever beam with an effective length d displayed in Fig.1.Here,the crack is assumed to go through the whole tooth width[1,4,13]W with a constant depth q0and a crack inclination angle a c.The bending,shear and axial compressive energy stored in a tooth can be represented by[12,13],U b¼F2b ;U s¼F2s;U a¼F2að1-a;b;cÞwhere K b,K s,K a are the bending,shear and axial compressive stiffness in the same direction under the action of the force F.Based on the beam theory,the potential energy stored in a meshing gear tooth can be calculated by[1,12,13],U b¼Z d0M22EI xdx;U s¼Z d1:2F2b2GA xdx;U a¼Z dF2a2EI xdxð2-a;b;cÞwhere U b,U s,U a are the potential energy stored in the bending,shear and axial compressive deformations,respectively under the action of the mesh force F.And F b,F a and M are calculated byF b¼F cos a1;F a¼F sin a1;M¼F bÁxÀF aÁhð3-a;b;cÞBased on Eqs.(1)–(3),the bending stiffness K b can be obtained as,1 K b ¼Z dðx cos a1Àh sin a1Þ2EI xdxð4ÞShear stiffness K s is calculated by,1 s ¼Z d1:2cos2a1xdxð5ÞAxial compressive stiffness K a is,1 a ¼Z dsin2a1xdxð6ÞIn the formulas(2)–(6),h,x,dx,a1;d are shown in Fig.1.E is the Young modulus.G represents the shear modulus.I x and A x represent the area moment of inertia and area of the section where the distance between the section and the acting point of the applied force is x,and they can be obtained by1 12ðh xþh xÞ3W;h x6h q(Fig.1.Model of the spur gear tooth as a non-uniform cantilever beam with a crack at tooth root.Z.Chen,Y.Shao/Engineering Failure Analysis18(2011)2149–21642151where v is the Poisson ratio.h q¼h cÀq0sin a c,q0and a c are the depth and the inclination angle of the crack,respectively.h x represents the distance between a point and the tooth’s central line and this point lies on the tooth profile curve where the horizontal distance from the tooth’s root is equal to d minus x.From the results derived by Yang and Sun[25],the stiffness of Hertzian contact of two meshing teeth is constant along the entire line of action.It is independent of the contact position and the interpenetration depth between meshing teeth.The Hertzian contact stiffness K h is given by1 K h ¼4ð1Àv2Þp EWð10ÞBesides the tooth deformation,thefillet-foundation deflection also influences the stiffness of gear tooth.Sainsot et al.[26] derived thefillet-foundation deflection of the gear based on the theory of Muskhelishvili[27].And then,they applied it to circular elastic rings to derive an analytical formula reflecting the gear body-induced tooth deflections by assuming linear and constant stress variations at root circle.It can be calculated as[3,4,7,26],d f¼F cos2a mWELÃu fS f2þMÃu fS fþPÃ1þQÃtan2a mÀÁ()ð11Þwhere W is the tooth width.u f and S f are given in Fig.2.The coefficients LÃ,MÃ,PÃ,QÃcan be approached by polynomial func-Fig.2.Geometrical parameters for thefillet-foundation deflection[3,4].Table1Values of the coefficients of Eq.(12)[22].A iB iC iD iE iF iLÃ(hfi,h f)À5.574Â10À5À1.9986Â10À3À2.3015Â10À4 4.7702Â10À30.0271 6.8045 MÃ(hfi,h f)60.111Â10À528.100Â10À3À83.431Â10À4À9.9256Â10À30.16240.9086 PÃ(hfi,h f)À50.952Â10À5185.50Â10À30.0538Â10À453.3Â10À30.28950.9236 QÃ(hfi,h f)À6.2042Â10À59.0889Â10À3À4.0964Â10À47.8297Â10À3À0.14720.6904 2152Z.Chen,Y.Shao/Engineering Failure Analysis18(2011)2149–2164The total equivalent mesh stiffness of one tooth pair in mesh can be obtained byK e¼11K b1þ1K s1þ1K a1þ1K f1þ1K b2þ1K s2þ1K a2þ1K f2þ1K hð14ÞHere,the subscripts1,2mean the pinion and gear,respectively.1.2.Mesh stiffness model with crack propagating along tooth widthAt very early stage of crack propagation,it usually starts from some local positions where the stress concentrations are observed.In order to investigate the effect of a tooth root crack propagating along tooth width non-uniformly,a mesh stiff-ness model is developed by dividing a gear tooth into some independent thin pieces like that shown in Fig.3b,so that the crack length along tooth width for each piece can be regarded as a constant which is reasonable when dx is small.Stiffness of each piece is denoted as K t(x)and can be calculated with taking tooth bending,shear and axial compress into account based on Eqs.(4)–(6).K t(x)can be obtained byK tðxÞ¼11b þ1sþ1að15ÞFig.3.Crack model at gear tooth root.Fig.4.Crack depth along tooth width.Z.Chen,Y.Shao/Engineering Failure Analysis18(2011)2149–21642153Although the proposed mesh stiffness model can also be suitable to a spatial gear tooth crack,this study assumes that the crack propagation is in plane shown as A–A in Fig.3a and c with different crack depth along tooth width for simplicity.The crack depth along tooth width can be described as a function of x in the coordinate system XOY in Figs.3c and 4.That meansqx ¼f ðx Þð18ÞFurther,the crack depth is assumed to distribute along tooth width as a parabolic function as shown in Fig.4.When the crack length W c is less than tooth width W ,the crack curve is denoted by the solid curve in Fig.4.While the crack propagates through the whole tooth width,the crack curve is described as the dashed curve which propagates along crack depth q 2.For the solid curve,q ðx Þ¼q 0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix þW c ÀWcq ;x 2½W ÀW c W q ðx Þ¼0;x 2½0W ÀW c(ð19ÞFor the dashed curve,q ðx Þ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiq 20Àq 22x þq 22r ð20Þ2.Investigation on effect of tooth crack on gear mesh stiffnessBased on the developed analytical model in this paper,effects of the tooth crack size,namely crack length along tooth width and crack depth,on the mesh stiffness of gear pair are able to be calculated and investigated.The main parameters used in this paper are from Ref.[4]and shown in Table parisons with FEA results in Ref.[4]In Ref.[4],healthy case and two crack cases were analyzed.They are:Crack No.1:p c =0.3mm,a c =33°,position:beginning at the root circle (in this study,just let q 0=q 2=0.3mm,a c =33°to set the same case).Crack No.2:p c =0.66mm,a c =70°,position:beginning at the root circle (in this study,just let q 0=q 2=0.66mm,a c =70°to set the same case).The comparisons made in Table 3and Fig.5between the mesh stiffness results from Ref.[4]by FEA and that from the analytical model developed in this study validate the developed model in this paper.2.2.Effect of tooth root crack propagating along tooth width on gear mesh stiffnessWhen the crack propagates through the whole tooth width,that means W c is equal to W shown in Fig.4,it continues to propagate along the depth direction labeled as q 2.The case where q 0=1mm,a c =60°is investigated.Table 2Parameters of the pinion-wheel set [4].PinionGear Teeth number 3025Module (mm)22Teeth width (mm)2020Contact ratio1.63 1.63Rotational speed (rpm)20002400Pressure angle20°20°Young modulus E (N/mm 2)2Â1052Â105Poisson’s ratio0.30.3Table 3Mesh stiffness comparison of single tooth pair.Gear tooth condition FEM results [4]Results obtained in this paper Difference (%)Healthy case 1.58Â108 1.52Â108 3.8Crack No.1 1.53Â108 1.47Â108 3.9Crack No.21.42Â1081.38Â1082.82154Z.Chen,Y.Shao /Engineering Failure Analysis 18(2011)2149–2164The mesh stiffness curves of a single tooth pair with different crack lengths are displayed in Fig.6.These curves are plot-ted versus the pinion angular position.And the mesh stiffness reflecting the alternative process between single-and double-tooth engagements are shown in Fig.7.In these two figures,distinct reductions of stiffness are observed when tooth cracks are introduced.The stiffness reduction increases with growth of crack length.The same phenomenon as stated in Ref.[4]can be observed that maximum stiffness reduction for a fixed crack appears where the cracked tooth of pinion is just going to engagement.This is an expected result because of the relative bigger flexibility of the tooth at the addendum circle compared to that at the position on the tooth profile which is closer to base circle.It is noted that the crack length of (20+1)mm refers the case when W c =W =20mm and q 2=q 0=1mm.In addition,a noticeable result can be obtained that the mesh stiffness reduction due to crack appears to increase more promptly when the crack propagates through the whole tooth width and continues to propagate along crack depth.2.3.Effect of tooth root crack depth on gear mesh stiffnessThe cases where W c =15mm,a c =60°and q 0increasing gradually from 0to 1.2mm with interval of 0.3mm are simulated to investigate the effect of tooth crack depth on gear mesh stiffness.The corresponding results for single tooth pair and the alternative process between single-and double-tooth engagements are shown in Figs.8and 9,respectively.Thesamemesh stiffness.(a)Gear mesh stiffness from Ref.[4]by FEA method.(b)Obtained from the modelFig.6.Mesh stiffness with different crack length along tooth width(single tooth pair).Fig.7.Mesh stiffness with different crack length along tooth width.phenomenon is also found that the maximum stiffness reduction during the mesh process for afixed crack appears at the beginning of the engagement when the cracked tooth of the pinion is getting into engagement.3.Dynamic simulation of spur gear system with gear tooth crack3.1.Spur gear systemBased on the mesh stiffness model of gear pair with or/and without a tooth root crack,a dynamic lumped parameter mod-el of a spur gearbox system comprising of six degrees of freedom(DOF)is established.A schematic of the gear dynamic mod-el is shown in Fig.10where the y axis is parallel to the line of action(LOA)of the gear pair.T p/T g is external/braking torque; X p/X g is nominal operational speeds of pinion/gear;J p/J g is inertial moment of pinion/gear;m p/m g is mass of pinion/gear;K iBj/C iBj is stiffness/damping of the supporting bearings and i=p,g for pinion and gear,respectively,j=x,y for x and y direc-tion.k(t)is time varying mesh stiffness by which the influence of gear tooth crack is incorporated and C m is the damping between gear teeth in mesh.F f is the tooth friction force caused by the sliding between the mating teeth.The design parameters of the spur gear system applied in this study are shown in Table4.And this spur gear system oper-ates under a load of60nm which is applied to the driven gear.The Coulomb friction model and the dynamic coefficient of friction u measured by Rebbechi et al.[28]are used in this paper.The equations of motion governing torsional vibration are represented by:J€h¼Tð21aÞJ¼Jp0Jg"#;h¼h ph g!;T¼T pÀM pNþM pfÀT gþM gNÀM gf!ð21bÞFig.8.Mesh stiffness with different crack depth(single tooth pair).Fig.9.Mesh stiffness with different crack depth.The equations of motion describing the translational vibration are as follows:M €X¼F ð22a ÞM ¼m Pm gm pm g2666437775;X ¼x p x g y p y g2666437775ð22b ÞF ¼F f ÀK pBx x p ÀC pBx _xp ÀF f ÀK gBx x g ÀC gBx _x g ÀN ÀK pBy y p ÀC pBy _y p N ÀK gBy y g ÀC gBy _yg 2666437775ð22c ÞHere,N is the net contact force due to the elasticity.h i =_h i =€h i is angular displacement/velocity/acceleration,m i denotes themass of gear.x i =_x i =€x i is lateral displacement/velocity/acceleration along x direction.y i =_yi =€y i is lateral displacement/velocity/acceleration along y direction.M iN and M if are the force moments induced,respectively by the normal mesh force along LOA and the corresponding surface friction force based on the method used by He et al.[29].The supporting bearing stiffness K iBj and damping C iBj are assumed to be constant although some time-varying models have been developed like [30–32]because its beyond the scope of this paper.The subscript i =p,g are for pinion and gear,respectively and j =x,y for x ,y directions shown in Fig.10.Statistical features which are commonly used to provide a measurement of the vibration level are widely used in mechan-ical fault detection [33–36].And Wu et al.[1]studied the performances of some of these statistical indicators whengearFig.10.Scheme of spur gear system with six degrees of freedom.Table 4Parameters of the gear system.PinionGear Moment of inertia (kg Ám 2)2Â10À30.96Â10À4Mass (kg)0.44390.3083Radial stiffness of the bearing (N/m) 6.56Â108 6.56Â108Damping of the bearing (Ns/m)1.8Â1031.8Â103Damping between meshing teeth (Ns/m)67Coefficient of friction0.06Fig.11.Displacement of pinion in y direction with crack depth:1.2mm,crack inclination angle:a c=60°and crack length:(a)0mm,(b)12mm,(c)16mm, (d)20mm,and(e)21.2mm.Fig.12.Change of statistical indicators along crack length.13.Spectrum of pinion vibration in y direction with different crack length.(a)Full scope.(b)Zoom plotFig.14.Amplitude of spectrum of pinion vibration versus crack length.Fig.15.Displacement of pinion in y direction with crack length:15mm,crack inclination angle:a c=60°and crack depth:(a)0mm,(b)0.6mm,(c)0.8mm, (d)1mm,and(e)1.2mm.Fig.16.Change of statistical indicators along crack depth.subroutine.And the results presented here are exhibited by statistical indicators and observations in time and frequency domain.17.Spectrum of pinion vibration in y direction with different crack depth.(a)Full scope.(b)Zoom plotIt is well known that,the tooth-meshing frequency and its harmonics,sometimes together with sideband structures due to modulation effects,are the most important components in gear vibration spectra [38].The increment in the number and amplitude of sidebands may indicate a gear fault condition,and the spacing of the side-bands is related to their source [39].Consequently,structures of sideband can be used as a useful diagnostic feature for gear fault detection.As the same as ob-served in published papers like Refs.[13,31,32,38–40],this paper will show the similar phenomenon and obtain some useful results.Influence of gear tooth crack propagating along tooth width on the frequency characteristics is investigated and shown in Figs.13and 14.In Fig.13,the plot (a)shows the spectrum of the dynamic response of the pinion in y direction while (b)is the zoomed plot exhibiting how the tooth crack changes the sidebands around the mesh frequency and its har-monics.And the changes in the amplitudes of the fourth harmonic component and one of its sideband are shown in Fig.14as the growth of tooth crack length.Consequently,a conclusion can be drawn that the amplitudes of the spectrum near mesh frequency and its harmonics are hardly changed by the gear tooth crack.By contrast,the sidebands begin to appear when the tooth crack appears and their magnitudes increase with the crack propagation which can be observed clearly in plot (b).It means that the sidebands are more sensitive to gear tooth crack propagation than the mesh frequency and its harmonics components.The same analysis are also carried out to study the changes of the dynamic response characteristics due to gear tooth crack propagation along crack depth while keeping the crack length and inclination angle unchanged (W c =15mm and a c =60°).And the corresponding results are shown in Figs.15–18.The displacements of pinion in y direction with different crack depth are shown in Fig.15.The statistical indicators –RMS and kurtosis defined by formulas (23)and (24),respectively are also applied to explore the effect of the crack propagation along depth and shown in Fig.16.As defined before,the 100%is equal to the indicators’largest value corresponding to the largest tooth crack depth (W c =15mm and q 0=1.2mm)minus that of the healthy tooth.When the tooth crack propagates along tooth depth while keeping the crack length and inclination angle constant values (W c =15mm and a c =60°),both RMS and kurtosis appear to be near a quadratic versus the crack length.Influence of gear tooth crack propagating along tooth depth on the frequency spectrum characteristics shown in Figs.17and 18is also performed.In Fig.17,the spectrum of the dynamic response of the pinion in y direction is plotted in (a)while plot (b)is the zoom plot which gives the information about how the tooth crack influences the sidebands around the mesh frequency and its harmonics.The fourth mesh harmonic component and one of its sideband changing with the tooth crack depth are shown in Fig.18.As suggested in Figs.17and 18,it can be concluded that the amplitudes at the frequencies near mesh frequency and its harmonics are nearly not affected by the gear tooth crack.However,the sidebands around the mesh frequency and its harmonics begin to appear with the presence of the tooth crack and their magnitudes increase with the crack propagation which can be observed clearly in plot (b).Likewise,it can be concluded that the sidebands are more sen-sitive to gear tooth crack than the mesh frequency and its harmonics.Observation in the change of the sidebands can offer more information on the presence and severity of tooth crack.4.ConclusionsAn analytical mesh stiffness model of spur gear with tooth root crack propagating along both tooth width and crack depth is proposed in this paper.It is validated by comparison with the FEA results.At the same time,effects of gear tooth crack propagating along tooth width and depth on gear mesh stiffness are investigated quantitatively.A dynamic model of spur gear pair system having six-degree-of-freedom is developed to examine the influence of gear tooth crack by incorporation of the developed mesh stiffness model.And two statistical indicators –RMS and kurtosis are used to assess the severityof Fig.18.Amplitude of spectrum of pinion vibration versus crack depth.。

齿轮箱中某工况下齿轮啮合动态激励计算及仿真一、研究齿轮啮合动态激励的意义齿轮箱作为机械设备中一种必不可少的传递运动和动力的通用零部件，在金属切削机床、航空工业、航海设备、电力系统、农业机械、运输机械、冶金等现代化工业发展中得到了广泛的应用。

齿轮系统是由齿轮、轴、轴承和箱体等组成的机械系统。

齿轮由于自身的制造误差和安装误差，在啮合过程中会引起周期性的加速分离或加速啮合，导致齿与齿之间的撞击，引起齿轮振动并产生啮合噪声。

齿轮的振动又会引起轴的振动，并通过轴承将振动传递给齿轮箱，引起箱体的振动，从而产生噪声。

所以齿轮激振是引起噪声的主要原因。

由于传统的齿轮箱结构设计基本上是凭经验进行的，仅停留在静态设计阶段，而没有从动态优化方面作认真考虑，因此迄今国产齿轮箱大多存在严重的振动和噪声问题。

为了解决这个问题，系统的方法是从结构动态性能优化出发，通过建立齿轮箱的动力学模型进行其动态特性分析，从而设计出全新的低噪声齿轮箱。

但是，目前更现实更迫切的针对已有的产品，进行动态分析和测试，找出它的主要振动源和噪声源，并采取有效的局部改进措施，降低它的噪声。

二、齿轮箱动力载荷计算分析2.1齿轮啮合动态激励齿轮啮合动态激励是齿轮系统产生振动和噪声的主要原因。

齿轮系统的动态激励有内部激励和外部激励两类。

内部激励是齿轮传动与一般机械的不同之处，它是由于同时啮合齿对数的变化、轮齿的受载变形、齿轮误差等引起了啮合过程中的轮齿动态啮合力产生的，因而即使没有外部激励，齿轮系统也会受这种内部的动态激励而产生振动噪声。

外部激励是指除齿轮啮合时产生的内部激励外，齿轮系统的其它因素对齿轮啮合和齿轮系统产生的动态激励。

如齿轮旋转质量不平衡、几何偏心、原动机(电动机、发动机等)和负载的转速与扭矩波动、以及系统中有关零部件的激励特性，如滚动轴承的时变刚度、离合器的非线性等。

在这些因素中质量不平衡产生的惯性力和离心力将引起齿轮系统的转子耦合型问题，它是一种动力耦合型问题。

第1篇一、实验背景齿轮作为机械传动系统中的重要组成部分，其性能直接影响着整个系统的效率和寿命。

为了提高齿轮设计的准确性和可靠性，本研究采用有限元分析（FEA）和刚柔耦合动力学仿真（Rigid-Flexibility Coupling）方法，对齿轮进行仿真耦合实验，以评估齿轮在实际工作条件下的力学行为和性能。

二、实验目的1. 建立齿轮的有限元模型，并进行网格划分。

2. 通过有限元分析，计算齿轮在静态载荷作用下的应力分布和变形情况。

3. 利用刚柔耦合动力学仿真，模拟齿轮在实际工作条件下的动态响应。

4. 分析齿轮的疲劳寿命和强度性能，为齿轮设计和优化提供理论依据。

三、实验方法1. 有限元模型建立与网格划分首先，根据齿轮的实际尺寸和材料属性，建立齿轮的几何模型。

然后，采用四面体网格对齿轮进行网格划分，确保网格质量满足仿真要求。

2. 静态载荷下的有限元分析在有限元分析中，将齿轮置于静态载荷作用下，通过求解非线性方程组，得到齿轮的应力分布和变形情况。

主要关注齿轮的齿面接触应力、齿根应力、齿面磨损和齿面疲劳寿命。

3. 刚柔耦合动力学仿真为了模拟齿轮在实际工作条件下的动态响应，采用刚柔耦合动力学仿真方法。

将齿轮视为柔性体，同时考虑齿轮与轴承、轴等部件的相互作用。

通过施加转速和扭矩等激励，模拟齿轮在旋转过程中的动态响应。

4. 疲劳寿命和强度性能分析在仿真过程中，对齿轮的疲劳寿命和强度性能进行分析。

通过计算齿面接触应力、齿根应力等参数，评估齿轮的疲劳寿命和强度性能。

四、实验结果与分析1. 静态载荷下的应力分布和变形通过有限元分析，得到齿轮在静态载荷作用下的应力分布和变形情况。

结果表明，齿轮的齿面接触应力主要集中在齿根附近，齿根应力较大。

同时，齿轮的变形主要集中在齿面和齿根处。

2. 刚柔耦合动力学仿真结果通过刚柔耦合动力学仿真，模拟齿轮在实际工作条件下的动态响应。

结果表明，齿轮的齿面接触应力、齿根应力等参数在旋转过程中发生变化，但总体上满足设计要求。

第一作者：赵重年，男，1994年生，硕士研究生，研究方向为军用车辆设计与试验。

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重庆理工大学毕业设计（论文）标准格式样本编号毕业设计（论文）题目汽车离合器结合性能仿真研究二级学院重庆汽车学院专业车辆工程班级学生姓名学号指导教师职称时间目录摘要 (Ⅰ)Abstract (Ⅱ)1 绪论 (1)AMT自动离合器的发展 (2)AMT自动离合器发展现状 (3)自动变速器的研究方向 (4)自动离合研究的难点与重点 (5)论文研究的主要内容 (6)2 AMT离合器工作原理和接合性能研究 (7)AMT原理和结构 (8)概述 (9)电控单元ECU (10)离合控制系统 (11)传感器、电控软件 (12)离合器接合特性分析 (13)力学模型分析 (14)离合器的三种状态分析 (15)AMT离合器起步过程分析 (16)离合器接合指标 (17)3 离合器的建模与仿真 (18)MATLAB/SIMULINK简介 (19)AMT离合器力学模型的建立 (20)发动机转矩输出模型 (22)离合器动力学模型建立 (23)4 离合器接合过程分析 (24)离合器角速度 (25)滑磨功和温度 (26)冲击度 (27)发动机输出转矩 (28)5 AMT离合器试验台搭建简介 (29)6 展望 (30)7 致谢 (31)参考文献 (32)附录 (33)摘要电控机械式自动变速器就是人们平常称的AMT，AMT为Automated Mechanical Transmission三个英文单词的缩写，能根据汽车的运行速度快慢，油门节气门的开度大小，驾驶人员的主观直接指令等一系列确定和模糊的参数，来选取合适的换挡时机，保证汽车行驶的最佳档位。

AMT没有增添新的机械操纵部分，保存了原本老式的变速箱机构，省略了驾驶员的踩离合，换挡等。

也就是在原有的变速箱基础上增加一个智能的控制器和执行机构，通过某种控制策略对发动机，离合器，整车传动机构进行协调控制，自动完成选挡和换挡操作。

AMT的核心技术是微机控制，电子技术质量，生产工艺的品质。

随着经济的发展，在环保和节约成为当今的主题，当前在中国对排放标准和燃料要求越来越符合环保节能的形势下。

Vol 121 No 110公 路 交 通 科 技J OURNAL OF HIGHWAY AND TRANSPORTATION RESEARCH AND DEVELOPME NT2004年10月文章编号:1002O 0268(2004)10O 0121O 05收稿日期:2003O 08O 11作者简介:王玉海(1977-),男,山东青岛人,博士研究生,研究方向为车辆自动变速理论与控制策略1(wyhai00@mails 1tsinghua 1edu 1cn)离合器动态过程建模与仿真王玉海,宋 健,李兴坤(清华大学汽车安全与节能国家重点实验室,北京 100084)摘要:在分析膜片离合器接合、分离过程动力学的基础上,根据摩擦学原理提出离合器过度动态过程的数学模型,此过程比静态模型更加准确地描述了离合器接合、分离的动态过渡过程,并给出仿真结果,为离合器自动控制提供理论基础。

关键词:离合器;动态过程;动力传动系统;仿真中图分类号:U4631211 文献标识码:AModeling and Simulation of Clutch Dyn am ic ProcessWANG Yu O ha i ,SONG Jian ,LI Xin g O kun(Tsinghua Universi ty State Key Laboratory of Automotive Safety and Energy,Beijing 100084,China)Abstract :This paper analyzes the dynamic process of clutch engagement and disengagement,then bri ngs up a new dynamic mathematic model of this transien t process 1This model describes the transient of clutch engagement and disengagement process more exactly than the static model 1The simulation result is provided and it will be applied to the con trol of automated clutch 1Key words :Clu tch;Dynamic transient process;Powertrain;Simulati on离合器是汽车动力传动系统的重要部件,它依靠主从动片之间的摩擦力矩来传递动力,并通过分离与接合来控制车辆动力传动系统的工作状态。