Proceedings of the Institution of Mechanical Engineers, Part D- Journal of Automobile Engineering

合集下载

拟投期刊的文章-可以引用的--Consensus-based reconfigurable controller design

followers [2, 3]. In this approach, the leader UAV tracks a predeﬁned trajectory, while the followers track the leader using the information receiving from the leader. It is easy to analyse and implement the leader–follower controller; however, this approach is not robust with respect to the failure of the leader. Wolfe et al. [4] investigated a decentralized controller for aircraft formation ﬂight, in which the formation consisted of a single line of decentralized control, with each aircraft ﬂying one wingspan behind the aircraft of its neighbour. In reference [5], the behaviour-based approach via a decentralized scheme was presented to achieve the formation manoeuvre of mobile robots using a feedback linearization method. In reference [6], navigation strategies for the ﬂeet of autonomous mobile robots were treated in which a sufﬁcient stability condition of a

Planning surface texturing for reduced friction……

/Tribology Engineers, Part J: Journal of EngineeringProceedings of the Institution of Mechanical/content/226/8/661The online version of this article can be found at:DOI: 10.1177/1350650112439809published online 7 March 2012 2012 226: 661 originallyProceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology intinζM Sedlacek, B Podgornik and J Vi parameters skewness and kurtosisPlanning surface texturing for reduced friction in lubricated sliding using surface roughnessPublished by: On behalf of:Institution of Mechanical Engineers can be found at:Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering TribologyAdditional services and information for/cgi/alerts Email Alerts:/subscriptions Subscriptions: /journalsReprints.nav Reprints:/journalsPermissions.nav Permissions:/content/226/8/661.refs.html Citations:What is This?- Mar 7, 2012OnlineFirst Version of Record- Jul 12, 2012Version of Record >>Original ArticlePlanning surface texturing for reducedfriction in lubricated sliding using surfaceroughness parameters skewness andkurtosisM Sedlacˇek1,B Podgornik2and J Vizˇintin1AbstractThe aim of this research was to confirm skewness and kurtosis parameters as two main roughness parameters which describe tribological properties of contact surfaces,especially pointing out their application in surface texturing.Based on our previous virtual texturing findings,steel samples were laser textured in a manner to achieve micro-channels with different spacing and width of the channels.Lubricated tests under different contact conditions were done to evaluate their influence on friction.It was confirmed that higher S ku and more negative S sk can be used for planning surface texturing.KeywordsBoundary lubrication,friction,roughness parameters,surface roughness,surface texturingDate received:21October2011;accepted:31January2012IntroductionIn recent years,surface texturing was introduced as a surface engineering technique to reduce friction.1,2 Reduction of friction was achieved with employment of diﬀerent patterns in the form of micro-dimples or channels on the surface.In general,it is assumed that in the case of dry sliding contact and boundary lubri-cation,textures act as micro-traps for wear particles3or micro-reservoirs which enable retention and supply of lubricants into the contact.On the other hand,in conditions of mixed and hydrodynamic lubrication micro-reservoirs act as micro-bearings and thereby improve the tribological properties of the contact.4 When textures act as micro-hydrodynamic bearings, theoretical studies and modelling enable us to study the eﬀect and optimization of surface texturing param-eters to improve tribological properties of contact surfaces.5–7Because of this,most research of surface texturing is done on theﬁeld of hydrodynamic lubrica-tion,especially in theﬁeld of mechanical seals and axial sliding bearings.5,8,9On the other hand,eﬀect of surface texturing in theﬁeld of boundary lubrication is rela-tively unexplored and research is still based on the try and error approach.10Possible idea to design surface contacts,especially in the boundary lubrication regime,which would result in lower friction,is by treating surface texturing as a predeﬁned roughness.11,12 By knowing which surface topography and especially which surface roughness parameters result in lower fric-tion,we should be able to select proper surface textur-ing parameters,and thus properly design the surface for given contact conditions.Knowledge about correlation between surface roughness and friction is essential for achieving this.Two of the most important surface properties are surface roughness and topography, which are described with surface roughness parameters. Unfortunately,standard surface roughness parameters R a and R q do not describe contact surfaces suﬃciently, with completely diﬀerent surfaces showing similar or even the same values of standard roughness parameters and vice versa–similar surfaces having much diﬀerent standard roughness parameters.In addition to that 1Centre for T ribology and T echnical Diagnostics,University of Ljubljana, Slovenia2Institute of Metals and T echnology,SloveniaCorresponding author:Marko Sedlacˇek,Centre for T ribology and T echnical Diagnostics, University of Ljubljana,Bogisiceva8,SI-1000Ljubljana,Slovenia. Email:marko.sedlacek@ctd.fs.uni-lj.siProc IMechE Part J:J Engineering Tribology226(8)661–667!IMechE2012Reprints and permissions:/journalsPermissions.navDOI:10.1177/1350650112439809diﬀerent standards use diﬀerent parameters.In prac-tice,most commonly used parameters for surface roughness description are R a and R q .Average surface roughness (R a )gives very good overall description of height variations,but does not give any information on waviness and it is not sensitive to small changes in proﬁle height.Root mean square deviation of the assessed proﬁle (R q )is more sensitive to deviations from main line than R a ,but it still does not give satisfactory description of the surface roughness.A parameter that describes non-Gaussian distribution of roughness proﬁle is the parameter R sk which is deﬁned as skewness and is sensitive on occasional deep valleys or high peaks.Zero skewness reﬂects in symmetrical height distribution,while positive and negative skew-ness describe surfaces with high peaks or ﬁlled valleys,and with deep scratches or lack of peaks,respectively.On the other hand,kurtosis (R ku )describes the prob-ability density sharpness of the proﬁle.For surfaces with relatively few high peaks and low valleys,R ku isless than 3,and more than 3for surfaces with relatively many high peaks and low valleys.13A lot of research has already been done in the ﬁeld of inﬂuence of rough-ness on tribological properties of contact surfaces.14–17It was shown that diﬀerent roughness parameters,as an average slope of the proﬁle Á ,mean peak spacing (S )and core roughness depth R k have an impact on fric-tion.However,a lot of questions remain open,the main one being the correlation between standard roughness parameters and the tribological behaviour of boundary lubricated contacts.Previous studies primarily focused on the parameters R a and R q .Few studies 18–20focused also on parameters R sk and R ku ,but only on the static coeﬃcient of friction for dry contact.In Wang et al.,21where the eﬀect of surface roughness parameters on mixed lubrication characteristics was investigated by modelling,it was found that skewness and kurtosis have a great eﬀect on the contact parameters of mixed lubrication.Attempt to correlate surface rough-ness parameters and tribological behaviour of textured surfaces was not found in our literature review.In our previous research 11,12where inﬂuence of sur-face roughness on friction was investigated,it was found that negative skewness (S sk )and high kurtosis (S ku )values lead to lower friction.Furthermore,asexplained in detail in Sedlacek et al.,22with use of NIST SMATS softgauge software,23virtually altered roughness proﬁles were investigated in terms of texture size and shape inﬂuence on surface roughness param-eters,especially on skewness and kurtosis.It was found that smaller width,larger spacing and wedge-shaped proﬁle of the channels reﬂect in higher R ku and more negative R sk parameters,which should give lower fric-tion under boundary lubrication.The aim of this research was to evaluate the inﬂuence of surface textur-ing parameters on friction,and to compare the results with the theoretical ﬁndings on thecorrelationFigure 1.Surface profiles and corresponding density of textured surface r ¼A T /A ,of specimens included in theinvestigation.Figure 2.Schematic illustration of the contact between pin and textured sample.662Proc IMechE Part J:J Engineering Tribology 226(8)between surface roughness parameters and friction.Furthermore,we investigated the possibility of using surface roughness parameters for planning surface tex-turing for improved tribological performances.ExperimentalTo conﬁrm the ﬁndings of roughness modelling,series of 100Cr6steel plate samples were laser textured pro-ducing micro-channels with diﬀerent channel width and spacings.Channels were chosen because in virtual tex-turing 22two-dimensional (2-D)proﬁles and roughness parameters were used.When 2-D proﬁles are converted into 3-D space by expansion in only one direction,grooved surfaces are formed.If expansion is done in two directions,surfaces with dimples would be obtained.Preliminary polished steel surfaces (100Cr6,S a ¼0.02m m,850HV),were surface textured usingNd-YAG laser,forming micro-channels with diﬀerent width and spacing.The depth of channels was kept constant at 11m m.Denotation of each sample according to the width and spacing of the channels,and the corresponding roughness proﬁles are shown in Figure 1.By keeping channel width ﬁxed at 80m m,spacing between channels was changed from 125to 500m m.Specimens with spacing of 125m m were denoted B1,with spacing of 250m m B2and with spa-cing of 500m m B3.Samples with spacing between the channels ﬁxed at 250m m and the width of the channels varied between 40and 120m m were denoted A2(40m m),B2(80m m)and C2(120m m).Finally,samples with a minimum channel width of 40m m and a max-imum spacing between channels of 500m m,were denoted A3.Diﬀerent spacing and width have inﬂuence also on density of textured surface r .On Figure 1,it can be also seen that with increase of width between the channels area ratio is decreased from 40%to16%,Figure 3.Roughness parameters for samples:(a)B1,B2,B3,G and T and (b)A2,B2,C2,G,T and A3.Sedlac ˇek et al.663and with decrease of channels width from 36%to 16%.The lowest area ratio of 8%was obtained with min-imum channel width and a maximum spacing between channels (A3).Channels with the width of 40m m (sample A),were made using a single mode laser beam,energy of 0.938mJ and ﬂash duration of 100ms.Samples B and C were made with a multimode laser beam with ener-gies of 2.79and 8.36mJ and the pulse duration of 259and 159ms,respectively.After laser texturing,all sam-ples were repolished to remove the bumps around the channels.The measurement of 3-D topography and belonging roughness parameters were performed prior to tribological tests using Hommeltester T8000stylus proﬁlometer.For all samples,the surface evaluation window was 4.8Â4.8mm 2,with a sampling interval of 10m m and a measurement speed of 0.05mm/s.Three-dimensional roughness parameters were calcu-lated using Hommel Map Expert software.Prior to the calculation,Gaussian ﬁltering was used with 0.8mm cut-oﬀlengths.If parameters are evaluated on the 3-D surface,parameters are denotated with the cap-ital letter S.For comparison,a ground sample (G)with average roughness S a of about 0.08m m and a sample produced by turning (T)with an average roughness S a of about 1.22m m were used.Values of surface roughness param-eters S a ,S q ,S ku and S sk for machined and laser surface textured (LST)samples are shown in Figure 3.Reciprocating sliding tests were carried out on a TE77device,using ﬂat-on-ﬂat contact.A ﬂat contact of $20mm 2in size was achieved using 100Cr6steel ﬂat ended pin with a diameter of 5mm,which was loaded against a textured plate.Schematic presentation of the contact can be seen in Figure 2.Before each sliding test,the ﬂat-ended pin was levelled and polished to ensure proper alignment with the textured surface and to dimin-ish the eﬀect of counterpart roughness.24To invalidate the impact of changing the orientation of channels according to the movement of the pin,reciprocating sliding was used.Sliding was always done in the direction perpendicular to the channels direction.Reciprocating sliding tests,withtheFigure 4.Coefficient of friction for samples:(a)B1,B2,B3,G and T and (b)A2,B2,C2,G,T and A3(v S ¼0.05m/s).664Proc IMechE Part J:J Engineering Tribology 226(8)stoke length of 6.8mm,were done at sliding speeds of 0.005,0.05,0.1,0.2and 0.3m/s corresponding to fre-quency 0.36,3.67,7.35,14.7and 22.05Hz,respectively.Normal load of 30N,corresponding to a nominal contact pressure of 1.52MPa was applied.Sliding distance of each test was 100m.For each sliding speed,tests were repeated at least three times to ensure proper repeatability.During testing,the coeﬃcient of friction was monitored as a func-tion of time.Tests were done under boundary lubrication conditions using pure Poly-Alpha-Oleﬁn oil (PAO 8;n 40¼46mm 2/s)and normal room conditions(T ¼23Æ2C;RH ¼50Æ10%).During the test,contact was immersed into the lubricant.Results and discussionValues of surface roughness parameters S a ,S q ,S ku and S sk for machined and LST samples are shown in Figure 3.In Figure 3(a),it can be seen that with increase in spacing (B1!B2!B3)S sk parameter is becoming more negative while S ku value increases.Smaller skewness and higher kurtosis were also achieved when smaller channel width was used (sample A2),as shown in Figure 3(b).The most nega-tive value of skewness,the highest kurtosis and lowest density of textured surface r were achieved with the sample A3,having the smallest channel width and the largest spacing.These results coincide with prediction obtained with virtual texturing,22and showing that changing width and spacing of textures is strongly cor-related with roughness parameter S ku and S sk and also density of textured surface r .Inﬂuence of spacing between channels on the coeﬃ-cient of friction at a sliding speed of 0.05m/s is shownin Figure 4(a).It can be seen that coeﬃcient of friction decreases with increased spacing between the channels.By increasing the spacing from 125to 500m m (B1!B3),S sk was reduced by 4times and S ku increased by 2.5times,which also resulted in $20%reduction of coeﬃcient of friction.If we compare textured surfaces with grounded sur-face (G)which has the lowest value of the parameters S a and S q ,the grounded one does not result in the lowest friction.These results clearly show that the roughness parameters S a and S q are not the main indi-cators of tribological properties of the contact surfaces.As it was shown in previous research,11,12roughness parameters S sk and S ku can have a signiﬁcant inﬂuence on tribological behaviour of contact surfaces.When comparing samples B3and T,which have comparable values of parameters S a and S q ,but diﬀerent values of S sk and S ku ,we can see that the sample B3shows much lower friction,conﬁrming the dominant inﬂuence of the parameters S sk and S ku on the coeﬃcient of friction,under the present contact conditions.Figure 4(b)shows the coeﬃcient of friction for sur-faces with diﬀerent channel width at a sliding speed of 0.05m/s.Smaller channel width was found to result in lower friction.Reducing the channel width from 80to 40m m,results in 22%lower friction.When comparing samples B2and C2,which show similar S sk values but diﬀerent S a ,S q and S ku values,it can be seen that sample C2shows higher value of the coeﬃcient of fric-tion,indicating on inﬂuence of area ratio r .Furthermore,comparison of samples C2and T,which have similar values of S a ,S q and S ku ,shows that the signiﬁcantly lower value of S sk for sample C2(nine times lower)also results in 30%lowerfriction.Figure parison of S sk /S ku ratio with coefficient of friction values for textured samples in lubricated sliding contact (v d ¼0.05m/s).Sedlac ˇek et al.665According to the predictions and results of virtual texturing,22sample A3,which has the smallest channel width and the largest spacing between the channels of all samples investigated,and consequently the lowest value of S sk and the highest value of parameter S ku ,also showed the lowest friction among all investigated samples.Despite comparable values of parameters S a and S q ,sample A3gives 45%lower friction than the sample produced by turning.When comparing textured samples C2and A3,which also have comparable values of parameters S a and S q ,lower value in S sk and higher value in S ku displayed by sample A3,also results in 33%lower friction.As in the case of wider channels (sample B),increase in spacing between the channels from 250to 500um (A2!A3)leads to more favour-able values of S sk and S ku and also to $15%lower friction.Figure 5shows a relationship between S sk and S ku parameters,and coeﬃcient of friction for textured sur-faces at sliding speed 0.05m/s.The results indicate thatparameters S sk and S ku inﬂuence tribological perform-ance of textured surfaces in lubricated sliding contacts.Higher on the ordinate axis (higher S ku value)and fur-ther down the abscissa (more negative S sk value)the surface is,lower friction can be expected,with the par-ameter S sk being the dominant one.Similar trends in tribological behaviour were observed also for other sliding speeds,as seen in Figure 6.With increase in spacing between the chan-nels,the diﬀerence between the coeﬃcient of friction remained constant regardless of the sliding speed used.For all sliding speeds,sample B3shows the lowest friction,except for sliding speed of 0.3,where friction of samples B2and B3is very similar.On the other hand,the highest friction at all sliding speeds was observed for sample B1.According to Figure 7,a decrease in the channel width will lead to lower friction at diﬀerent sliding speeds,with sample A2showing the lowest friction among the samples with the same channel width (A2,B2and C2),up to the sliding speed of 0.3m/s.Furthermore,as compared to ground sample (G),which shows a sharp increase in friction when the slid-ing speed is reduced to 0.05m/s,the textured ones show only very moderate friction increase.At lowest sliding speed (0.005m/s),textured samples show lower friction than the ground sample (G).On the other hand,sample A3,which has the lowest channel width and largest spacing and consequently the lowest S sk value and the highest S ku value among all samples investigated,shows much lower coeﬃcient of friction than all other sam-ples.Furthermore,sliding speed has almost no inﬂu-ence on its coeﬃcient of friction.This indicates that negative S sk and high S ku can be used for planning surface texturing in boundary and also in hydro-dynamic lubrication regime.However,comparison of samples C2and G at sliding speed 0.1m/s,points out that a wrong selection of texturing parameters can des-troy favourable tribological behaviour,leading to increase in friction instead of expected reduction.Due to laser limitations,only textures with channels were investigated in this study.It is expected that with implementation of dimples,which would result in even more favourable surface roughness parameters,even lower friction could be obtained.However,this still has to be experimentally investigated and conﬁrmed.ConclusionsBased on the experimental work performed,the follow-ing conclusions can be drawn:1.The surface roughness parameters S ku and S sk can be used under boundary lubrication for designing textured surfaces with desired coeﬃcient offriction.Figure 6.Influence of sliding speed and spacing between the channels on the coefficient of friction in lubricated slidingcontact.Figure 7.Influence of sliding speed and channels width on the coefficient of friction in lubricated sliding contact.666Proc IMechE Part J:J Engineering Tribology 226(8)2.Friction tends to get lower when the parameter S kuis getting higher.However,the most dominant par-ameter is the parameter S sk and the more negative it is the lower friction we can expect.Friction also depends on the density of textured surface r.Lower it is,lower friction can be expected.3.Surface texturing,which result in greater S ku andmore negative S sk values and consecutively reﬂect in lower friction is characterized by smaller width of the channels and wider spacing between them.4.The correct choice of roughness parameters(nega-tive S sk and high S ku)in textured surfaces can result in lower coeﬃcient of friction and reduced sensitiv-ity of the contact on sliding speed.FundingThis research received no speciﬁc grant from any funding agency in the public,commercial,or not-for-proﬁt sectors. References1.Etsion I.Improved tribological performance of mechan-ical components by laser surface texturing.Tribol Lett 2004;17(4):733–737.2.Etsion I.State of the art in laser surface texturing.J Tribol2005;127:248–253.3.Suh NP,Mosleh M and Howard PS.Control of friction.Wear1994;175:151–158.4.Hamilton DB,Walowit JA and Allen CM.A theory oflubrication by microasperities.ASME J Basic Eng1966;88(1):177–185.5.Etsion I and Halperin ser surface textured hydro-static mechanical seal.Sealing Technol2003;2003(3): 6–10.6.Zhu D,Nanbu T,Ren N,et al.Model-based virtual sur-face texturing for concentrated conformal-contact lubri-cation.Proc IMechE Part J:J Engineering Tribology 2010;224:685–696.7.Dobrica MB,Fillon M,Pascovici MD,et al.Optimizingsurface texture for hydrodynamic lubricated contacts using a mass-conserving numerical approach.Proc IMechE Part J:J Engineering Tribology2010;244: 737–750.8.Brizmer V,Kligerman Y and Etsion I.A laser surfacetextured parallel thrust bearing.Tribol Trans2003;46: 397–405.9.Etsion I,Halperin G and Brizmen V.and Kligerman,Y.Experimental investigation of laser surface textured par-allel thrust bearings.Tribol Lett2004;17(2):295–300. 10.Pettersson U and Jacobson S.Textured surfaces in slidingboundary lubricated contacts mechanisms,possibilities and limitations.Tribol Mater Surf Interfaces2007;l1(4): 181–189.11.Sedlac ek M,Podgornik B and Viz intin J.Influence ofsurface preparation on roughness parameters,friction and wear.Wear2009;266:482–487.12.Sedlac ek M,Podgornik B and Viz intin J.Correlationbetween standard roughness parameters skewness and kurtosis and tribological behaviour of contact surfaces.Tribol Int2012;48:102–112.13.Gadelmawla ES,Koura MM,Maksoud TMA,et al.Roughness parameters.J Mater Process Technol2002;123:133–145.14.Menezes PL,Kishore and Kailas SV.Influence of rough-ness parameters on coefficient of friction under lubricated conditions.Sadhana2008;33(3):181–190.15.Hu ZM and Dean TA.A study of surface topography,friction and lubricants in metal forming.Int J Mach Tools Manuf2000;40:1637–1649.16.Lundberg J.Influence of surface roughness on normal-sliding lubrication.Tribol Int1995;28(5):317–322. 17.Wieleba W.The statistical correlation of the coefficient offriction and wear rate of PTFE composites with steel counterface roughness and hardness.Wear2002;252(9–10):719–729.18.Tayebi N and Polycarpou AA.Modeling the effect ofskewness and kurtosis on the static friction coefficient of rough surfaces.Tribol Int2004;37:491–505.19.Liu X,Chetwynd G and Gardner JW.Surface character-ization of electro-active thin polymeric film bearings.Int J Mach Tools Manuf1998;38(5–6):669–675.20.Komvopoulos K.Surface engineering and microtribologyfor MEMS.Wear1996;200:305–327.21.Wang W-Z,Chen H,Hu Y-Z,et al.Effect of surfaceroughness parameters on mixed lubrication characteris-tics.Tribol Int2006;39:522–527.22.Sedlac ek M,Podgornik B and Viz intin J.Surfacetopography modelling for reduced friction.Strojnisˇki ves-tnik–J Mech Eng2011;57:674–680.23.National Institute of Standards and Technology.Internet based surface metrology algorithm testing system/VSC/jsp/index.jsp(2002,acces-sed2009).24.Vilhena LM,Podgornik B,Viz intin J,et al.Influence oftexturing parameters and contact conditions on tribo-logical behaviour of laser textured surfaces.Meccanica 2009;46:567–575.AppendixNotationr density of textured surface(%)S a arithmetic average height of the surface(m m)S ku kurtosis of height distributionS q root mean square height of the surface(m m)S sk skewness of height distributionv S sliding speed(m/s)Sedlacˇek et al.667。

Proceedings of the Institution of Mechanical Engineers, Part F- Journal of Rail

Special Issue ArticleDynamics of a vehicle–track couplingsystem at a rail jointIlaria Grossoni,Simon Iwnicki,Yann Bezin and Cencen GongAbstractThe dynamic behaviour at a rail joint is examined using a two-dimensional vehicle–track coupling model.The track system is described as a finite-length beam resting on a double-layer discrete viscous-elastic foundation.The vehicle is represented by a half car body and a single bogie.The influence of the number of layers considered,the number of elements between two sleepers,and the beam model is investigated.Parametric studies,both of the coupling model and the analytic formulae,are carried out in order to understand the influence of the main track and vehicle parameters on the P1and P2peak forces.Finally,the results in terms of P2force from the proposed model are compared,not only with measured values but also with other simulated and analytical solutions.An excellent agreement between these values is found.KeywordsRail joints,vehicle–track interaction,dynamic behaviour,P1force,P2forceDate received:9December2013;accepted:1September2014IntroductionWhen a train runs over a joint,large dynamic impact forces are developed that lead to vibrations in the structures and a higher probability of component fatigue and damage.Thus,it is clear that rail joints can aﬀect the maintenance costs,ride comfort and running security on a modern railway.Although there is currently a worldwide trend towards using continuously welded rails to minimize the wheel–rail impact forces,rail joints are still common in some areas.For example,insulated rail joints are required for track electrical insulation to detect the train location and to isolate sections such as those near road crossings.Many studies have focused on the dynamic response of the railway track under moving vehicles.Some of these studies consider the track system to solely con-sist of a beam on an elastic foundation subjected to moving point loads.1–3Although this approach is simple to implement it is insuﬃcient to fully model the dynamic behaviour of the track and vehicle systems as it neglects the eﬀects of wheel–rail contact. Some other studies4–7take the coupling aspects into account,but only a few apply these aspects to model the dynamic behaviour with a rail joint.8,9In this paper,a two-dimensional vehicle–track cou-pling model is established.The track system is described as aﬁnite-length beam supported on a two-layer discrete elastic foundation.The vehicle is represented using a half car body.These sub-systems are solved independently and coupled together through a Hertzian wheel–rail contact model,4where the irregularity due to the rail joint is modelled as a second-order polynomial.The inﬂuence of the number of layers considered,the number of elements between two sleepers and the beam model is investi-gated.An extensive parametric study has been carried out using aﬁnite element model and analytical for-mulae,through which it is possible to point out the diﬀerences using a predictive model and an analytical one.The main results show that theﬁrst impact force P1is greatly inﬂuenced by the wheelset mass,the rail mass and the joint angle,whereas the second peak force P2is largely aﬀected by the wheelset mass,the rail-pad stiﬀness,the support stiﬀness and the joint angle.The parametric study using the analytic formu-lae demonstrates the robustness of the established coupling model.Finally,the results in terms of the P2force from this model have been compared with measured data,8another simulated model8and ana-lytical solutions.10,11An excellent agreement has been found between the measured data and simulated model.Institute of Railway Research,University of Huddersfield,UK Corresponding author:Ilaria Grossoni,Institute of Railway Research,University of Huddersfield,Queensgate,Huddersfield,HD13DH,UK.Email:i.grossoni@Proc IMechE Part F:J Rail and Rapid Transit2015,Vol.229(4)364–374!IMechE2014Reprints and permissions:/journalsPermissions.navDOI:10.1177/0954409714552698Modelling the vehicle–track coupling systemThe vehicle–track coupling model with a rail joint is shown in Figure 1.Fundamental assumptionsThe following assumptions were made in this study.1.Only vertical dynamic forces were considered.Due to the track symmetry,it was possible to consider a single rail in the calculations.2.The track system was modelled using a two and three-layer discretely supported ballast track model.A ﬁnite straight track without imperfec-tions was considered.The number of beam elem-ents considered was 90,because in this way it was possible to avoid overlapping between the increas-ing static load during the transient time and the dynamic forces due to the rail joint.3.A half car body was considered for the vehicle model.All the masses were assumed to be concen-trated at the centre of gravity of the corresponding element.The two wheelsets masses and proﬁles were assumed to be the same.4.A nonlinear Hertzian contact model was used to couple the vehicle and track models.It was also assumed that there was only one contact point at each wheel.5.An iterative scheme was used in order to solve the coupling problem.Modelling the track systemA ﬁnite element (FE)analysis was developed to approximate the deformation within an element using nodal values of displacement and rotation.The third-order Hermitian interpolation was assumed to be valid in this study.The Euler–Bernoulli mass,stiﬀness and damping matrices of the generic i th element are reported in Appendix 1.The moving force is characterized by a constant value of speed V .Thus,a simple formula for the uniform linear motion was used.Modelling the vehicle systemThe model consisted of a half-car supported by a bogie through the secondary suspension and a bogie supported by two half wheelsets through the primary suspension.All the bodies were assumed to be rigid.The vehicle mass,stiﬀness and damping matrices are reported in Appendix 2.Modelling the irregularityA quadratic function can be used to describe the deformed shape of the rail,as highlighted in a com-parison with measured values reported in Wu and Thompson.12It was assumed that at the start and ﬁnal point of the joint the ﬁrst derivative of the function was equal to zero.The idealized form of the joint used in the model is presented in Figure 2.The quadratic function describing the irregularity irr(x )can be established asirr ðx Þ¼4D 2x 204x 4L 4D L 2x ÀL 2ÀÁ2À4D L xÀL 2ÀÁþDL24x 4L(where D is the maximum depth of the rail joint and L is its eﬀective length.In particular,the length of the rail joint L is deﬁned as the sum of the horizontal projection of the tangential lines that start fromtheFigure 1.Vehicle–track coupling model with a rail joint (Mc:car-body mass;Ks2:secondary suspension stiffness;Cs2:secondary suspension damping;Mt:bogie mass;Jt:bogie pitch moment of inertia;Ks1:primary suspension stiffness;Cs1:primary suspension damping;Mw:wheelset mass;Kc:contact stiffness;mr:rail mass per unit length;E:Y oung’s modulus of the rail;I:rail inertia;kr:rail-pad stiffness;cr:rail-pad damping;ms:sleeper mass;ks:support stiffness;cs:support damping).Grossoni et al.365dip bottom and have an inclination equal to,respect-ively, 1and 2.ResultsThe parameter values used to solve the coupling system are reported in Grossoni et al.13The response in terms of wheel–rail contact force as a function of time is shown in Figure 3.The displacement and acceleration of the cen-tral node and in the central sleeper (45th sleeper)are presented in Figure 4.The two peaks are due to the passage of each of the two wheelsets,which occurs respectively at 0.56and 0.63s.Due to the con-nection between the leading and the trailing wheelset,the second peaks are larger than the ﬁrst ones in Figure 4.A comparison between models (i.e.two-and three-layer models which includes additional masses for the ballast layer)and diﬀerent beam types (i.e.Euler–Bernoulli and Timoshenko beams)inboth the time and frequency domains is presented in Figure 5.Figure 5(a)shows that the ﬁrst peak value is of the same order for both the two-layer and three-layer models and that the second peak force is mostly aﬀected.Adding a layer to represent the ballast mass aﬀects the results;a larger inertia results in a shift of the two characteristic peaks in the frequency domain (Figure 5(b)).A comparison in terms of the number of elements in a sleeper bay is shown in Figure 6.The model used in the comparison is a two-layer discretely supported ballast track with an Euler–Bernoulli beam.As expected,the more elements that are considered,the more stable the results are and fewer oscillations occur.It is worth noting that when the number of elements is greater than four,the diﬀerences are negligible,this is also true in terms of the maximum peak force.On the other hand,increasing the number of elements leads to an increase in the computational costs.As an exam-ple,the running times required in each case (the PC used for the simulation was an Intel(R)Core(TM)i7-3770Figure 3.Wheel–rail contact force against time:leading and trailingwheels.Figure 2.The idealized form of the joint used in the model (irr(x ):irregularity value at point x ).10The dotted lines are the geometrical constructions for the calculation of the effective length.366Proc IMechE Part F:J Rail and Rapid Transit 229(4)with 16GB RAM)and the maximum forces are pre-sented in Table 1.Analysing Figure 3,it is also possible to recognize two peak forces,frequently called the P 1and P 2forces.The P 1force is a high-frequency force (approximately 500–1000Hz)and it is characterized by a high magni-tude,which has been reported to be approximately ﬁve times greater than the unsprung static load.10It is mainly associated with the clattering of the unsprung mass on the rail-end and is mainly absorbed by the iner-tias of the rail and sleeper.In the example shown in Figure 2,the force peak occurs 0.3ms after crossing the joint,which is within the typical range of between 0.25and 0.5ms.10The P 2force,which occurs several milliseconds after the impact,is a medium-frequency force (approximately 30–100Hz)and its peak is lower than the P 1force,being around three times bigger than the static force.10Contrary to the P 1force,the P 2force depends on the rail bending resilience and it is transmitted to the ballast,producing an accel-eration in the deterioration of the whole track system.From the vehicle standpoint,the extent of the trans-mitted load depends solely on the unsprung masses,as the other masses are suspended via primary and sec-ondary suspensions.This is the reason why vehicle designers should reduce them as much as possible.The P 1and P 2forces can be determined in a ﬁrst approximation 10as in equations (1)and (2)P 1¼P 0þ2 VﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃK H m e1þm e =m u ðÞs ð1ÞP 2¼P 0þ2 V 1Àc t4k t ðm t þm u ÞÂﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ11þm t =m u ðÞk t m u s ð2Þwhere P 0is the static wheel load (unit:N),2 the total joint angle (unit:rad),V is the travelling speed (unit:m/s),K H the linearized Hertzian contact stiﬀness (unit:N/m)as deﬁned in Jenkins et al.,10m u the vehi-cle unsprung mass (unit:kg),m e is the eﬀective track mass (unit:kg)and m t ,k t and c t are the equivalent track system parameters deﬁned in Jenkins et al.10The UK standard GM/TT0088states that:‘vehicles shall be able to run over the normal range of vertical track irregularities at normal operating speeds without generating excessive vertical loads and stresses in the rails and track’.11There is a limit only for the P 2force,which cannot exceed a totalvalueFigure 4.Plots of:(a)the rail displacement at the central node against time;(b)the rail acceleration at the central node against time;(c)the mid-sleeper displacement against time;and (d)the mid-sleeper acceleration against time.Grossoni et al.367of 322kN per wheel at the maximum operating speed.This limit is applied because,as previously mentioned,this force is directly transmitted to the ballast.In par-ticular,an analytical formula has been proposed 11P 2¼Q þA z V m MCKð3Þwhere Q is the maximum static wheel load (unit:N),A z is the total angle of the vertical ramp discontinuity and is ﬁxed at 0.02rad,V m is the maximum normal operating speed (unit:m/s),M v is the eﬀective vertical unsprung mass per wheel (unit:kg),and M ,C and K are parameters that are discussed in the standard.11The RSSB 14have noted that:‘although the concept of eﬀective unsprung mass is simple,its accurate evalu-ation is not always straightforward’.Parametric study of the FE modelNumerical examples are shown and the eﬀects of some parameters are investigated in this section.The parameters of the track,vehicle and joint models that were used in the simulation studies are reported in Table 2.From Figure 7(a),it can be seen that the trends of the P 1and P 2forces with the rail-pad stiﬀness are diﬀerent.For the case of the P 1force,there is an initial constant trend for low stiﬀness values (10–100MPa)and then a linearly increasing trend for higher stiﬀness values (500–1000MPa).The slope increases with increasing speed.For the case of the P 2force,instead,there is a relatively rapid increasing trend at low stiﬀness values (10–100MPa)and thenaFigure parison of the two-and three-layer models for different beam types (Euler–Bernoulli and Timoshenko beams)in (a)the time domain and (b)the frequency domain (central sleeper).368Proc IMechE Part F:J Rail and Rapid Transit 229(4)relatively slower increasing trend for higher stiﬀness values (500–1000MPa)with a slope signiﬁcantly lower than the ﬁrst part.Regarding the support stiﬀness (Figure 7(b)),it can be stated that the trend observed for the P 1force is relatively constant whereas P 2grows more than lin-early.The average slope increases with increasing the speed.This means that decreasing the ballast stiﬀness has little eﬀect on the P 1force,whereas it can reduce the P 2force.As shown in Figure 7(c),the impact of the mass of the wheelsets is very large in both cases.In particular,the trend for the P 1force is asymptotic,that is the change in the mass of the wheelset plays a limited role in the impact forces for wheel mass greater than 600–800kg.The P 2force increases proportionally with the mass of the wheelset;the average slope increases with increasing speed.Finally,from Figure 7(d)it can be deduced that the impact forces are diﬀerent for diﬀerent eﬀective lengths,even if the joint angle is ﬁxed to 25mrad.Thus,the dynamic response in terms of wheel–rail contact forces is closely related to the actual shape of the rail joint under loading.This conclusion contradicts the formulae proposed by Jenkins et al.10(equations (1)and (2)),according to which the forces are constant for constant value of total dipangle.Figure 6.Wheel–rail contact force as a function of the number of elements between two sleepers (two-layer model and Euler–Bernoulli beam).T able 2.Parameters used in the simulation studies.T rack modelVehicle model Joint model T ravelling speed VT ravelling speed V T ravelling speed V Rail mass per unit length m Wheel mass M w Affected length L Rail-pad stiffness k r Bogie mass M tT otal joint angle 2Support stiffness k s Car body mass M c T otal joint angle 2T otal joint angle 2In the following discussions,only the most relevant graphs are reported.T able parison between different models in terms of running time required and maximum force.Number of elements 1234567Running time (s)75199400728122319172315Maximum force (kN)375389387385384383383Grossoni et al.369Parametric study of the analytical modelA parametric study has been performed using the ana-lytic models deﬁned in equations (2)and (3)presented in Figure 8and 9respectively.10,11For the ﬁrst model,six parameters were used in the simulations:the travelling speed V ,the foundation stiﬀness k t ,the joint angle 2a ,the rail section properties (mass per unit length m and inertia I )and the unsprung mass M u .For the second model,only three parameters were used:the travelling speed V ,the maximum static wheel load,and the unsprung mass M u .In fact,in this case all the other parameters regarding the track properties,both rail and support,were ﬁxed to typical values.From Figure 8(a)it can be observed that there is a relatively rapid increasing trend for smaller proﬁles (50–60kg/m)and then a relatively slower increasing trend for bigger proﬁles (60–320kg/m)with a slope signiﬁcantly lower than the ﬁrst part.Finally,increas-ing the rail proﬁles beyond values around 320kg/m leads to a decrease in extent of the peak force.All ﬁgures show that there is an increasing impact of the unsprung mass on the P 2force when increasing the travelling speed.This trend was also observed with the FE model (Figure 7(c)).Figure 8(b)shows that the unsprung mass has a strong inﬂuence on the P 2peak force.As shown in Figure 8(c),the inﬂuence of the support stiﬀness is signiﬁcant.The increasing trend is reasonably linear at low speeds (60–80km/h)and the slope rises with increasing speed.However,at higher speeds (120–160km/h)the growth is more than linear,as previously observed in Figure 7(b).Finally,from Figure 8(d)it can be deduced that the joint angle plays an important role in determining the impact force level,as expected.The variation of the P 2force is linear and the average slope increases with increasing speed.Figure 9(a)shows that the variation of the impact force with the unspung mass is linear and the slope increases with increasing speed (as found in Figure 8(b)).Figure 9(b)shows that there is alinearFigure 7.The variation of P 1(bold lines)and P 2(normal lines)forces as a function of:(a)rail-pad stiffness (k r );(b)support stiffness (k s );(c)wheel mass (M w );(d)joint shape fixing the total joint angle to 25mrad at a fixed speed of 160km/h (Case 1:joint depth equal to 1mm and effective length equal to 0.25m;Case 2:joint depth equal to 2mm and effective length equal to 0.5m;Case 3:joint depth equal to 4mm and effective length equal to 1m;Case 4:joint depth equal to 6mm and effective length equal to 1.5m).370Proc IMechE Part F:J Rail and Rapid Transit 229(4)Figure 8.Variation of the P 2force with:(a)rail mass (m );(b)unsprung mass (M u );(c)foundation stiffness (k t );(d)joint angle (2a )using equation (2)varying the travelling speed (V ).The dashed line represents the P 2force limit based on the UK standard GM/TT0088.11Figure 9.Variation of P 2force with (a)unsprung mass (M u );(b)maximum static wheel load (Q )using equation (3)varying the travelling speed (V ).The dashed line represents the P 2force limit based on the UK standard GM/TT0088.11Grossoni et al.371increasing trend of the P 2force with the static load,as expected from equation (3).To conclude,it is worth remarking that the created FE model reproduces the trends found by applying the well-known analytic formulae of equations (2)and (3)(Figure 8and Figure 9)and also allows other important factors to be taken into account with a relative low computational cost (Table 1).ComparisonThe present FE model has been compared with the above analytical models and a reference from the lit-erature.The analysis reported in Zhai and Cai 8on measurements for two diﬀerent Chinese freight vehi-cles was used in the comparison.The main character-istics of two diﬀerent freight vehicles,C62A and C75,are reported in Zhai and Cai.8A comparison between the results in terms of P 2force for the cases of C62A and C75freight vehicles with increasing travelling speed is shown in Figure 10.In particular,for each speed and vehicle type ﬁve diﬀerent values of the peak force were considered:measured data,8simulated value,8two diﬀerent analytical solutions 10,11and the present model.Figure 10shows that in this case the analytical for-mula in Jenkins et al.10overestimates the peak force whereas the one in UK standard GM/TT0088under-estimates it.11This can be explained by remembering that in the latter case the track parameters,including the mass,stiﬀness and damping properties,are ﬁxed.It is noticeable that the results are close to each other,particularly the measured data,simulated values and the present model.The percentage diﬀer-ences between the present model and measured data or simulated values are reported in Table 3.ConclusionsThe primary objective of this study was to investigate the characteristics of the vertical dynamic response at a rail joint using a comprehensive FE model ofaFigure parison between the results in terms of the P 2force on C62A and C75freight vehicles.T able 3.Percentage differences between the present model and measured data 8and simulated values.8C62AC75T ravelling speed (km/h)Measured data (%)Simulated values (%)Measured data (%)Simulated values (%)30 4.5 3.2 3.20.860 3.710.9 2.2 1.6806.54.43.70.6372Proc IMechE Part F:J Rail and Rapid Transit 229(4)vehicle–track coupling system.The utilized two-dimensional model was established by iteratively mer-ging three basic models,which are the track model, the vehicle model and the contact model.This strategy was shown to be eﬃcient in obtaining numerical solu-tions in the time domain.In order to achieve a rea-sonable model size that is compatible with the available computing facility,several assumptions were made in the rail joint model,track model and boundary conditions.The wheel–rail impact mechanism can be explained in terms of a discontinuity of the stiﬀness of the joint structure.At impact,two peak contact forces develop. The main characteristics,such as the frequency and the magnitude,are quite diﬀerent.It has been demon-strated that the lower-magnitude force is the force that actually causes the track to degrade,due to its characteristic frequencies matching with the typical frequencies of the track.Through a series of sensitivity studies of several parameters,it has been demonstrated that the dynamic response can be signiﬁcantly improved by optimized design parameters.Parametric simulations have shown that theﬁrst impact force P1is greatly inﬂuenced by the mass of the wheelsets,the mass of the rail and the joint angle,whereas the second peak force P2is aﬀected by the mass of the wheelset, the rail-pad stiﬀness,the support stiﬀness and the joint angle.The model has highlighted that the impact forces depends on the actual shape of the rail joint. Therefore,major reductions in peak force values can be obtained through an appropriate joint design.The parametric study using analytical formulae pointed out that the FE model established in this study can reproduce the same trends and also allows other important factors to be taken into account with a relative low computational cost.Finally,the results in terms of P2force from the present model were compared not only with measured values but also with both simulated and analytical solutions.An excellent agreement between values was found,with a maximum percentage diﬀerence of10%.FundingThis work was partially supported by the European Commission within the FP7SUSTRAIL project(grant 265740).References1.Thambiratnam D and Zhuge Y.Dynamic analysis ofbeams on an elastic foundation subjected to moving loads.J Sound Vib1996;198(2):149–169.2.Wang Y,Wang Y,Zhang B,et al.Transient responses ofbeam with elastic foundation supports under moving wave load excitation.Int J Engng Technol2011;1(2): 137–143.3.Grassie SL,Gregory RW,Harrison D,et al.The dynamic response of railway track to highfrequency vertical excitation.J Mech Engng Sci1982;24(2):77–90.4.Lei X and Noda NA.Analyses of dynamic response ofrailway track to high frequency vertical excitation.J Sound Vib2002;258(1):147–165.5.Zhai W,Wang K and Cai C.Fundamentals of vehicle–track coupled dynamics.Veh Syst Dyn2009;47(11): 1349–1376.6.Lu F,Kennedy D,Williams FW,et al.Symplectic ana-lysis of vertical random vibration for coupled vehicle–track systems.J Sound Vib2008;317(1–2):236–249. 7.Diana G,Cheli F,Collina A,et al.Modelli matematiciper lo studio della interazione veicolo-struttura-arma-mento.Ingegneria ferroviaria1995;12:126–140.8.Zhai W and Cai Z.Dynamic interaction between alumped mass vehicle and a discretely supported con-tinuous rail put Struct1997;63(5):987–997.9.Dukkipati RV and Dong R.The dynamic effects ofconventional freight car running over a dipped-joint.Veh Syst Dyn1999;31(2):95–111.10.Jenkins HH,Stephenson JE,Clayton GA,et al.Theeffect of track and vehicle parameters on wheel/rail ver-tical dynamic forces.Railway Engng J1974;3(1):2–16. standard GM/TT0088:1993.Permissible trackforces for railway vehicles.12.Wu TX and Thompson DJ.On the impact noise gen-eration due to a wheel passing over rail joints.J Sound Vib2003;267(3):485–496.13.Grossoni I,Iwnicki S,Bezin Y,et al.Dynamic responseof vehicle-track coupling system with an insulated rail joint.In:The11th international conference on vibration problems(eds Dimitrovova Z,Rocha de Almeida J and Goncalves R),Lisbon,Portugal,9–12September2013, pp.185–194.AMPTAC.14.RSSB.A review of dynamic vertical track forces.Reportn.ITLR/T11289/001,2002.London,UK:RSSB.Appendix1In order to establish the mass matrix for the generic i th element,it is necessary to integrate the vibrational kinetic energy expressing the squared speed of rail displacement at point x in terms of nodal displace-ments using the Hermitian interpolation.Therefore ½m i¼ml420Â15622l54À13l22l4l213lÀ3l25413l156À22lÀ13lÀ3l2À22l4l226643775where m is the mass per unit length of the rail(unit: kg/m)and l the length of the element(unit:m).The stiﬀness matrix of the generic i th element is formed by two contributions:the contribution fromthe rail½k riand the contribution from the rail-pad½k rpi.Similar to the previous case,theﬁrst part is calculated integrating the bending strain energy and expressing the rail displacement in terms of nodal dis-placement.The second part,on the contrary,is concentrated.Grossoni et al.373Thus½k i¼½k ri þ½k rpi¼EIlÂ126lÀ126l6l4l2À6l2l2À12À6l12À6l6l2l2À6l4l22666437775þk rÂ1000 0000 0010 0000 2666437775where EI is the uniformﬂexural rigidity of the beam (unit:Nm2),l the length of an element(unit:m)and k r the stiﬀness of the rail-pad(unit:N/m).Finally,the damping matrix of the generic i th element depends only on the concentrated contribu-tion of the rail-pad½c i¼c rÂ1000 0000 0010 0000 26643775where c r is the damping due to the rail-pad (unit:NÁs/m).Appendix2The mass[M],damping[C]and stiﬀness[K]matrices are established imposing the vertical and rotational e-q-uilibrium of the bodies,which are the car body,the bogie and the wheelsetsM½ ¼M c00000M t00000J t00000M w00000M w266664377775C½ ¼C s2ÀC s2000ÀC s2C s2þ2C s10ÀC s1ÀC s100C s1l2tÀC s1l t C s1l t0ÀC s1ÀC s1l t C s100ÀC s1C s1l t0C s1 266664377775 K½ ¼K s2ÀK s2000ÀK s2K s2þ2K s10ÀK s1ÀK s100K s1l2tÀK s1l t K s1l t0ÀK s1ÀK s1l t K s100ÀK s1K s1l t0K s1 266664377775where M c is the car body mass(unit:kg),M t is the bogie mass(unit:kg),J t is the pitch moment of the bogie(unit:kgÁm2),M w is the wheelset mass(unit:kg), C s1is damping due to the primary suspension(unit: NÁs/m),C s2is the damping due to the secondary sus-pension(unit:NÁs/m),l t is the distance between the centre of the bogie and the centre of the wheelset (unit:m),K s1is the stiﬀness of the primary suspension (unit:N/m)and K s2is the stiﬀness of the secondary suspension(unit:N/m).374Proc IMechE Part F:J Rail and Rapid Transit229(4)at Southeast University on May 10, 2015Downloaded from。

期刊名缩写——精选推荐

期刊名縮寫
原名
Acta Mechanica ASCE - Journal of Engineering Mechanics ASCE - Journal of The Engineering Mechanics Division ASME Applied Mechanics Reviews Advances in Engineering Software Advances in Computational Mathematics Archives of Computational Methods in Engineering Applied Mathematical Modelling Applied Ocean Research Applied Scientific Research
Computers, Materials and Continua Computational Mathematics and Mathematical Physics
CMC Comput. Math. Math. Phys.
Engineering Analysis with Boundary Elements European Journal of Mechanics - A/Solids
J. Comput. Phys.
Journal of Engineering Mathematics Journal of Mathematical Physics /dbt/dbt.jsp?KEY=JMAPAQ Journal of Fluid Mechanics Journal of Sound and Vibration Journal of the Australian Mathematical Society Journal of the C hinese Institute of Engineers Journal of the Optical Society of America A

A thermal model of a ball screw feed drive

/Engineering Science Engineers, Part C: Journal of MechanicalProceedings of the Institution of Mechanical/content/225/1/186The online version of this article can be found at:DOI: 10.1177/09544062JMES21481862011 225:Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science X Min and S JiangA thermal model of a ball screw feed drive system for a machine toolPublished by: On behalf of:Institution of Mechanical Engineers can be found at:Science Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical EngineeringAdditional services and information for/cgi/alerts Email Alerts:/subscriptions Subscriptions: /journalsReprints.nav Reprints:/journalsPermissions.nav Permissions:/content/225/1/186.refs.html Citations:What is This?- Jan 1, 2011Version of Record >>186A thermal model of a ball screw feed drivesystem for a machine toolX Min and S Jiang∗School of Mechanical Engineering,Southeast University,Nanjing,People’s Republic of ChinaThe manuscript was received on13December2009and was accepted after revision for publication on25March2010. DOI:10.1177/09544062JMES2148Abstract:The feed drive system is a major heat source of machine tools,which results in consid-erable thermal drift at the tool.Therefore,there is a need to establish a scientiﬁc and systematicmodel that can be used to predict the temperature distribution of the feed drive system.In thisresearch,considering the thermal contact resistance between the bearing and its housing,anintegrated thermal model has been developed by the aid of theﬁnite-element method to analysethe temperature distribution of a ball screw feed drive system,in particular the theoretical deter-mination of power losses caused by the friction in ball screw pair,rolling bearings,and guideways.Thermal boundary conditions including the convective heat transfer coefﬁcients and heatﬂux have been obtained using the Fourier’s law.Results reveal that the ball screw shaft surfacehas a uniform temperature rise of4.2◦C under a given condition.The temperature rise agreeswith the data obtained by an infrared thermometer.Keywords:ball screw feed drive system,thermal model,ﬁnite-element method,temperature rise1INTRODUCTION1.1Background and motivationA ball screw feed drive system is widely used in a machine tool because of its high efﬁciency,great stiff-ness,and long life.However,with increase in feed rates, the power losses in the frictional transmission com-ponents of mechanical structure will increase,which leads to a lower positioning accuracy of the machine. As a result,the feed drive system becomes a major heat source resulting in a considerable thermal drift for the machine tool,which can contribute40–70per cent to the overall error[1].In recent years,the thermal behaviour of the ball screw feed drive system for a machine tool has been discussed.Linear grating and thermal imaging sys-tem are employed to measure the thermal error and the temperature rise of ball screw feed drive sys-tem[2,3].Research also has considered many ways ∗Corresponding author:School of Mechanical Engineering,South-east University,Jiangning District,Nanjing,Jiangsu211189,Peo-ple’s Republic of China.email:jiangshy660118@ of forecasting a ball screw system temperature distri-bution and thermal deformation,such as the multiple regression analysis,the modiﬁed lumped capacitance method,the least square method,and theﬁnite-element method(FEM)[4–9].Although all the results are accepted,experiments must be conducted to iden-tify factors needed in the multiple regression analysis and the modiﬁed lumped capacitance method[4–6]; this has limited the wide application of these methods in the machine tool industry.When the least square method is employed,simulation is needed to perform the system model identiﬁcation[7].For theﬁnite-element approach[8,9],heat conduction between the bearings and their supports is neglected.Schulz and Schmitt[10]investigated the heat generation in a mechanical transmission path of high-speed feed drive system in view of the empirical expression.The literature review shows that no comprehensive thermal model exists for the ball screw feed drive system that can be used to predict its thermal prop-erties.Thus,the main objective of this study is to establish a thermal model using FEM,where heat gen-eration in a mechanical structure of the ball screw feed drive system is derived from the friction in ball screw pair,rolling bearings,and guide ways.The thermal contact resistance between the bearing and its hous-ing is deduced from the rolling bearing analysis andProc.IMechE Vol.225Part C:J.Mechanical Engineering ScienceA thermal model of a ball screw feed drive system for a machine tool 187heat transfer theory.Thermal boundary conditions including the convective heat transfer coefﬁcients and heat ﬂuxes have been obtained by using the Fourier’s law.Utilizing an infrared thermometer,the tempera-ture rise of the test ball screw-tested drive system is measured for comparison with the data estimated by FEM.1.2Experimental set-upIn this study,a ball screw feed drive system of a vertical machining centre (as shown in Fig.1)is taken as the object for investigating the thermal behaviour,which includes a ball screw pair,a driving motor,and a bed saddle.The ball screw shaft is supported by two pairs of the angle contact rolling bearings with a back-to-back arrangement,which are preloaded by a preload nut.The ball screw shaft bearing system is driven directly by a servo motor rated at 3kW.The bearings are installed in the housings located inside the bed saddle.There are two guiding surfaces on the upper and lower sides of the bed saddle.The fundamental speciﬁcation of the system is listed in Table 1.2THERMAL MODELFigure 2shows the ﬁnite-element model representing a simpliﬁed ball screw feed drive system.An eight-node element is chosen to calculate the ball screw system temperature ﬁeld.To get satisfactory results,the contacting elements are used to simulate the con-tact areas connecting the bearings and the housings.Each element has a single degree of freedom(whichFig.1Schematic of the feed drive systemTable 1Speciﬁcation of the ball screw feed drive systemParametersValue Maximum speed 2000r/min Stroke 600mm Nut length 60mm Preload of nut 5268NNut typeDouble nut Nominal outer diameter of the screw shaft 40mmLead10mmBearing type30TAC62A(NSK)Dimension of the bed saddle 1240×297×418mm 3Mass of the bed saddle 296kg Mass of the table202kgFig.2The FEM model of the ball screw feed drive systemis temperature).There are a total of 454340solid elements and 1994contact elements in the FE model.In order to simplify the thermal model,the following assumptions are made:1.Friction heat between the moving nut and the screw is uniform and proportional to the contacting time;half of the heat generated between the screw shaft and the nut is supposed to be transferred to the ball screw shaft;the screw shaft is simpliﬁed to be a solid cylinder with uniform heat generation rate.2.Support bearings,another uniform heat source,are hollow cylinders.3.Heat conduction from the motor is replaced by heat ﬂuxes directed to its installed surface.4.The radiation term can be neglected for a lower temperature rise.2.1Heat generationFor a ball screw feed drive system,there are four major heat sources in the feed drive system:(a)heat generated by support bearings due to thefriction between the balls and races;(b)heat generated between the nut and screw shaft;(c)heat generated by the motor;(d)heat generated by the guide way.2.1.1Heat generation of bearingsHeat is mainly generated at bearing raceways and balls due to the friction inﬂuenced by speed,preload,and lubricant.The empirical heat generation in the bearing is given by [11,12]H b =1.047×10−4nM b (W )(1)A reasonable estimate of the total friction M b of a given ball bearing under moderate preload,lubricant,and speed conditions is the sum of the load torque and viscous friction torque.M b =M l +M v(2)Proc.IMechE Vol.225Part C:J.Mechanical Engineering Science188X Min and S Jiang where M l is the load-dependent friction torque because of imperfect mechanical bodies under load.The following equation is given to describe thistorque[11]M l=f1p1d m(N mm)(3)in which the parameter f1is a factor dependent onbearing design,and the relative bearing preload,p1, depends on the magnitude and direction of theapplied load.For angular contact ball bearingsf1=0.001p0c00.33(4)p1=1.4F a−0.1F r(5) For single and thrust bearings(θ=90◦)p0=2.3F r tanθ+F a(6) M v in equation(2)is the viscous friction torque and can be empirically expressed as follows[11]M v=10−7f0(ν0n)2/3d3m(N mm)ifν0n>2000cSt r/min(7) M v=160×10−7f0d3m(N mm)ifν0n<2000cSt r/min(8)where f0is a factor that depends on bearing type and lubrication type.The speciﬁcation of bearings can be found inTable2. According to the viscosity–temperature characteristics of the base oil of the lubricated grease,as shown in Table3,how the heat generation varies with tempera-ture of each bearing can be determined.Table2Speciﬁcation of bearingsBearing Front/rearContact angle60◦Inner diameter30mmOuter diameter62mmMean diameter46mmWidth16mmPreload3040NLubrication mode GreaseTable3Viscosity–temperature characteristic ofthe basic oil of the lubricated greaseTemperature(◦C)Kinematic viscosity (mm2/s)2535 4018 60102.1.2The heat generation of ball screw pairIn order to maintain a high rigidity and accuracy,an appropriate preload must be applied to the screw–ball–nut system.The preload will produce heat due to friction.As a result,the friction heat generation between the moving nut and the ball screw is another important heat source.According to the work by Tenjitus[13],heat generation is as followsH s=0.12πnM s(9)where M s is the total friction torque of the ball screw system,which consists of the friction torque M d and the resistance torque M pl.So the total friction torque isM s=M d+M pl(10)The friction torque M d isM d=T D(1−η)(11)whereη=0.95;T D is the torque used to overcome axial load related to friction force and cutting force,which can be written as[14]T D=FL2πη(12)The resistance torque M pl is required to drive the preloaded ball screw without axial load,which can be written asM pl=F p L2πη(1−η2)(13) 2.1.3Heat generated by the guide wayThe guide way is also one of the heat sources of the machine tool,especially for the high-speed machining process with a super high feed rate.Assuming that the friction coefﬁcient of the sliding guide way is0.12,the heat generation isH g=μF n V(14) In this article,the no-load test condition is inves-tigated;therefore,the only load applied to the guide way is from gravities of the table or bed saddle.In the simulating process,only half of the heat generation is assumed to transfer into the bed saddle,and the rest into the table or the bed.2.2Conduction between outer bearing rings andhousingWhen two surfaces are in contact,the presence of surface roughness produces imperfect contact at theProc.IMechE Vol.225Part C:J.Mechanical Engineering ScienceA thermal model of a ball screw feed drive system for a machine tool189 joint in spite of a relative large pressure existing onthe interface.The imperfect contact results in a sharptemperature drop across the joint owing to the thermalcontact resistance.Therefore,it is necessary to studythe thermal characteristics of this contact pair.The following calculations of the thermal contactresistance between the outer ring and the housingare based on the work by Bossmanns[15].Conduc-tion through the mating surfaces of the bearing outerring and the bearing housing is modelled as a func-tion of temperature-related clearanceﬁt.For thermalpermissivity,the temperature nodes lie at the centreof the ring cross-section and the opposite of the mat-ing surface in the housing.The equivalent thermalpermissivity is[15]=1(h r/λr)+(h g/λa)A(W/K)(15)Considering the difference of the linear expansion between the mating materials,the average air gap between the housing and the outer ring h g around the perimeter can be computed ash g=h0−[(T r−T0)αr−(T h−T0)αh]r h(16) Here,h0=8μm,h0=26.5◦C.2.3Heat transfer from structure into ambient air The calculation of heat transfer coefﬁcient for convec-tion follows a series of steps.First,the feature size and the mean velocity of theﬂuid with respect to the solid surface are determined.When the two parameters are known,the Reynolds number is determined.The heat dissipates from the ball screw system into ambient air by forced convective heat transfer.For the ball screw shaft,the Reynolds number isRe=udνﬂuid(17)The following equation is used to determine Nusselt number.Nu=0.133Re2/3Pr1/3(18) The equation is valid forRe<4.3×1050.7<Pr<670where Pr is0.707for the air.The heat transfer coefﬁcient is then calculated byα=Nuλﬂuidd(19)The effect of the airﬂow velocity on the convective heat transfer coefﬁcient can be neglected because the feed speed of the bed saddle is relative low.The con-vective heat transfer coefﬁcient of12W/m2K is used for the surface of the bed saddle[16].3THERMAL CHARACTERISTICSOn the basis of the preceding derivation and the ther-mophysical properties of materials(provided by the manufacturer)and the air listed in Tables4and5,the thermal property of the feed drive system,including the steady-state and the transient characteristics,has been analysed using the ANSYS software package.Dur-ing the process of calculation,the heat conducted into the screw shaft is converted into the heat generation power of the shaft and is uniformly applied to the screw shaft covered by the stroke.As shown in Fig.2,the blue areas are covered with the recommended convective heat transfer coefﬁcient and the green areas are cov-ered with the convective heat transfer coefﬁcient of 12W/m2K.Figure3shows the steady-state temperature dis-tribution of the feed drive system under a feed rate of20m/min and a room temperature of26.5◦C.It can be seen that the screw shaft surface covered by the stroke has an almost uniform temperature distri-bution,and the maximum temperature rise reaches 21.2◦C.The result also shows that the temperature rises of the front and the rear bearing supports are 8.2and10.4◦C,respectively.The temperature rise of the left bearing is higher than that of the right because the left end is dominated by not only the rolling bear-ing but also the servo motor,whereas the temperature of the right end of the ball screw shaft is only affected by the rolling bearing.The temperature jumps appear at the interfaces between the bearing outer rings and the housings due to the thermal contact resistances existing there,leading to a higher temperature rise of the bearings.For the bed saddle,the higher tempera-ture rises are located at two ends of the guiding surface, Table4Thermophysical properties of materialsThermalconductivity(W/m K)Linearexpansioncoefﬁcient(1/K)Speciﬁcheatcapacity(kJ/kg K)Density(kg/m3)Screw shaft49.84657858 Bearing60.5 3.2×10−54607800Bed saddle48 1.17×10−55207350 Table5Thermophysical properties of air Temperature(◦C)Thermalconductivity(W/m K)Kinematicviscosity(mm2/s)20 2.59×10−218.1×10−6 30 2.67×10−218.6×10−6 40 2.73×10−219.1×10−6Proc.IMechE Vol.225Part C:J.Mechanical Engineering Science190X Min and SJiangFig.3The temperature distribution of the feed drivesystem under the heat transfer coefﬁcient of 37.4W/m 2Kwhich results from the heat generation of the nearby rolling bearings.For the convenience of representation,total seven points at the ball screw system (as shown in Fig.4)are focused on to discuss their temperature rises:two points (numbered 1and 7)are located on the support surfaces of the front and the rear bearings,respec-tively;two points (numbered 4and 5)are on the nut surface;and the other points (numbered 2,3,and 6)are on the surface of the ball screw.To further understand the thermal behaviour,the transient-state temperature rise of the ball screw sys-tem has been predicted by the proposed method.The variation in temperatures at ﬁve points (nos.1,2,3,6,and 7)with the test duration are given in Fig.5;the results show that it takes only half an hour for the ball screw shaft to reach the thermal equilibrium.However,at least 2.5h are needed for the bearing supports to reach the steady state.This is because much of the heat generated by the rolling bearing transfers into the bed saddle with a relatively large heat capacity.Fig.4Locations of measured points for temperaturesT e m p e r a t u r e (oC )Time(min)Fig.5Variation in temperatures with the test duration(the room temperature,26.5◦C)4DISCUSSION AND VALIDATIONExperiments were performed with the arrangement shown in Fig.6.Temperatures of the seven points as already stated in Fig.4were measured by a portable infrared thermometer.In the experiment,each point is marked so that the measuring process can be conve-nient;the ball screw rotates at a speed of 2000r/min.The temperature measurement is taken at an interval of 10min.Figure 7shows a comparison between the theoreti-cal analysis and the test result of the temperature rises at ﬁve points (from no.2to no.6)on the screw shaft.The deviation may be caused by the following reasons.(a)(b)Fig.6Photographs of (a)the feed drive system and (b)the instrumentation planStroke range of the screw shaft (m)2730333639424548T e m p e r a t u r e (oC )Fig.7Surface temperature along the screw shaftProc.IMechE Vol.225Part C:J.Mechanical Engineering ScienceA thermal model of a ball screw feed drive system for a machine tool 191The convective heat transfer coefﬁcient calculated from the heat transfer model is lower than the actual value,because the effect of the shaft spiral grooves on the heat transfer property is neglected.A higher convection heat transfer coefﬁcient is required for the ball screw shaft with the spiral grooves on its sur-face,because the movement of the air surrounding the shaft is reinforced,thus enhancing the heat transfer between the screw surface and the air.Using equations (17)to (19),the forced convective heat transfer coefﬁcient of the screw shaft is obtained,and the original theoretical value is 37.4W/m 2K when the screw rotates at a speed of 2000r/min.However,the author thinks that the heat convection of the shaft is more activated.To obtain the convective heat transfer coefﬁcient,the effect of the variation in the coefﬁcients on the temperature rises of the screw shaft was studied,in which the coefﬁcient changes from the original value of 37.4to 187W/m 2K with a step value of 37.4W/m 2K.The probable value of the con-vective heat transfer coefﬁcient can be identiﬁed by comparing the theoretical temperature rise with the experimental result.Figure 8shows the change in the temperature rises with the convective heat transfer coefﬁcients of the screw shaft surface;it can be seen that the temper-ature rise decreases with the increase in the heat transfer coefﬁcient,and the theoretical temperature rises agree with the experiment when the heat trans-fer coefﬁcient is 187W/m 2K and the corresponding temperature rise is about 4.2◦C.Figure 9presents the temperature distribution of the feed drive system under the heat transfer coefﬁcient of 187W/m 2K;the result shows that the ball screw surface covered by the stroke also has a uniform temperature distribution.As a result,the value equal to ﬁve times of the original theoretical value is recommended as the convective heat transfer coefﬁcient for the analysis of the thermal behaviour of the ball screw.Surprisingly,an identical mechanism was found by Choi and Lee [17],in which the thermal behaviour of a spindle bearing system wasT e m p e r a t u r e (oC )Stroke range of the screw shaft (m)Fig.8Temperature of the screw shaft surface withrespect to the heat transfer coefﬁcientsFig.9Temperature distribution of the feed drive systemwith the heat transfer coefﬁcient of 187W/m 2KTable 6Temperatures of bearing supportsLocation Numerical result (◦C)Measuring result (◦C)133.034.5731.030.5analysed,and a similar mechanism can also be found by Guo and Sun [18],where thermal characteristics and thermal deformation of high-speed spindle sys-tem in an numerical control (NC)precision lathe was studied.Furthermore,when the screw shaft rotates at 500,1000,and 1500r/min,the temperature rises pre-dicted by the proposed model are 2.4,3.0,and 3.4◦C,respectively,which agrees with the measurement,and the maximum error is less than 5per cent.The comparison of temperatures of the bearing sup-ports (listed in Table 6)shows that the numerical results are well in agreement with the measured ones.5CONCLUSIONSIn this article,considering thermal contact resistance between bearings and its housings,a systematic ther-mal model is developed using FEM to investigate the thermal characteristics of a ball screw feed drive system,in particular characterization of heat gener-ation caused by the friction in transmission compo-nents.The simulating results are compared with the experimental results obtained from an actual mea-surement of a vertical machining centre.The following conclusions can be obtained:1.The value equal to ﬁve times of the original theoret-ical value is recommended as the convection heat transfer coefﬁcient for the analysis of the thermal behaviour of the ball screw.In this article,the con-vection heat transfer coefﬁcient of 187W/m 2K of the rotational screw shaft surface,instead of the original coefﬁcient of 37.4W/m 2K,is applied as the thermal boundary condition to calculate the temperature distribution.For the steady state,the predicting results reveal that the screw shaft surface has an almost uniform temperature rise of 4.2◦C,which agrees with the measurement.2.The proposed thermal model is independent of the experiment,which can be used to predict theProc.IMechE Vol.225Part C:J.Mechanical Engineering Science192X Min and S Jiangsteady-state temperature rise of a ball screw system.Furthermore,the ball screw thermal expansion in axial direction can also be obtained with this model, which can supply the basic data for compensating the thermal error of the feed drive system. ACKNOWLEDGEMENTSThe authors gratefully acknowledge the support of the National Science Foundation through grant nos. 5047507and50775036,and Jiangsu Science and Technology Project through grant nos.BK2002059, BG2006035,and BK2009612.©Authors2011REFERENCES1Bryan,J.International status of thermal error research (1990).CIRP Ann.–Manuf.Technol.,1990,39(2),645–656. 2Junyong,X.,Bo,W.,Youmin,H.,and Tielin,S.Experi-mental research on factors inﬂuencing thermal dynam-ics characteristics of feed system.Precis.Eng.,2010, 34(2),357–368.3Heisel,U.,Koscsák,G.,and Stehle,T.Thermography-based investigation into thermally induced positioning errors of feed drives by example of a ball screw.CIRP Ann.–Manuf.Technol.,2006,55(1),423–426.4Kim,S.K.and Cho,A.W.Real-time estimation of temper-ature distribution in a ball screw system.Int.J.of Machine Tools&Manufacture,1997,37(4),451–464.5Yun,W.S.,Kim,S.K.,and Cho,D.W.Thermal error anal-ysis for a CNC lathe feed drive system.Int.J.Mach.Tools Manuf.,1999,39(7),1087–1101.6Huang,S.-C.Analysis of a model to forecast thermal deformation of ball screw drive system.Int.J.Mach.Tools Manuf.,1995,35(8),1099–1104.7Junyong,X.,Youmin,H.,Bo,W.,and Tielin,S.Research on the thermal dynamic characteristics and modeling approach of ball screw.Int.J.Adv.Manuf.Technol.,2008, 43(5–6),421–430.8Horejš,O.Thermo-mechanical model of ball screw with non-steady heat sources.In Proceedings of the First International Conference on Thermal issues in emerg-ing technologies,theory and applications,ThETA1,Cairo, 3–6January2007,pp.133–137(IEEE Computer Society, USA).9Wu,C.-H.and Kung,Yu.-T.Thermal analysis for the feed drive system of a CNC machine center.Int.J.Mach.Tools Manuf.,2003,43(15),1521–1528.10Schulz,H.and Schmitt,T.Model-based determination of heat generation in the mechanical structure of high speed feed drive systems.Prod.Eng.,1994,1(2),89–92. 11Harris,T.A.Roll bearing analysis,1991(Wiley Sons,New York).12Palmgren,A.Ball and roller bearing engineering,1959 (S.H.Burbank,Philadelphia,PA).13Tenjitus,W.Solution for heating of ball screw and envi-ronment engineering.Key C Mach.Tool, 2004,3,65–67.14Guangren,C.Foundation of Ball screw drive design,1987 (Mechanical Industry Press,Beijing).15Bossmanns,B.and Tu,J.F.A thermal model for high speed motorized spindles.Int.J.Mach.Tools Manuf., 1999,39(9),1345–1366.16Tanabe,I.and Takada,K.Thermal deformation of machine tool structures using resin concrete.Jpn.Soc.Mech.Engrs C,1994,37(2),384–389.17Choi,J.K.and Lee,D.G.Thermal characteristics of the spindle bearing system with a gear located on the bearing span.Int.J.Mach.Tools Manuf.,1998,38(9), 1017–1030.18Ce,G.and Qinghong,S.Analysis of thermal character-istics and thermal deformation of high-speed spindle system in NC precision lathe.J.Southeast Univ.,Nat.Sci.Ed.,2005,35(2),231–234.APPENDIXNotationA cylinder outside surface area of theringC0basic rating static loadd feather size-diameterd m mean diameterf1,f0friction torque parametersF axial load of nutF a axial load of bearingF n normal loadF p preloadF r radial loadh0initial clearanceﬁth g average air gap between housing andouter ringh r thickness of the outer ringH b heat generated power of bearingH s heat generated power of the ball screw pair H g heat generated power of guiding waysL lead of ball screwM b total friction of ball bearingM d resistance torque of ball screwM l load dependent torqueM pl friction torque of ball screwM v viscous friction torquen rotational speedP0equivalent static radial loadP r Prandtl numberP1equivalent loadr h inner diameter of housing matingbearingRe Reynolds numberT0initial temperatureT D driving torqueT h temperature of housing inner faceT r temperature of outer ringu mean velocity of surfaceV velocity of moving partProc.IMechE Vol.225Part C:J.Mechanical Engineering ScienceA thermal model of a ball screw feed drive system for a machine tool193αh linear thermal expansion coefﬁcient of the housingαr linear thermal expansion coefﬁcient of the outer ringηefﬁciency of the ball screw pairθcontact angleλthermal conductivityλa thermal conductivity of airλh thermal conductivity of outer ringλﬂuid thermal conductivity of theﬂuid μfriction coefﬁcientν0kinematic viscosity of the lubricantνﬂuid kinematic viscosity ofﬂuidequivalent thermal permissivity Subscriptsa refers to airh refers to housingr refers to bearing outer ringProc.IMechE Vol.225Part C:J.Mechanical Engineering Science。

英国机械工程师学会的影响因子

英国机械工程师学会的影响因子英国机械工程师学会的影响因子在今天的文章中，我们将深入探讨英国机械工程师学会的影响因子，并对其对于机械工程行业的影响进行全面评估和分析。

1. 英国机械工程师学会的概述英国机械工程师学会（Institution of Mechanical Engineers，简称IMechE）是世界上最早的机械工程专业学会之一，成立于1847年。

IMechE的使命是通过其会员、出版物和活动，促进机械工程学科的发展和创新，为社会和经济发展做出贡献。

2. 影响因子的定义和意义影响因子（Impact Factor，IF）是一种衡量学术期刊影响力的指标，通常被用于评价期刊的质量和重要性。

影响因子越高的期刊，意味着其发表的论文被引用的频率越高，从而具有更大的学术影响力。

3. IMechE的影响因子排名根据最新的数据，IMechE旗下的《Proceedings of the IMechE, Part C: Journal of Mechanical Engineering Science》期刊在机械工程领域的影响因子排名中处于领先地位。

这一排名反映了IMechE在机械工程学术领域的重要地位和影响力。

4. IMechE对机械工程行业的影响IMechE作为机械工程领域的权威机构，通过其出版物、学术会议和专业培训，为机械工程师们提供了丰富的学术资源和专业支持。

IMechE 致力于推动机械工程的创新和发展，促进行业内的知识交流和合作，对于提升整个行业的水平和声誉起到了重要作用。

5. 个人观点和理解在我看来，IMechE的影响因子不仅反映了其学术期刊的影响力，更体现了其在机械工程行业中的声誉和地位。

作为一家具有百年历史的专业学会，IMechE在学术研究、行业标准和人才培养等方面都发挥着重要作用，对于推动行业发展和提升工程师素质具有不可或缺的意义。

总结回顾通过今天的文章，我们对英国机械工程师学会的影响因子进行了全面的评估和分析。

SCIlist

英文
39
SCI
英国
International Journal of Solids and Structures
固体与结构国际期刊
ISSN 0020-7683
双周刊
Pergamon-Elsevier Science Ltd
英文
40
SCI/EI
美国
Journal of Applied Mechanics-transactions
岩土工程
ISSN 1353-2618, E-ISSN 1751-8563
6期/年
Proceedings of ICE
英文
32
SCI
英国
Geosynthetics International
国际土工合成
ISSN 1072-6349, E-ISSN 1751-7613
月刊
Thomas Telford Publishing
英国
Computer-Aided Civil and Infrastructure Engineering
计算机辅助民用和基础工程学
ISSN 1093-9687
期刊
Blackwell Publishers
英文
17
SCI/EI
英国
Computers & Geosciences
计算机与地球科学
ISSN 0098-3004
ISSN 0016-8505
双月刊
Thomas Telford Publishing
英文
30
SCI
英国
Geotextiles and Geomembranes
土工合成材料与土工用膜
ISSN 0266-1144

工业摩擦润滑技术国家地方联合工程研究中心技术委员会成立

108润滑与密封第45卷轮轨空间动态行为的影响，结果表明，轮轨系统动态响应随着非圆化磨耗幅值的增大而增大，但随非圆化磨耗阶次和车辆运行速度则呈非线性变化趋势。

参考文献[1]JOHANSSON A,NIELSEN J0.Out-of-round railway wheels:wheel-rail contact forces and track response derived from field tests and numerical simulations[J].Proceedings of the Institution of Mechanical Engineers,Part F:Journal of Rail and Rapid Transit,2003,217(2)：135-146.[2]TAOG Q,WANG L F,WEN Z F,et al.Measurement and assessment of out-of-round electric locomotive wheels[J].Proceedings of the Institution of Mechanical Engineers,Part F:Journal of Rail and Rapid Transit,2018,232(1)：275-287.[3]MORYS B.Enlargement of out-of-round wheel profiles on highspeed trains[J].Journal of Sound and Vibration,1999,227(5): 965-978.[4]ZHONG S Q,XIONG J Y,XIA0X B,et al.Effect of the first twowheelset bending modes on wheel-rail contact behavior[J].Journal of Zhejiang University Science A,2014,15(12)：984-1001.[5]TAO G Q,WANG L F,WEN Z F,et al.Experimental investigation into the mechanism of the polygonal wear of electric locomotive wheels[J]. Vehicle System Dynamics,2018,56(6)：883-899.[6]JIN X S,WU L,FANG J Y,et al.An investigation into the mechanism of the polygonal wear of metro train wheels and its effect on the dynamic behaviour of a wheel/rail system[J].Vehicle System Dynamics,2012,50(12):1817-1834.[7]王科，崔晓璐,陈光雄，等.高速铁路车轮多边形磨耗影响因素仿真研究[J].润滑与密封,2017,42(10):31-34.WANG K,CUI X L,CHEN G X,et al.Numerical study on the influence factors of wheel polygonalization of high-speed trains [J].Lubrication Engineering,2017,42(10)：31-34.[8]陈光雄，金学松,鄒平波，等•车轮多边形磨耗机理的有限元研究[J].铁道学报,2011,33(1):14-1&CHEN G X,JIN X S,WU P B,et al.Finite element study on the generation mechanism of polygonal wear of railway wheels[J].Journal of the China Railway Society,2011,33(1):14-18.[9]肖乾,郑继峰，昌超，等.高速列车谐波磨耗车轮滚动接触疲劳特性分析[J].润滑与密封,2017,42(1):1-7.XIAO Q,ZHENG J F,CHANG C,et al.Analysis of harmonic wear wheels/rail rolling contact fatigue of high speed train[J].Lubrication Engineering,2017,42(1):1—7.[10]LIU X Y,ZHAI W M.Analysis of vertical dynamic wheel/railinteraction caused by polygonal wheels on high-speed trains [J].Wear,2014,314(1/2)：282-290.[11]韩光旭，张捷，肖新标，等•高速动车组车内异常振动噪声特性与车轮非圆化关系研究[J].机械工程学报,2014,50(22)：113-121,HAN G X,ZHANG J,XIAO X B,et al.Study on high-speed train abnormal interior vibration and noise related to wheel roughness[J].Journal of Mechanical Engineering,2014,50(22)：113-121.[12]王兴宇，范军.高速列车车内噪声与车轮不圆顺关系的研究[J].铁道学报,2013,35(9)=14-18.WANG X Y,FAN J.Research on relation between interior noises and out-of-round wheels of high-speed EMU[J].Journal of the China Railway Society,2013,35(9):14-18.【13】刘佳，韩健，肖新标，等.高速车轮非圆化磨耗对轴箱端盖异常振动影响初探[J].机械工程学报,2017,53(20)：98-105.LIU J,HAN J,XIAO X B,et al.Influence of wheel non-circular wear on axle box cover abnormal vibration in high-speed train [J].Journal of Mechanical Engineering,2017,53(20)：98-105.【14】Railway applications:Noise emission:Rail roughness measurement related to rolling noise generation:BS EN15610：2009 [S].BSI British Standards,2009.[15]翟婉明•车辆-轨道耦合动力学[M].3版.北京:科学出版社,2007：12-84.[16]SHEN Z Y,HEDRICK J K,ELKINS J A.A comparison of alternative creep force models for rail vehicle dynamic analysis [J].Vehicle System Dynamics,1983,12(1/2/3)：79-83. [17]LIU P F,ZHAI W M,WANG K Y.Establishment and verification of three-dimensional dynamic model for heavy-haul traintrack coupled system[J].Vehicle System Dynamics,2016,54(11):1511-1537.工业摩擦润滑技术国家地方联合工程研究中心技术委员会成立2020年11月25日，工业摩擦润滑技术国家地方联合工程研究中心技术委员会成立大会暨第一次全体会议在依托单位——广州机械科学研究院有限公司召开。

杂志英文简写-全称

J. Contam. Hydrol. Journal of Contaminant HydrologyJ. Controlled Release Journal of Controlled ReleaseJ. Coord. Chem. Journal of Coordination ChemistryJ. Cryst. Growth Journal of Crystal GrowthJ. Dairy Sci. Journal of Dairy ScienceJ. Dispersion Sci. Technol. Journal of Dispersion Science and Technology J. Elastomers Plast. Journal of Elastomers and PlasticsJ. Electroanal. Chem. Journal of Electroanalytical ChemistryJ. Electroceram. Journal of ElectroceramicsJ. Electrochem. Soc. Journal of the Electrochemical SocietyJ. Electron. Mater. Journal of Electronic MaterialsJ. Electron Microsc. Journal of Electron MicroscopyJ.Electron.Spectrosc.Relat.Phenom.Journal of Electron Spectroscopy and Related PhenomenaJ. Endocrinol. Journal of EndocrinologyJ. Endotoxin Res. Journal of Endotoxin ResearchJ. Eng. Mater. Technol. Journal of Engineering Materials and Technology J. Environ. Biol. Journal of Environment biologyJ. Environ. Eng. Journal of Environment EngineeringJ. Environ. Health Journal of Environment HealthJ. Environ. Manage. Journal of Environment ManagementJ. Environ. Monit. Journal of Environmental MonitoringJ. Environ. Qual. Journal of Environment QualityJ. Environ. Radioact. Journal of Environment RadioactivityJ. Environ. Sci. Health., Part A Journal of Environment Science and Health, Part A Environmental ScienceJ. Environ. Sci. Health., Part B Journal of Environment Science and Health, Part B PesticidesJ. Enzym Inhib. Journal of Enzyme InhibitionJ. Essent. Oil Res. Journal of Essential Oil ResearchJ. Ethnopharmacol. Journal of EthnopharmacologyJ. Eur. Ceram. Soc. Journal of the European Ceramic SocietyJ. Exp. Biol. Journal of Experimental BiologyJ. Exp. Bot. Journal of Experimental BotanyJ.Exposure Anal.Environ.Epidemiol.Journal of Exposure Analysis and Environment EpidemiologyJ. Ferment. Bioeng. Journal of Fermentation and BioengineeringJ. Fire Sci. Journal of Fire SciencesJ. Fluid Mech. Journal of Fluid MechanicsJ. Fluids Eng. Journal of Fluids EngineeringJ. Fluorine Chem. Journal of Fluorine ChemistryJ. Food Biochem. Journal of Food BiochemistryJ. Food Eng. Journal of Food EngineeringJ. Food Lipids Journal of Food LipidsJ. Food Prot. Journal of Food ProtectionJ. Food Sci. Journal of Food ScienceJ. Gen. Appl. Microbiol. Journal of General and Applied Microbiology J. Gen. Microbiol. Journal of General MicrobiologyJ. Hazard. Mater. Journal of Hazardous materialsJ. Heat Transfer Journal of Heat TransferJ. Heterocycl. Chem. Journal of Heterocyclic ChemistryJ. High. Resolut. Chromatogr. Journal of High Resolution Chromatography J. Histochem. Cytochem. Journal of Histochemistry and CytochemistryJ. Hypertens. Journal of HypertensionJ. Imaging Sci. Technol. Journal of Imaging Science and TechnologyJ. Inclusion Phenom. Mol. Recognit. Chem. Journal of Inclusion Phenomena and Molecular Recognition in ChemistryJ. Ind. Microbiol. Journal of Industrial MicrobiologyJ. Indian Chem. Soc. Journal of the Indian Chemical SocietyJ.Ind.Microbiol.Biotechnol.Journal of Industrial Microbiology and Biotechnology J. Inorg. Biochem. Journal of Inorganic BiochemistryJ. Inorg. Nucl. Chem. Journal of Inorganic and Nuclear ChemistryJ. Inorg. Organomet. Polym. Journal of Inorganic and Organometallic Polymers J. Inst. Chem. Journal of Institute of Chemists (India)J. Inst. Environ. Sci. Journal of the Institute of Environment SciencesJ.Inst.Water Environ.Manage.Journal of the Institution of Water and Environment ManagementJ. Intell. Mater. Syst. Struct. Journal of Intelligent Material Systems and StructuresJ. Interferon Cytokine Res. Journal of Interferon and Cytokine Research J. Interferon Res. Journal of Interferon ResearchJ. Jpn. Inst. Met. Journal of the Japan Institute of MetalsJ. Korean Chem. Soc. Journal of the Korean Chemical SocietyJ. Labelled Compd. Radiopharm. Journal of Labelled Compounds andRadiopharmaceuticalsJ. Lipid Mediators Journal of Lipid MediatorsJ. Lipid Mediators Cell Signalling Journal of Lipid Mediators and Cell Signalling J. Lipid Res. Journal of Lipid ResearchJ. Liq. Chromatogr. Journal of Liquid ChromatographyJ. Liq. Chromatogr. Related Technol. Journal of Liquid Chromatography and Related TechnologiesJ. Low Temp. Phys. Journal of Low Temperature PhysicsJ. Lumin. Journal of LuminescenceJ. Macromol. Sci., Phys. Journal of Macromolecular Science - Physics J. Macromol. Sci., Polym. Rev. Journal of Macromolecular Science Polymer Reviews J. Macromol. Sci., Pure Appl. Chem. Journal of Macromolecular Science Pure and Applied ChemistryJ. Macromol. Sci., Rev. Macromol. Chem. Phys. Journal of Macromolecular Science -Reviews in Macromolecular Chemistry and PhysicsJ. Mass Spectrom. Journal of Mass SpectrometryJ. Mater. Chem. Journal of Materials ChemistryJ. Mater. Civ. Eng. Journal of Materials in Civil EngineeringJ. Mater. Cycles Waste Manage. Journal of Material Cycles and Waste Management J. Mater. Eng. Perform. Journal of Materials Engineering and Performance J. Mater. Process. Manuf. Sci. Journal of Materials Processing and Manufacturing ScienceJ. Mater. Process. Technol. Journal of Materials Processing Technology J. Mater. Res. Journal of Materials ResearchJ. Mater. Sci. Lett. Journal of Materials Science LettersJ. Mater. Sci. - Mater. Electron. Journal of Materials Science - Materials in ElectronicsJ. Mater. Sci. - Mater. Med. Journal of Materials Science Materials in Medicine J. Mater. Sci. Technol. Journal of Materials Science and TechnologyJ. Mater. Synth. Process. Journal of Materials Synthesis and Processing J. Math. Chem. Journal of Mathematical ChemistryJ. Med. Chem. Journal of Medicinal ChemistryJ. Membr. Biol. Journal of Membrane BiologyJ. Membr. Sci. Journal of Membrance ScienceJ. Microbiol. Biotechnol. Journal of Microbiology and BiotechnologyJ. Microbiol. Methods Journal of Microbiological MethodsJ. Microcolumn Sep. Journal of Microcolumn SeparationsJ. Microelectromech. Syst. Journal of Microelectronic SystemsJ. Microencapsulation Journal of MicroencapsulationJ. Mol. Biol. Journal of Molecular BiologyJ. Mol. Catal. Journal of Molecular CatalysisJ. Mol. Catal. A:Chem. Journal of Molecular Catalysis A:ChemicalJ. Mol. Catal. B:Enzym. Journal of Molecular Catalysis B:Enzymatic J. Mol. Graphics Modell. Journal of Molecular Graphics and Modelling J. Mol. Liq. Journal of Molecular LiquidsJ.Mol.Microbiol.Biotechnol.Journal of Molecular Microbiology and Biotechnology J. Mol. Model. Journal of Molecular ModelingJ. Mol. Spectrosc. Journal of Molecular SpectroscopyJ. Mol. Struct. Journal of Molecular StructureJ. Nanopart. Res. Journal of Nanoparticle ResearchJ. Nat. Prod. Journal of Natural ProductsJ. Near Infrared Spectrosc. Journal of Near Infrared SpectroscopyJ. Neurochem. Journal of NeurochemistryJ. Neurosci. Journal of NeuroscienceJ. Neurosci. Res. Journal of Neuroscience ResearchJ. New Mater. Electrochem. Syst. Journal of New Materials for Electrochemical SystemsJ. Non-Cryst. Solids Journal of Non-Crystalline SolidsJ. Non-Equilib. Thermodyn. Journal of Non-Equilibrium Thermodynamics J. Nucl. Mater. Journal of Nuclear MaterialsJ. Nucl. Sci. Technol. Journal of Nuclear Science and TechnologyJ.Opt.Soc.Am.B:Opt.Phys.Journal of the Optical Society of America B:Optical PhysicsJ. Org. Chem. Journal of Organic ChemistryJ. Organomet. Chem. Journal of Organometallic Chemistryzwz1012发布日期:2006-4-03J. Organomet. Chem. Journal of Organometallic ChemistryJ. Pet. Sci. Technol. Journal of Petroleum Science and TechnologyJ. Pharm. Biomed. Anal. Journal of Pharmaceutical and Biomedical Analysis J. Pharm. Pharmacol. Journal of Pharmacy and PharmacologyJ. Pharm. Sci. Journal of Pharmaceutical SciencesJ. Pharmacol. Exp. Ther. Journal of Pharmacology and Experimental Therapeutics J.Pharmacol.Toxicol.Methods Journal of Pharmacological and Toxicological Methods J. Phase Equilib. Journal of Phase EquilibriumJ. Photochem. Photobiol., A Journal of Photochemistry and Photobiology A J. Photochem. Photobiol., B Journal of Photochemistry and Photobiology B J. Photopolym. Sci. Technol. Journal of Photopolymer Science and Technology J. Phys. A:Math. Gen. Journal of Physics A:Mathematical and General J.Phys.B:At.,Mol.Opt.Phys.Journal of Physics B:Atomic Molecular and Optical PhysicsJ. Phys. Chem. Journal of Physical ChemistryJ. Phys. Chem. A Journal of Physical Chemistry AJ. Phys. Chem. B Journal of Physical Chemistry BJ. Phys. Chem. Ref. Data Journal of Physical and Chemical Reference Data J. Phys. Chem. Solids Journal of Physics and Chemistry of SolidsJ. Phys. D:Appl. Phys. Journal of Physics D:Applied PhysicsJ. Phys. G:Nucl. Part. Phys. Journal of Physics G:Nuclear and Particle Physics J. Phys. I Journal de Physique IJ. Phys. II Journal de Physique IIJ. Phys. III Journal de Physique IIIJ. Phys. IV Journal de Physique IVJ. Phys. Org. Chem. Journal of Physical Organic ChemistryJ. Phys. Soc. Jpn. Journal of the Physical Society of JapanJ. Phys.:Condens. Matter Journal of Physics:Condensed MatterJ. Planar. Chromatogr. - Mod. TLC Journal of Planar Chromatography - Modern TLC J. Plant Biochem. Biotechnol. Journal of Plant Biochemistry and Biotechnology J. Polym. Eng. Journal of Polymer EngineeringJ. Polym. Environ. Journal of Polymers and the EnvironmentJ. Polym. Mater. Journal of Polymer MaterialsJ. Polym. Sci., Part A:Polym. Chem. Journal of Polymer Science Part A:Polymer ChemistryJ. Polym. Sci., Part B:Polym. Phys. Journal of Polymer Science Part B:Polymer PhysicsJ. Porous Mater. Journal of Porous MaterialsJ. Porphyrins Phthalocyanines Journal of Porphyrins and Phthalocyanines J. Power Sources Journal of Power SourcesJ. Prakt. Chem. /Chem-Ztg Journal fur Praktische Chemie - Chemiker Zeitung J. Propul. Power Journal of Propulsion and PowerJ. Protein Chem. Journal of Protein ChemistryJ. Pulp Pap. Sci. Journal of Pulp and Paper ScienceJ. Quant. Spectrosc. Radiat. Transfer Journal of Quantitative Spectroscopy and Radiative TransferJ. Radioanal. Nucl. Chem. Journal of Radioanalytical and Nuclear Chemistry J. Radioanal. Nucl. Chem. Art. Journal of Radioanalytical and Nuclear Chemistry ArticlesJ. Radioanal. Nucl. Chem. Lett. Journal of Radioanalytical and Nuclear Chemistry LettersJ. Raman Spectrosc. Journal of Raman SpecroscopyJ. Rapid Methods Autom. Microbiol. Journal of Rapid Methods and Automation in MicrobiologyJ. Reinf. Plast. Compos. Journal of Reinforced Plastics and Composites J. Rheol. Journal of RheologyJ. S. Afr. Inst. Min. Metall. Journal of the South African Institute of Ming and MetallurgyJ. Sci. Food Agric. Journal of the Science of Food and AgricultureJ. Sci. Ind. Res. Journal of Scientific and Industrial ResearchJ. Serb. Chem. Soc. Journal of the Serbian Chemical SocietyJ. Sep. Sci. Journal of Separation ScienceJ. Sol-Gel Sci. Technol. Journal of Sol-Gel Science and TechnologyJ. Solid State Chem. Journal of Solid State ChemistryJ. Solid State Electrochem. Journal of Solid State ElectrochemistryJ. Solution Chem. Journal of Solution ChemistryJ.Steroid Biochem.Mol.Biol.Journal of Steroid Biochemistry and Molecular Biology J. Strain Anal. Eng. Des. Journal of Strain Analysis for Engineering Design J. Struct. Chem. Journal of Structural ChemistryJ. Supercrit. Fluids Journal of Supercritical FluidsJ. Synth. Org. Chem Jpn. Journal of Synthetic Organic Chemistry, Japan J. Test. Eval. Journal of Testing and EvaluationJ. Therm. Anal. Journal of Thermal AnalysisJ. Therm. Anal. Calorim. Journal of Thermal Analysis and Calorimetry J. Therm. Spray Technol. Journal of Thermal Spray TechnologyJ. Thermophys Heat Transfer Journal of Thermophysics and Heat Transfer J. Thermoplast. Compos. Mater. Journal of Thermoplastic Composite Materials J. Toxicol. Environ. Health Journal of Toxicology and Environment Health J. Toxicol., Clin. Toxicol. Journal of Toxicology - Clinical Toxicology J.Toxicol.,Cutaneous Ocul.Toxicol.Journal of Toxicology -Cutaneous and Ocular ToxicologyJ. Toxicol., Toxin Rev. Journal of Toxicology - Toxin ReviewsJ. Trace Elem. Exp. Med. Journal of Trace Elements in Experimental Medicine J. Trace Elem. Med Biol. Journal of Trace Elements in Medicine and Biology J. Trace Microprobe Tech. Journal of Trace and Microprobe Techniques J. Vac. Sci. Technol., A Journal of Vacuum Science and Technology AJ. Vac. Sci. Technol., B Journal of Vacuum Science and Technology BJ. Wood Chem. Technol. Journal of Wood Chemistry and TechnologyJACS Journal of the American Chemical SocietyJOM JOM Journal of the Minerals Metals and Materials SocietyJPC J. Planar Chromatogr. - Mod. TLC JPC Journal of Planar Chromatography Modern TLCJpn. J. Appl. Phys., Part 1 Japanese Journal of Applied Physics Part 1Jpn. J. Appl. Phys., Part 2 Japanese Journal of Applied Physics Part 2Jpn. J. Cancer Res. Japanese Journal of Cancer ResearchJpn. J. Pharmacol. Japanese Journal of PharmacologyJpn. J. Toxicol. Environ. Health Japanese Journal of toxicology and Environment healthJSME Int J., Ser. A JSME International Journal Series A:Mechanics and Material EngineeringJSME Int J., Ser. B JSME International Journal Series B:Fluids and Thermal EngineeringJSME Int J.,Ser.C JSME International Journal Series C:Mechanical Systems Machine Elements and Manufacturing11/ 11。

采用MATLAB+Simulink的液压管路瞬态压力脉动分析

p 向量的后 n − 1 个元素 q = q0 p = p0
图3
选择算子常数
分别加上两个边界条件
p2 p3 Μ p′ = p n p0
则构成两个新的向量
q0 q q′ = 1 Μ qn −1
∂p 在 Simulink 中的表达方式 ∂x ∂p Fig.3 Simulink diagram of ∂x
整个管路动态压力脉动特性分析的 Simulink 仿真块图如图 4 所示其中子系统 subsystem 为包括稳态项和瞬态项的摩擦力项
常数 2
积分器 1 选择算子 2
选择算子 1 常数 1 积分器 2
子系统
图4 Fig.4
Simulink 仿真块图
Simulink simulating module 表2 Table 2 仿真参数
q ðr02
=
其中系数 ni 和 mi 采用日本研究人员 KAGAWA 给出的数值[5] 如表 1 所示
表1 Table 1 系数 ni 和 mi 值
Coefficients ni and mi
t
1 2 3 4 5 6 7 8 9 10
ni
2.63744×101 7.28033×101 1.87424×102 5.36626×102 1.57060×103 4.61813×103 1.36011 ×104 4.00825×104 1.18153×105 3.48316×105
Abstract: The mathematical model of fluid transients inside hydraulic pipelines is introduced including the unsteady friction item. A new method using SELECTOR block in MATLAB Simulink is developed to handle the integration in spatial domain when solving the partial differential equations. Using this method, the pressure transients inside hydraulic pipelines can be predicted both in time and spatial domains. A straight pipeline with a hydraulic valve on one side and a reservoir on the other side is studied as an example. The pressure pulsations inside the pipeline after the valve is shut off are simulated using the new method. The simulation results are given and compared with the predictions from characteristics method and finite element method published previously. The high frequency oscillation problem created by the numerical analysis is also discussed. Key words: pressure pulsations; pipeline transients; MATLAB Simulink; hydraulic pipeline; partial differential equation 在石油输送管网系统航空航天燃油供给系统以及液压传动系统中由于阀门的突然开关泵的失效以及执行元件止动等原因管道中将产生沿管路传播的压力脉动波这种现象会导致传输传动及控制系统性能的下降例如泵效率的降低系统

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

951 Dynamics and control of gearshifts on twin-clutch transmissionsM Goetz*,M C Levesley,and D A CrollaSchool of Mechanical Engineering,University of Leeds,Leeds,UKThe manuscript was received on14May2004and was accepted after revision for publication on30March2005.DOI:10.1243/095440705X34720Abstract:Based on a detailed dynamic model of an automotive powertrain containing a twin-clutchtransmission,an integrated powertrain control for gearshifts is developed.The operation of this con-troller is demonstrated on the basis of simulation results for upshifts,downshifts,and multiple gear-shifts taking place within the same half of the transmission.The control algorithm makes use ofclosed-loop control of clutch slip for a smooth transfer of engine torque with the aim of reproducingthe operation of a one-way clutch.Further elements are a closed-loop control of engine speed througha combination of a manipulation of engine controls and clutch pressure.In addition,it is demonstratedthat the control of transmission output torque during gearshifts can add robustness to the controland provides a means to manipulate directly the gearshift character.Finally,the dynamic eﬀects ofgear preselection through conventional hydraulically actuated cone-type synchronizers on the overallshift quality are discussed.Keywords:twin-clutch transmission,dual-clutch transmission,gearshift control,automatictransmission control,clutch control1INTRODUCTION friction clutch.The two halves of the twin-clutchtransmission consist of simple gear sets and syn-chronizers such as found on conventional manual The design principle of the twin-or dual-clutchgearboxes.This mechanical design oﬀers superior transmission originates in a patent by Ke´gresse[1]mechanical eﬃciency to that of planetary-type auto-back in1939.The idea behind this transmission con-matic transmissions equipped with a hydraulic torque cept is to split a manual gearbox into two halves.Oneconverter and explains why the twin-clutch trans-half of the transmission carries the odd gear ratiosmission is of interest from an economical and driving while the other carries the even gear ratios,as shownperformance point of view.in Fig.1.Each of the two halves(each half consistsHowever,the automatic control of the two friction of an input shaft,gears,synchronizers and a layshaft)clutches during gearshifts has to be performed with of the twin-clutch transmission is connected to thegreat care.In particular,the lack of one-way clutches engine through a separate friction clutch.The torque(i.e.clutching element that engages when running of both transmission halves is gathered at the out-in one direction of rotation and disengages when put of the transmission by a gear stage meshing withrunning in the other direction),which help to smooth output gears located on both layshafts.Gearshiftsthe transfer of engine torque in the torque phase can be accomplished as clutch-to-clutch shifts byof gearshifts on planetary-type automatic trans-changing from one half to the other,thereby retain-missions,seemed for a long time diﬃcult to com-ing full traction at the wheels.This characteristic ofpensate through clutch control.Also,the inability to the twin-clutch design enables powershifts as on askip one gear(i.e.multiple gearshifts such as from conventional planetary-type automatic transmissionfourth to second gear)without disengaging the and thus eradicates the principal disadvantage oftorque-transmitting clutch was considered a major automated manual transmissions utilizing only oneshortcoming.After renewed interest in the1980s *Corresponding author:School of Mechanical Engineering,[2,3],where the twin-clutch design had been applied University of Leeds,Woodhouse Lane,Leeds LS29JT,UK.email:to race cars,only the advent of faster and morecapable electronics at the end of the1990s led to full menmg@952M Goetz,M C Levesley,and D A CrollaFig.1Twin-clutch transmission of two-layshaft typeinterest from all major car and transmission manu-for gearshifts,which produces high shift quality facturers.In2003,the twin-clutch transmission[4]comparable with that of planetary-type automatic wasﬁnally put into production for theﬁrst time.transmissions.Another important aim is to create a The problems of the control of both a singlegearshift control that is robust against changes in gearshift and multiple gearshifts on twin-clutch the clutch friction coeﬃcient and allows the track-transmissions are addressed in this paper.Theing of transmission output torque trajectories,thus requirement for robust operation of the control of providing a basis for integration in torque-based gearshifts under a variety of operating points andpowertrain control schemes.conditions(e.g.changes in clutch friction)necessitatethe employment of closed-loop control techniques.For conventional automatic transmissions,closed-2DYNAMIC POWERTRAIN MODELloop control has been mainly applied to enginesynchronization[5],leaving the control of the engine For the simulation of gearshift performance,adynamic model of a vehicle powertrain was torque transfer to a combination of one-way clutchoperation and open-loop clutch pressure manipu-developed.lation.For twin-clutch transmissions the potentialsThe whole powertrain model is depicted in Fig.2 of various gearshift control concepts applied to up-and features a mean value torque production model shifts was compared in reference[6].The solutionof a spark ignition engine that was given in reference that oﬀered the best gearshift performance was a[8]and that makes use of regression functions for closed-loop strategy,where the transmission outputairﬂow through throttle body and intake manifold torque was controlled throughout the whole gear-and for the torque generated in the combustion shift.The control of multiple gearshifts was addressedprocess.Also included in the engine model are the in reference[7]where a solution for so-called‘double rotational dynamics of the engine and accessory shifts’was proposed.The control described in thatloads.Inputs to the engine model are throttle angle article used the second clutch to provide someﬁll-and spark advance.The block representing the twin in torque for the time that the torque-transmittingclutch transmission in Fig.2consists of two parts: clutch has to be disengaged in order to be able to the rotational dynamics of clutches,synchronizers change the gear in that particular transmission half.and geartrain,and the dynamics of the hydraulic The control strategy presented in that paper,how-system.Inputs to the transmission block are pressure ever,made exclusive use of open-loop techniques.values for clutches and synchronizers,which are The objectives of this paper are to investigate the actually voltage inputs to the solenoid valves con-dynamics of gearshifts on twin-clutch transmissionstrolling the hydraulic actuation of clutches and and to develop an integrated powertrain control synchronizers.Dynamics and control of gearshifts on twin-clutch transmissions953Fig.2Model of a vehicle powertrain including a twin-clutch transmissionThe dynamic models of powertrain and hydraulic components of the transmission,while massless system were created in MATLAB/Simulink A,whichspring–damper elements are employed to model the was also used to generate the simulation results compliances of the shafts in the gearbox.To model presented in this paper.the drag that is created in the twin-clutch trans-mission,the inertias are‘connected’to the groundvia damper elements.2.1Rotational dynamics of the twin-clutchIn order to model the dynamics of a shift from transmissionsynchronizer to synchronizer where both gear ratios Figure3shows the dynamic model of the twin-clutch(i.e.synchronizers)are located within the same half transmission,which is based on the layout presented of the transmission,the dynamic model of the in Fig.1.twin-clutch transmission depicted in Fig.3had to Inputs to this part of the transmission model are be extended by an additional synchronizer model the clamp forces at clutches and synchronizers.Non-(indicated by the dashed rectangle in Fig.3).This compliant discs represent the inertias of the internalprovided the basis for realistic modelling of a changeFig.3Rotational dynamics of the twin-clutch transmission,depicted for the conﬁguration of ﬁrst and second gears.Extension is shown for third gear954M Goetz,M C Levesley,and D A Crollabetween synchronizers without producing discon-additional rules given bytinuities in the simulation results.This extension to IF {v in =v out }AND {x s Áx s,max }THENthe transmission model is used later in sections 3.3and 4.{dog clutch is engaged}(6)Both the synchronizer and the clutch models con-IF {x s <x s,max}THEN {dog clutch is disengaged}sist of a friction model that describes the torque transmitted in the slipping and in the sticking states.(7)It also contains the logic of the transitions between the two states.The synchronizer model incorporates These two equations essentially reﬂect the fact that a third state,which accounts for a mechanical lock-the dog clutch can be engaged once the two halves ing of its two halves via the dog-clutch-like part of of the synchronizer run with the same speed and the synchronizer.The friction behaviour of clutch thus the teeth can slide to their maximum axial dis-and synchronizer is given by the equations placement,thereby mechanically locking the syn-chronizer.If the teeth of the dog clutch are slid back T C =sgn(v in −v out )R m F N m k z (1)into their initial position,the mechanical coupling is neutralized.The information about the displacement with of the dog clutch comes from the actuator model of the synchronizer.m k=f (D v )(2)for the clutch,and 2.2Hydraulic actuation of clutches andsynchronizersTsyn =sgn(v in −v out )Rm sin a F N m kz (3)The hydraulic system of the transmission model gen-erates a clamp force at its output (i.e.input to the rotational dynamics described in the last section)withfrom a voltage input to the solenoid valves.The hydraulic actuation scheme is the most commonly m k=constant (4)used so far,particularly in conjunction with wet friction clutches.Electric actuation in conjunction for the synchronizer.If the clutch–synchronizer slips with dry friction clutches o ﬀers increased simplicity (v in ≠v out),the friction torque is given by equation and e ﬃciency but tends to show more compliance (1)for the clutch and equation (3)for the syn-in the actuation system and hence slower response chronizer.The friction coe ﬃcient of the clutch is times.dependent on the sliding speed across the clutch and First,a detailed dynamic model of the hydraulic was represented by a higher-order polynomial as a actuation system was developed.The hydraulic clutch function of the sliding speed.This allowed modelling actuation consists of a proportional solenoid valve,of various friction materials of both wet and dry which controls oil ﬂow to the hydraulic actuator.friction types.The friction coe ﬃcient at the syn-Increasing the pressure in the hydraulic actuator chronizer has been assumed constant.extends the actuator piston,which acts on the clutch If both halves of the clutch–synchronizer stick pack,thus producing a clamp force.The model of together (v in =v out)the torque at the clutch–synch-the clutch pack essentially contained the equations ronizer is determined by the applied load torques of motion of the piston including the opposing forces and inertial torques and is limited by of the return spring and the clutch pack.This clutch pack model permits a simulation of the dynamic |T C,syn|∏m s R m F Nz(5)behaviour of the hydraulic clutch actuation at the A frictional lock-up of the clutch–synchronizer takes point where the clutch piston has ended its idle place if the di ﬀerential speed across the clutch stroke and makes contact with the clutch pack,lead-vanishes and the criterion of equation (5)is fulﬁlled.ing to a sharp rise in clutch pressure.Based on The frictional contact of the clutch–synchronizer the detailed model,a simpliﬁed phenomenological breaks apart if the torque at the clutch–synchronizer model was generated for the development of the exceeds the limit given by equation (5).gearshift controller,since it was less complex and The additional state coming from a mechanical more ﬂexible.The simpliﬁed model of the hydraulic locking of the synchronizer through engagement actuation is depicted in Fig.4and consists of two linear transfer functions and a feedback loop.of the dog clutch was accounted for by simpleDynamics and control of gearshifts on twin-clutch transmissions955Fig.4Simpliﬁed dynamic model of the hydraulic actuation and clutch pack in the s domain3INTEGRATED POWERTRAIN CONTROL OF of engine torque transfer without creating too much GEARSHIFTSvehicle jerk.If it is possible to mimic the operationof a one-way clutch by careful control of a friction Gearshifts on twin-clutch transmissions can beclutch,then the optimal transfer of engine torque accomplished as so-called clutch-to-clutch shifts could be accomplished even on a twin-clutch trans-by changing from one half of the transmission tomission.Such a control was suggested in references the other.However,before commencing the clutch-[9]and[10]and requires closed-loop control of to-clutch shift,the target gear needs to be engagedclutch slip.(preselected)on the opposite half of the trans-The problem of obtaining the torque signal and mission.Essentially,the gearshift on a twin-clutchthe advantages and disadvantages of each technique transmission consists of two parts:(sensor measurement versus mathematical observer)are not discussed here but are well covered in the (a)the preselection of the target gear on the torque-literature(see,for example,references[6],[11],and free half of the transmission;[12]).(b)the clutch-to-clutch shift.The clutch-to-clutch shift is the subject of this3.1Control of upshiftssection whereas the preselection(in particular,thedynamic eﬀects of the gear change)is discussed in The control algorithm for power-on upshifts is section4.depicted in Fig.5.The control sequence is shown in The clutch-to-clutch shift consists of two distinctive the clutch pressure proﬁles of the simulation result parts:a‘torque phase’where engine torque is trans-(upshift fromﬁrst to second gear)in Fig.6.In step1 ferred from the oﬀgoing clutch to the oncoming of the control algorithm,hydraulic pressure is reduced clutch and an‘inertia phase’where the speed of theat the oﬀgoing clutch.The nearer the pressure is engine is synchronized to that of the target gear.decreased to the value where the clutch starts to The order of the two phases depends on the type ofslip,the smaller are the resulting torque vibrations shift(i.e.upshift or downshift)and the direction coming from the stick–slip transition.However,theactual transition from stick to slip at this clutch of the transmission of drive power(i.e.power-on orpower-oﬀ).is accomplished by the clutch slip control,which is The clutch-to-clutch shift can be controlled inactivated in step3.Prior to activation of the clutch principle in the same manner as on planetary-type slip controller,the oncoming clutch is preﬁlled in transmissions.However,because of diﬀerences instep2.This pressure needs to be selected on the the design(in particular,the absence of one-way basis of a compromise between fastﬁlling on one clutches on twin-clutch transmissions)the transferhand and little eﬀect on driveline torque on the of engine torque in the torque phase becomes more other.The closed-loop control of clutch slip main-tains a small clutch slip reference value(5rad/s)by diﬃcult to control.This is due to the diﬃculty incontrolling the timing of the application and release manipulating the pressure at the oﬀgoing clutch.By of the two clutches.One-way clutches and theirramping up the pressure at the oncoming clutch ability to disengage automatically once the trans-(step4),the slip controller automatically reduces the mitted torque has become negative aid the controlpressure at the oﬀgoing clutch,thus transferring956M Goetz,M C Levesley,and D A CrollaFig.5Algorithm for upshift controlFig.6Simulation result of an upshift fromﬁrst to second gear(BTDC,before top dead centre).The arrows and numbers indicate the steps of the control algorithm depicted in Fig.5engine torque without creating negative torque at In this phase,the engine speed is synchronized to this clutch.At the point where the pressure at thethat of the target gear while tracking a reference oﬀgoing clutch has become zero,the slip controller speed proﬁle.The closed-loop speed controller,whichis activated in step5,achieves this by manipulating is deactivated and the control can proceed to theinertia phase.both engine throttle angle and spark advance(SA),957 Dynamics and control of gearshifts on twin-clutch transmissionsthus uniting the advantages of large engine torque From the output torque proﬁle in Fig.6,it can be variations and fast engine response.In the inertiaseen that the torque does not show any abrupt phase,transmission output torque control can be changes at the point of the transition from the torque activated(step6)in which closed-loop trackingto the inertia phase,thus verifying the smooth of a reference torque proﬁle is achieved through control of the engine torque transfer by the clutch manipulation of pressure at the oncoming clutch byslip controller.the controller.The reference torque proﬁle used heregoverns the transmission output torque to a level3.2Control of downshiftscorresponding to the change in gear ratio over thewhole gearshift.At the end of the inertia phase the The power-on downshift starts with the inertia phase clutch pressure is raised to the line pressure(step7),where the engine is synchronized to the target gear, which is the main pressure in the hydraulic system.followed by the torque phase where engine torque istransferred between the two clutches.The control It was observed that the torque vibrations createdat the end of the gearshift where the clutch locks up algorithm for downshifts is depicted in Fig.7.Again could be reduced by abruptly raising the sparkthe steps of the control algorithm are indicated in the advance to its original value at this point.Further simulation result depicted in Fig.8.At the beginning details of the upshift control including a discussionof the inertia phase(step1in Fig.7),the pressure at of robustness against changes in the clutch friction the oﬀgoing clutch is reduced in a similar way as in material have been given in reference[13].the torque phase of the upshift control.Through-Figure6shows a simulation result for an upshift out the inertia phase of the downshift the engine from theﬁrst to second gear.The graph depicts theneeds to be accelerated in order to reach the syn-time proﬁles of transmission output torque T out,the chronous speed of the target gear.A combination rotational speeds v at both clutches including engineof an increase in throttle angle(step2)and clutch speed(denoted as input speed),the pressure pro-pressure modulation by the speed controller(step3)ﬁles p C at both clutches,the throttle angle and theallows tracking of a reference speed proﬁle without spark advance(denoted Throttle and SA).In general,having to decrease the clutch pressure too much, good tracking of the reference proﬁles for enginethus transmitting as much engine torque as possible. speed(second graph)and transmission output torque Prior to the end of the inertia phase,the oncoming (uppermost graph)can be observed.clutch is preﬁlled in step4(low pressure to suppressFig.7Algorithm for downshift control958M Goetz,M C Levesley,and D A CrollaFig.8Simulation result of a downshift from second toﬁrst gear(BTDC,before top dead centre).The arrows and numbers indicate the steps of the control algorithm depicted in Fig.7torque vibrations)and the throttle angle is decreased a downshift from second toﬁrst gear is depicted again in step5.in Fig.8.Once again,it can be seen that the track-In a similar way as previously explained for the ing performances of speed and torque reference upshift,clutch slip control is employed in the torquetrajectories are good.The output torque proﬁle of phase for a smooth transfer of engine torque(step6).the downshift depicted in Fig.6looks reasonably In parallel with the clutch slip control,the optionalsmooth,owing to the relatively shallow gradient transmission output control can be activated(step7).of the reference torque trajectory selected in the Although the clutch slip controller takes care oftorque phase.the engine torque transfer,the transmission outputtorque proﬁle can take diﬀerent shapes depending3.3Control of multiple gearshiftson the operating point of engine and the gear ratio.To be able to manipulate the proﬁle of the trans-As explained in the introduction,gearshifts thatchange between gears within the same half of the mission output torque,closed-loop torque controlcan be activated in the torque phase.To implement transmission(e.g.from fourth to second gear)cannot the output torque control without losing the functionbe accomplished as simple clutch-to-clutch shifts. of the clutch slip control,the pressure manipulation During the period of time where the original gear is at the oncoming clutch is split into two actions.Thedisengaged and the target gear engaged,the appro-ﬁrst action requires ramping up the pressure,but at priate half of the transmission needs to be torque a lower rate than required in the torque phase of thefree.This means,however,that since both the upshift.This is necessary to force the slip controller original gear and the target gear are located within to transfer engine torque gradually.Then,the secondthe same half of the transmission,the torque-action comes from the closed-loop torque control,transmitting clutch has to be disengaged for the which adds its contributions in the pressure manipu-change in gears.The result would be a gearshift lation to the pressure ramp of theﬁrst control action.similar to a manual or automated manual trans-Further details of the downshift control havemission with interruption in traction,which is not been given in reference[14].A simulation result for acceptable for a powershift transmission.959 Dynamics and control of gearshifts on twin-clutch transmissionsTwo or more consecutive gearshifts would fulﬁl the transferred to the other clutch in steps5and6.The requirement of transmitting power to the wheelsremainder of engine torque is used for continuing during the gearshift,but these would result in un-the acceleration of the engine.The change of clutch acceptably long shift times and would be distinguish-in steps5and6is accomplished through conven-able as two separate gearshift events by the driver.tional open-loop pressure ramps.Owing to the small To solve the problem,it was proposed to use theamount of engine torque transferred,no signiﬁcant second clutch during the gear change in order to improvement in clutch slip control over the open-provide someﬁll-in torque[7].This technique isloop controlled clutch change was noticed.A second adopted here and combined with the techniques reason why the clutch slip control was not aseﬀective here as it was in the normal torque phase of engine control,clutch slip,and torque controldeveloped in the previous sections.Since multiple is that,for its operation,the engine needs to be downshifts are,because of the importance ofdecelerated to the input shaft speed of the inter-response time,more critical than multiple upshifts,mediate gear,which would result in increased vehicle only multiple downshifts are discussed here.Thejerk.control algorithm for multiple downshifts is depicted While the gear is changed in the torque-free halfof the transmission through a change in synchronizer in Fig.9.The steps in the control algorithm that arediﬀerent from the control of single downshifts are in steps8and9,the engine speed controller is active indicated by arrows in the simulation result shownat the torque-carrying clutch(step7).The pressure in Fig.10.value at the engaging synchronizer is mainly deter-Up to step4,the control algorithm in Fig.9is themined by the time available for synchronization and same as for single downshifts.However,instead of the gear ratio.After synchronization of the input transferring the full amount of engine torque in theshaft to the target gear is completed,the syn-subsequent phase,only a part of engine torque is chronizer pressure is raised to line pressure(step10).Fig.9Control algorithm for multiple downshifts960M Goetz,M C Levesley,and D A CrollaFig.10Simulation result of a downshift from fourth to second gear(BTDC,before top dead centre).The arrows and numbers indicate the steps of the control algorithm depictedin Fig.9Subsequent to the preﬁlling of the original clutch In this section,the dynamic eﬀects of preselection (step11)the actual torque phase begins,which ison the overall gearshift quality will be investigated. controlled in the same way as for single downshifts,A simple preselection strategy is employed thatrequires that a gear lower than the presently engaged again employing clutch slip control and transmissionoutput torque control.gear has to be selected on the torque-free half of the Figure10depicts a simulation result for a down-transmission.This has the advantage that the trans-shift from fourth to second gear.The speed trajectory mission is always prepared for a downshift without of the engine in Fig.10clearly indicates that theﬁrst having to change the target gear.engine accelerates constantly throughout the whole The engagement of the target gear ratio on the inertia phase,comparable with a single gearshift.torque-free half of the transmission requires syn-Thus,the driver experiences the multiple–gearshift chronization of the input shafts to the speed level event as a single gearshift event.Traction is inof the target gear.When changing to a target gear general maintained throughout the gearshift.In the lower than the gear currently engaged,the input torque phase the reference torque proﬁle is trackedshaft needs to be accelerated.When changing to a accurately apart from an initial deviation.target gear higher than the gear currently engaged,the input shaft needs to be decelerated.If this syn-chronization process is carried out by use of conven-tional synchronizers,the energy for this speed change 4DYNAMIC EFFECTS OF GEAR PRESELECTIONis transferred from the output of the transmission.ON GEARSHIFT PERFORMANCE Other methods of synchronization include central syn-chronization with an external energy supply(external As mentioned at the beginning of section3,a gear-brake and electric motor)or synchronization via shift on a twin-clutch transmission consists of pre-engine control,both requiring only simple dog selection of the target gear on the torque-free halfclutches.The latter is only reasonably applicable of the transmission and a clutch-to-clutch shift.to automated manual transmissions featuring only。