您的当前位置:首页正文

英文翻译[1]

2022-09-19 来源:步旅网
Impact of regenerative braking on vehicle stabilityTopic 6: Modelling and Control Authors:Dr. Matthew Hancock (corresponding author), JLR Advanced Engineering, SMG Simulation and ControlsTeam, Jaguar Cars Ltd, Engineering Centre, Whitley, Coventry CV3 4LF UKTel: +44 24 7620 6199, Fax: +44 24 7620 6533email: mhancocI1 jaguar.comDr. Francis Assadian, JLR Advanced Engineering, SMG Simulation and Controls Team, Jaguar Cars Ltd,Engineering Centre, Whitley, Coventry CV3 4LF UKTel: +44 24 7620 4955, Fax: +44 24 7620 6533email: fassadia~jaguar.comAbstractIn a series regenerative braking system, regenerative braking is generally used to themaximum extent prior to the introduction of friction braking. During the regenerative brakingphase, this generally means that the front to rear braking distribution will be less than idealsince it is often only possible to apply braking torque to a single axle. This can havesignificant implications for vehicle handling and stability during cornering, particularly if theaxle concerned is the rear axle.The first part of this paper considers the impact on vehicle stability of applying regenerativebraking through the rear axle of a sports utility vehicle. It is shown that, on low p. surfaces inparticular, a moderately sized electric motor has the capability to significantly compromisevehicle stability during cornering. The second part of the paper then considers how this issuemay be resolved. Various solutions are considered and it is shown that redistributing theregenerative braking torque using active driveline devices allows vehicle stability to beprotected whilst maintaining maximum energy recovery.1 IntroductionA key feature of mild and full hybrid vehicles is the conversion of the vehicle's kinetic energyto electrical energy during braking. This is achieved by using the vehicle's electric motor(s),instead of the friction brakes, to apply 'regenerative' braking torque to the wheels. However,whilst this approach has obvious benefits for fuel economy, it cannot fully replicate thefunctionality of the friction brakes. There are two reasons for this. Firstly the wheel torquecapacity of the electric motors used in hybrid vehicles is generally less than that of the frictionbrakes. Regenerative braking alone cannot therefore deliver adequate deceleration capabilityand the vehicle's conventional friction brakes must be retained. For maximum energy173recovery, series (as opposed to parallel) regenerative braking systems are used whereregenerative braking is generally used to the maximum extent (defined by the power limit ofthe motor) prior to the introduction of friction braking.The second limitation of regenerative braking is its ability to control the distribution ofbraking force between the front and rear axles. Brake force distribution is important both forextracting optimum braking performance and for protecting vehicle stability. Ideally, thedistribution should match the ratio of the available tyre forces at the front and rear [1]. For agiven vehicle on a homogeneous surface, this ratio is simply a function of the load on eachwheel and therefore deceleration or total braking force. A typical ideal brake forcedistnibution curve is shown in Figure 1. If the actual brake force distribution follows thiscurve, both the front and rear brakes will be utilised to their maximum extent and both willreach saturation (lock) simultaneously. If the actual distribution is below the ideal curve, therear brakes will be under utilised and the front brakes will reach saturation first. However, ifit is above the ideal curve the rear brakes will saturate first. When a tyre becomes locked orgoes into high slip it loses the majority of its lateral force capacity and hence if this happens atthe rear axle before the front, vehicle stability will be heavily compromised.0U.0 01 0.1 ~~ 0.1--- 0.2-- 0.3---- 0.4--- 0.5--- 0.6---- 0.----Fr n A-----e ------ Force- I ------oa -----------F i- gu --r e : I d e-1 a-l-- -b --r -k f o c d i st r ib u ti oregeneative rakingis conected ronth rAr xle. Thise Is thrfoeteoosacsdceaifrom ~ ~ ~ ~~igr a:Ida brake force prpcieadrpeet distribution infcn hleg ntrsoguaranteeng ve hicle sabilinertywist exracting maximum acnergy brecoery Inorder dsrbtion asssthiesclannareo the o raralem, prob Theiistprsoh paper asse considers hr the impactri moon vsehiclestability of applying regenerative braking through the rear axle of a sports utility vehicle(SUV). A number of solutions are then proposed and assessed in the second part of the paper.2 Vehicle Model174The model investigation used is Figure is carried representative out in the simulation 2. As of a hybrid SUV environment with using the a full drivetrain vehicle model. configuration Therear can axle be observed and also from that features the allows a figure, part the front time the vehicle has an electric shown motor indriving theand all wheel drive (AWD) system with a centre couplingstated rear in axles the following to be fully analysis, locked this together. coupling However, is always unless open.otherwiseEngineTrans.-MotorT fFigure 2: Drivetrain configuratiou~rthe consider Coupling _dvhcedvhce2.1 Mo -I OverviewCentre The full #ehicle \" model Six [2] body used degrees for this analysis of has the following features:* freedom Non-linear and four tyres wheel rotational degrees of freedom-utilises * the Longitudinal Magic Formula * and Steering, lateral Tyre Model weight [3]driveline transfer * Full and electronic suspension includedstability systems program assumed to be rigid body\" traction (ESP) Brakes, control model which includes yaw stability control,centre (TCS) coupling and anti-lock and motor braking all (ABS) modelled [4].as perfect actuators (no dynamics).Note that aerodynamic (driving/braking drag torques and driveline was are employed thus dynamics applied and directly are not is used throughout to the included wheels). in the modelthis paper.The SAE sign conventionTo facilitate the analysis employed of the [2]. vehicle model's behaviour, a simple driver model was alsoany The predefined objective series trajectory of this model of points as precisely was to as control possible. the steering The demanded of the vehicle trajectory to followof it and using the a model variable operates angle required preview by selecting is defined as ato system. reach this A the PID most appropriate 'target point' aheadpoint controller and the actual then uses yaw angle the error to give between the required the yawsteering angle.2.2 Friction Braking ModelFor simulations according carried to out the with of front 'regenerative 61% to front rear distribution braking and shown off, in the Figure friction 3. brakes are applieddetermined 39% rear purely is employed Here a fixed brake distributionforce by distribution the physical up to O.6g sizing deceleration. of This distribution isconsistent is maintained the front and rear brakes. Beyond 0.6g, the brakewith [5], conventional just below a system which vehicles the ideal curve (Figure 3). This characteristic isuses that a control feature electronic brake force distribution (EBD)brake valve to pressure electronically split.adjust the front to rear hydraulic175-- -0.3 -- S0 .25 -------------------0 .2 --------------- -----------------------------140.-Actual Friction Brake Distribuition0.6 0.700 0.1 0.5 0.4 0.3 0.2 Front Axle Force t WeightFigure 3: Actual friction brake force distribution employed in the vehicle model2.3 Regenerative Braking Modelthat appliesRegenerative braking is modelled using a simple model of an electric motor betweentorque directly to the rear axle. A 37kW motor is assumed with a gear ratio of 9.25:1 in Figure 4.the motor and the rear wheels. The torque characteristic of the motor is shown brakingThe braking torque requested from the motor is controlled using a series regenerative extent possiblestrategy. Here, regenerative braking torque is generally used to the maximum An example(up to the torque limit of the motor) to fulfil the driver's braking torque request. friction brakingof how the requested braking torque is distributed between regenerative and motor (at theat S0kph is shown in Figure 5. At the speed shown the torque limit of the is deliveredwheels) is 2000Nm. Therefore up to this point all of the requested braking torque and thenby the motor. Above 2000Nm, additional torque is first provided by the front brakes been exceededalso by the rear brakes once the conventional front to rear braking ratio has (see Section 2.2).-200 -- ----400- -4 ----- ----------------------------------- ---0 ------------- ---W 6 0 ------ --------------~- 800 ------ -1200 -14000 ----- ---- ----T---- ----I---- ----1E160---140--- 120--- 100--- 80--- 40-- 60--- 20---- Veil ped pfuntio-o-speda---- whel as--- the--- at---- torque- limit-- Motor-- Fiur 4:20 176z0S IM -3000 -- ------- ---------% ---000------0-5000 --- Front Friction BrakesRear Friction Brakes400 Regenerative Braking -------- 0 --------------- --- --------------------- ------------S--------100002000 4000 6000 8000 Total Braking Torque Request, NmFigure 5: Braking torque distribution at 5Okph3 Dynamic Analysis of the Impact of Rear Axle Regenerative BrakingThe simulation model is used to assess the impact of regenerative braking on vehicle stabilityby analysing the vehicle's response during braking in a turn manoeuvres on various surfaces.Even on high-ji surfaces it is shown that, without ESP, applying regenerative braking on therear axle can degrade stability. This is illustrated with a braking in a turn manoeuvre on p. =1. Here the vehicle is initially driven at a constant speed of 1 30kph whilst the steering isbeing controlled to follow a 1 85m radius trajectory (yielding a near limit lateral accelerationof 0.8g). Once a steady state cornering condition is reached a constant total braking torque isapplied (yielding a peak deceleration of approximately 0.2g) whilst the steering continues tobe controlled to maintain the 1 85m radius trajectory.Results are shown in Figure 6 with regenerative braking off (conventional brakes used) andwith regenerative braking on. Such a manoeuvre typically causes instability in even aconventional vehicle because the brake application causes weight transfer onto the frontwheels which in turn results in a loss of lateral force at the rear. The resulting oversteer iscontrolled via the application of counter steer and this can be observed as the negativesteering input that is applied after the brake application begins at 10 seconds (Figure 6). If thetest is repeated with regenerative braking applied, it can be observed that the driver workloadincreases, as evidenced by a 20% increase in the steering correction required from the driver(Figure 6a). The further reduction in stability here is due to the fact that the rear tyres nowhave to generate the majority of the required braking torque (Figure 6b), which increases theirlongitudinal slip and hence further reduces their lateral force capacity.1771 0 0 --------------------------- -----10...............Front -Regan]ff~0 --50 ----------- --r -----Rear -ReganOff--- -----50 ----------- ----------- 410 0 -----------48 1- --- 12 Tiez------b--------- ------- .2 0 ------ 10a g13 14Regan OffRegen On80 9 10 11 Time, s1 P2 1 3 114Figure 6: Driver workload during a 185m radius, l3Ok-ph braking in a turn test. Brakeapplication at 10 seconds, ESP off in all cases.However, on this surface it can also be shown that ESP can comfortably compensate for anytheloss of stability caused by the application of regenerative braking. To illustrate this, Figure 7.results for the same braking in a turn manoeuvre with ESP switched on are shown in andAs can be observed from Figure 7a, vehicle stability for both the conventional noregenerative braking cases is markedly improved with ESP and there is also now though,significant difference between them in terms of driver workload. There is a penalty as the additional instability caused by regenerative braking increases the peak brake pressuresapplied by ESP by around 10% (Figures 7b and 7c).C30Time, sa)041---- --- -- --- ----- ---- -- ----- --- --- --- -------------310 ----------- C0-----------------2'CL1'W8e% 910----1--- 'I Time, s121'14b)Figure 7: Driver and ESP workload during a 185m radius, l3Okph braking in a turn test.Brake application at 10 seconds, ESP on in all cases.178On low-p. surfaces the impact on stability is much more dramatic. This is because on surfacessuch as ice (p. -0. 1), even at moderate speeds (up to around 1 O~kph), the motor has enoughbraking torque capacity to lock the rear wheels, causing an almost total loss of lateral forcecapacity and hence stability. This can be illustrated with an open loop braking in a turn teston p. = 0. 1. Here the vehicle is initially driven at a constant speed of 50kph with a fixedsteering input of 200. Whilst the vehicle is in a steady state cornering condition a constanttotal braking torque of 400Nm is applied. In a conventional vehicle, without ESP, this is notsufficient braking torque to cause either the front or the rear wheels to go into high slip and sothe vehicle remains stable (does not spin). This is indicated by the fact the vehicle's sideslipangle does not significantly increase after the brake application (Figure 8). However, withregenerative braking applied, the additional braking torque applied to the rear wheels causesthem to lock and hence the vehicle loses the majority of its rear lateral force capacity andbecomes unstable (Figure 8). Unlike in the high p. test, ESP is unable to offer a significantimprovement in stability in this case, as shown by the fact that the vehicle sideslip angle is notsignificantly reduced compared to the ESP off case (with regenerative braking on, Figure 8).0.2-25 -Regen Off, ESP Off -Regen Regen On, On, ---ESP ESP OffOn---- ----- -------30 4 4.5 5 5.5 Time, 6 s6.5 7 7.5 8Figure 8: Vehicle sideslip angle during a 20', 50kph open loop braking in a turn manoeuvreon p.= 0. 1. Brake application at 5 seconds.5 Potential Solutions to the ProblemHaving illustrated that regenerative braking are can have a severe impact on vehicle stability, twomethods \" of combating off this issue considered braking in once this the section:longitudinal Switching regenerative slip of either rear tyreexceeds \" Locking a certain centre threshold.coupling the under braking.Regenerative slip of the braking rear are off tyres therefore regenerative at the rear to axle a degrades conventional reducing stability braking the slip of the because system). the tyres it increases Both of The a 20% the the longitudinalconsidered(relative solutions switching a means braking to of rear rear tyres. exceed effectiveness slip threshold ofiswhen either 179illustrated in the same p. = 0.1, 50kph, braking in a turn test as described in the previoussection. As can be observed from Figure 9b, without the slip threshold, the application ofregenerative braking causes the inside rear wheel to go into high slip and eventually lock.With the slip threshold applied, regenerative braking is switched off at the instant that theinside rear wheel reaches 20% slip (Figure 9b). Beyond this point the longitudinal slip of therear wheels then reduces because the majority of the braking torque is now being applied tothe front wheels by the friction brakes. The net result is that the lateral force capacity of therear tyres is maintained and hence the vehicle remains stable (Figure 9a). Note that only thelongitudinal slip of the inside rear wheel is discussed here because it is the more lightlyloaded rear wheel and therefore has the highest slip value.It should be noted however that the vehicle's sideslip angle still increases beyond that of thevehicle without regenerative braking. This is because of the initial regenerative brakingperiod between 5 and 5.6 seconds when the longitudinal slip of the rear tyres is significantlygreater than that observed with the conventional vehicle (Figure 9b). Clearly, if the slipthreshold at which regenerative braking is switched off were to be reduced, there would alsobe a corresponding reduction in the difference in sideslip angle between the two cases. Forexample, if the slip threshold is reduced to 10%, the peak sideslip angle of the vehicle withregenerative braking reduces to 1.40, just 0.30 higher than the conventional vehicle and 2.60less than the vehicle with the 20% threshold.-20- -1) Regen-On--N-Slip-Threshol-Regen -25-4 0 On, 20%/ Slip Threshold4.5 5 5.5 6 Time, sa)-------- 6.6 7 7.5 8---- ........... ..----- --- -------1gn ----4 * ~----- ~~ gn-n-20-Slp-hrshlf---4.5 5 5.5 6 Time, sb)6.5 7 7.5 8Figure 9: Impact of using a slip threshold to disable regenerative braking during a 200, 50kphopen loop braking in a turn manoeuvre on g. = 0. 1. Brake application at 5 seconds. ESP offin all cases.The second solution that is considered is to lock the centre coupling under braking. Asdescribed in Section 2, the vehicle under consideration has a part time all wheel drive system180that allows the rear axle to be connected to the front axle via an electronically controlledcentre coupling. If this coupling is locked such that the front and rear axles become rigidlyconnected, then any regenerative braking torque applied by the electric motor will bedistributed between the front and rear axles instead of only being applied to the rear.Moreover, the rigid connection between the front and rear axles means that the torque will bedistributed according to the grip available at each axle and therefore will match the idealbrake force distribution described in Section 1.The effectiveness of this solution is illustrated with the same [L = 0. 1, 50kph, braking in a turntest as used above. As can be observed from Figure 10, with the centre coupling locked, thelongitudinal slip of the inside rear wheel does not exceed 5% and is only marginally higherthan it is with the conventional vehicle. Consequently, the lateral force capacity of the reartyres is not degraded at any point in the manoeuvre and vehicle stability is maintained (Figure10a). The sideslip angle with the coupling locked is still higher than it is with theconventional vehicle because, as described in Section 2.2, at low decelerations theconventional vehicle's braking distribution is significantly more front biased than the idealdistribution. As discussed, with the coupling locked, the braking distribution will be closer tothe ideal curve and hence more braking torque is applied to the rear axle, as evidenced by thefact that the longitudinal slip of the inside rear is still higher than it is for the conventionalvehicle (Figure l0b).Raa)< ----------------------------- ------4 4.5 5 556 lime, sb)6 6.5 7 7.5 8Fg r 10 : Impact---F--------------- of locking---- cetr coupling--- du n a 20I -------- kph--- ope -----loop -brking-i-a-turmaour on 0.1 ------- Brake application --- at secons.----off-n-allcases------- In terms vehicle saIiy --- both souin have--- therefore.ben .shown.to.e.effectivetheFirstly,... locking.. in----- other-- aesteeaesgiiatdfeecsbwenhm. However, of------- centre ~ ~ avid ~~---- having couplin toreuc-te-eenraiv -bain- trqe-tan-pin.-o181example, in the braking in a turn manoeuvre described above, 53kJ of energy is recoveredwith the coupling locked whereas with the 20% slip threshold solution just 8kJ of energy isrecovered. Clearly, it is possible that more than 8kJ could be recovered if the regenerativebraking was controlled such that the longitudinal slip of the rear tyres was maintained at anacceptable level, rather than being simply switched off when a certain threshold wasexceeded. However the energy recovery would still not be as high as with the centre couplinglocked as the overall level of regenerative braking torque that can be applied is still limited bythe longitudinal force capacity of the rear axle. This would also be a significantly morecomplex solution to implement, as it would require the motor control to be integrated or atleast synchronised with the slip controls in the friction brake controller (ABS).However, locking the centre coupling also has disadvantages. The proposed solution implieslocking the coupling every time the driver applies the brakes and this will not always bedesirable for vehicle handling below the limit. There are also implications for ABS and ESPbecause with the coupling locked:\" The front and rear axle speeds are synchronised and this make it more difficult toaccurately estimate longitudinal slip.\" The ability of ESP and ABS to distribute friction braking torque to individual wheels islimited.For these reasons ABS and ESP algorithms normally require the coupling to be open whilstthey are active. This is generally not an issue in conventional vehicles because the coupling isable to open in sufficient time for ABS and ESP operation not to be effected. However, inthis case regenerative braking would also have to be switched off before the coupling could beopened and so the impact of the dynamics of the three actuators (motor, coupling and brakes)on the synchronisation with ESP/ABS would need further consideration.6 ConclusionIt has been shown that applying regenerative braking to the rear axle can degrade vehiclestability. For a given manoeuvre, the severity of this degradation is dependant upon motorsize and road surface friction coefficient. With a moderately sized motor it has been shownthat on high [t, reduction in stability can be contained by ESP without a large increase in ESPbrake pressures. However, on low gi the reduction is stability is much more severe and cannotbe compensated for with ESP. In order to resolve this issue two solutions have beenconsidered that effectively prevent regenerative braking from causing the wheels to go intohigh slip; firstly switching to friction braking once the longitudinal slip of either rear wheelexceeds a specified threshold and, secondly, locking the centre coupling. Both solutions haveproved to be effective from a vehicle stability perspective but locking the centre coupling hasthe advantage that it maximises energy recovery. However, before such a solution could beimplemented, further work would be required to assess the impact of locking the coupling onsub-limit handling and ABS/ESP performance. The influence of actuator dynamics on theeffectiveness of the solution also requires further consideration.7 AcknowledgementsThe authors would lie to thank Jaguar Cars Ltd and Land Rover Ltd for supporting thepublication of this paper.1828 References1. Gillespie, T. 'Fundamentals of Vehicle Dynamics,' SAE, 1992, pp. 60.2. Hancock, M. 'Vehicle Handling Control using Active Differentials', PhD thesis,Loughborough University, April 2006.3. Pacejka, H and Besselink, 1, 'Magic formula tyre model with transient properties,'Vehicle System Dynamics Vol. 27 No. 4, 1997, pp. 234-249.4. van Zanten, A. 'VDC, The Vehicle Dynamics Control System of Bosch,' SAE Paper9507595. Buschmann, G. 'Electronic Brake Force Distribution Control -A SophisticatedAddition to ABS,' SAE Paper 920646.List of FiguresFigure 1: Ideal brake force distribution.Figure 2: Drivetrain configuration of the considered vehicle.Figure 3: Actual friction brake force distribution employed in the vehicle modelFigure 4: Motor torque limit at the wheels as a function of speed.Figure 5: Braking torque distribution at 50kph.Figure 6: Driver workload during a 185m radius, 13Okph braking in a turn test. Brakeapplication at 10 seconds, ESP off in all cases.Figure 7: Driver and ESP workload during a 185m radius, l3Okph braking in a turn test.Brake application at 10 seconds, ESP on in all cases.Figure 8: Vehicle sideslip angle during a 20', 50kph open loop braking in a turn manoeuvreon g. = 0. 1. Brake application at 5 seconds.183Figure 9: Impact of using a slip threshold to disable regenerative braking during a 20', 50kphopen loop braking in a turn manoeuvre on gi = 0. 1. Brake application at 5 seconds. ESP offin all cases.Figure 10: Impact of locking centre coupling during a 200, 5Okph open loop braking in a turnmanoeuvre on g= 0. 1. Brake application at 5 seconds. ESP off in all cases.184

因篇幅问题不能全部显示,请点此查看更多更全内容