CONTROL ALTERNATIVES FOR YAW ACTUATED FORCE STEERED BOGIES. Scott Simson, Colin Cole. Centre For Railway Engineering, Central Queensland University

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1 Proceedngs of the 17th World Congress The Internatonal Federaton of Automatc Control CONTROL ALTERNATIVES FOR YAW ACTUATED FORCE STEERED BOGIES Scott Smson, Coln Cole Centre For Ralway Engneerng, Central Queensland Unversty Abstract: A new desgn for actvely steered boges (Smson S., 2007) has been proposed for tractve rollngstock to mprove not only wheel ral wear and rollng contact fatgue but to also mprove wheel ral adheson. The new boge desgn features forced steerng wth actve yaw control of the secondary suspenson. The control alternatves for the new boge desgn are lmted by the need for the control to act ndependently to wheel ral creep forces. Two control alternatves are presented, a full actve method where the control s appled based on known track algnment and the vehcles poston. And a sem actve method where the track curvature s estmated from gyroscope nputs wth no pror knowledge of the track and a target algnment s estmated. Copyrght 2008 IFAC Keywords: Applcaton of mechatronc prncples; Mechatronc systems; Modellng; Ralway Vehcle Dynamcs; Tran Dynamcs. 1. INTRODUCTION The steerng task for tracton curvng of ralway boges s sgnfcantly dfferent to the non-tractve or dle case. The dfference s due to the large longtudnal creep forces from tracton that saturate and dmnsh other creep force effects. Creep and creep forces s the phenomena of frcton between rollng contacts such as a wheel and ral. Rollng contacts have creepage and creep forces n three drectons, longtudnal, lateral and spn. Under hgh tracton loads for the ral frcton the moment forces due to longtudnal creep force dfferences that provde steerng and lateral forces due to spn creep that counter gravtatonal stffness are dmnshed. The deal for steerng boges perfect steerng (Goodall R. M., Me T. X. 2006; Goodall R. M., et. al. 2006) s no longer the mnmal wear soluton and s not applcable to haulng locomotves and the alternate concept of deal steerng has been proposed (Smson S. A., Cole C., 2007). Ideal steerng allows for dfferent longtudnal creep at the wheel contacts, whch has mnmal effect on the wheel ral wear rates, but allows offsettng of the lateral trackng poston so that lateral forces can be balanced by the lateral components of the normal wheel ral contact forces nstead of lateral creep forces. Ideal steerng requres the boge to control the steerng angle and boge yaw angle where as perfect steerng requres addtonal control of the wheelset angle of attack or warp angle, (see Fgure 1a). A new desgn for actvely steered boges (Smson S., 2007) (see Fgure 1b) has been proposed for tractve rollngstock to mprove not only wheel ral wear and rollng contact fatgue but to also mprove wheel ral adheson. Adheson beng the amount of tractve force acheved by the locomotve and s often a lmtaton to tran haulage performance. Improvng wheel ral adheson n curvng requres the steerng control to be ndependent of wheel ral creep forces so that all the avalable creep force can be used for tracton. The new boge desgn features forced steerng wth actve yaw control of the secondary suspenson. Forced steerng s a lnkage arrangement that forces the yaw angles of the wheelsets at the prmary suspenson to match the yaw angle of the secondary suspenson n radal algnment of the boge wheelsets /08/$ IFAC / KR

2 steerng have not consdered hgh tracton curvng cases where creep forces become saturated. Huntng nstablty whch any mode of wheelset lateral oscllaton those stablty decreases wth wheel concty and tran speed. Huntng s major lmtaton to the maxmum safe runnng speed of trans. The control task n actve steerng s both curve steerng and vehcle stablty. Secondary yaw actvaton control s a system whch controls the boge yaw angle by movng ether the bolster or boge frame wth no change n the steerng angle of the wheelsets. It can therefore be used to stablse boge huntng modes permttng the use of shorter boge axle spacngs. The man advantage n curve steerng n secondary yaw actvaton control s the reducton n peak lateral track shftng forces by balancng the lateral wheel forces on the two or more wheelsets n the boge. Lateral track shftng forces are the gross lateral forces transmtted to the rals by a wheelset that can cause ral sleepers to move. Fgure 1 Boge and wheelset angles nvolved n dealsed steerng and the three axle arrangement of a yaw actuated force steered boge (Smson S., 2007). Forced steerng boges are only partally dependant on creep forces for steerng, (Smson S. A., Cole C., 2008a; Smson S. A., Cole C., 2008b). As such the wear rate on tght radus curves under tracton wth forced steered boges only deterorates slghtly from the performance of deal steerng (Smson S. A., Cole C., 2008b). Early lnear modellng nvestgaton of the stablty of self steerng and forced steerng boge desgns dentfed a low frequency nstablty mode assocated wth low wheel conctes (Wckens A. H., 2003). Recent studes of force steered boges have dentfed mprovements n lateral wheel forces from ncreasng the steerng angle produced from boge yaw rotaton to exceed radal steerng, (Sato E., et. al. 2003). 1.1 Actve Steerng Research on actve steerng (Goodall R. M., Me T. X. 2006; Goodall R. M., et. al. 2006) has focused on actuated wheelset yaw (Schneder R., Hmmelsten G., 2004) and secondary yaw actvaton (Braghn F., et. al. 2006) wth prototype developments seen on both concepts targetng hgh speed passenger operatons. Theoretcal research has looked at the capabltes of ndependent wheel desgns and drectly steered wheels (Goodall R. M., et. al. 2006). Prevous nvestgatons on actve For secondary yaw actvaton total creep forces causng wheel ral wear are not greatly altered (Goodall R. M., Me T. X. 2006) though there s lkely to be some mprovement n tracton adheson due to reduced creepages present on the front wheelset. Studes on curvng adheson performance of ths concept have not been conducted. Actuated wheelset yaw control s a system whch controls the wheelset steerng angle wth no drect control of the boge yaw angle. It would also be possble to have a desgn that controls wheelset warp angle Fgure 1. The authors are not aware of any actuated wheelset yaw controller desgn that makes use of warp angle. The tracton steerng performance of actuated wheelset yaw boge depends on the controller used and the relance on creep forces to generate control. Controllers that are dependant on creep force nputs perform smlarly to self steerng boges (Smson S. A., Cole C., 2008b). Alternatvely actuated wheelset yaw controllers can be made to mtate forced steerng boges by elmnatng the dependence on creep forces as a control nput. 2. ACTUATED YAW FORCE STEERED (SIMSON) BOGIES A provsonal patent for a force steered boge wth a secondary yaw control system has been made (Smson S., 2007) coverng two and three axle varatons. The general confguraton of a three axle, yaw actuated, force steered boge s shown n Fgure 1b. The desgn features actuators on ether sde of the boge that control the yaw movement of the secondary suspenson and force steerng lnkages that control the yaw movement of the end axles to match the yaw movement of the secondary suspenson. Three axle force steerng can be mplemented n two alternatve forms, the dfference 8282

3 n the two boge desgns s the stffness n the lateral connecton of the mddle axle to the steerng arm. Optons range from a stff connecton (e.g sold bar) to soft connectons ncludng free floatng. Under deal steerng, correct boge trackng n a curve s acheved wth a combnaton of wheelset steerng angles and boge yaw angle (see Fgure 1a). The yaw actuated force steered boge (Smson S., 2007) has drect control of the boge yaw angle and the force steerng lnkages set the wheelset steerng angle. Ths s acheved wth the placement of actuators at or above the vehcle s secondary suspenson and wth potental redundancy from duplcate actuators gvng a sgnfcantly more robust desgn than actuated wheelset yaw permts. 2.1 Egen Mode Analyss An Egenvalue analyss has been conducted on the lnearsed vehcle models for Smson boge wthout actuator control. The Egenvalue analyss dentfed numerous dstnct modes nvolvng yaw or lateral movement of the wheelsets across the rals. Selected results form the Egenvalue analyss are gven n Table 1. It was noted that not all of these modes can be descrbed as huntng modes and only those modes that become unstable wth changes n runnng speed or concty are termed huntng modes. The unstable modes dentfed can be broadly classfed as: vehcle huntng; boge huntng; prmary suspenson huntng. All of these modes occur wth frequences under 7 Hz for the modelled vehcle. Addtonal modes nvolvng boge sway and yaw oscllatons of the wheelsets and steerng lnkages where dentfed at frequences above 12 Hz. None of these hgher frequency modes were unstable for speed or conctes tested. The vehcle huntng mode, Table 1 (note: conctes reported are and 0.05 for ths mode), can be dsmssed n that t s unstable only at low wheel profle conctes and then only f the boge rotaton frcton s made very low as was the case n the lnearsed model. The vehcle huntng mode operates well below the frequences of knematc wheelset oscllaton descrbed by Klngel (Wckens A. H., 2003). The vehcle huntng mode was prevously dentfed by Wckens Table 1. At lower speeds and conctes boge huntng modes for front and rear boges, are the same and are so heavly damped that they do return egenvalues for the model evaluated. As speed and concty ncrease the rear boge mode becomes dstnct wth a hgher frequency than the front boge huntng. Huntng of the front and rear boges are dfferent as the force steerng lnkage to the vehcle body on the rear boge steers the axles n the opposte drecton to the boge yaw moton. Consequentally both boge huntng modes yaw the vehcle body wth lmted connecton to the body sway motons. The Egen values for boge huntng vary between 2 4 Hz for a wde range of tran speeds ( kph), wth the crtcal speed beng dependant on wheel concty. There are several prmary suspenson huntng modes all of whch ether correspond or closely match the natural frequency for longtudnal oscllatons of the end axles on the steerng lnkages. That frequency for the tested vehcle model s approxmately 5 Hz. All of these modes go unstable at close to 250 kph n the lnearsed model except for the case when the mddle axle s dsconnected to the steerng lnks whch hunts at a lower speed. Actve control of any of these nstablty modes wth lnkage based forced steerng s unlkely as they are essentally oscllatons of the steerng lnkage connecton stffness. 2.2 Control Task Smson Boge As wth any actvely steered boge the controller has two prmary functons whch are curvng and stablty. The control target durng curvng for the Smson boge (Smson S., 2007) s to keep the boge yaw poston tangental to the rals. The controller must also control huntng and boge oscllatons wth frequences up to 4 Hz for the modelled vehcle. Table 1 Egenvalue analyss, undamped natural frequences and dampng rato 50 kph, λ = kph, λ = kph, λ = kph, λ = 0.50 Mode [Hz] [%] [Hz] [%] [Hz] [%] [Hz] [%] Vehcle Huntng * Front Boge Huntng Rear Boge Huntng Prmary Huntng A type Prmary Huntng B type End axle longtudnal oscllaton The concty (λ) for the vehcle huntng mode are and

4 The vehcle huntng mode, whch has frequences under 0.2 Hz for the smulated speeds, can probably be gnored as t lkely that passve frcton n the boges secondary yaw suspenson n real boge systems wll be suffcent to control ths mode. 3. CONTROL SYSTEMS Two control approaches are reported on n ths paper. Full actve control method (has pror knowledge of the track algnment) sensng boge frame msalgnments to a predetermned target yaw. Sem actve control method that uses a track curvature estmate based on sensng boge angular velocty wth tran speed and determnng msalgnments to a calculated target yaw whch s set by the track curvature estmate. The control feedback loop for both the full actve and sem actve control methods used n smulaton testng ncludes low pass flters to model sensor and actuator delays that would occur n actual mplementatons. Both the control nput and output sgnals are fltered wth a 3 pole 16 Hz low pass flter. Smulatons have also been done usng a feed forward controller to determne the boges ultmate capablty. Fgure 2 Control feedback for actve steerng smulatons The fnal control equaton (Equaton 1) s based on the calculated yaw msalgnment of the boge to the rals. Equaton 1 Fnal control equaton. X = G p X ψ G G t G p t s ψ + G d dψ dt + G t t s ψ dt Control for boge Msalgnment yaw boge Gan ntegral Gan dervatve Gan proportonal tme Integral tme 3.1 Full Actve Curvature Msalgnment Under full actve control track geometry data, determned for the track poston s used to determne a target yaw angle requred for each boge. Control s then determned by Equaton 1 based on the msalgnment to the target yaw, (Equaton 2). The stablty of ths control method depends on the phase shft poston of the control n relaton to the oscllaton response, (Tananfuj K., et. al. 2003). Dampng of the response s acheved wth the actuator force beng ¼ wavelength behnd the yaw msalgnment. The authors (Tananfuj K., et. al. 2003) use a half wavelength of knematc oscllaton for a phase shft delay of the control. Sgnal processng and actuator responsveness mean a proportonal control nput has a small phase shft delay to the yaw msalgnment and ncreases the huntng nstablty. Stablty of the Smson boge (Smson S., 2007) s thus obtaned wth a dampng force opposng the yaw msalgnment velocty (.e dervatve control). The dervatve control used has a negatve gan settng compared to proportonal gan on the steerng control. The stablty control feature therefore has a drect and negatve mpact on steerng control responsveness. Equaton 2 Full actve msalgnment. ψ = ϕ ϕt ( x) ψ Msalgnment yaw boge ϕ t (x) Yaw target algnment boge, a functon of x ϕ Measured yaw algnment boge x poston along the track The steerng task changes n curve transtons requrng good steerng responsveness, so t s n curve transtons where stablty control competes wth steerng control. The use of a yaw velocty dervatve (yaw acceleraton) can mprove the responsveness of the stablty control but a dervatve can not be appled to the steerng control. Determnng a target yaw for use n the curve transton s more dffcult than n the regular part of the curve. Artculated or force steered boges are notable for the curvng dffculty they experence n transton curves. The boge yaw angle requred for tangental algnment n transton curves s dependant on the changng curvature between the boges and the resultng steer angle of the wheelsets do not match the present curvature. To mnmse creep forces the Smson boge (Smson S., 2007) needs some angle of attack durng the transton n order to change the lateral poston of the wheelsets to and from a curvng algnment. The transtonal curve control can be mplemented wth a weghted curvature assessment where the curvature at each boge s used to determne a target yaw (see Equaton 3, Fgure 3). Ths method can be further adapted wth a delay factor where the curvature s determned for a pont ahead of the 8284

5 vehcles current poston thus gvng the boge an angle of attack throughout the curve transton. On a short transton (~6 tmes the boge sem spacng) usng a weghtng rato (n) of 3 and a delay factor of 1.3 tmes, the boge sem spacng of X m, has gven mnmumm wear energy n smulaton usng deal steerng as the control target. Further work s requred to assess the optmal steerng target yaw for a range of transton curves. Fgure 3 Target yaw calculaton Equaton 3 Boge 1 target yaw angle. ϕ = A t1 n C x + C x n +1) ( 1( ) ( )) ( ϕ t Target yaw boge (1 or 2) A Boge sem spacng C (x) Curvature at boge (1 or 2) centre poston, a functonn of track poston n weghtng rato for boge curvature 3.2 Sem Actve Estmated Curvature Msalgnment Actve steerng wth curvature estmaton has been mplemented n a smulaton of a prototype secondary yaw control boge (Braghn F., et. al. 2006). In practce gyroscopes can be mounted to provde the yaw velocty of the boge and the vehcle body so these measurements, together wth the tran speed, allow the nstantaneous curvature to be estmated. The control can then be appled based on the boge msalgnment to a estmated target yaw, Equaton 4. In such as system, there s the problem that boge yaw velocty could also be due to lateral boge frame oscllatons or a huntng nstablty descrbedd n secton 2.1 gvng a unstable feedback loop. The presence of yaw velocty dependent term n Equaton 4 creates addtonal feedback to the full actve method. 2 steerng yaw angle s opposte to the curvature. The vehcle huntng mode (secton 2.1) s also not excted by the curvng estmates as the yaw veloctes are to low. At very hgh speeds, vehcle huntng could be excted by the curvng control however such speeds are unlkely, for the locomotves smulated, due to prmary suspenson huntng modes. Equaton 4 Sem actve msalgnment. dϕ ψ = ϕ ϕ e dt ψ Msalgnment yaw boge ϕ e Yaw algnment estmate boge ϕ Measured yaw algnment boge x poston along the track t tme Yaw velocty oscllaton for: the vehcle body; the front boge; and the rear boge are shown n Fgure 4 together wth the boge yaw oscllatons durng hgh speed huntng nstablty smulaton. A modfed yaw oscllaton for each boge s also shown n Fgure 4 whch s boge yaw velocty wth the boge to body relatve yaw angle velocty subtracted. The body yaw velocty s the most stable curve estmate nput to the front boge huntng. The alternatve would be to flter nput for curve sensng wth a low pass flterng to remove the 2-4 Hz frequency of the boge huntng modes. All these curve sensng approaches place consderable delay to determnng the start of curve transton for the lead boge. The body yaw acceleraton can be used wth a low pass flterng to remove nstablty effects, to dentfy the change n curvature durng the curve transton. The yaw acceleraton has to be dvded by tran velocty to gve change n curvature per unt length. Together wth the body yaw velocty used to dentfy the track curvature under the vehcle we can now estmate the change n curvature under the vehcle. The target yaw for each boge can then be set based on the estmated current track curvature and estmated change n track curvature. The flterng requred on the estmate of change n curvature wll cause some trackng errors at the ends of the transton curve. Durng curvng, the lateral oscllatons on the front boge are detrmental to the control as addtonal yaw s requred n the same drecton to match a calculated target yaw. The rear boge huntng mode, however, s damped by the steerng control as the 8285

6 reducng steerng performance on curvature entrances and exts. ACKNOWLEDGEMENTS Ths research has been founded and supported by the Central Queensland Unversty. The vehcle dynamcs modellng has used VAMPIRE verson 4.32 suppled by DeltaRal. REFERENCES Fgure 4 Boge and Body Yaw Velocty Durng Huntng 4. CONCLUSIONS The control problem for all steerng boge desgns must be a trade-off between the lateral stablty performance and the curve transton performance. Lateral stablty of actuated yaw force steered boges at hgh speeds requres the boge huntng mode to be controlled. To control boge huntng the yaw velocty of the boge has to be damped. The front boge of a actuated yaw forced steered vehcle, the same yaw dampng ressts boge algnment on the curve entrance transton. Sem actve control faces added challenges of detectng curve transtons and dstngushng curvng from lateral nstablty movements. Improved steerng control s acheved wth systems that estmate both the curvature and the change n curvature usng the vehcle body yaw acceleraton. Front boge huntng nstablty requres the use of low pass flterng of the change n curvature estmatons based on body yaw acceleratons. The flterng delays ths nput sgnal Smson S., Ralway Boge, (2007), Australan Provsonal Patent Applcaton No Smson S. A., Cole C., (2007) Idealsed Steerng for Haulng Locomotves, Rals & Rapd Transt, Part F Proceedngs Insttute of Mechancal Engneers, UK., Vol. 221, No. 2, pp Goodall R. M., Me T. X. (2006) Chapter 11 Actve Suspensons, Handbook of Ralway Vehcle Dynamcs, Ed. Iwnck S., Taylor & Francs Group, Boca Raton, FL, USA Goodall R. M., Brun S., Me T. X. (2006) Concepts and prospects for actvely-controlled ralway runnng gear, Vehcle Systems Dynamcs, Vol. 44, Supplement 1, pp Taylor and Francs. Smson S. A., Cole C., (2008a) Smulaton of Tracton and Curvng for Passve Steerng Haulng Locomotves, Rals & Rapd Transt, Part F Proceedngs Insttute of Mechancal Engneers, UK., (Preprnt) Smson S. A., Cole C., (2008b) Parametrc Smulaton Study of Tracton Curvng of Three Axle Steerng Boge Desgns, Vehcle Systems Dynamcs, Vol. 46, Supplement 1, (pre prnt) Taylor and Francs. Wckens A. H., (2003) Fundamentals of ral vehcle dynamcs: gudance and stablty, Swets & Zetlnger B.V., Lsse, The Netherlands. Sato E., Kobayash H., Tezuka K. (2003) Lateral Force durng Curve Negotaton of Forced Steerng Boges, Quarterly Report or Ralway Technology Research Insttute, Vol. 44, No. 1, pp 8-14 RTRI Japan. Schneder R., Hmmelsten G., (2004), The Mechatronc Boge State of Development, Proceedngs 6th Internatonal Conference on ralway boges and Runnng Gears, Budapest, Sept. 2004, pp 23-32, Department of Ralways Vehcles, BME, Budapest. Braghn F., Brun S., Resta F., (2006), Actve yaw damper for the mprovement of ralway vehcle stablty and curvng performances: smulatons and expermental results, Vehcle System Dynamcs, Vol 44, No.11 Nov 2006, pp , Taylor & Francs Tananfuj K., Sato T., Goodall R., (2003) Actve steerng of a Ral Vehcle wth Two-Axle Boges Based on Wheelset Moton, Vehcle System Dynamcs, Vol. 39, No. 4, pp , Taylor & Francs 8286