Measurement of Tractive Force in the Creep Region and Maximum Adhesion Control of High Speed Railway Systems

Transcription

1 Measurement of Trative Fore in the Creep Region and Maximum Adhesion Control of High Speed Railway Systems Atsuo Kawamura (Yokohama National University, Japan) Meifen Cao (Corporation for Advaned Transport & Tehnology, Japan) Yosuke Takaoka, Keiihi Takeuhi,Takemasa Furuya, KantaroYoshimoto (Yokohama National University, Japan) Abstrat The aeleration and deeleration rate of the train depend on the trative fore. When the wheels of the train slip on the rails, the torque is dereased to avoid the ontinuous slipping. This reason is that the trative oeffiient between the wheels and the rails has a peak at a ertain slip veloity. But this adhesive phenomenon is not learly examined or analyzed. Thus we have developed a new adhesion test equipment.in this paper, we measured the trative fore with this equipment, and larified the adhesive phenomenon. Then we proposed a new trative fore ontrol and verified the effetiveness of the proposed ontrol sheme. 1. Introdution The strong demands for Shinkansen are the speed up of the trains, and the inrease of the passenger transportation apaity while preserving the safety of high-speed railway systems. One possible approah for this is to enhane the speed adjustment apability. The end results are 1) the safety will be improved by reduing the distane for the urgent stop, 2) the train running density an be improved by inreasing the average speed for the existing lines with many urves, that is alled the high-density-sheduling. Generally, the speed adjustment performane an be enhaned through inreasing driving or braking fore that is mostly ahieved by the maximum adhesion fore between wheels and rails. It is said that the trative fore between the wheel and the rail depends on the slip veloity between the wheel and the rail. And it is also said that this trative fore inreases when the slip veloity inreases a little, but if the slip beomes too large, it now goes down. However, it seems that there is no elaborated paper in whih this phenomena were atually measured under the repeatedly measurable and reproduible onditions [1]~[3]. In [2], [4], the measured data on the peak of the trative oeffiients have large variations. On the other hand, there are a number of papers on the re-adhesion ontrol. In [4], under the assumption that the trative fore has a peak at a ertain slip veloity, the slipping ondition was estimated from the slip veloity, and the torque was redued. In [5], the motor speed referene is redued for re-adhesion. In [6], this approah was improved, and the torque harateristi of the motor has the drooping. Also in [7], the slip referene speed is adjusted based on the error of the atual slip and the slip referene. In [8], the slipping was deteted from the slip speed of the multiple axles, and the trative fore was estimated. As a result, a sophistiated anti-slip re-adhesion

2 ontrol was proposed and tested in the atual trains. In [5]~[8], the slipping was estimated from the slip veloity. However in [9]~[12], the trative fore was diretly estimated by the disturbane observer, and the avoidane of the slipping and the use of the maximum adhesion fore were proposed. In [9], [10], from the division of the derivative of the estimated trative fore based on the observer and the derivative of the slip veloity, the derivative of the trative oeffiient was alulated, and the maximum trative fore ontrol was proposed. In [11], [12], also from the derivative of the estimated trative fore based on the disturbane observer, the anti-slip ontrol was proposed. In [9]~[12], only the simulation results were presented. In this paper, the following will be desribed. (1) The preise measurement method for the trative fore and the trative oeffiient are proposed, and these values are repeatedly measured by the newly developed adhesion testing equipment. Through the measurements, it is onfirmed that the trative oeffiient has a peak at the ertain slip veloity. (2) Based on the proposed real time trative fore measurement method, a new maximum trative fore ontrol is proposed, and the proposed approah was verified through the test equipment. (3) Future problems on the proposed approah are summarized, and the road map for the further developments for this approah is larified. The hapter 1 is the introdution of the paper, and in the hapter 2 a new measurement method of the trative oeffiient is proposed, and using the newly developed adhesion test equipment the measured data are shown. In the hapter 3 a new maximum trative fore ontrol is proposed and verified by the test equipment. The hapter 4 is on the disussions and the hapter 5 onludes this paper. 2. Proposal of the Trative Coeffiient Measurement 2.1 Mathematial Model for Trative Fore Measurement For the measurement of the trative fore, one axle model as shown in Fig.1 is assumed, and the following differential equations are proposed [9]. Fig. 1: One axle train model. dω J = Te Fr Bω (1) dt

3 dv 2 M = F Cv dt (2) F = µmg (3) where T e is the input motor torque, ω is the motor speed, v is the train speed, F is the trative fore, µ is the tration oeffeient, and g is the gravity aeleration. Other parameters are shown at Table 1. Table 1. Parameters for simulations. J R B M C Wheel inetia Wheel radius Visoity frition Train mass Aerodynami oeffiient (kg m 2 ) (m) (kg m/se) (kg) (se 2 /m 3) The slip veloity is defined as the absolute value of the differene between the train body veloity and the wheel veloity, as follows. slip = ω r v (4) The following state equation is obtained if the trative fore F hanges as a step funtion. B d ω 1 ω 1 J J + J Te dt T = L T (5) L where the trative torque T L = Fr (6) If the wheel angular veloity is measurable, the following output equation is obtained. ω = [ 1 0][ ω T ] T L (7) Equation (5) and (7) are observable, and the state variables an be observed. Thus, the minimal order observer is derived as follows [13]. T ˆ ω L = [ Te ( J ns Bn ) ω] s + ω + (8) where the suffix of n denotes the nominal value. Also the ω an be free parameter and it is the pole of the observer. The above-mentioned algorithm was reported in [9],[10] by authors; however, the experimental measurement was not done yet. 2.2 The Adhesion Test Equipment and Parameters The Adhesion Test Equipment The adhesion test equipment was developed for larifiation of the adhesion phenomena and also for the preise measurement of the trative fore. The size of the setup is one eight of the atual Shinkansen wheel. The outlook is shown in Fig.2 and the funtion blok diagram is in Fig.3. The material of the setup is the same as the Sinkansen wheel and rail. The diameter of the train wheel (train wheel for abbreviation) is one eight of the atual train wheel. And the rail is represented five times larger diameter wheel (rail wheel for abbreviation) as shown in Fig.4. The detailed parameters

4 are listed in Table 2. The 1:8 redution gear is installed between the rail wheel and rail side driving motor. The axle weight is ontinuously ontrollable by the servomotor. Fig. 2: Adhesion test equipment. Fig. 3: Funtion blok of the adhesion test equipment.

5 Fig. 4: Train(upper) and rail(lower) wheels. In this paper, all data are based on the rude data in this adhesion test equipment. For example, the speed 10 km/h of the train wheel is effetively 8 times larger in the atual model, that is 80 km/h. In this setup the maximum speed is designed to be 40km/h or the 8 times larger equivalent train speed of 240 km/h Parameter Measurements For the estimation of the trative fore Tˆ L in (8), the inertia J n, the visosity frition onstant B and the observer pole ω are required. The ω is seleted by the trial and error approah in the experiments, and the other two parameters are seleted as follows. Table 2. Parameters for experiment equipment Length Width Height Total weight Train side motor Rail side motor Rated torque Train side maximum revolution Rail side maximum revolution Train side wheel diameter Rail side wheel diameter Maximum load 3106(mm) 107.5(mm) 1115(mm) 2000(kg) 7.5(kw) 7.5(kw) 47.7(Nm) 1600(rpm) 2500(rpm) 107.5(mm) 537.5(mm) 686(N)

6 As for the B ω, first the train wheel was rotated until the motor temperature beomes the onstant without ontating the rail wheel. Seond, the speed referene is inreased from zero to the high speed. Under the steady state, the speed and the torque referene of the inverter were measured at several speed points. As a result, the B=0.07(N m se/rad) was obtained. As for the J, the following proedure was employed. In equation (1), if F = 0 or without ontating the rail wheel, and the train wheel is aelerated or deelerated at the onstant rate, the speed inrease ω and speed derease ω an be expressed in the next equations. 1 t1 ω = ( Te Bω) dt J (9) t0 1 t2 ω = ( Te Bω) dt J (10) t1 where [ t 0, t 1 ] is the aeleration period and [ t 1, t 2 ] is the deeleration period. By ontrolling the inverter it is easy to make t1 t0 = t2 t1 and the veloity hange rate is the same. The subtrating equation (10) form (9) yields the next equation. 1 t1 t2 2 ω = ( Tedt Tedt) (11) J t0 t1 Under the assumption that the torque referene of the inverter is the same as the atual torque, the inertia was obtained to be J=0.021(kg m 2 ) from equation (11). 2.3 Measurement of the Trative Fore and the Trative Coeffiient From the steady state that the both wheels are rotating at the same surfae veloity under the ontat, the torque of the motor of the train wheel was suddenly inreased, and the slipping was generated. The trative fore was measured by the disturbane observer in (8). The trative oeffiient is alulated by the division of the estimated trative fore and the axle weight based on the definition in (3). The ω is 100 (rad/se). The results are shown in Fig.5 ~ Fig.7. Fig.5 depits the trative oeffiient and the slip ratio, Fig.6 and Fig.7 denotes the motor torque and train wheel speed, in whih the symbols (+!) show the lapse of time. If we repeat this experiment, the wheel surfae is terribly damaged by the instantaneous heat, thus we also aelerate the rail wheel by the following equation, whih means that the mass M of the train is aelerated by the estimated trative fore. 1 Tˆ L ω rail = dt (12) 2 r weight g On the other hand, the slip ratio in the horizontal axis in Fig.5 is alulated from (4), however, in this figure the alulated slip ratio is the output of the low pass filter of the ut-off frequeny ω, whih is the same as the observer pole. This reason is that sine the estimated trative fore is obtained through the low pass filter, both trative fore and slip veloity should have the same time delay. Fig.5 implies that the maximum trative oeffiient is about 0.28 around the slip ratio of Above this slip ratio the

7 trative effiient gradually dereases. This tendeny was observed through various experiments with different axle weight and different train speed. Fig. 5: Trative oeffiient (axle weight 500 N). Fig. 6: Motor torque.

8 2.4 Disussion of the Measurement Fig. 7: Wheel and slip veloity. To enhane the auray of the measurement of the trative fore, the following points should be more elaborated. (1) The preise measurement of the visosity frition B ω (2) Measurment under the onstant speed of the rail wheel (3) Additional measurement of the tray loss suh as wind loss of the wheels (4) Chek the influene of different axle weight (5) Chek the influene of the steady state speed of the rail wheel just when the torque is suddenly inreased (6) Large variation of the trative oeffiient by the water wet surfae ondition As for (1), the measured Bω is shown in Fig.8, in whih the B is not onstant. At present the experimental data were taken under the almost onstant B region, however, the B should be on line hanged to have more preise trative oeffiient. As for (2), the surfae of the iron wheels was worn out in this ondition, thus we quitted this setting. We measure the (3), but it was very small and negligible. As for (4) and (5) we had the very similar urve like Fig.5. We will investigate more on (4), (5) and (6).

9 Fig. 8: Parameter 3. Maximum Trative Fore Control 3.1 Proposed Algorithm B ω. The trative oeffiient has a peak in terms of the slip veloity as shown in Fig.5, thus the maximum trative fore an be available at the point when df / dslip = 0. The following approximation is assumed. df dfˆ dslip / (13) dslip dt dt To alulate the d F ˆ, the quasi-derivative ( sg, g = 100 ) of the estimated trative dt s + g fore is proposed [15]. The value of g is heuristially seleted so as to redue the effet of the noise. In [9], [10], the derivative of the trative fore is modeled as a part of the state equation, and this value is estimated by the full order observer, however, dslip it is sensitive to the noise around the peak of the trative fore. Also is diretly dt alulated from the veloity of the train and rail wheels, but as mentioned in setion 2.3, it is low pass filtered with the ut off frequeny of ω, and quasi-derivative is taken. The optimal slip veloity whih makes the trative fore maximum is generated in the slip referene generation blok as shown in Fig.9.

10 Fig. 9: Blok diagram of maximum trative fore ontrol. The optimal proedure is based on the steepest gradient method as follows. df (1) ˆ df is alulated from ˆ dslip and dslip dt dt dfˆ (2) The slip veloity referene is slipref ( k + 1) = slipref ( k) + α, where α is a dslip 5 onstant, and in the experiment it was seleted as (3) go bak to (1) Dividing the sum of the train speed and slip veloity by the radius of the train wheel generates the motor speed referene. The motor speed regulation is done by the PI ontroller. The features of this proposed algorithm are (1) trative fore is diretly alulated by the disturbane observer, (2) the optimal slip veloity is generated as the referene, (3) steepest gradient method is used for optimization. 3.2 Verifiation by Experiments The proposed algorithm was tested using the adhesion test equipment as mentioned in Chapter 2. In the experiment the train speed is needed, thus using (2), the train speed was alulated by the omputer in real time. The train mass is seleted as the axle weight divided by the gravity onstant g. The axle weight was hanged in several ases, however similar urves were observed, thus one of the typial available trative oeffiient with the axle weight 400(N) is shown in Fig.10.

11 Fig. 10: Avaliable trative oeffiient. The initial slip referene was given as 1 km/h and the proposed maximum trative ontrol was begun at t=0(s). It is observed that the most of the trative oeffiients were loated around the peak region. In this experiment a pulse sensor of 1024 (ppr) was used, however, in the existing train system usually 60 (ppr) sensor is widely installed. In the referene [17], the simulation studies of 60 (ppr) sensor was performed and the very good results were obtained in the mid and high speed region. Due to the hardware modifiation in the experiments, the final results with 60 (ppr) sensor will be shown at the onferene. From Fig.10 it is onfirmed that the maximum trative fore is atually realized in the experiments based on the proposed algorithm. 3.3 Disussions on the Maximum Trative Fore Control We believe that there are following items that we should investigate more. (1) In the very low speed region, the pulse from the pulse sensor is very little, thus the train speed estimation is diffiult, whih, in turns, makes the trative fore estimation diffiult. (2) If the trative fore hanges very muh, the effetiveness of the propose algorithm is not yet heked. As for (1) we are investigating in [16], and if less than one pulse is observed within one sampling interval, the instantaneous speed observer looks very attrative. As for (2) we will make experiments, however, in simulations the validity of the proposed algorithm was heked in [17].

12 4. Disussions The future problems for the measurement and ontrol were already mentioned in setion 2.4 and 3.3. As we reviewed the literatures in the introdution, the diret estimation of the trative fore is relatively new approah in the train field, however, in the field of tration ontrol of eletri vehiles, it was already reported to be measurable [18]. In ase of the rubber tire, the slip ratio beomes larger when the trative oeffiient has a peak ompared with iron wheels. And it was reported that it was observed that the trative fore had a peak at a ertain slip speed. Very important information for the diret measurement of the trative fore is the exat values of parameters, and also the train veloity. The following future problems should be investigated. (1) How to measure the preise values of inertia J and visosity frition B and the train speed v. Or new approah to estimate the slip veloity without the train speed [19]. (2) Train speed estimation at the very low speed region (3) Theoretial equation for the trative fore (4) Tested data at the atual Shinkansen trains Authors are investigating the above targets, however, due to the limitation of the available spae those will be reported at the next opportunity. 5. Conlusions First, the preise measurement method for the trative fore is proposed, and these values are repeatedly and re-produtively measured by the newly developed adhesion testing equipment. Through the measurements, it is onfirmed that the trative oeffiient has a peak at the ertain slip veloity. Seond, based on the proposed real time trative fore measurement method, a new maximum trative fore ontrol is proposed, and the proposed approah was verified through the testing equipment. Third, future problems on the proposed approah are summarized, and the road map for the further developments for this approah is larified. Referenes [1] Oyama: "High speed and high adhesion" (in Japanese),RRR,pp.9-14,1994 [2] Uhida, Oyama, Nomura: "Appropriate brake based on adhesin harateristis''(in Japanese), RTRI report, Vol.14, No.5, pp.5-10, 2000 [3] W.D.May, E.L.Morris, D.Atak: ''Rolling frition of a hard ylinder over a visoelasti material'', Applied Physis, Vo.30, No.11, pp , 1959 [4] F.Kok,M.weinhardt: ''Trative effort and wheel slip ontrol of loomotive type 120'', IFAC, pp , 1987 [5] S.Anderson,J.Shwartz: ''Digital simulation of an inverter fed indution motor loomotive drive with wheel reep ontrol'', Eletrial Drive Symposium, Capri, pp , 1990 [6] Hariyama, Hoshi, Nakmura, Toda, Nakazawa, Yuki, Tkahara: ''Wheel slip and readhesion ontrol by indution motor vetor ontrol for high speedshinkansen''(in Japanese), IEE of Japan JIASC, pp , 1997

13 [7] Sekimoto, Nakamura, Mohizuki, Toda, Takahara: ''Wheel slip amd re-adhesion ontrol for high speed shinkansen train - for individualmotor ontrol system''(in Japanese), IEE of Japan Trans.D, Vol.116, No.7, pp , 1996 [8] Yamanaka, Watanabe, Hariyama, Nakamura: ''Anti-slip readhesion ontrol with presumed adhesion fore'' (in Japanese), IEE of Japan Trans.D, Vol.119, No.2, pp , 1997 [9] Y.Ishikawa, A.Kawamura: ''Maximum adhesive fore ontrol in super high speed train'', PCC-Nagaoka, pp , 1997 [10] Ishikawa: ''Theoretial analysis of adhesion ontrol for high speed trains'' (in Japanese), Yokohama National University Graduation Theses, 1996 [11] Ohishi, Nakano: ''Anti-slip ontrol of eletri motor oah using adhesion fore oeffiient estimator based on disturbane obsevers'' (in Japanese), IEE of Japan, JIASC, No.71, 1998 [12] Ohishi, Ogawa, Nakano, Miyashita, Yasukawa: ''An approah of anti-slip readhesion ontrol of eletri motor oah based onfirstorder disturbane obsever'' (in Japanese), IEE of Japan, JIASC, No.117,1999 [13] Ohnishi: ''Robust Control based on the disturbane observer'' (in Japanese), Journal of Robotis Soiety of Japan, Vol.11, No.4, pp , 1993 [14] Takeuhi, Takaoka, Yoshimoto, Cao, Kawamura: ''Solution Experiment of Adhesive Phenomenon by Testing Equipment for Shinkansen'' (in Japanese),IEE of Japan, SPC, SPC-01-37,2001 [15] Takaoka, Kawamura: ''Maximum adhesive fore ontrol in high speed train based on seond-order differentiation of slip frequeny'' (in Japanese), IEE of Japan, IIC, IIC , 2000 [16] Cao, Takaoka, Kawamura: ''A Proposal of Adhesion Control using Disturbane- Instantaneous Speed Observer and Train Speed Estimation'' (in Japanese),IEE of Japan, National Convention, 5-267, 2001 [17] Takaoka, Kawamura: ''Maximum adhesion ontrol for eletri ars with onsideration the quantization of motor shaft sensor emits sixty pulse per revolution'' (in Japanese), IEE of Japan, IIC, IIC-01-5, 2001 [18] Sado, Sakai, Uhida, Hori: ''Tration Control for Eletri Vehile based on Road Condition Estimation and Slip Ratio Control'' (in Japanese), IEE of Japan, JIASC, No.283, 1998 [19] Yoshimoto,Takaoka,Takeuhi,Kawamura: ''Wheel Slip Ratio Estimation without Train Veloity'' (in Japanese), IEE of Japan, National Convention, 5-265, 2001