PAPER Brakng Force Estmaton of Each Car Dasuke HIJIKATA Brake Control Laboratory, Vehcle Control Technology Dvson Toshharu NISHIMURA Brake Control Laboratory, Vehcle Control Technology Dvson (Former) Generally brakng performance of tran sets s evaluated by stoppng dstance or deceleraton. However, stoppng dstance and deceleraton are performance ndces establshed for a whole tran set, and do not represent performance of each car ndvdually. For more detaled analyss of detal brakng performance, t s useful to have the brakng force n each car. Ths paper descrbes a method desgned to estmate the brakng force n each car based on the acceleraton and coupler force, by usng couplng devces as force sensors. Runnng tests results on an 8-car freght tran usng the devsed method showed that t was possble to estmate the brakng force of each car and that the estmated was close to the theoretcal. Keywords: brakng performance, stoppng dstance, deceleraton, brakng force, coupler force. Introducton Brakes are extremely mportant devces used for deceleratng and haltng trans, and ther performance must therefore be fully understood. Brakng performance, frequently evaluated through stoppng dstance and deceleraton, s typcally udged n the case of conventonal ralway lnes from the dstance requred for trans to brake for an emergency, from the maxmum commercal runnng speed. The procedure used to test brakng performance also reflects brakng performance durng operaton. The method also saves tme and effort, because t measures the sngle-axs velocty of trans. Gven these advantages, ths method could be consdered to be a fundamental method for measurng brakng performance. Stoppng dstance and deceleraton however only gve an ndcaton of brakng performance for a whole tran set, and do not gve any nsght nto the brakng of ndvdual vehcles. If the fnal brakng dstance s the same for two cases beng compared, t s mpossble to tell f deceleraton was gradual and smooth throughout the tran set n one case or f there was a sudden drop n one vehcle n the other. Whereas n realty, tran sets have varyng characterstcs and contan dfferent vehcle types. Therefore, n order to further mprove brakng performance and relablty, t s crtcal to be able to get a more detaled pcture of actual brakng performance, based on ndvdual vehcles. As part of efforts for ths problem, the followng methodologes are tred out: determnng one-wheel or one-axle brakng force by measurng the forces actng on the brake shoe hanger n the foundaton brake [,2], and calculatng one-boge brakng forces by focusng attenton on the tractve force actng on a sngle lnk connectng the vehcle and the boge [3]. Ths study offers a procedure to estmate the brakng force on an arbtrary vehcle n a tran set by applyng a vehcle coupler as a sensor usng the force actng on t (coupler force, herenafter) and the vehcle acceleraton [4]. Ths paper frst proposes a dynamc model to estmate the brakng force from the coupler force and acceleraton. Then, test results from applyng ths procedure to actual freght trans n operaton are addressed. 2. Brakng force actng on each vehcle n a tran set In a tran comprsng n vehcles, a model dagram of the forces actng on each deceleratng vehcle n consderaton of only the longtudnal movement s sketched n Fg. (a) wth symbol defntons lsted n Table. The knetc equaton wth multple-degree of freedom systems connected by sprngs and dampers s defned as (). Mx + Cx + Kx = f () Where, M s a mass matrx n response to each vehcle, C attenuaton matrx of dampers, K rgdty matrx of sprngs, x, x, and x are vectors respectvely of deceleraton, velocty, and dsplacement. f s an external-force vector, showng here a brakng force actng on each vehcle. Each vehcle n a tran set ndvdually exerts a brakng force to decelerate tself and transmts the force va the buffer and coupler to the neghborng vehcles. Whle sprngs and dampers act on buffer rubbers popularly used, sprngs partcularly exhbt non-lnear rgdty that gradu- Symbol Table Symbol defnton Defnton m, M Vehcle mass x k c Dsplacement Sprng constant Attenuaton coeffcent f, F Brakng force R Coupler force Acceleraton 98 QR of RTRI, Vol. 57, No. 2, May 26
Travelng drecton No. vehcle k No. 2 vehcle k 2 k n-2 No. n- vehcle k n- No. n vehcle x m m 2 c x f f 2 x 2 x 2 c 2 x n m n- c n-2 x f n- n- x n m n c n- x n fv (a) Multple-degree of freedom model Travelng drecton No. vehcle No. 2 vehcle No. n- vehcle No. n vehcle m R m 2 R 2 R n-2 m n- R n- m n f f 2 f n- f n (b) Smplfed model Travelng drecton Head vehcle(locomotve) Intermedate vehcle (No. freght car) No. freght car ) Intermedate vehcle (No. freght car) Tal vehcle (No. freght car ) M R m R 2 R R + m m R F f f f Σm, Σf (c) Locomotve and freght-car model Fg. Model dagrams of the forces actng on each vehcle ally ncreases wth dsplacements. In order to handle the brakng force for each vehcle as a dynamc model wth multple degree of freedom, a precse model capable of descrbng t and numercal smulaton are requred. References [5-8] have been reported as the research handlng these ssues whch employ a model addressng translaton and rotaton of wheelsets, boges, and vehcles after precse consderaton of the non-lnearty of sprngs and accompanyng components. These studes, amed at bucklng analyss and reducton of maxmum coupler forces, have collected many fndngs on the coupler-force response wth a certan level of brakng force (or acceleraton force) as an nput, by comparng the coupler-force smulatons wth actual measurements. Aganst formal-order analyses that smulate the system moton from an external force n a knetc equaton, however, the reverse analyss estmatng the nput from actual measurements lke ths study needs pre-known parameters and movements to solve t. The output however may be msleadng, dependng on the measurement results (3 requrements must be satsfed: exstence, unqueness, and contnuty of soluton). As t s not easy through such an approach to estmate the brakng force on each vehcle, a procedure compatble for both practcal use and precson s preferable. Model smplfcaton as shown n Fg. (b) s then consdered on the followng premses. If the brakng force actng on each vehcle has steady s (the s themselves for each vehcle can dffer), the relatve movement of each vehcle should converge once a certan perod passes, physcally resultng n ts equal acceleraton. Defnng the acceleraton of the whole tran set as and further assgnng the sum of matrx terms of attenuaton and rgdty as R (coupler force), the brakng force at each vehcle s expressed as (2). f k mk Rk ( k = ) = mk + Rk Rk ( < k < n) mk + Rk ( k = n) Where, Suff. k and n are natural numbers satsfyng k n, and (2) mples head, ntermedate, and tal vehcles n top-to-bottom order. The acceleraton takes a negatve as a deceleraton. When the tran runs through an nclned secton, a slope-converted should be assgned as for the secton correspondng to horzontal runnng. When runnng resstance s n consderaton, the runnng resstance correspondng to the vehcle runnng should be deducted from the rght member of (2). A freght tran comprsng a locomotve postoned at the head and other freght cars as shown n Fg. (c) s consdered here. Renamng the locomotve mass and brakng force as M and F to dstngush the symbol of the locomotve from those for freght cars, t s expressed as (3), (4). (2) F = M R (3) f m R R = + < + ( ) m + R ( = ) Meanwhle, takng the grand sum of the equatons for all freght cars, (5) s derved from Σ f (total brakng force) (4) QR of RTRI, Vol. 57, No. 2, May 26 99
and Σ m (total mass of freght cars). f = ( m ) + R (5) = = The above tells that the brakng force for the locomotve s determned from ts mass, acceleraton, and the neghborng coupler force, smlar for the total brakng forces of freght cars. It s also found that the brakng force on an ntermedate vehcle s calculated from ts mass, acceleraton, and ts neghborng two coupler forces. 3. Verfcaton through runnng tests 3. Test process Usng the test trans (Fg. 2) consstng of a locomotve (DF2 type) and contaner-freght cars (4 and 6 types), runnng tests were conducted. Fgure 3 gves an outlne. A 6-vehcle tran consstng of locomotve and 5 freght cars was frst tested to assess the applcablty of ths procedure. Then, usng an 8-vehcle tran ( locomotve + 7 freght cars), estmaton of breakng forces wth ths procedure was studed n comparson wth theoretcal data and an estmaton was made of the brakng force of an arbtrary freght car. The mass of each car was adusted to smulate full-loaded condtons, by usng dead weghts. Coupler forces (+ for tensle and - for compressve) were measured by equppng the couplers wth stran gauges. Velocty was calculated from the wheel revolutons of the locomotve. Acceleraton was measured wth sensors whch mounted on the locomotve and the frst freght car (rght behnd the locomotve). Brakng force was estmated for the locomotve usng ts own acceleraton and for freght Fg. 2 Test tran cars by that of the frst freght car. 3.2 Test wth locomotve + 5 freght cars 3.2. When only locomotve brakes are appled Fgure 4 shows results for velocty, acceleraton, coupler force, and estmated brakng force when applyng 2-notch brakng only on the locomotve (ndependent brake, herenafter) at tme s from the ntal velocty of 25 km/ h. Ths operaton, causng only the locomotve to decelerate, makes the followng freght cars push the locomotve. A compressve force s therefore exerted on the coupler between the locomotve and freght cars. The coupler force actually measured exhbts ths trend, showng that a com- Travelng drecton Locomotve No. freght car No. 2 freght car No. 5 freght car M m m 2 m 5 F f f 2 f 5 Measurement tems Velocty Acceleraton R Coupler force Acceleraton Σm,Σf (a) locomotve + 5 freght cars Travelng drecton Locomotve No. freght car No. 2 freght car No. 7 freght car M F m m 2 m 7 f f 2 f 7 Measurement tems Velocty Acceleraton R R 2 Coupler force Acceleraton Coupler force BC pressure Σm,Σf (b) locomotve + 7 freght cars Fg. 3 Outlne of test tran QR of RTRI, Vol. 57, No. 2, May 26
pressve force mpacts rght after the brake s appled and vbratons gradually fall to a stable state over a certan perod. In ths status wth stable coupler forces, the acceleratons of the locomotve and freght cars almost concde wth each other, showng the convergence of relatve movement of the vehcles. Estmated brakng force, ndcatng steady s at the locomotve from startup to the end, stays roughly level at kn after a certan amount of tme despte vbratonal movement occurrng mmedately after the brake s appled. Ths result concdes wth brakng only beng appled to the locomotve. Whle the estmated brakng force n the locomotve shows stable s even f the coupler force stays n a transent response regon because t s canceled out by ts own transent acceleratve response. However, the estmated brakng force totaled over the freght cars, whch represents the relatve moton of the 5 cars only by -car acceleraton, exhbts the errors reflectng relatve moton between cars before they become statonary and Coupler force [kn] Acceleraton [km/h/s] Velocty [km/h] Estmated brakng force [kn] 3 25 2 5 5 5 5 2 25 3 35 4 4 3 2 - -2-3 -4 5 5 2 25 3 35 4 4 2-2 -4-6 -8 5 5 2 25 3 35 4 3 2 No. freght car Locomotve Locomotve No. 5 freght car - 5 5 2 25 3 35 4 Tme [s] Fg. 4 Independent 2-notch brakng also ndcates reasonable s after full convergence. 3.2.2 When both locomotve and freght cars are braked Fgure 5 shows a result of velocty, acceleraton, coupler force, and estmated brakng force when 3-notch brakng s appled to both the locomotve and freght cars (contnuous brake, herenafter) at tme s from the ntal velocty of 25 km/h. Contnuous brake s regularly used whle runnng between statons. Ths operaton s programmed so as to roughly equalze the deceleratons between the locomotve and freght cars. Deletng the acceleraton from (3) and (5) to sort them by R, (6) s gven. Coupler force [kn] Acceleraton [km/h/s] Velocty [km/h] Estmated brakng force [kn] M f ( m ) F = = R = M + m 3 25 2 5 5 = Fg. 5 Contnuous 3-notch brakng (6) 5 5 2 4 3 2 - -2-3 No. freght car Locomotve -4 5 5 2 4 2-2 -4-6 -8 5 5 2 3 2 Locomotve No. 5 freght car - 5 5 2 Tme [s] QR of RTRI, Vol. 57, No. 2, May 26
If the masses of locomotve and freght cars and brakng forces are controlled n adequate proporton n (6), the numerator of the rght member approaches, ndcatng that there s no large force actng on the coupler. The coupler forces actually measured, exhbtng ths tendency, transts here a moderate path almost wthout forces except a few nstantaneous compressve forces. These spky responses, appearng when there s a constant dfference of acceleratons between locomotve and freght cars (partcularly appearng frequently for large opposte peaks at the same tme), s deemed to be ndcatve of mpacts due to relatve movements. Steady-state s are observed here for the estmated brakng force of the locomotve smlar to when ndependent brakng s appled. For ndependent 2-notch and contnuous 3-notch brakng, the brake-cylnder pressure (BC pressure, herenafter) s almost evenly set. Judgng from the s of the both estmated brakng forces almost equvalent at about 6 kn, t s found here that the brakng forces of the locomotve can be detected separately from those of freght cars. Meanwhle, the freght-totaled brakng force also ndcates comparatvely large fluctuatons although t stays almost at a constant except for the regon rght after brakng begns. These fluctuatons, concdng wth the tmng of the spky responses of the coupler force, are consdered to be errors caused by the relatve movement of vehcles, smlar to what occurred wth ndependent brakng. Whle the freght cars n ndependent brakng are relatvely stable wth only coupler forces beng exerted, brakng forces ndvdually act on each freght car for contnuous brakng. The brakng force exerted on each vehcle further exhbts a transmsson delay of the brakng commands and unevenness n frcton between wheels and brake shoes. From these factors, contnuous brakng s prone to relatve movements among vehcles, probably affectng the estmated brakng force. 3.2.3 When freght-car brakng condton s ntentonally vared Transtons n estmated brakng forces were observed for contnuous 3-notch brakng when brakng of freght cars was ntentonally vared. The brakng condton of freght cars s altered here by turnng the manually operated valves for each boge on and off. Table 2 shows the test condtons and Fg. 6 the test results. As stated n Secton 3.2., estmated brakng forces for freght cars durng contnuous brakng are prone to fluctuatons n terms of Estmated freght-totaled brakng force [kn] Fg. 6 2 8 6 4 2 8 6 4 2 2 3 4 5 6 Freght-totaled number of vehcles wth brakes enabled Relatonshp between freght-totaled number of vehcles wth brakes enabled and estmated freght-totaled brakng force vbratonal s. Therefore, the dead tme and transentresponse characterstcs of BC pressure have been consdered here. In other words, the estmated brakng force n each condton s calculated by takng a tme-averaged over a runnng secton requred for stoppng after the BC pressure reaches 63.2 % of a steady and further by takng a frequency-averaged over the test wth same condtons. The calculated s exhbted a trend n proporton to the number of vehcles wth brakes enabled. Each of the plots shows a hgh lnearty, thereby demonstratng that the brakng force estmated usng ths procedure possesses a resoluton at least equvalent to boge for contnuous 3-notch brakng. 3.3 Test wth locomotve + 7 freght cars 3.3. Comparson between estmated and theoretcal s Fgure 7 (a) shows total brakng forces estmated and those wth theoretcal s for 7 freght cars when the tran emergency brakes at tme s from the ntal velocty of 75 km/h. The theoretcal here s a brakng force that s expected at the desgn phase, defned as (7) for freght car and as (8) for all freght cars (totaled). ^f = τ κ η S P µ (7) Table 2 Brakng condton for freght cars Number of vehcles wth brakes enabled Brakng condton for freght cars 5 Brake on for every freght car 4 Brake off for freght car 3 Brake off for 2 freght cars 2.5 Brake on for only one sde of boges for every freght car 2 QR of RTRI, Vol. 57, No. 2, May 26
8 5 Estmated caton s large compared to that n Secton 3.2.2 because of the ncrease n brakng force due to added vehcles and emergency brakng. Brakng force [kn] 2 9 6 3 2 5 5 2 25 Tme [s] Theoretcal (a) 7 freght cars (totaled) 3.3.2 Brakng force of an arbtrary vehcle The car subect to ths procedure s can be selected randomly. For example, when the frst freght car s selected: f = m + R R (9) 2 s derved from (4), whch can be used to estmate the brakng force of ths vehcle f ts acceleraton and neghborng 2 coupler forces are obtaned. In the same test as Fg. 7 (a), the estmated brakng force and theoretcal for the frst freght car are shown n Fg. 7 (b). Observatons from ths test produce the same outcome as n Fg. 7 (a),.e. that the estmated brakng force follows the theoretcal whle showng some vbratonal behavor. Therefore, ths procedure can be appled to any car n the tran set. Verfcatons were then made to see f ths method could be appled to estmate the brakng force for each vehcle n a tran set. Brakng force [kn] 8 6 4 2 Fg. 7 Estmated 5 5 2 25 Tme [s] Theoretcal (b) No. (Frst) freght car (sngle) Comparson between the estmated and theoretcal s 4. Conclusons In ths study, a procedure was developed to estmate the brakng force actng on each vehcle n a tran set usng coupler forces and acceleratons, based on the assumpton that the relatve movements among vehcles converge. By applyng ths process to runnng tests usng a freght tran, t was verfed that ths procedure can be used to estmate any brakng force n a tran set wth to a reasonable degree of accuracy and that the brake force estmaton exhbts a trend followng the theoretcal s except fluctuatng components. Whle a large relatve movement among vehcles may cause some errors, the only alternatves are measurng ndvdually the acceleratons of vehcles or averagng the results. Further work about the problems on smplfcaton of measurements and mprovement of estmaton precson requre studes to make ths procedure more practcal. ^f = τ κ η S P µ (8) = Where, τ : Number of brake cylnders per boge, κ : Lever rato, η : Mechancal effcency, S : Brake-cylnder area, P : BC pressure, μ : Frcton coeffcent between wheels and brake shoes. τ, κ, and S are constants nherent n vehcle parameters, η s an approxmate obtaned from prelmnary study, P s a actually measured at No. freght-car whch s appled to all cars. Frcton coeffcent between wheels and brake shoes, generally dependng on velocty, pressng force, temperature, dry-wet condton and so forth, s approxmated as a functon of velocty. The results show that the theoretcal s grow wth the passage of tme. The estmated brakng forces totaled over the all freght cars exhbt a farly good result followng the theoretcal data curve on average although ndcatng some vbratonal behavor. It s thought that amplf- Acknowledgment The authors would lke to thank staff from the Japan Freght Ralway Company who cooperated ths study. References [] Uchda, S., Obara, T., Brake Control for Speedup of Shnkansen EMU Based on the Effectve Use of Adheson, RTRI Report, Vol. 7, No. 3, pp. 4-48, 993 (n Japanese). [2] Hasegawa, I., Kayashma, K., Brake Technology for 4 km/h Operaton of Narrow-Gauge Lnes, RTRI Report, Vol. 3, No., pp. 35-4, 999 (n Japanese). [3] Saga, S., Myabe, M., Kawamura, J., Sugta, H., Chkuma, K., An Evaluaton Method of the Brakng Performance Usng Boge Tracton Force, Quarterly QR of RTRI, Vol. 57, No. 2, May 26 3
Report of RTRI, Vol. 56, No. 4, pp. 256-26, 25. [4] Hkata, D., Brake Force Estmaton of Arbtrary Cars on Tran Set, In Proceedngs of the 23rd Transportaton and Logstcs Conference 24 (Translog 24), the Japan Socety of Mechancal Engneers, pp. -4, November 24 (n Japanese). [5] Matsu, S., Coupler Force Due to Longtudnal Wave n the Braked Tran : An Example of Numercal Analyss of the Impact of Contnuous Body, Transactons of the Japan Socety of Mechancal Engneers, Seres C, Vol. 74, No. 629, pp. 74-7, June 97 (n Japanese). [6] Hayase, T., Chonan, S., Numercal Analyss on Bucklng of Tran Set, Transactons of the Japan Socety of Mechancal Engneers, Seres C, Vol. 66, No. 646, pp. 943-95, June 2 (n Japanese). [7] Hayase, T., Chonan, S., Fukazawa, K., Optmum Desgn of a Hgh Functonal Buffer or Ralway Vehcles, Transactons of the Japan Socety of Mechancal Engneers, Seres C, Vol. 67, No. 654, pp. 49-498, February 2 (n Japanese). [8] Hayase, T., Fukazawa, K., Numercal Analyss of Tran Set Bucklng, RTRI Report, Vol. 5, No. 5, pp. 29-34, 2 (n Japanese). Authors Dasuke HIJIKATA Researcher, Brake Control Laboratory, Vehcle Control Technology Dvson Research Areas: Brakng performance evaluaton, Wheel slde protecton Toshharu NISHIMURA Researcher, Brake Control Laboratory, Vehcle Control Technology Dvson (Former) Research Areas: Brakng performance evaluaton 4 QR of RTRI, Vol. 57, No. 2, May 26