() () Study on e-adhesion control by monitoring excessive angular momentum in electric railway traction Takafumi Hara, Student Member, Takafumi Koseki, Member, Yutaka Tsukinokizawa, Non-member Abstract Suppression of a slip and reduction of a friction between rail and wheel are important in railway systems. This paper proposes a new slip re-adhesion control based on excessive torque and excessive angular momentum. The effectiveness of the proposed method has been confirmed by the calculation. Furthermore, the proposed method has been evaluated by two performance indicator, frictional force reduction and effective utilization of adhesive force. As a result, it has been found that effective use of adhesive force is achieved and frictional force can be reduced up to 21% by the proposed method. Keywords: slip slip velocity tractive force electric railway adhesion control excessive angular momentum 1. (1) (2) (3) (4) (5) 2 2 (6) 2. 21 1 1 (1)(4) ω w = G r T m T L (1) M v b = T L r F d (2) v s = rω w v b (3) ω s = ω w v b r (4) Table 1 = 1 4 M r 2 = 1 2 Mr2 (1) (2) rm ω s (5) ω s = 1 { ( G r T m 1 + ) T L + } rf d (5) (6)
Table 1. Parameters explanation Item Value Comment Inertia moment around wheel kg m 2 Equivalent inertia moment of drive axis kg m 2 ω w Driving wheel angular velocity rad/s G r Gear ratio - M Equivalent inertia weight around wheel kg M Mass per axis kg v b Velocity rad/s v s m/s ω s Slip angular velocity m/s T m Motor torque N m T L Adhesive torque N m r adius of wheel m F d Travel resistance N T ex = ω s = G r T m ( 1 + ) T L + rf d (6) G r T m (1 + )T L (7) { ( L ex = G r T m 1 + ) T L + } rf d (7) (8)(9) ω s = 1 L ex dt (8) ω s = 1 T ex (9) Fig. 1 0 22 L ex T ex T L (10) T L T L ˆTL = 0 H [ ] [ ][ ] [ d 0 1 Gr = + dt 0 0 ˆω w ˆT L ˆω w ˆT L 0 ]T m +H(ˆω w ω w ) (10) Fig. 1. Excess torque T ex Fig. 2. Disturbance torque and angular momentum L ex estimation [ y = 1 0 ] [ ˆω w ˆT L ] (11) 23 t slip t detect t T down t T up τ 1 τ 2 Fig. 2 G r T m ( 1 + ) ˆTL ( 1 + ) ˆTL rf d 1 (Case A) 2 (Case B) 2 Fig. 3 (Case A) (Case B) 231, Case A T ex,slip τ 1 s T ex,τ1 2 L ex,τ1 (12) Fig. 4
Fig. 3. Case analysis of re-adhesion control Table 2. Torque pattern Time Explanation t slip Slip generation Infinitesimal time T m = T m t detect Slip detection τ 1, T m = T m t T down Torque down τ 2, T m = T m down t T up Torque up Time constant G up Table 3. Parameters single axis bogie model g 9.81 2.22 10 3 159 r 0.412 G r 5.28 L ex,τ1 = τ 1 2 (T ex slip + T ex,τ1 ) (12) 232, Case B τ 1 s G r T m ( 1 + ) ˆTL T ex,τ1 L ex,τ1 (13) Fig. 5 L ex,τ1 = τ 1 2 T ex,τ 1 (13) 233 T m T m T L detect T L detect (14) G up 4. T m (t slip < t < t T down ) T m down (t T down t t T up ) T m = (14) T m down + G up (T m T m down )(t t T up ) (t T up < t) t slip < t < t detect T m down (15) 231232 L ex,τ1 = τ 2 (T L detect T m down ) (15) Table 2 Fig. 4. Calculation of excessive 234 Fig. 5. Calculation of excessive angular momentum, Case A angular momentum, Case B T min Fig. 6 T min 3. t = 0.00 s T m = 1.00 10 3 G 1.00 s t = 6.00 s Fig. 7 (a) (b) t = 15.00 s Fig. 7 (b) (a) (a) (b) MATLAB/Simulink T min = 10.0 t = 24.00 s 30.0 Table 3 2 41 (7) µ max
Table 4. Tractive coefficient µ ur and Loss friction force around driving wheel F slip (τ 1 ) τ 1 [ms] Tractive Loss friction force coefficient µ ur around driving wheel F slip 50.0 92.6 (100 % ) 68.4 (100 % ) 100 92.4 (100 % ) 111 (162 % ) 200 81.2 (87.7 % ) 245 (358 % ) 400 61.2 (66.1 % ) 933 (1.34 10 3 % ) Tractive coefficient 0.25 0.2 5 Fig. 6. Torque limitation (a) (c) (a) (c) 0 0 5 0.2 0.25 0.3 0.35 0.4 [m/s] Fig. 7. Characteristic change between tractive coefficient and slip velocity (16) µ ur 1 µ ur = t finish t start tfinish t start µ(t) µ max 100 dt(16) t start = 6.00 s t finish = 15.00 s Fig. 7 µ max 0.09 42 (8) F slip T L W slip (17) W slip = µ(v s )W g v s (17) W slip F slip (18) F slip = tfinish t start tfinish µ(v s )W g v s dt t start v b dt t start = 6.00 s t finish = 15.00 s (18) 5. 51 τ 1 = 100 ms k = 0.250 Fig. 8 Fig. 10 Fig. 8 (1 + ) ˆT L G r T m (1 + ) ˆT L G r T m Fig. 10 0 0 τ 1 s τ 1 100 ms τ 2 250 ms 1 2 3 T ex L ex 52 3 3 τ 1 k G up τ 1 τ 1 40 ms Table 4 k 0.200G up 1.00 s τ 1 50.0100200400 ms 50 ms τ 1 = 100 ms k G up 2
7000 Torque[N m] Fig. 11. Tractive coefficient µ ur 0 Fig. 8. Motor torque and adhesive torque ( Proposed ) 0.09 0.08 0.07 before 6[s] after 6[s] Fig. 12. Loss friction force around driving wheel F slip 0.06 0.04 0.03 0.02 0.01 0 Fig. 9. ( Proposed ) Fig. 13. A block diagram of re-adhesion controller Torque[N m] 7000 0 Excess torque Slip information 8 8.5 9 9.5 10 Fig. 10. Motor torque andadhesive torque ( Proposed, t=8.00-10.00 s Fig. 11Fig. 12 Fig. 14. Nonliner table charactarictic between 1.00 s 2.00 s 1.00 s 2.00 s 2 τ 1 = 100 ms, G up = 1.00 s, k = 0.200 53 531 (6) (6) Fig. 13 (6) α w α ref T ref T m ref T v Fig. 14 (19) (19) α
Torque[N m] 7000 Torque[N m] 7000 2 k G up 6. 0 0 Fig. 15. Motor torque and Fig. 16. Motor torque and adhesive torque ( Proposed ) adhesive torque ( Conventional ) 0.4 0.35 0.3 0.25 0.2 5 v before 6[s] top after 6[s] 0 Fig. 17. ( Proposed ) slip velocity[m/s] 0.4 0.35 0.3 0.25 0.2 5 v before 6[s] top after 6[s] 0 Fig. 18. ( Conventional ) Table 5. Comparison between conventional and proposal re-adhesion control Method Tractive Loss friction force coefficient µ ur around driving wheel F slip Proposed 92.4 ( 0.500 % ) 111 ( 21.3 % ) Conventional 91.9 (100 % ) 142 (100 % ) α 0 α w (> 0) ADL 1 (α α 0 ) ADL = 1 α α 0 (α 0 < α < α 0 + α w ) (19) α w 0 (α 0 + α w α) 0.09 1 2 3 T ex L ex 2 0.500 % 21.3 % α α 0 ADL = 1 T mref T ref α α 0 +α w ADL = 0 T mref 0 α α 0 α +α w ADL 532 (6) Figure 15 16 Figure 17 18 Table 5 Table 5 0.500 % 21.3 % 2 1 1 No. 673 (1998) 2 1 D 1203 pp.382.389 (-3) 3 2M1C D 12111pp.1192.1198 (2001-11) 4 205 D 1249pp.909.916 (2004-9) 5 ( 3 ) 24 (1987)pp. 282-286 6 TE-08-37 (2008-9) 7 (2MIC) IEE Trans. IA, Vol.127, No.8, 2007 8 TE- 10-38 (2010-7)