Investigation on a Power Coupling Steering System for Dual-Motor Drive Tracked Vehicles Based on Speed Control

Transcription

1 energies Article Investigation on a Power Couplg Steerg System for Dual-Mor Drive Tracked Vehicles Based on Speed Control Li Zhai 1,2, * ID, Hong Huang 1,2 Steven Kavuma 1,2 1 National Engeerg Laborary for Electric Vehicles, Beijg Institute Technology, Beijg 181, Cha; @bit.edu.cn (H.H.); stevenkavuma@hotmail.com (S.K.) 2 Co-Innovation Center Electric Vehicles Beijg, Beijg Institute Technology, Beijg 181, Cha * Correspondence: zhaili26@bit.edu.cn; Tel.: Received: 24 June 217; Accepted: 28 July 217; Publhed: 1 August 217 Abstract: Double-mor drive tracked s (2MDTV) are widely used tracked dustry due development electric drive systems. aim th paper solve problem sufficient propulsion mor rque low-speed, small-radius steerg sufficient power high-speed large-radius steerg. In order do th a new type steerg system with a designed a closed-loop strategy based on speed adopted improve lateral stability. work done entails g simulatg 2MDTV proposed strategy RecurDyn Matlab/Simulk. simulation results show that 2MDTV with outputs more rque power both steerg cases compared 2MDTV without, steerg stability improved by usg strategy based on speed. Keywords: track ; dual-mor; dynamic steerg; power 1. Introduction addition a track a improves s traction on st surfaces, refore tracks are found on a variety s such as bulldozers, excavars, tanks, tracrs any whose application would benefit from creased traction. Such s are widely used many areas such as military, agriculture, construction, mg, daster rescue [1]. Although re are many studies on traditional tracked s [2 4], re still a need for more vestigations on electric tracked s. In recent years, with development high-power electronic s, computer technology drive mors with high power high efficiency, electrical drive technology has made a breakthrough [5]. An electric drive system can be used not only meet required dynamic performance, but also provide energy for electromagnetic weapons [6]. hybrid electric powertra with energy management strategies can provide more flexibility meet driver dem improve fuel economy [7]. Moreover, compared traditional s, electric tracked s CO NO x emsions are reduced [8], makg electric drive technology an important research direction regard tracked propulsion. dual-mor dependent drive configuration most widely used configuration electric tracked s [9 11]. Th electric propulsion system which composed two AC duction mors, fal drives runng gears characterized by complicated multi-variables nonlearity [12]. need for high speed, heavy load aumation has imposed higher higher requirements on stability, reliability, lability maneuverability s [13]. Energies 217, 1, 1118; doi:1.339/en

2 Energies 217, 1, Skid steerg predomantly used with tracked s, that say s are steered by forcg traction elements on opposite sides run at different speeds [14]. re have been many or vestigations steady-state hlg charactertics steerg mechanms [15]. steady-state hlg ory based on analyzg slidg motion track over ground however few studies focus on electric stability dynamic steerg. rque outer mor required for small radius steerg will be quite large durg a dynamic steerg situation. At higher speeds rque output propulsion mors limited by ir power ratg, so y could not necessarily contribute so much steerg. In order solve above problems dual-mor dependent drive tracked, it necessary design a power steerg. An electro-mechanical drive system with a horizontal ax steerg structure proposed solve problem needg use large electric mors whose power requirements are far beyond those pure drive power [16]. However se needs lots idle gears th creases size assembly. A mechanical used decrease traction power unilateral drive mor, which allows regenerated power flow from low-speed side high-speed side mechanically [17]. Th quite complex due application three planetary gear systems. A planetary gear proposed improve efficiency ner side mor [18]. Though efficiency mor higher with two planetary gear system, it requires higher accuracy for system. An electromechanical transmsion with an auxiliary mor was proposed crease output rque or power mor [19], however workg prciple structural design system were not described detail. re are many studies which focus on lateral dynamic motion electric s [2,21], some which cover electric tracked s [15,22], but few studies take dynamic steerg account. rque or power required by will be much larger durg transients. Th paper aimed at solvg followg problems by designg a power steerg system: (1) shortage propulsion mor rque at low speeds small radius steerg, (2) sufficient power at high speed large radius steerg. lateral stability improved by employg a closed loop strategy based on speed. On runng simulation RecurDyn Matlab/Simulk, results show yaw rate for s with creases ideal value rapidly achieves better trajecry followg. 2. Mamatical Model for Dynamic Steerg In order steer a tracked, it necessary drive one track faster than or, causg turn slower track. One ways th executed by usg a dual-mor dependent drive with two mor lers rque speed two mors which drive sprocket. Th called an electronic differential steerg system (ECDS) which can improve s stability, hlg flexibility. objective th paper solve problems sufficient rque durg small radius steerg shortage power high-speed large radius steerg. First we selected a tracked which object our mamatical g analys. selected s configuration shown Table 1. Secondly, we analyzed tracked s kematics dynamics for stationary steerg dynamic steerg order study rque power required by propulsion mor both steerg cases.

3 Energies 217, 1, Table 1. Vehicle parameters. Parameters Value Vehicle tread, B (m) 1.3 Ground contact length, L (m) 1.7 Rollg restance coefficient, f.4 Transmsion efficiency, η.9 Drive ratio, i g 6.35 Mass, m (kg) 2 Mass ga coefficient, δ 1.5 Moment ertia, J (kg/m 2 ) 3 To do th we ok right steerg as an example, F L tractive force on outer track, F R tractive force on ner track, R L rollg restance force on outer track, R R rollg restance on ner track, M µ steerg restance moment, v L track speed on outer side, v R track speed on ner side ω yaw rate. Steerg maneuvers with different radiuses can be shown 1. M µ defed as follows: µ max M µ = 1 4 µmgl = RB mgl (1) where µ coefficient roll restance, µ max maximum rollg restance coefficient, R steerg radius. rollg restance two tracks which same magnitude but opposite direction expressed as follows: R L = R R = 1 f mg (2) 2 Accordg dynamics performance dicars: First, maximum speed should be 72 km/h. Second, maximum climbg degree should be 32 climbg speed 2 km/h. Third, acceleration capability: 32 km/h less than 8 s. parameters mor are determed as shown Table 2. Table 2. Mor parameters. Parameters Rated Power (kw) Rated Torque (N m) Rated Speed (r/m) Power (kw) Torque (N m) Speed (r/m) Value In th paper, dynamic balance correspondg different steerg maneuvers analyzed obta rque or power required by an unilateral mor. n we could fd out wher it can meet requirements durg different steerg radius R.5 B Steerg equilibrium relationship between force moment when turng from restg, as shown 1a, can be expressed as: { F L F R + R R R L = δm dv dt (F L + F R ) B2 (R L + R R ) B2 M µ = J dω dt where F L F R are tractive force but opposite direction. It s worth mentiong that when R =, F L = F R, V L = V R, lateral acceleration zero, dv/dt =, when R =.5 B, V R =, R R =. (3)

4 dv FL FR + RR RL = δ m d t B B dω ( FL + FR) ( RL + RR) Mμ = J 2 2 dt (3) Energies where FL 217, 1, 1118 FR are tractive force but opposite direction. It's worth mentiong that when 4 R = 17, FL = FR, VL = VR, lateral acceleration zero, dv/dt =, when R =.5 B, VR =, RR =. 1. Force analys: R.5 B steerg; R >.5 B steerg. 1. Force analys: R.5 B steerg; R >.5 B steerg. mor speed on both sides can be expressed as { nl = 1i g 12πr z 3.6 ω ( B 2 R) n R = 1i g 12πr z 3.6 ω ( B 2 + R) (4) where r z radius sprocket, r z = 15 mm. From Equations (1) (4), mor rque power can be obtaed as follows: { TL,R = F L,R i g η r z P L,R = T L,R n L,R 9549 T tractive rque but opposite direction. P consumed power used drive track. Subscript L or R means left or right side R >.5 B Steerg Accordg dynamic balance, followg formula can be obtaed from 1b: { F L F R R R R L = δm dv dt (F L + F R ) B2 + (R R R L ) B2 M µ = J dω dt where F L tractive force. If we assume followg equation: F R = µmgl 4B (5) (6).5 f mg = (7) We will get solution R = R = m. When R > R, F R tractive force same direction with track. While when R < R, F R brake force, generated by mor. direction between F R V R opposite th situation. th steerg case can be divided static startg steerg drivg steerg, mor rque power required vary with steerg radius speed. From Equations (1) (7), Table 3 shows steerg power rque required by dual mors durg dynamic steerg maneuvers with,.2 B,.5 B steerg radii stationary steerg maneuvers with,.2 B,.5 B, 2 B, 5 B, 8 B, 1 B steerg radii. From Table 3 we can see that when R.5 B, both dynamic steerg stationary steerg, mor rque required exceeds mor s peak rque (15 N m). When R = 5 B, power required by outer side mor larger than mor s maximum power (4 kw). When R = 8 B or R = 1 B, power required by both side mors larger than mor s maximum power (4 kw). Accordg results we can fd that durg small-radius steerg ( R.5 B) rque required by a sgle mor dynamic steerg 1.5 times that durg stationary steerg. Durg large-radius steerg (R = 1 B) power required by mor 1.5 times mor s maximum power refore mor s rque power should crease by 5% at least, which

5 Energies 217, 1, results large size mass mor or power verters. As a result, superiority ECDS not highlighted, although Zhai [1] proposed a sgle mor steerg mor system, providg larger rque durg small-radius steerg, additional power durg high speed large-radius steerg while workg prciple structural design coupled system were not described detail. Table 3. Dynamic stationary steerg rque power required by two mors. Energies 217, 1, Situation R (mm) T L (N m) T R (N m) n L (r/m) n R (r/m) P L (kw) P R (kw) V (km/h) R = 8 B or R = 1 B, power required by both side mors larger than mor s maximum power Dynamic (4 kw)..2 B Accordg 279 results 252 we can fd 482 that durg 26 small-radius 14.1 steerg 5.5 ( R B) rque required.5 B by 258 a sgle mor 181 dynamic 688 steerg 1.5 times 18.6 that durg stationary 3.6 steerg. Durg large-radius 192 steerg 192(R = 1 B) 344 power 344 required by 6.9 mor times mor's maximum.2 B power 187refore 187 mor's rque 482 power 26 should 9.4crease 4. by 5% at 1.22 least, which results.5 B large size 179 mass 168 mor 688 or power 12.9 verters. As a result, 3.6 Stationary 2 B superiority ECDS not highlighted, although Zhai [1] proposed a sgle mor steerg 5 B mor 8 Bsystem, providg 9 larger 69 rque 5847 durg small-radius 5159 steerg, additional power 49. durg high speed 1 B large-radius 8 steerg 59 while 7223 workg 6535 prciple 6.3structural 4.5 design 61.2 coupled system were not described detail. 3. Steerg System Design 3. Steerg System Design 3.1. Steerg Couplg Drive System 3.1. Steerg Couplg Drive System A steerg drive system composed a new type center steerg mor, two A steerg drive system composed a new type center steerg mor, two electromagnetic electromagnetic clutches, clutches, two two planetary planetary gear gear couplers, couplers, two two propulsion propulsion mors mors designed designed shown shown parameters parameters steerg steerg mor mor are determed are determed as lted as lted Table 4. Table 4. steerg mor can canproduce large large rque rque at low at low rotation rotation speed. speed. A reverse A reverse mechanm mechanm designed designed steerg mor achieve positive negative rotation rotation direction. direction. When When rque rque power or power sufficient, electromagnetic clutch engaged rque or or power drivg drivg wheel wheel satfied satfied by by steerg mor propulsion mor. Parameters Rated Power (kw) Steerg drive system configuration. Rated Torque (N m) Table 4. Steerg mor parameters. Rated Speed (r/m) Power (kw) Torque (N m) Speed (r/m) Value

6 Energies 217, 1, Table 4. Steerg mor parameters. Parameters Rated Power (kw) Rated Torque (N m) Rated Speed (r/m) Power (kw) Torque (N m) Speed (r/m) Value Energies 217, 1, Planetary Gear Coupler Design A planetary gear coupler proposed couple rque or power propulsion mor steerg mor. output rque transmitted sprocket creased usg rque mode durg low-speed small-radius steerg. steerg. output output power power transmitted transmitted sprocket sprocket creased usg creased power usg power mode durgmode high-speed durg large-radius high-speed steerg. large-radius refore steerg. rque refore power rque dem or for power different dem radius for steerg different satfied radius steerg satfied steerg performance steerg improved. performance improved. planetary gear couplers consts two electromagnetic (EM) clutches, two two gear gear pairs pairs a a planetary gear gear unit, unit, which which consts consts a sun a sun gear, gear, a rg a rg gear, gear, a planet a planet carrier carrier three planet three planet gears, shown gears, shown 3. Gear3. pair Gear 1 contas pair 1 contas gear 1 gear gear 1 2 (rg gear gear), 2 (rg whereas gear), whereas gear pairgear 2 contas pair 2 gear contas 3 gear gear 3 4. It sgear worth 4. It's notg worth that notg gear 1that gear 13 are mounted gear 3 are onmounted steerg on mor steerg shaft without mor shaft a sple, without transmittg a sple, transmittg rque occurs only rque when occurs one only EM when clutches one engaged. EM clutches dual mor engaged. dual drivemor steerg cludesdrive a sgle steerg side cludes mode a sgle aside double side mode mode. a We double takeside one side as anmode. example, We as take shown one side as an example, 3. as shown Components planetary gear coupler. When drivg straight, rg gear (R) fixed by brake while both EM When drivg straight, rg gear (R) fixed by brake 1 while both EM clutch EM clutch are dengaged. power transmitted sun gear (S) clutch 1 EM clutch 2 are dengaged. power transmitted sun gear (S) planetary gear unit (transmsion ratio 6.35) from propulsion mor, outputted through planetary gear unit (transmsion ratio 6.35) from propulsion mor, outputted through planet carrier (C) sprocket. Durg steerg, if rque or power does not meet dem, planet carrier (C) sprocket. Durg steerg, if rque or power does not meet dem, rque or power coupled by th planetary gear. mode rque or power coupled by th planetary gear. mode cludes cludes rque mode speed mode, as shown Table 5. rque mode speed mode, as shown Table 5. Table 5. Couplg mode operation each component. Table 5. Couplg mode operation each component. Mode Braker 1 EM Clutch 1 EM Clutch 2 Steerg Mor Propulsion Mor Mode Straight Braker engaged 1 dconnected EM Clutch 1 dconnected EM Clutch 2 Steerg f Mor Propulsion workg Mor Torque Straight engaged dconnected combed dconnected workg f workg workg Torque Power dengaged dconnected combed dconnected combed workg workg Power dengaged combed dconnected workg workg rque mode active when turng a small radius at low speed. In rque mode EM clutch 1 dconnected while EM clutch 2 engaged brake 1 dengaged. n rque steerg mor propulsion mor are coupled sun gear (S) through gear pair 2, transmitted sprocket through planet carrier (C). power transmsion path shown 4a. power mode active when turng big radius at high speed. In

7 Energies 217, 1, Energies 217, 1, rque mode active when turng a small radius at low speed. In pair 1 rque power mode propulsion EM clutch mor 1 transmitted dconnected while sun gear EM clutch (S). n 2 engaged power brake coupled 1 dengaged. transmitted n rque sprocket through steerg mor planet carrier propulsion (C). power mortransmsion are coupled path sun shown gear (S) through 4b. gear pair 2, transmitted sprocket through planet carrier (C). power transmsion path shown 4a Torque Torque transmsion transmsion mode; mode; Power Power transmsion transmsion mode. mode. rque power output drivg sprockets on both sides under different steerg power mode active when turng big radius at high speed. In radius conditions with th are shown Table 6. performance power mode EM clutch 1 engaged while EM clutch 2 dconnected brake 1 without also shown Table 6. engaged. power steerg mor transferred rg gear (R) through gear pair 1 Table power 6. Mors propulsion condition mor comparon transmitted between sun gear with (S). n without power. coupled transmitted sprocket through planet carrier (C). power transmsion path shown TL TR Ts PL PR Ps nl nr ns Radius 4b. Couplg (N m) (N m) (N m) (kw) (kw) (kw) (r/m) (r/m) (r/m) rque power output drivg sprockets on both sides under different steerg B without radius conditions with th are shown Table 6. performance (dynamic) with without also shown Table 6..5 B without (dynamic) with Table 6. Mors condition comparon between with without. B without (stationary) with Radius Couplg T L (N m) T R (N m) Ts (N m) P L (kw) P R (kw) Ps (kw) n L (r/m) n R (r/m) ns (r/m).5 B B without without (stationary) (dynamic) with with B without without (dynamic) with (stationary) with B without B without (stationary) with (stationary) with B (stationary) without with It B can without be seen from 148 Tables that 26.7maximum 13.7 rque propulsion mor 15 (stationary) with N m, which cannot meet steerg requirement whereas with a maximum 8 B without rque (stationary) 28 with N m, can 9 be transmitted 69 from propulsion 37.1 mor 14.8 sprocket 4244 meet 5129 dynamic 942 or stationary small-radius steerg requirements. When turng a big radius, peak It power can be seen from mor Tables 4 3 kw without 6 that, maximum which rque not enough, propulsion while with mor, 15 N m, which cannot can output meet a large steerg enough requirement power (6 whereas kw at with most) meet 8 B a steerg maximum requirement rque 28 shown N m, can Table be 3. transmitted from propulsion mor sprocket meet dynamic or stationary small-radius steerg requirements. When turng a big radius, peak power 3.3. Planetary Geaer System Design mor 4 kw without, which not enough, while with, can output a large enough power (6 kw at most) meet 8 B steerg requirement shown Table Selection Prelimary Calculation planetary gear transmsion type 2Z-X (A) (defed by former Soviet Union), that NGW type, selected. transmsion ratio number teeth each gear: sun gear Za

8 Energies 217, 1, Planetary Geaer System Design Selection Prelimary Calculation planetary gear transmsion type 2Z-X (A) (defed by former Soviet Union), that NGW type, selected. transmsion ratio number teeth each gear: sun gear Z a = 17, rg gear Z b = 91, planetary gear Z c = 37, so actual gear ratio i = gear ratio error.5%. material sun gear planetary gear are 2CrMnTi, level 6 precion. material rg gear 42CrMo, level 7 precion. Calculate gear module itially accordg bendg fatigue: m = K m 3 TK A K F K Fp Y Fa1 φ d z 2 aσ Flim (8) where K m formula coefficient, K A usg coefficient, K F comprehensive coefficient, K Fp bendg coefficient, Y Fa1 oth shape coefficient, φ d oth width coefficient. σ Flim permsible stress. refore gear module 2.5. centre dtance 7 mm with a spiral angle Geometric Size Calculation geometric sizes sun gear (with subscript 1), planet gear (with subscript 2) rg gear (with subscript 3) are shown Table 7. Table 7. Geometric sizes each gear pair (mm). Gear Pair Reference Circle Diameter (d) Basic Circle Diameter (d b ) Tip Circle Diameter (d a ) Root Circle Diameter (d f ) Breadth Tooth External gear pair d 1 = d 2 = d b1 = d b2 = d a1 = d a2 = d f1 = d f2 = b sun = 43 b planet = 48 Internal gear pair d 2 = d 3 = d b2 = d b3 = d a2 = d a3 = d f2 = d f3 = b planet = 48 b rg = Checkg Strength To make sure coupler can work extreme condition, teeth contact stress teeth bendg strength checked as shown Table 8. stress suffered by gear teeth lower than allowed value so coupler can meet strength requirements. Table 8. Checkg each gear pair (MPa). Checkg Pair σ H1 σ H2 σ F1 σ F2 σ HP1 (allowed) External gear pair (teeth contact stress) External gear pair (teeth bendg strength) Internal gear pair (teeth contact stress) Internal gear pair (teeth bendg strength) σ HP2 (allowed) σ FP1 (allowed) σ FP2 (allowed) Checkg σ H1 σ HP1 σ H2 σ HP2 σ F1 σ FP1 σ F2 σ FP2 σ H1 σ HP1 σ H2 σ HP2 σ H1 σ HP1 σ H2 σ HP EM Clutch EM Brake Accordg maximum rque charactertics steerg mor planetary gear coupler Table 3, maximum required rques EM clutch 1 EM clutch 2 3 are 15

9 Energies 217, 1, N m, respectively. overall size EM clutch 1 EM clutch 2 Φ = 9 mm 1 mm. maximum Energies 217, required 1, 1118 brakg rques size electromagnetic brake 15 N m 9 17 Φ = 31 mm 55 mm, respectively. important design parameters electromagnetic clutches clutches electromagnetic electromagnetic brakes are proposed brakes are for proposed manufacture. for manufacture. Based on Based above on calculations, above calculations, overall size designed as 468 mm 364 mm 378 mm. overall size designed as 468 mm 364 mm 378 mm. 4. Control Strategy 4. Control Strategy 4.1. Driver Inputs Modelg 4.1. Driver Inputs Modelg put angle signal steerg wheel dplacement shown 5. Accordg different put steerg angle signal wheel angle signals, steerg wheel desired dplacement turng radius can shown be calculated. 5. Accordg different steerg wheel angle signals, desired turng radius can be calculated. θ θ - θ + 1 θ 1 2 θ 2 3 θ θ 3 θ 4 θ 4 5. Input angle signal steerg wheel. 5. Input angle signal steerg wheel. dplacement acceleration pedal or brake pedal assumed be lear output rque dplacement mor. acceleration coefficient pedal oracceleration brake pedal (A) assumed brake pedal be lear dplacement output signal (D) rque mor. are given as follows: coefficient acceleration (A) brake pedal dplacement signal (D) are given as follows: α α A A= α α α max α α B = β β (9) (9) β β B = β max β βmax β where α β are dplacements acceleration brake pedals, respectively. α β are free dplacements where α β are acceleration dplacements brake acceleration pedals, respectively. brake pedals, α max respectively. β max are α maximum β are dplacements free dplacements acceleration acceleration brake pedals, respectively. brake pedals, Arespectively. range α max from β max 1, are where outputmaximum rque dplacements propulsion mor acceleration range brake frompedals, Trespectively. max. And DA range from 1 1,, where where output output rque rque propulsion propulsion mor mor range range from from T max Tmax.. And D range from 1, where output rque propulsion mor range from Tmax Torque Dtribution Strategy Based on Speed 4.2. Torque Dtribution Strategy Based on Speed A rque dtribution strategy based on speed proposed shown 6. AccordgA rque A, B dtribution steerg wheel strategy angle signals, based on based speed on proposed above calculation, shown rque 6. rotation Accordg speed A, desired B can steerg be determed. wheel angle signals, based dtribution above ler calculation, used rque regulate rotation speed desired can be determed. dtribution ler used regulate rque each mor track driver puts based on real-time rotation speed (n L-real /n R-real ) rque each mor track driver puts based on real-time rotation speed (nl-real/nr-real) reved rque ( T reved rque 1 / T (ΔT1/ΔT2) 2 ) from slip-ratio ler. rque generated by each mor from slip-ratio ler. rque generated by each mor coupled through electromechanical transmitted sprocket. coupled through electromechanical transmitted sprocket Ideal Vehicle Ideal Vehicle Body Body Model Model Accordg Accordg dynamic dynamic analys, analys, ideal ideal can be summarizedas as follows: follows: ω des = { vl,r vlr, ( Rdes = ) 1.8B ωdes = v des vdes ( Rdes ) 3.6Rdes 1.8B (R des = ) 3.6R (R des des = ) (1) (1) where ω desired yaw rate, V L,R left or right side track speed center steerg which can be calculated from accelerar pedal position, v des desired speed, R des ideal steerg radius.

10 Energies 217, 1, where ω desired yaw rate, VL,R left or right side track speed center steerg which can be calculated from accelerar pedal position, vdes desired speed, Rdes ideal steerg radius. Energies 217, 1, Torque dtribution strategy based on on speed. desired speed ideal steerg radius can be determed by driver. se signal are puts ideal ideal body body desired desired sprocket sprocket rotation rotation speed speed rque are rque calculated. are calculated Couplg Dtribution Controller 7 shows workflow dtribution ler. ler receives signals (Tdes,, ndes) n ) calculated from ideal. Usg fuzzy proportion tegration differentiation (PID) ler based based on on error error between between reference reference rotational rotational speed speed actual rotational actual rotational speed speed produce produce rque T 11 rque. fuzzy T11. rulesfuzzy shown rules shown 8a c. rque 8a c. signal (T rque LL ) sent signal (TLL) sent judgment module judgment given module as follows: given as follows: T = T +Δ T (11) T LL LL= T 11 + T1 1 (11) where ΔT1 where T obtaed by slip ratio ler, which will be troduced next section. Similarly, 1 obtaed by slip ratio ler, which will be troduced next section. Similarly, rque rque signal signal (T (TRR) sent judgment module given as follows: RR ) sent judgment module given as follows: TRR = T22 +Δ T2 (12) T RR = T 22 + T 2 (12) flowchart judgment module shown 9. Dependg on different flowchart TLL TRR obtaed, judgment module module will output shown different rque 9. Dependg comms on different mor Tler. LL T RR When obtaed, required module rque will output power different does rque not exceed comms ir peak value, mor ler. steerg When mor does required not work, rque Ts =. When power does required not exceed rque ir exceeds peak value, peak rque steerg mor propulsion does not work, mor, Ts =. steerg When mor required operates rque generate exceeds additional peak rque rque meet propulsion rque mor, requirements. steerg mor When operates power generate mor additional sufficient, rque power meet rquemode requirements. active, When steerg power mor mor generates sufficient, relevant rque power meet mode active, conditions, steerg output mor enough generates power. relevant rque meet conditions, output enough power.

11 Energies 217, 1, 1118 Energies 217, 1,1, 1118 Energies 217, Energies 217, 1, Couplg dtribution ler Couplg dtribution ler. Couplg dtribution ler. 7. Couplg dtribution ler. p rules Ki rules (c) Kd rules. 8.Fuzzy Fuzzyrules: rules: Krules KiKrules (c)(c) KdKrules Fuzzy KpK ii rules dd rules. 8. K Fuzzyrules: rules: rules rules. pp rules 9. Flowchart judgment module Flowchart judgment module. Flowchart judgment module Slip Ratio Controller Slip Ratio Controller Usually, tracked s turns are accompanied by a slip phenomenon: Slip Ratio Controller Usually, tracked s turns are accompanied byby a slip phenomenon: Usually, tracked s turns are accompanied a slip phenomenon: (c) (c)(c)

12 Energies Energies 217, 217, 1, 1, Energies 217, 1, rω u rω s = u rω = 1 rω (rω u ) = accompanied rω phenomenon: u) u = 1 uby a (slip Usually, tracked s turns sare u u ( rω u u rω u= = 11 urω (rω(r ω > u) ss =s==rωruω = 1 rωu (rω >u)u ) u s = rrω u ωrω u = 1 rω rω (rω > u ) Slip Ratio Controller (13) (13) (13) where n = rω sprocket rotation speed, u track longitudal speed, generally u = V. where n = rω sprocket rotation speed, u track longitudal speed, generally u = V. Innorder improve rotation tracked speed, usteerg stability use speed, energy efficiently, where = rω sprocket track longitudal generally u = V. slip In order improve tracked steerg stability use energy efficiently, slip ratio Inorder led with reasonable range. stability choice slip ratio related improve atracked steerg use energy efficiently, road slip ratio led with a reasonable range. choice slip ratio related road parameters, normally sdes =.15 for an asphalt road. ler designed based ratio led with a reasonable range. choice slipslip ratioratio related road parameters, parameters, normally sdes =.15 for an asphalt road. slip ratio ler designed based on fuzzy spid method (similar rque ler mentioned above) mata normally =.15 for an asphalt road. slip ratio ler designed based on fuzzy PID des on fuzzy PID method (similar rque ler mentioned above) mata actual slip ratio(similar closedrque ideal slip ratio, as shown 1. actual method ler mentioned above) mata actual slipslip ratioratio closed actual slip ratio closed ideal slip ratio, as shown 1. actual slip ratio calculated Equation (13). 1. actual slip ratio calculated from Equation (13). idealfrom slip ratio, as shown calculated from Equation (13). sl-des sl-des V V Slip ratio sl-real ratio sl-real nl-real Slip calcular nl-real calcular -V V nr-real nr-real d d dt dt Slip ratio Slip ratio s R-realcalcular calcular s R-real sr-des sr-des d ddt dt Fuzzy PID Fuzzy PID1 ler ler 1 Fuzzy PID Fuzzy PID2 ler ler 2 T1 T1 Couplg Couplg dtribution dtribution ler ler T2 T2 1. Slip 1. Slip ratio ratio ler. ler. 1. Slip ratio ler. 5. Modelg Simulation Results 5. Modelg Simulation Simulation Results Results 5. Modelg steerg steerg co-simulation shown built by multi-body stware 6 66 built by by multi-body stware steerg co-simulation co-simulation shown shown built multi-body stware stware Matlab/Simulk. ground are developed stware Matlab/Simulk. ground are developed stware Matlab/Simulk. ground are developed as shown driver puts, based on speed as shown driver puts,, based on speed mor as shown 11. driver puts based on speed mor system are developed Simulk. module seamlessly system are developed Simulk. module module seamlessly terfaced mor system are developed Simulk. seamlessly terfaced with Matlab/Simulk. parameters simulation dynamic simulation parameters are shown with Matlab/Simulk. parameters dynamic parameters are shown Table terfaced with Matlab/Simulk. parameters dynamic simulation parameters are shown9. Table 9. reaction charactertic mors can be aumatically generated by mor ler reaction charactertic mors can be aumatically generatedgenerated by mor by ler Table 9. reaction charactertic mors can be aumatically mor ler Simulk transferred as put mor. Simulk transferred as put mor. Simulk transferred as put mor. 11. Track g; Vehicle g Track Track g; g; Vehicle Vehicle g. g.

13 Energies 217, 1, Energies 217, 1, Table 9. Dynamic simulation parameters. Component Table 9. Dynamic simulation parameters. Number Inertia (kg mm²) Stiffness Coefficient Dampg Coefficient Component Sprocket Number 2 Inertia 279,379 (kg mm 2 ) Stiffness 18, Coefficient Dampg1 Coefficient Sprocket Road Wheel , ,379 12, 18, 1 RoadCarrier Wheel , , 12, 1 Carrier Track lk , Track Track subsystem lk ,6, 9 1, 1 Track subsystem - 1,6, 1, 5.1. Center Steerg 5.1. Center Steerg When steerg wheel turned left, accelerar pedal pushed botm, When begs steerg turn wheel from its static turned position. left, comparative accelerar trajecry pedal pushed shown botm, 12a. begs without turn from its static turns position. slowly due comparative its sufficient trajecry output shown rque. When 12a. without used, yaw rate turns slowly due creases its sufficient rapidly output ideal rque. value When (1.3 rad/s) whereas when used, yaw rate not used creases yaw rate rapidly gradually creases ideal value (1.3.8 rad/s rad/s) as whereas shown when 12b. It can be seen not from used yaw 12c rate that gradually creases with.8 rad/s as shown outputs 12b. a larger It can rque be seen from itial movement 12c that meet with needs small-radius dynamic outputs a steerg. larger rque As steerg itial enters movement steady meet state, needs output small-radius rque decreases dynamic fally steerg. tends As a steerg constant enters value. steady power state, generated output by rque sprockets decreases shown fally tends 12d. a constant power output value. creased power generated with, by sprockets but has a shown small value as a 12d. whole. power output creased with, but has a small value as a whole. Y(m) w(rad/s) Yaw rate(w/o) Yaw rate(w) -1.5 Trajecry (w/o) Trajecry (w) X(m) T(N*m) P(kW) (c) (d) Simulation Simulation results results center center steerg: steerg: Trajecry; Trajecry; Vehicle Vehicle yaw rate; yaw (c) Sprocket rate; (c) Sprocket rque; (d) rque; Sprocket (d) power. Sprocket power B Steerg

14 Energies 217, 1, Energies 217, 1, B Steerg steerg wheel manipulated output R =.5 B, accelerar pedal pushed steerg wheel manipulated output R =.5 B, accelerar pedal pushed botm begs turn from its static position. trajecry shown botm begs turn from its static position. trajecry shown 13a. If not added, due limited rque, sprocket cannot 13a. If not added, due limited rque, sprocket cannot always generate required rque, so rque on both sides always at upper limit always generate required rque, so rque on both sides always at upper limit (15 N m). (15 N m). In 13b it can be seen that yaw rate about 1.2 rad/s when In 13b it can be seen that yaw rate about 1.2 rad/s when turng with turng with, but only.8 rad/s without it. 13c shows that durg, but only.8 rad/s without it. 13c shows that durg itial dynamic itial dynamic steerg phase, required rque quite large. with steerg phase, required rque quite large. with can satfy can satfy rque requirement rque tends a smaller constant value steady rque requirement rque tends a smaller constant value steady state. power state. power generated by sprockets shown 13d. power on outer side generated by sprockets shown 13d. power on outer side creases with creases with power on ner side slightly reduced, but power on ner side slightly reduced, but overall power not overall power not very large. very large Trajecry(w/o) Trajecry(w) Y(m) w(rad/s) Yaw rate(w/o) Yaw rate(w) X(m) T(N*m) P(kW) (c) (d) Simulation Simulation results results.5 B.5 steerg: B steerg: Trajecry; Trajecry; Vehicle Vehicle yaw rate; yaw (c) Sprocket rate; (c) Sprocket rque; (d) rque; Sprocket (d) power. Sprocket power B B Steerg Steerg steerg steerg wheel wheel manipulated manipulated output output R R = =.5.5 B, B, accelerar accelerar pedal pedal pushed pushed botm botm begs begs turn turn from from its its static static position. position. trajecry trajecry shown shown 14a. 14a. It It can can be be seen seen that that understeer understeer improved improved with with.. From From 14b, we can see that fally yaw rate 1.2 rad/s, which close 14b, we can see that fally yaw rate 1.2 rad/s, which close oretical value, yaw rate without only.8 rad/s. As oretical value, yaw rate without only.8 rad/s. shown 14c, sce used, outer side output rque creased, ter side sprocket regenerates brakg rque. power generated by outer sprockets regenerated by ter sprocket are shown 14d. Th time ner mor

15 Energies 217, 1, As shown 14c, sce used, outer side output rque Energies creased, 217, 1, 1118 ter side sprocket regenerates brakg rque. power generated by15 17 outer sprockets regenerated by ter sprocket are shown 14d. Th time ner regenerates brakg power, while outer mor output maximum power. Although mor regenerates brakg power, while outer mor output maximum power. Although oretical rque power don t exceed maximum value accordg Table 3, rque oretical rque power don t exceed maximum value accordg Table 3, rque power outer side sprocket simulation much larger than oretically calculated, meang power outer side sprocket simulation much larger than oretically calculated, meang steerg restance moment may be larger than we expected. steerg restance moment may be larger than we expected. Y(m) Trajecry(w/o) Trajecry(w) X(m) w(rad/s) Yaw rate(w/o) Yaw rate(w) T(N*m) P(kW) (c) (d) Simulation Simulation results results 2 2 BB steerg: steerg: Trajecry; Trajecry; Vehicle Vehicle yaw yaw rate; rate; (c) (c) Sprocket Sprocket rque; rque; (d) (d) Sprocket Sprocket power. power B Steerg B Steerg steerg wheel manipulated output R = 8 B, accelerar pedal led steerg wheel manipulated output R = 8 B, accelerar pedal led make accelerate from 3 km/h drive steerg. trajecry shown make accelerate from 3 km/h drive steerg. trajecry shown 15a. understeer charactertic improved. yaw rate 15a. understeer charactertic improved. yaw rate shown 15b not as large as that small-radius steerg due high speed shown 15b not as large as that small-radius steerg due high speed.. power outer sprocket larger thanks, while power power outer sprocket larger thanks, while power without always at maximum value as shown 15f. without always at maximum value as shown 15f. Without Without, speed decreases rapidly, as shown 15c., speed decreases rapidly, as shown 15c. rque rotation speed rque rotation speed sprocket are shown 15d,e. sprocket are shown 15d,e.

16 Energies 217, 1, Energies 217, 1, Y(m) Trajecry(w/o) Trajecry(w) X(m) w(rad/s) Yaw rate(w/o) Yaw rate(w) (c) v(m/s) Speed(w/o) Speed(w) T(N*m) n(r/m) P(kW) (d) (e) (f) Simulation Simulation results results 8 B steerg: steerg: Trajecry; Trajecry; Vehicle Vehicle yaw yaw rate; rate; (c) (c) Vehicle Vehicle speed; speed; (d) (d) Sprocket Sprocket rque; rque; (e) (e) Sprocket Sprocket rotation rotation speed speed (f) (f) Sprocket Sprocket power. power. 6. Conclusions 6. Conclusions In th paper, we found that rque power required by propulsion mor are quite In th paper, we found that rque power required by propulsion mor are quite large accordg dynamic analys 2METV. refore, a new steerg large accordg dynamic analys 2METV. refore, a new steerg designed without creasg peak rque or power propulsion mor. consts designed without creasg peak rque or power propulsion mor. consts a planetary gear system, two gear pairs, two electromagnetic clutches a braker. By a planetary gear system, two gear pairs, two electromagnetic clutches a braker. By rque or power steerg mor propulsion mor, rque or power put rque or power steerg mor propulsion mor, rque or power put sprocket creased meet steerg performance requirements different radius. Based sprocket creased meet steerg performance requirements different radius. Based on on th, a rque-coupled dtribution strategy based on speed proposed. simulation th, a rque-coupled dtribution strategy based on speed proposed. simulation RecurDyn RecurDyn Matlab/Simulk shows that can improve output rque or Matlab/Simulk shows that can improve output rque or power power sprockets, usg proposed strategy can achieve better trajecry sprockets, usg proposed strategy can achieve better trajecry followg. followg. Acknowledgments: Th work was supported by National Natural Science Foundation Cha for fancially supportg Acknowledgments: th project Th ( ). work was supported by National Natural Science Foundation Cha for Author fancially Contributions: supportg Li th Zhai project proposed ( ). novation overall system designed methods, Hong Author Huang Contributions: are responsible Li for Zhai proposed design coupled novation systems overall simulation system system, designed Steven Kavuma performed simulation methods. Li Zhai Hong Huang wrote manuscript Steven Kavuma polhed methods, Hong manuscript. Huang All are authors responsible read for approved design coupled manuscript. systems simulation system, Steven Kavuma performed simulation methods. Li Zhai Hong Huang wrote manuscript Conflicts Steven Interest: Kavuma polhed authors declare manuscript. no conflict All authors terest. read approved manuscript. References Conflicts Interest: authors declare no conflict terest References Zhai, L.; Sun, T.M.; Wang, Q.N.; Wang, J. Lateral stability dynamic steerg for dual mor drive high speed tracked. Int. J. Aum. Technol. 216, 17, [CrossRef] Kettg, Zhai, L.; M.; Sun, Frohner, T.M.; F.; Wang, Wottawah, Q.N.; V. Wang, Drive J. Cha Lateral for stability Tracked Vehicle. U.S. dynamic Patent steerg A, for 7 dual November mor 2. drive 3. LI, high J.; Zhang, speed tracked H.; Meng,. H.; Tang, Int. J. R. Aum. Research Technol. tracked 216, 17, compliance simulation. Armor. Veh. Enge 2. 23, Kettg, 92, 4 7. M.; Frohner, F.; Wottawah, V. Drive Cha for Tracked Vehicle. U.S. Patent A, 7 4. Kim, November M.S.; Woo, 2. Y.H. Robust design optimization dynamic responses a tracked system. 3. Int. LI, J. J.; Aum. Zhang, Technol. H.; Meng, 213, H.; 14, Tang, R. Research [CrossRef] tracked compliance simulation. Armor. Veh. Enge 23, 92, Kim, M.S.; Woo, Y.H. Robust design optimization dynamic responses a tracked system. Int. J. Aum. Technol. 213, 14,

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