ESTIMATION OF AUTOMOTIVE TIRE FORCE CHARACTERISTICS USING WHEEL VELOCITY

Transcription

1 Copright IAC th Triennial World Congre, Barcelona, Spain ESTIMATION O AUTOMOTIVE TIRE ORCE CHARACTERISTICS USING WHEEL VELOCITY Eiichi Ono*, Katuhiro Aano*, Maaru Sugai*, Shoji Ito**, Aira Tanaa**, Mamoru Saada*** and Yohiui Yaui**** * Toota Central R & D Lab. Inc., ** Toota Motor Corporation, *** Deno Corporation, **** Aiin Seii Co., Ltd. Abtract: It i important to etimate friction force characteritic beteen tire and road in order to improe the control performance of a ehicle in critical motion. In thi paper, an etimation method hich etimate parameter concerned ith friction force margin i propoed b appling the on-line leat quare method to heel rotational elocitie. The effect of the etimation i ealuated b appling the method to the braing control. Copright IAC Keord: automobile, ehicle dnamic, heel, elocit, leat-quare etimation, brae, tre, friction, ero, control. 1. INTRODUCTION or anali and computer imulation, ariou tire model for automotie ehicle are propoed (Bernard et al., 1977; Baer et al., If the friction force margin of each heel can be etimated b uing tire model, it i epected that the control performance of the ehicle can be improed. Hoeer, the parameter of the tire model are changed depending on condition of tire and road. Then, it i difficult to ue the tire model for etimating friction force margin, and a robut control approach hich treat tire characteritic a plant perturbation i propoed (Ono and Hooe,. In thi paper, e etimate friction force characteritic beteen tire and road uing heel elocit. The parameter concerned ith friction force margin i etimated b the method. The method bring high performance ehicle control hich cannot be achieed b the robut control approach. The lope of friction force againt lip elocit at the operational point, or Etended Braing Stiffne (hereafter XBS, i an important parameter of tire/road friction characteritic. Maimum braing force can be obtained at the point XBS= (ee ig. 1, and a decreae in XBS indicate a decreae in the margin of friction force. In the folloing ection, e propoe the etimation method of XBS from heel elocit b appling the on-line leat quare method. riction force XBS Operational point Slip elocit heel elocit ig. 1. Tire/road characteritic and etended braing tiffne (XBS

2 urther, e ealuate the propoed method b appling XBS to the braing control.. ESTIMATION O EXTENDED BRAKING STINESS (XBS.1 Wheel deceleration model The pneumatic tire of the ehicle hae rotational reonance from the heel inertia and the ideall pring (Umeno et al.,. Hoeer, the reonance anihe hen braing becaue of brae pad friction. Then, the rotational dnamic of the heel (ee ig. are modeled b the equation & = r rt + r d, (1 here, : moment of inertia of heel, r : radiu of heel, : friction reaction force beteen tire and road, T : brae torque (in proportion to heel clinder preure, d : diturbance from road, and : heel elocit. B auming that ehicle dnamic are ufficientl loer than heel dnamic and i a function of lip elocit, the Wheel Deceleration Model can be obtained from (1. r && = & + : Etended Braing Stiffne (XBS, : diturbance from road and brae torque fluctuation ( = r d& rt&. If e aume contant deceleration braing, for eample, µ-pea braing on contant µ road, brae torque T can be treated a a diturbance b differentiating (1. Thi implie that XBS can be etimated from heel elocit. It i not necear to ue the heel clinder preure alue. ( decribe the dnamic of heel deceleration, and XBS i proportionate to the brea point frequenc of the heel deceleration model. Then, XBS can be etimated b identifing the brea point frequenc of (. Moment of inertia of the heel riction force Brae torque T ig.. Rotational dnamic of the heel ( Radiu of the heel r (a Soft braing: = 1MPa ig. 3. Eperimental reult of the ehicle braing ith contant heel clinder preure on paced no road. ig. 4. Eperimental reult of the frequenc characteritic of heel elocit ith contant heel clinder preure on paced no road. Hard braing: heel clinder preure = 3 MPa (ig. 3 (b, moderate braing: heel clinder preure = MPa, oft braing: heel clinder preure = 1 MPa (ig. 3 (a. igure 3 ho eperimental reult of the ehicle braing ith contant heel clinder preure on paced no road. While there i ufficient margin of friction force in ig. 3 (a, it ho critical braing near µ-pea in ig. 3 (b. igure 4 ho the eperimental reult of the frequenc characteritic of heel elocit hon in (b Hard braing: = 3MPa PSD MPa MPa 3 MPa - 1 requenc [H]

3 ig. 3 during braing. The magnitude of poer pectrum denit in lo frequenc increae according to the increae in heel clinder preure, and brea point frequenc hift to the left (lo frequenc. Thi indicate that XBS decreae according to the decreae in margin of friction force.. Appling on-line leat quare method XBS [N/m] Ice Paced no B auming that i hite noie, XBS can be etimated b appling the leat quare method (Ljung, 1987 to ( a follo: τ ˆ τr φ (3 [ i] = ( [ i 1] [ i ] [ i] = [ i] + [ i 1] [ i ] P [ ] [ i 1] φ[ i] L i = λ+ φ[ i] P[ i 1] 1 φ [ ] [ ] [ i] P[ i 1] [ ] [ ] = P i 1 λ λ+ φ i P i 1 ˆ[ i] = ˆ [ i 1] + L[ i] [ i] [ i] ˆ [ i 1] P i λ (4 ( ( (6 φ (7 : ampling time, : filtered (- H band pa heel elocit, : etimated XBS, and : forgetting factor. The algorithm decribed b (3-(7 etimate XBS from the fluctuation phenomenon of heel elocit. igure ho etimated XBS b (3-(7 of the eperimental reult hon in ig. 3 (b. XBS i on the decreae according to hard braing. XBS [N/m] ig.. Etimated XBS b (3-(7 of the eperimental reult hon in ig. 3 (b 1 3 [MPa] ig. 6. Relation beteen aeraged XBS during braing and heel clinder preure igure 6 ho the relation beteen aeraged XBS during braing and heel clinder preure. According to the decreae in margin of friction force on each road urface, etimated XBS i on the decreae. Thi implie that the maimum braing force on each road urface can be obtained b the XBS ero control, i. e., actuation of heel clinder preure hich control etimated XBS to the mall alue. 3. EVALUATION O ESTIMATED XBS The etimated XBS can be applied for brae control, e.g. ABS. In thi paper, e propoe the brae control hich obtain a contant µ rate to ealuate the XBS etimation method. or an eperimental ehicle, a conentional ABS actuator i ued. Hoeer, the conentional on-off ABS ale ma not be uitable for the propoed tem. Therefore, e onl ealuate ABS performance uch a topping ditance, teerabilit and tabilit. Noie and ibration due to the conentional ABS ale are not ealuated. 3.1 XBS ero control A control tem to follo the reference alue of XBS (XBS ero control i realied b a 3 laered hierarch control a hon in ig. 7. In order to follo the reference of XBS, the XBS ero calculate the reference alue of heel deceleration, the deceleration ero calculate the reference alue of the preure of the heel clinder, and the brae ero calculate the ale command of ABS. reference + - XBS ero Decel. ero Brae ero Etimation of XBS Vehicle ig. 7. Control tem tructure of XBS ero

4 Since etimation of XBS ue the fluctuation phenomenon of heel elocit, the deceleration ero influence the etimation of XBS. The deceleration ero or on the tabiliation of heel dnamic. The Wheel Deceleration Model ith the deceleration ero can be decribed a r & e = a + & e +. (8 & e = & &, (9 & : reference alue of deceleration ero, and a : feedbac gain of deceleration ero. Then, the etimation algorithm i modified a ˆ [ ] ˆ [ ] a d i = i. ( r ˆ d : etimated alue of XBS under the deceleration ero. rom (8, it i obiou that the robut tabilit of the deceleration ero i compenated b deigning feedbac gain a min r a >, (11 here, min : minimum alue of XBS at arbitrar lip elocit on ariou road. 3. Braing control trateg baed on XBS riction force characteritic during combined teering and braing maneuer are decribed b the bruh model (Bernard et al., In thi paper, the folloing ariable are defined in order to implif the model. = = (1 1 K β = (13 K = + (14 : lip rate, : longitudinal elocit of heel, : lateral elocit of heel, K : longitudinal tiffne of tire, and K β : lateral tiffne of tire. Auming that the direction of the friction force θ coincide ith the lip direction, a tanθ =, ( the friction force can be decribed a follo. K Cae 1: ξ = 1 > 3µ 3 ( 1 ξ = µ coθ (16 3 ( 1 ξ = µ inθ (17 K Cae : ξ = 1 < 3µ = µ coθ (18 = µ inθ (19 µ : maimum friction coefficient, : longitudinal friction force, : lateral friction force, and : load force. urther, e define µ rate (i.e. generated friction force / maimum friction force a + γ = =. ( µ µ rom (1-(, the lope of friction force againt γ < 1 a lip can be decribed uing γ ( = K ( 1 γ 3 (1 i decribed a a function of K and γ. Thi mean that a contant µ rate i obtained b a control hich gie a contant, een if the maimum friction coefficient µ change. urthermore, XBS can be decribed a = 1 K = ( 1 γ 3 co θ in θ ( 1 γ 3 + ( 1 γ 3. ( 3 Thi mean that a contant µ rate i obtained b the XBS ero control that follo (. In (, force direction θ can be etimated from teer angle and ehicle elocit. 4. EXPERIMENTAL RESULTS 4.1 Braing on contant µ road igure 8 and igure 9 ho eperimental reult of traight line braing on an artificial lo friction road ith the XBS ero hich follo ( and conentional ABS. luctuation of heel elocit and the preure of the heel clinder are uppreed b the XBS ero and a larger friction force i obtained than ith conentional ABS. igure ho - plot, the approimated bruh model and the operational point of the XBS ero on an artificial lo friction road. In order to meaure - plot, the heel clinder preure of front heel equipped ith heel dnamometer (Burard and Calame, 1998 increae at a contant rate until the front heel are loced (Yaui et al.,. Vehicle elocit i alo meaured b optical enor, and i calculated b (1. The parameter K and µ of the bruh model (16 are decided o that the model

5 approimate to - plot. The operational point of the XBS ero indicate aerage and during XBS ero operation (eperimental reult hon in ig. 8. Each eperiment, i. e. meaurement of friction force characteritic and the XBS ero, ha the ame initial elocit of m/. igure alo ho aerage alue of calculated b multipling the etimated XBS b. Thi figure ho that deirable friction force can be obtained b the XBS ero. The effect of the XBS ero during combined teering and braing maneuer i hon in ig. 11. The brae i applied on ehicle turning ith a contant teering heel angle on an artificial lo friction road from an initial elocit of m/, and the longitudinal and lateral force of the front heel are meaured b heel dnamometer. igure 11 ho the aerage longitudinal friction coefficient µ = and the lateral friction coefficient ( ( = [N] µ for econd from appling the brae. ig. 8. Eperimental reult ith XBS ero on artificial lo friction road ig. 9. Eperimental reult ith conentional ABS on artificial lo friction road Etimated ( = Reference [N] ig.. riction force characteritic on artificial lo friction road µ = / ig. 11. riction force characteritic on artificial lo friction road The point O and X indicate four eperimental reult of the XBS ero and conentional ABS, repectiel. Thi figure ho that combined µ = µ + µ i alo improed b the XBS ero. 4. Adaptation to change of road friction characteritic XBS ero aail a µ pea folloing control een if maimum friction coefficient µ change. In thi ection, e ealuate the adaptation of the XBS ero to change in road friction characteritic. igure 1 ho the eperimental reult of the XBS ero during change in road friction characteritic from an artificial lo friction road to a dr road. When the ehicle tranition from an artificial lo friction road to a dr road, etimated increae according to the increae in the Etimated ( = Operational point of XBS ero Bruh model..1. margin of friction force. Then, the XBS ero or to increae heel clinder preure more rapidl than conentional ABS, a hon in ig µ = / Conentional ABS (Combined µ =.18 XBS ero (Combined µ =.1

6 [N] Lo friction road Etimated Dr road ( = Reference ig. 1. Eperimental reult of XBS ero during change of road friction characteritic from artificial lo friction road to dr road Lo friction road Dr road REERENCES Baer, E., L. Nborg and H. B. Paceja (1987. Tre modelling for ue in ehicle dnamic tudie, SAE paper, Bernard,. E., L. Segel and R. E. Wild (1977. Tire hear force generation during combined teering and braing maneuer. SAE paper, 778. Burard, H. and C. Calame (1998. Rotating heel dnamometer ith high frequenc repone. Tire Technolog International 1998, pp onner, W. D., H. Winner, L. Dreilich and E. Schunc (1996. Electrohdraulic brae tem, The firt approach to brae-b-ire technolog. SAE paper, Leffler, H. (1996. Electronic brae management EBM, Propect of an integration of brae tem and driing tabilit control. SAE paper, Ljung, L (1987. Stem Identification, Theor for the uer. pp , Prentice-Hall. Maron, C., T. Diecmann, S. Hauc and H. Prinler (1997. Electromechanical brae tem, Actuator control deelopment tem. SAE paper, Ono, E. and S. Hooe (. Technique in ehicle integrated control for teering and traction tem. In: Mechatronic tem technique and application: Volume Tranportation and ehicular tem (Leonde, C. T. (Ed, pp Gordon and Breach Science Publiher. Umeno, T., E. Ono, K. Aano, A. Tanaa, S. Ito, Y. Yaui and M. Saada (. Etimation of tireroad friction uing tire ibration model, To appear in SAE paper. Yaui, Y., H. Nitta, T. Yohida, T. Hoome and K. Kaamura (. Eperimental approach for ealuating tire characteritic and ABS performance. SAE paper, ig. 13. Eperimental reult of conentional ABS during change in road friction characteritic from artificial lo friction road to dr road. CONCLUSION XBS i an important parameter in identifing tire/road friction characteritic. In thi paper, the etimation method of XBS i propoed and the performance of the XBS etimation i eperimentall erified. urthermore, e demontrate the XBS ero control hich obtain a contant µ rate a compared ith conentional ABS. In the future, e epect that XBS can be applied for brae control tem, e.g. Electro Hdraulic Brae EHB (onner et al., 1996; Leffler, 1996 and Electro Mechanical Brae EMB (Maron et al., 1997, to greatl enhance ehicle control performance.