Optimal Regenerative Braking with a push-belt CVT: an Experimental Study

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1 AVEC 1 Optimal Regenerative Braking with a push-belt : an Experimental Study Koos van Berkel 1, Theo Hofman 2, Bas Vroemen 3, Maarten Steinbuch 4 1,2,4 Eindhoven University of Technology Den Dolech 2, P.O. Box 513, 56 MB Eindhoven, The Netherlands Phone: Fax: k.v.berkel@tue.nl, 2 t.hofman@tue.nl, 4 m.steinbuch@tue.nl 3 Drivetrain Innovations Croy 46, 5653 LD Eindhoven, The Netherlands Phone: Fax: vroemen@dtinnovations.nl This paper describes the approach and the results of efficiency experiments on a push-belt Continuously Variable Transmission () in a new hybrid drive train. The hybrid drive train uses the push-belt to charge a flywheel, with the kinetic energy of the vehicle during regenerative braking and discharge during flywheel driving. The experiments are performed on a test rig with two electric machines following prescribed speed and torque trajectories, representing the flywheel and vehicle load. The approach includes the design of a control strategy for the variator, which enables regenerative braking. The experiments show that the can be used very efficiently in the proposed hybrid drive train. Topics / Powertrain & Drivetrain Control, Electric Vehicle, Hybrid Vehicle & Fuel Cell Vehicle, Energy Efficient Vehicles 1. INTRODUCTION The market share of Continuously Variable Transmissions (s) is still growing, especially in the A-B-C vehicle segment in Asia. s enable efficient engine operation, thereby increasing the fuel efficiency of the vehicle. Due to an increasing oil price and stricter environmental regulations, a higher fuel efficiency is still desired. Hybrid transmissions can give a significant improvement (2 3%) as shown in many hybrid vehicles(e.g., by Toyota and Honda). Current battery-based systems, however, are too expensive for this segment, due to large battery packs and additional electric machine(s). As a low-cost alternative, a new mechybrid-drive train design is presented, using a flywheel module and a push-belt for energy storage and power transmission, respectively. The topology, which describes how the energy sources are connected, is shown in Fig. 1. This concept uses the push-belt to charge the flywheel (F) with load (L) (kinetic energy of the vehicle) during regenerative braking and discharge during flywheel driving. To make maximum use of the recuperation energy, the should be controlled by changing the speed ratio such that the hybrid system is operated at the most efficient operation points [1]. This requires extensive knowledge F E Fig. 1: Hybrid drive train topology with flywheel (F), combustion engine (E), vehicle load (L),, clutches and brake. of the hybrid system components, in particular the efficiency of the under flywheel driving and regenerative braking conditions. 1.1 Main contribution of the paper A small number of publications is found concerning the efficiency of s during static [2] and conventional dynamic driving[3, 4], yet not under regenerative braking or flywheel driving conditions. This paper focuses on the approach and the results of efficiency experiments on the, under these hybrid driving conditions. The experiments are performed on a test rig with two electric machines following prescribed speed and torque trajectories, representing the flywheel and vehicle load. The approach includes the design of a control strategy for the varia- L 67

2 AVEC 1 tor, which differs from many traditional designs, to enable regenerative braking. The experimental results form a solid basis for future work on an efficiency model of the, which is a valuable input for the Energy Management Strategy of the mechybrid-drive train. The outline is as follows: Section 2 describes the experimental setup; Section 3 describes the simulation models of the hybrid drive train and the experimental setup; Section 4 describes the control design of the variator; finally, Sections 5 and 6 discuss the experimental results and the conclusions. 2. SYSTEM DESCRIPTION The hybrid topology of Fig. 1 supports several functionalities. For the experimental setup, it is sufficient to have a drive train topology that supports regenerative braking and flywheel driving. Hence, a reduced drive train topology is chosen, which represents a series connection of the flywheel (F), and vehicle load (L), as shown in Fig. 2. The engine (E) has been left out. and flywheel. Then, the model of the experimental setup is described on system level. These models are used (1) to define the efficiencies of the, for the analysis of the experimental results in Section 5 and (2) to derive the setpoints (torques, speeds, speed ratio) for the experiments at the end of this section. 3.1 model The consists of a series connection of various components, such as the pump, torque converter, DNR, push-belt variator, final drive and differential. Its quasi-static model is shown in Fig. 3. In this model, thetorques(t i )andspeeds(ω i )areevaluated at four locations, being the engine (subscript e ) and wheel side (subscript w ) of the and the primary (subscript p ), and secondary side of variator (subscript s ). The push-belt variator, which is considered as the key component of the, enables a continuously variable speed ratio, defined by r cvt (t) := ω s(t) ω p (t). (1) electric machine F electric machine L T pu ( e,p pu ) var (T p p,r ) d e p s w J p T e T s T w T p J s J w torque and speed sensors pump variator final drive inertia prim. side inertia sec. side inertia wheel side Fig. 2: Photo of the experimental setup. In this figure, the left and right electric machine represent the flywheel and the vehicle load, respectively. The flywheel is coupled to the primary pulley shaft of the. The considered is a conventional, mass-production system with integrated pump, torque converter, Drive / Neutral / Reverse (DNR), variator, final drive and differential. For the considered experiments, the DNR is put in Drive and the torque converter and differential are locked. The vehicle load is coupled to the locked differential. For determining the efficiency, torque measuring shafts and speed sensors are mounted on both shafts at each side of the. 3. MODELING & SIMULATION The electric machines and the need to track setpoints, such that all torques and speeds in the reduced drive train (experimental setup), mimic the behavior of the hybrid drive train with sufficient accuracy, described by a reference vehicle driving a given velocity profile v(t). First, this section describes the quasi-static simulation models of the hybrid drive train, which consists of the, vehicle Fig. 3: Quasi-static model of the. For the considered experiments, the DNR is put in Drive and the torque converter is locked, such that ω p (t) = ω e (t). The inertias acting on the primary shaft, such as the DNR, torque converter and primary pulley set, are lumped to inertia J p. The inertia of the secondary pulley set is J s. The inertias of the final drive and differential are lumped to inertia J w. The transmission efficiency of the, as a total system, is defined by η cvt := { Pw Pe, P e > P e P w, P e, (2) with the powers P e = T e ω e and P w = T w ω w. In this model, power is dissipated by the pump, final drive and the variator, which will be discussed below. Pump: The pump provides pressure p pu for actuation of the. The power dissipation of the pump, is described by a torque T pu (ω e (t),p pu (t)), whichdependsonthespeedω e (t)andgeneratedpressure p pu (t). Values of T pu are obtained from a measured look-up table, provided by the manufacturer. 68

3 AVEC 1 Final drive: The final drive gear set gives a speed reduction with a constant gear ratio, defined by r d := ω w(t) ω s (t) = (3) The power dissipation is modeled as a constant transmission efficiency of η d =.99, which is defined by the powers P s = T s ω s and P w = T w ω w : η d := { Ps(t) P w(t), P w(t) > P w(t) P s(t), P w(t). (4) Push-belt variator: The push-belt variator dissipates power, mainly due to mechanical friction, slip within the push-belt and deformation of the pulleys and pulley shafts, among others [5]. The transmission efficiency of the variator, depends on the torque (T p (t) or T s (t)), speed (ω p (t) or ω s (t)), speed ratio r cvt (t) and the safety strategy in the variator control system (see Section 4.1), and is defined by η var (t) := { Ps(t) P p(t), P p(t) > P p(t) P s(t), P p(t), (5) with the powers P p (t) = T p (t)ω p (t) and P s (t) = T s (t)ω s (t). For the experiments, T p and T s can be calculated, using torques and speeds measured by the torque measuring shafts (T e,t w,ω e and ω w ) and the pump pressure, by the torque balances: d T p (t) = T e (t) T pu (ω e (t),p pu (t)) J p dt ω e(t), (6) T s (t) = r ( d 1 T w (t)+ J s + r ) d d J w η d r d η d dt ω w(t), (7) 3.2 Vehicle model The parameters of the reference vehicle (Toyota Vitz) are given in table 1. The angular velocity of the wheels ω w (t) [rad/s] is, for a given speed profile v(t) [m/s] of the vehicle, modeled as ω w (t) = 1 R w v(t), (8) with R w [m] the dynamic wheel radius, which includes a constantsmall slip between the tires and the road surface. The torque acting on the drive shaft, T w (t), is modeled as the sum of the roll resistance, air drag and inertia torques, and holds Table 1: Vehicle System Parameters J w 1.5 kgm 2 inertia of driven wheels m 1134 kg vehicle mass R w.282 m dynamic wheel radius C d.3 - air drag coefficient A 2.15 m 2 frontal area vehicle F r 133 N roll resistance ρ 1.25 kg/m 3 air density at 15 o C with a constant roll resistance F r, air drag coefficient C d, frontal area of the vehicle A, air density ρ, inertiaofthedrivenwheelsj w andvehiclemassm. 3.3 Flywheel model The flywheel is modeled as an inertia J f =.3 kgm 2, in series with a gear set and the. The gear set gives a constant gear ratio r f := ω e(t) ω f (t) = 1 12, (1) with ω f (t) the speed of the flywheel. The torque losses, generated by, e.g., air drag, bearings and gears, are assumed to be negligible compared to the torque required for flywheel driving and braking. Then, the torque generated by the flywheel T f (t) equals T f (t) = J f d dt ω f(t). (11) 3.4 Experimental Setup Model Figure 4 shows the quasi-static model of the experimental setup. The electric machine on the left side (subscript 2 ) represents the flywheel, whereas the electric machine on the right side (subscript 1 ) represents the wheels. The electric machines have an inertia (J i ) and generate torques (T i ) and speeds (ω i ), that are measured by the torque measuring shafts on both sides of the. For a given velocity profile v(t) and initial flywheel speed (ω f, ), the setpoints of the electric machines are calculated using (8), (9), (1), (11). Here, the torque required by the flywheel T f, is estimated with an estimated constant transmission efficiency of the, of η cvt =.85: d T 1 (t) = T w +J 1 dt ω w, (12) ( t T f ω 2 (t) = r (t) ) f J f +rf 2J dt+ω f,, (13) 2 T f (t) = r fr cvt (t)η cvt T w(t). (14) T w (t) = R w (F r C daρv 2 (t) +( J w Rw 2 +m) d (9) dt v(t)), 3.5 Setpoints for the Experimental Setup A velocity profile v(t) is chosen, with constant velocities (3 and 5 km/h) and constant accelerations (.8and.8m/s 2 )thatarecommonindrivecycles, 69

4 AVEC 1 T (T e e,r ) 2 e w 1 J 2 J 1 T 2 T 1 T e T w or (2), which is determined by the control switching strategy, as will be explained later. p T p F p Fig. 4: Quasi-static model of the experimental setup. p s p p as shown in the upper graph of Fig. 5. The corresponding reference trajectories of the speed ratio of the r cvt,d (t), flywheel speed ω f,d (t) with ω f, = 3. rpm and wheel torque T w,d (t) as a function of time are depicted in the lower three graphs of Fig. 5. Setpoints for flywheel driving and regenerative braking 5 velocity profile [km/h] ratio [ ] flywheel speed [rpm] wheel torque [Nm] Fig. 5: Velocity profile and setpoints for the speed ratio r cvt, flywheel speed ω f and wheel torque T w. 4. VARIATOR CONTROL SYSTEM For the considered experiments, the variator control system is of significant importance as: (1) the level of the clamping forces influences the transmission efficiency of the ; and(2) regenerative braking, with negative power flow through the variator (T p < ), requires a specific control design. Fig. 6 gives a schematic view of the variator. The variator consists of a metal push-belt, which is clamped between a pair of pulleys on each side of the variator (primary side, subscript p, and secondary side, subscript s ). Each pulley pair consists of one axially fixed sheave and one axially moveable sheave. On each moveable sheave, an axially pulley force (F p and F s ) is generated by an oil pressure, controlled by a hydraulic system. The level of the clamping forces determines the maximum allowable torque transfer, without macroscopic slip between the push-belt and pulley sheaves, whereas the ratio of the clamping forces determines the speed ratio. Hence, the objective for the variator control system is twofold: (1) transfer of torque T p or T s ; and (2) tracking of the reference speed ratio r cvt,d. The control objective of each pulley set may be decoupled, i.e., either (1) F s Fig. 6: Schematic view of the push-belt variator. 4.1 Torque Transfer Control The level of the clamping forces determines the amount of slip between the push-belt and pulley sheaves. When the clamping force is too low, the increased slip may cause heavy damage and reduced efficiency. When the clamping force is too high, the increased friction losses compromise the transmission efficiency ofthevariatorandraisethepumpload. Theminimal clamping force, required to transfer torque without macroscopic slip (i.e., slip that may cause damage), is computed by means of a Coulomb based friction model of the variator (see, e.g., [2], [6]): F x,min = cosθ Tx 2µR x, x {p,s}, (15) with θ half the pulley wedge angle, µ the friction coefficient between the pulleys and the belt and R x the geometric running radii of the belt on the pulleys. In most production s, a safety strategy is employed to compensate for disturbances and uncertainties in the variator model. Typically, safety strategies combine a relative f r with an absolute safety factor f a. In case the variator efficiency is sufficiently high, one may assume that F p,min F s,min. Hence, theminimal safe clampingforcef safe,which holds for both pulleys, is formulated as: F safe = cosθ( (1+fr)Tp +fatp,max) 2µR p. (16) For the experiments, common values are used: f r =.15, f a =.2 and T p,max = 124 Nm. 4.2 Speed Ratio Control The ratio of the clamping forces determines the speed ratio of the variator. The speed ratio is controlled with a feedforward (open-loop) controller and a feedback (closed-loop) controller. For the design of a feedforward controller, static and dynamic models are used, to prescribe reference trajectories for the clamping forces. The static model, relates the static pulley-thrust ratio κ(r cvt,t p ) with the speed ratio(r cvt )andprimarytorque(t p )foragivensafety strategy in the torque transfer control: κ(r cvt,t p ) = F p F s ṙcvt= s T s, (17) 7

5 AVEC 1 with ṙ cvt the rate of ratio change. Here, pulleythrust ratioκ(r cvt,t p )is basedon static experiments under various conditions, such as different engine speeds, wheel torques and speed ratios, see Fig. 7. ln(κ) [ ] ln(κ) [ ] Nm Nm.5.5 ln(r ) [ ] Nm Nm κ for T p > κ for T p <.5.5 ln(r ) [ ] Fig. 7: Static pulley-thrust ratios plotted on logarithmic scale as a function of speed ratio, for positive and negative torques, based on static experiments (ṙ cvt = ) under various conditions. For the dynamic model, several designs are proposed in literature, among others, by Ide et al [7] and Carbone et al [8]. Ide introduces a relatively simple grey-box model, which reasonably describes the dynamic shift behavior, validated by various experiments, e.g., in[5]. Carbone introduces a theoretical model (CMM-model), which accurately describes the dynamic shift behavior, validated by experiments under various operating conditions. Carbone found, that Ide s model appears to be a first order approximation of the CMM-model. Here, Ide s model is chosen, due to its simple implementation and its reasonable accuracy. This model relates the rate of ratio change (ṙ cvt ), the speed ratio (r cvt ), primary pulley speed (ω p ) with a shifting force: F shift = ṙ cvt k r (r cvt ) ω p. (18) Here,k r (r cvt )isanexperimentallyobtaineddamping. The models (17) and (18) are used to derive the following control laws (F p,ratio and F s,ratio ) to track the desired speed ratioand change(r cvt,d and ṙ cvt,d ): F p,ratio = F shift,d +κf safe, (19) F s,ratio = F shift,d + F safe κ, (2) ṙ cvt,d +u F shift,d = k r (r cvt,d ) ω p, (21) using a linear feedback control action u (with PID-control). Further details regarding the design of a ratio controller can be found, e.g., in [2] and [6]. 4.3 Control Switching Strategy The clamping force on each pulley controls either the torque transfer or the speed ratio. Traditionally, the majority of the approaches control the torque transfer via the secondary pulley (F s F safe ) and speed ratio via the primary pulley (F p F p,ratio ), see, e.g., [9]. This control approach is based on the observation, that in conventional driving conditions (T p > ), the static pulley-thrust ratio κ 1 is such that F p F s, see Fig. 7. In this situation, macroscopic slip is avoided when F s F safe > F s,min, such that with a sufficiently large safety factor (see Section 4.1), F p F s F safe > F p,min. However, duringregenerativebraking(t p < ), the static pulley-thrust ratio (κ) changes, as shown in Fig. 7. Especially when r cvt < 1, F p << F s holds, such that the control objectives need to be switched in order to avoid macroscopic slip. Hence, in that situation, the torque transfer needs to be controlled via the primary pulley (F p F safe ) and speed ratio via the secondary pulley (F s F s,ratio ). This is employed with the following control switching strategy [6]: } F p,d = F p,ratio F s,d = F safe } F p,d = F safe F s,d = F s,ratio if F shift,d +κf safe F safe, (22) if F shift,d +κf safe < F safe,(23) with F p,d and F s,d the reference trajectories for the clamping forces F p and F s, respectively. 5. EXPERIMENTAL RESULTS The flywheel driving and regenerative braking experiment is performed using the setpoints derived in Section 3 and the variator control system of Section 4. The resulting control actions and the efficiency of the are evaluated in the following sections. 5.1 Variator control system Figure 8 shows the tracking results of the speed ratio controller and the corresponding clamping forces. From this experiment, the following observations can be made: (1) the variator control system is able to accurately track its reference r cvt,d ; (2) indeed, during regenerative braking, the control objectives are switched, e.g., F p (instead of F s ) tracks F safe. 5.2 Transmission efficiency of the The resulting transmission efficiency of the as a system, as defined by (2), and of the variator separately, as defined by (5), are shown in Figure 9. From this experiment, the following observations can be made: (1) This can be used very efficiently for regenerative braking, e.g., during this period, the average efficiency is 85%. (2) This and variator have a relatively high transmission efficiency during acceleration, medium vehicle velocity and deceleration, e.g., 81 91% and 88 97%, respectively. The difference between the transmission efficiencies of the and the variator, are caused by the pump and the final drive, but also due to the kinetic energy storage in the inertias. The energy losses are shown in figure 1. From this figure, it can be observed that the energy losses are dominated by the 71

6 AVEC 1 Speed ratio [ ] Force [kn] Force [kn] Tracking of speed ratio and clamping forces.5 2 F p,d r cvt r cvt,d 1 F safe 1 F s 5 F s,d F safe F p Energy [kj] Energy losses in during experiment pump variator 5 final drive inertia 5 Fig. 1: Experimental result: energy losses of each component. Fig. 8: Experimental result: tracking of clamping pressures for torque transfer and speed ratio control. Efficiency [%] Efficiency [%] Push belt and variator efficiency during experiments η cvt flywheel driving η var flywheel driving η cvt regenerative braking η var regenerative braking Fig. 9: Experimental result: transmission efficiency of the as a system and the variator separately. pump (average of 57%) and the variator (average of 43%). The energy loss due to the pump is relatively high, especially during periods with low power demand. This is mainly due to the relatively high speeds of the pump caused by the flywheel, which is almost proportional to the power consumed by the pump. Based on this result, it can be concluded that the transmission efficiency of the may be further increased, by revision of current hydraulic scheme for the mechybrid drive train. 6. CONCLUSIONS In this paper, an approach is described for efficiency experiments on the push-belt, under regenerative braking and flywheel driving conditions. From the measured static pulley-thrust ratio it can be concluded, that to enable regenerative braking, a control switching strategy needs to be adopted in the variator control system. From the experiments it can be concluded that a can be used very efficiently for regenerative braking, flywheel acceleration and flywheel driving at medium velocity. The transmission efficiency of the may be even further increased, by the design of a hydraulic scheme which reduces the pump load during flywheel driving. Basedontheseresultsitcanbeconcludedthata push-belt, in combination with a flywheel system, can be a promising design solution for efficient hybrid vehicle propulsion. REFERENCES [1] H. Yeo, S. Hwang, and H. Kim. Regenerative braking algorithm for a hybrid electric vehicle with cvt ratio control. 22(11): , 26. [2] B.G. Vroemen, A.F.A Serrarens, and F.E. Veldpaus. Hierarchical control of the zero inertia powertrain. JSAE Review, 22(4): , 21. [3] A. Bonthron. Cvt: Efficiency measured under dynamic running conditions. In SAE Int. Con. and Exp., number 85569, [4] T. F. Chen, D. W. Lee, and C. K. Sung. An experimental study on transmission efficiency of a rubber v-belt cvt. Mechanism and Machine Theory, 33(4): , [5] B.G. Vroemen. Component Control for The Zero Inertia Powertrain. PhD thesis, Technische Universiteit Eindhoven, Eindhoven, 21. [6] M. Pesgens, B. Vroemen, B. Stouten, F. Veldpaus, and M. Steinbuch. Control of a hydraulically actuated continuously variable transmission. Int. Journal of Vehicle Mechanics and Mobility, 44(5):387 46, 26. [7] T. Ide, A. Udagawa, and R. Kataoka. A dynamic response analysis of a vehicle with a metal v-belt cvt. JSAE Review, 16(2):23 235, [8] G. Carbone, L. Mangialardi, B. Bonsen, C. Tursi, and P.A. Veenhuizen. Cvt dynamics: Theory and experiments. Mechanism and Machine Theory, 42(4):49 428, 27. [9] W. Ryu, J. Nam, Y.. Lee, and H. Kim. Model based control for a pressure control type cvt. Int. Journal of Vehicle Design, 39(3): ,