Simulated behavior of a vehicle with V-belt type geared neutral transmission with variator slip control

Transcription

1 1 Simulated behavior of a vehicle with V-belt type geared neutral transmission with variator slip control P.A. Veenhuizen, B. Bonsen,.W.G.L. Klaassen, K.G.O. van de Meerakker, H. Nijmeijer and F.E. Veldpaus Abstract Combining both launch and reverse drive functions with the ratio change function in a geared neutral continuously variable transmission (GN-CV), thus making a launch device like a torque converter and a drive-neutral-reverse set obsolete, is attracting considerable attention. his paper covers modelling and simulation of a V-belt type geared neutral transmission in and around the geared neutral point. Due to the specific nature of the geared neutral state, conventional driveline simulation models are shown to be inadequate. Experimental results are presented allowing for a more detailed description of the functional properties of the V-belt type variator, especially those related to small amounts of slip between the belt and the pulleys. he measured data will be analyzed to obtain grey model fitting parameters, which allow the data to be used in a simulation program, based on a dynamic driveline model. It will be shown that with a GN-CV stall and launch performance can be considerably better than that to be achieved with a driveline with torque converter. Keywords: continuously variable transmission, CV, infinitely variable transmission, IV, power train modelling, efficiency, slip, geared neutral p r F r GN r ω, r, r G r ω r s ω F pri, F sec P circgn P lossgn R I. NOAION Hydraulic pressure Fixed chain ratio Geared neutral ratio Ratio of annulus to sun radius of epicyclic gear Speed, orque, Geometric ratio Speed ratio at zero speed loss orque ratio at zero torque loss Speed slip Primary, secondary clamping force Circulating power in GN state Loss power in GN state Radius echnische Universiteit Eindhoven, Departement of Mechanical Engineering, P.O. Box 513, 56 MB Eindhoven, he Netherlands, corresponding author: P.A.Veenhuizen@tue.nl orque β Pulley sheave angle η var+, (η var ) Efficiency for positive (negative) power flow from primary to secondary variator shaft µ Friction coefficient µ eff Effective friction coefficient ω Angular speed Subscripts F Fixed ratio path Low, OD Low, Overdrive in, out Input, output eng Engine load Road load pri, sec Primary, secondary side of variator sun, pla, ann sun, planet carrier, annulus II. INRODUCION Efficiency improvement has been the main reason for developing split-path transmissions based on hydrostatic variators. By transmitting part of the engine power through conventional gears, the load on the variator and thereby power losses are reduced. With increasing engine torque levels for passenger cars, the main reason for developing split-path V-belt type CV s is improvement of the CVs torque capacity [1]. Partial unloading of the variator creates room for higher transmission input torque with comparable variator endurance life expectation. he price for this increased torque capacity is a reduced CV ratio range. Usually this is solved by adding two clutches, allowing for an additional direct Low mode, significantly extending the ratio range at the cost of an, albeit synchronous, shift. Apart from this development, there has been significant interest in so-called Infinitely Variable ransmissions (IVs). An interesting feature of this type of transmission is that it allows for a so-called

2 geared neutral state. In this state, a running engine can be connected to the drive shafts of a vehicle standing still, without the use of a slipping clutch. For this purpose, the possibility of an epicyclic gear to subtract two input angular speeds to generate a zero output speed is considered. By changing one of the input speeds, the output speed starts to deviate from zero, causing the vehicle to take off. A research study on an IV based on the PIVchain variator, was reported on already in the early nineties [2], [3]. Nowadays, an IV is under development by orotrak [4]. It is based on a full toroidal variator. Another development by Nissan MC is based on a half toroidal variator [5]. A very recent paper by GM [6] covers the control of the geared neutral point in a half toroidal traction drive split power CV. he main advantages and disadvantages on system level of a GN-CV over a conventional CVbased driveline with a torque converter (C) or with conventional wet plate clutches are: No separate starting device needed. No drive-neutral-reverse (DNR) set required. Oil development can be focused on compatibility with variator related functions, since C and slipping clutches are absent. Extra fixed gear set or chain, as well as an epicyclic gear required. wo clutches required to extend the ratio range. Both clutches are only actuated at or near synchronization. Running variator at stall and launch. An important difference between toroidal and belt type variators regarding control is the fact that the reaction force of the power roller inside the toroid variator is a direct measure for the transferred torque. Controlling this force means controlling the output torque. Nowadays, most developments use this feature in some way, including arrangements without geared neutral capabilities. A V-belt type variator does not have this intrinsic feature. herefore, controlling a V-belt type transmission at or near the geared neutral point requires special attention. his issue is addressed in a previous paper [7]. Since the present paper is concerned with the geared neutral state obtained with V-belt type variators, the layout and transmission parameters of the IV as described in [2] and [3] were taken as reference albeit with minor modifications. his paper first describes a basic geared neutral layout and its kinematic, torque and power relationships in section 3. While deriving a model for the GN-CV (section 4), the necessity of more detailed knowledge of variator loss mechanisms becomes apparent. he experimental determination of these quantities is the subject of section 5. he simulation model of the GN-CV driveline is outlined in section 6 and used in section 7. he results are discussed in section 8. Finally, section 9 gives some conclusions and recommendations for future work. A. Layout III. RANSMISSION MECHANICS A typical layout of a driveline with a geared neutral transmission is presented in Fig. 1. he sun C1 Fig. 1. Schematic representation of a typical Geared Neutral ransmission. of the epicyclic gear is connected to the engine shaft via the V-belt variator. he variator transfers torque by means of friction forces, due to clamping forces, which in turn are generated by hydraulic cylinders. he planet carrier is also connected to the engine shaft via a fixed-ratio mechanical path and clutch C1. he annulus drives the final drive reduction (r d ) and differential gear. By closing clutch C2 and opening C1, the epicyclic gear becomes a direct link between the secondary variator shaft and the final drive and the transmission behaves like a conventional CV. he Low mode of the transmission is realized by closing C1 and releasing C2. In this mode, the GN-CV exhibits the geared neutral state. In the rest of this paper, C1 is closed and C2 is open, since this is the relevant case for geared neutral behavior. he synchronous transition to the state with C2 closed and C1 open is beyond the scope of this paper. B. Kinematics From the kinematics of the epicyclic gear it is seen that: ω sun = ω pla + (ω pla ω ann ), where C2 2

3 , the planetary ratio, is the ratio of the annulus radius and the sun radius. he sun speed is always equal to the speed ω sec of the secondary variator pulley, whereas the annulus speed ω ann is always equal to the output speed ω out. With C1 closed, the carrier speed ω pla is equal to r F ω pri = r F ω in, where r F is the fixed chain transmission ratio. Combining these relations results in ω out = ω in 1 [r GN r ω ] (1) where r ω is the variator speed ratio, i.e. ω sec = r ω ω pri. Furthermore, r GN is a characteristic parameter, given by r GN (1 + )r F. (2) Obviously, the GN-state which is the state where ω out = and ω in, can only be realized when r ω = r GN. C. orque and power For the following all losses are assumed to originate in the variator. A free body diagram, shown in Fig. 2, can be used for the determination of torque level at various relevant nodes inside the transmission. Both clutches have been removed and a direct link has been substituted for C1. On noting that in = pri + F, F = r F pla, he engine supplies the power that is lost inside the GN-CV which is given by P lossgn = 1 (r GN r ) out ω in. (5) On noting that, contrary to the common case, positive power flows from secondary to primary shaft, variator efficiency is given by η var = priω pri sec ω sec = r r ω. (6) he minus sign subscript to η var indicates that this efficiency is defined for positive power flow from secondary to primary shaft. Now, Eq. (3) goes over in in = out r GN [ 1 ηvar ], (7) showing that high variator efficiency may cause excessive output torque, even at moderate input torque levels. he relation out = sun = sec = pri = F (8) r r GN shows that then also the loading of various other components, including the variator, may become excessive. However, the variator will be shown to be a suitable component for controlling the output torque, since the transferable torque can be limited by limiting the level of clamping force. in pri F Fig. 2. r w,r sec F sun r F pla pla sun pla ann A free body representation of the GN-CV. pri = r sec, sun = sec, ann = out and sun : pla : out = 1 : (1 + ) :, a relation between in- and output torque can be derived: in = out 1 [r GN r ]. (3) In the GN state, the circulating power, loading both chain and variator, is given by P circgn = out r GN ω in. (4) out 3 IV. VARIAOR MODEL Usually, a V-belt variator in a conventional drive train is modelled as a reduction with a controllable ratio r = ω sec/ ωpri = pri/ sec. Often efficiency η is assumed to depend on this ratio and on input torque only. Variator shift dynamics can be approximated by for instance the model by Ide [8]. Variator slip is usually neglected, using the argument that slip losses are generally much smaller than torque losses. Modelling a transmission in the launch condition requires the introduction of a state with zero transmission efficiency. Since output power is zero at stand still and input power is finite (running engine delivering torque) the transmission should be capable of absorbing all engine power. Usually, this function is realized by either a C or a slipping clutch. For this reason, losses play a significant role for the modelling of the GN-CV in and around the GN-state. hese losses can be assumed to originate mainly inside the V-belt variator. When clutches C1 and C2 from Fig. 1 are present, these too may be used for absorbing engine power. Within the

4 scope of this paper, however, this case is not further investigated. he following sections will cover the experimental determination of variator losses and traction curves. he measured data will be analyzed in terms of grey model fitting parameters, which allow the data to be used in a dynamic simulation of the GN-CV. V. DEERMINAION OF V-BEL VARIAOR RACION CURVES AND LOSSES A. Introduction his section on experimental results refers to measurements carried out on a single variator with push-belt, not in a geared neutral arrangement, manufactured by van Doorne s ransmissie bv. he position of the moveable sheave on the primary shaft was mechanically blocked. Different blocking rings were used for measurements in overdrive, medium and low ratio. Positive power flows from primary to secondary shaft. V-belt variator torque and slip losses, defining efficiency, are described in terms of the following experimental variables: in- and output speed, in- and output torque and clamping force. By assuming that all variator components have infinite stiffness, a straightforward way to account for torque losses can be represented by sec = pri loss r. (9) loss represents the torque losses that are generated by friction inside the V-belt when it is in contact with the pulley sheaves. Both r and loss can be found by fitting Eq. (9) to the experimental data. Similarly, slip losses may be accounted for by using ω sec = (ω pri ω loss ) r ω (1) with the related dimensionless quantity called (speed) slip: s ω = ω loss ω pri = 1 r ω r ω. (11) Both r ω and r represent the speed and torque ratios in a state where torque loss and slip loss are zero and η var+ = r ω /r = 1. With Eq. (9) and Eq. (1) this leads to r = r ω = r G, where r G = R pri /R sec, with R pri and R sec representing the primary and the secondary V-belt running radius, respectively. Since torque is transmitted by friction in a typical V-belt arrangement, an effective friction coefficient for a blocked variator can be defined by (see [9]): µ eff (s ω ) = sec(s ω ) cos(β). (12) 2F sec R sec By measuring secondary torque sec and secondary clamping force F sec while varying s ω and deriving the secondary running radius R sec from variator geometry, the effective friction coefficient can be determined. For the measurement of F sec the pressure p sec in the secondary clamping cylinder is measured. An additional clamping force component, originating from centrifugal forces on the rotating oil must be taken into account. B. Experimental setup Motor dspace Fig. 3. Hydraulics Valves Belt- Box Brake Schematic representation of experimental setup. he experimental setup is shown schematically in Fig. 3. he main part of the system is the P811 type belt box. It is driven and loaded by Siemens asynchronous motors ( Motor and Brake in Fig. 3). hese motors deliver a maximum torque of 298 [Nm] with a maximum speed of 525 [rad/s]. Both motors are equipped with a Heidenhain ERN1381 incremental rotary encoder with 248 [ppr]. he torque at both sides is measured using a HBM 2WN torque sensor. he maximum allowable torque is 2 [Nm] up to 15 [rad/s]. A separate hydraulic unit is used to provide the required flow and pressure for actuating the variator as well as for lubrication and cooling purposes. More details can be found in [9]. During measurement, the clamping force on the secondary pulley F sec was held constant, while the primary pulley sheave was mechanically blocked, fixing primary belt running radius R pri. Assuming fixed belt length a constant belt running radius, R sec is also defined by geometry. During the experiments, the speed of the motor was held constant and the speed of the brake was varied such that a well defined amount of variator speed slip s ω could be realized. 4

5 Low Medium µ eff [ ] µ eff [ ] loss [Nm] loss [Nm] η var+ η var Overdrive µ eff [ ] s ω loss [Nm] s ω η var s ω Fig. 4. ypical results of the measurement of the friction coefficient µ eff, torque loss loss and variator efficiency η var+ as function of speed slip s ω. op row: Low ratio, middle row: medium ratio; bottom row: Overdrive ratio. C. Experimental results Fig. 4 shows typical results of the measurement of the effective friction coefficient µ eff, torque loss loss and variator efficiency η var+ as function of speed slip s ω, at three ratios: Low, medium and OD. Input speed was ω pri = 15[rad/sec], secondary clamping force was F sec = 8[kN]. Additional experiments at different input speeds (225[rad/sec] and 3[rad/sec]) and at different secondary clamping force levels (5[kN] and 12[kN]) were carried out. raction curves (µ eff (s ω ) vs s omega at fixed r G and F sec ) show roughly linear behavior at low slip values, whereas a rather sharp transition to a virtually constant value at about 1% slip (medium and OD) to 2.5% (Low) can be seen. he maximum friction coefficient proves to depend weakly on r G and on F sec, being typically µ max =.9 in Low up to µ max =.15 in OD. loss Proves to be almost independent from slip, but the value depends considerably on r G and on F sec. Efficiency shows a maximum at about 2.5% slip in Low and at 1 to 1.5% in medium and overdrive. he slight lowering of efficiency with increasing slip for large slip values can be attributed entirely to slip losses, whereas torque losses dominate at very low slip values. he experimental results also show that r ω equals r to within measurement accuracy, so that the relation r = r ω = r G, which was derived for the loss-free case in section 5.1, can also be used for the case with variator losses. VI. SIMULAION MODEL OF BASIC DYNAMICS OF A DRIVELINE WIH GN-CV A. Description and assumptions A schematic representation of the simulation scheme is given in Fig. 5. he relevant degrees of freedom for the GN-CV model are the input speed ω in (equal to engine speed) and output speed ω out, with their respective associated Engine Side Inertia and Wheel Side Inertia. he inertia s are linked by the GN-CV. he slip and torque losses are modelled by assuming infinite variator stiffness. Although the experimental results have 5

6 eng Engine Side Inertia in in Geared Neutral ransmission r out out Vehicle Side Inertia load the engine is only loaded by the transmission losses. Opening the throttle will quickly lead to maximum engine speed, quite opposite to the case with a C, where the engine will speed up to stall speed. herefore, the engine speed should be controlled independently. Fig. 5. Variator Shift Dynamics ppri psec Basic GN-CV simulation scheme. been obtained on a variator with blocked primary pulley sheave, it is assumed that the measured data also hold for the case in which the variator changes ratio. Using Eq. (11) variator slip can be calculated by deriving r ω from Eq. (1). By using the semiempiric models given in [8], the dynamics of the variator shifting process is represented. his model relates primary and secondary clamping forces to variator shift speed ṙ G. Although variator shift speed is known to depend on variator slip, this in not taken into account during the simulations, due to lack of data. Slip s ω can be converted into sec by using a look-up table based on the measured traction curves and Eq. (12). In this look-up table, only the dependence of µ eff on r G and s ω are taken into account. Calculation of pri follows from pri = loss + r sec, with loss also taken from a look-up table, based on the measured data. Both pressures p pri and p sec can be regarded as control inputs. For the look-up table representing loss only dependence on r G and on F sec are taken into account. B. Driveline control In a vehicle stall condition, control of the output torque out cannot be accomplished by control of engine speed as is customary with conventional drivelines comprising a C. Equation Eq. (8) shows a linear relation between out and sun = sec. his means that sec would be a candidate for output torque control in and around stall condition. Should the transmission contain a sensor for measuring sec, output torque control can be carried out by using this sensor signal. In most cases, however, such a sensor is not present. In the following section a control technique is proposed which relies on the specific friction characteristics of the V-belt variator. In the geared neutral point, C. Variator slip control he relation out = sec = 2 F sec µ eff (s ω )R sec, cos(β) (13) derived from Eqs. (8) and (12), shows that by controlling F sec the transmission output torque can be controlled. µ eff ( s ω ) µ max Micro slip Intermediate slip Macro slip s ω Fig. 6. Schematic representation of friction coefficient versus speed slip. Illustration of three slip regimes. An important parameter in this equation is the slip dependent friction coefficient µ eff (s ω ). As can be seen from the measurement results, schematically reproduced in Fig. 6, µ eff (s ω ) is approximately constant within the so-called intermediate slip region. he intermediate slip region is defined as the region beyond the micro slip region and below the macro-slip region where damage to belt and/or sheaves can be expected after prolonged running. A recent paper [1] shows that the variator based on push-belt technology can safely withstand slip up to 6% under otherwise normal running conditions. As long as slip is controlled to be in the intermediate slip region, µ eff (s ω ) is approximately equal to µ max and out is linearly dependent on F sec at a fixed ratio. Controlling F sec by controlling p sec is standard practice in many CV applications, but controlling slip s ω requires a separate measurement of this quantity. An interesting suggestion for the measurement of s ω has been given in [12] using a lock-in technique. Another approach for measuring variator slip is by 6

7 accurately calibrating the geometric axial position of a variator sheave position to r G = r ω and then use Eq. (11) to estimate s ω (for details see [11]). It is interesting to note that a limited amount of noise and DC offset in the measured value for s ω has little effect on the realized output torque, since µ eff / s ω in the intermediate slip region. his only holds of course, as long as their combined effect does not cause s ω to leave the intermediate slip region. A proposal for a variator control scheme is given in [7] and reproduced in Fig. 7. he reference input for clamping force control is not actual torque, but the desired output torque as it results from the accelerator pedal interpreter. his value is then used for the calculation of clamping force that would just be adequate for transfer of this torque. It is the purpose of the slip controller to obtain variator slip within the Intermediate Slip Region (see Fig. 6). his is realized by shifting the variator. herefore the shift force, which is the force that causes the variator to change ratio, should become larger when the slip error becomes larger. his is realized by the P-controller, indicated in Fig. 7. More advanced controllers may lead to better control performance, but obscure the working principle. he sign of the slip error determines whether an up- or downshift should be made, in order to reduce slip error. Since the shift force should always be positive, so that the clamp force is always the lowest of the primary and secondary actuating forces on the variator, the only way to allow for up- and downshifts is to interchange clamp and shift forces between primary and secondary pulley, depending on the sign of the slip error signal. VII. SIMULAION RESULS he dynamic model with the mentioned control scheme has been implemented in Matlab/Simulink. Results from a simulation run, depicted in Fig. 8, show the transition at t=3 [sec] from idle state, with low engine speed (8 [rpm]) and zero commanded output torque to a stall-state with output torque of 4 [Nm] and engine speed equal to 22 [rpm]. At t=5 [sec] the engine speed is increased to 45 [rpm] and the brakes are released, causing the vehicle to accelerate. he variator slip setpoint is equal to 3.5 during the whole simulation, since the traction curve is known to be approximately independent from slip at this value for all variator ratio s. During stall (t=3 to 5 [sec]), engine torque and power is seen to be low, whereas the absolute value of the secondary torque exceeds 16 [Nm]. Variator power is seen to be appreciable ( 5 [kw]) in this state, whereas engine power is still small, reminiscent of the power circulation state. Sharp peaks of engine power can be seen at those instances where engine speed setpoint is sharply increased. When the brake is released (t=5 [sec]) the vehicle starts to accelerate and the variator starts shifting towards Low, in order to maintain the requested amount of slip. Due to physical shift speed limitation and limited control gain, slip can be seen to drop to values close to zero at t=1 [sec]. his also leads to reduction of output torque, due to the reduction of µ eff when s ω tends to zero. Engine power is seen to increase now that power can be applied to both vehicle acceleration and road load losses. Variator torque can be seen to be limited during both stall and launch. VIII. DISCUSSION A clear distinction with a drive train with C is the fact that the GN-CV does not have a component capable of taking up large amounts of power and transform it into heat. Instead, the GN-CV recycles the power efficiently, and during stall, engine output power can and must drop back to low values once its speed has been increased to the desired value as can be seen in the simulation results. Contrary to the driveline with C, the generation of stall torque does not require an engine speed increase and can therefore be expected to be much more dynamic, if requested. his is also clearly shown in the simulation results, where at t=3 [sec], output torque is increased very rapidly, without any engine speed increase. Since the engine is only loaded by the variator and hydraulic pump losses, more torque is available for speed increase as compared to the C case, where the engine is increasingly loaded with C impeller torque. his also will lead to a more responsive stall and launch behavior. It is interesting to note that during launch, engine sided inertia s do not play a role. his is easily seen by taking the time derivative of Eq. (1): ω out = ω in 1 (r GN r ω ) ω in ṙ ω. (14) he first term equals zero in the geared neutral state, so that the initial launch acceleration is completely described by the ratio change dynamics of the variator. Aiming for maximum initial acceleration calls for high engine speed and high ratio change speed, limited by the power recirculating capabilities of the variator. his situation is quite 7

8 Desired Output orque sec DV = r outdv P F clamp sec DV cos( λ) = 2µ R max sec Clamp Force reference Setpoint Primary Clamping Force Controller Slip error Sign Measured Slip Percentage 3.5% Desired Absolute Slip Value Sign + Shift Force + u P Offset + - P-Controller Slip controller Shift Force reference Force Interchanger Setpoint Secondary Clamping Force Controller Fig. 7. Variator control scheme Ang. Speed [rpm] setpoint ω eng Slip setpoint orque [Nm] 4 2 out eng setpoint 2 sec pri Acceleration [m/s 2 ] r ω [ ] ime [s] Power [kw] 1 5 P eng 5 P pri ime [s] Fig. 8. Simulation of geared neutral CV during stall and launch 8

9 opposite from the usual case, where extreme low ratio s lead to a negative effect on acceleration due to large contribution of engine side inertia. Low efficiency of the power recirculating transmission, often mentioned as an argument against GN-CV s, is largely irrelevant, since efficiency of any drive train is zero at stall/launch. It can be expected that the fuel consumption of a vehicle with GN-CV will be lower than that of a vehicle with C, since the ability of transforming substantial amounts of mechanical power into heat is considerably lower for the former. It can be easily shown that absolute value of power flowing through the variator becomes even lower than the r power at the output when ω out > ω GN in 2. On the other hand, launch of the vehicle in the reverse direction leads to higher circulating power levels than forward launch when similar acceleration is requested. IX. CONCLUSIONS AND RECOMMENDAIONS Making use of specific properties of the variator can render a viable proposition V-belt based GN- CV. he approach used with toroidal variators, using control of the power roller support pressure in order to control output torque, cannot be used with V-belt variators. However, using the specific properties regarding slip and traction coefficient of the V-belt variator, a new type of control system has been included in the simulation. Experimental data has been presented, allowing this control system to be used in dynamic simulation of a GN-CV driveline. By means of this simulation it has been shown that variator slip control presents an interesting option for controlling the GN-CV output torque. he simulation also shows that the stall and launch performance of a vehicle with GN-CV can be considerably better than what can be achieved with a driveline with C. Lower fuel consumption can be expected, since vehicle launch can be carried out with considerably better efficiency. Launch behavior is strongly dependent on variator shift speed. Both stall and launch are basically limited by the power recirculating capabilities of the variator. Variator shift speed should be adequate for launch performance. his paper focuses only on the behavior in and around the geared neutral point, especially during high torque operation. Extending the research beyond these limits is recommended. Also further investigations of the Intermediate slip regime and into variator slip reconstruction techniques is recommended. REFERENCES [1] Märkl, J. and M. Schencker, Konzeptstudie zu stufenlosen Getrieben für Höhermotorisierungen, Wissensforum Oktober 21, Stuttgart. [2] Vehabzadeh, H., J.P. Macey, O. Dittrich, A Split-orque, Geared-Neutral Infinitely Variable ransmission Mechanism, FISIA Paper 9589, May 199. [3] Vehabzadeh, H., and S.M. Linzell, Modelling, Simulation, and Control Implementation for a Split-orque, Geared Neutral, Infinitely Variable ransmission, SAE Paper 9149, [4] Soar, G., I. James, M. Headley, G. Briffet, A. Lee, J. Newall, he orotrak IV - Passing hrough Concept Readiness, VDI conference Getriebe in Fahrzeugen (ransmission in vehicles), Friedrichshafen, Germany, 19-2 June 21. [5] Yamada, K., Parametric Modelling and Analysis of IV, Proc. of the International Congress on Continuously Variable Power ransmission, CV 99, Eindhoven, he Netherlands, [6] Hebbale, K. and M. Carpenter, Control of the Geared Neutral Point in a raction Drive CV, Proceedings of the American Control Conference, Denver, Colorado, June 4-6, 23 [7] Veenhuizen, P.A., B. Bonsen,.W.G.L. Klaassen, K.G.O. van de Meerakker and F.E. Veldpaus, Variator loading and control in a V-belt type geared neutral transmission in and around the geared neutral point., In CV 22 Congres, VDI-Berichte 179, pages , 22. [8] Ide,., H. Uchiyama and R. Kataoka, Experimental investigation on shift-speed characteristics of a metal V- belt CV, JSAE, no , [9] Vroemen, B.G. Component Control for the Zero Inertia powertrain. PhD thesis, Eindhoven University of echnology, 21. [1] Drogen, M. van, and M. van der Laan, Determination of Variator Robustness under Macro Slip Conditions for a Push Belt CV, SAE World Congress, Detroit, 24, SAE , to be published. [11] Bonsen, B.,.W.G.L. Klaassen, K.G.O. van de Meerakker, M. Steinbuch, P.A. Veenhuizen, Measurement and control of slip in a continuously variable transmission, Proceedings of the 3rd IFAC Symposium on Mechatronic Systems, September 6-8, 24, Sydney, Australia, to be published. [12] Faust, H., M. Homm, F. Bitzer, Efficiency-optimised CV Clamping System, 7. LuK Symposium, April 22. 9

10 LIS OF FIGURES 1 Schematic representation of a typical Geared Neutral ransmission A free body representation of the GN- CV Schematic representation of experimental setup ypical results of the measurement of the friction coefficient µ eff, torque loss loss and variator efficiency η var+ as function of speed slip s ω. op row: Low ratio, middle row: medium ratio; bottom row: Overdrive ratio Basic GN-CV simulation scheme Schematic representation of friction coefficient versus speed slip. Illustration of three slip regimes Variator control scheme Simulation of geared neutral CV during stall and launch