Simulation and Control of slip in a Continuously Variable Transmission

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1 Simulation and Control of slip in a Continuously Variable Transmission B. Bonsen, C. de Metsenaere, T.W.G.L. Klaassen K.G.O. van de Meerakker, M. Steinbuch, P.A. Veenhuizen Eindhoven University of Technology Department of Mechanical Engineering Den Dolech, 56MB Eindhoven, The Netherlands Abstract: Continuously Variable Transmissions are used to optimize engine efficiency in automotive drivelines. The efficiency profit however, is lost due to inefficiencies in the CVT itself. These losses occur mainly in the (hydraulic) actuation system and in the variator. The losses can be lowered by minimizing the clamping force of the pulleys on the belt. Lowering the clamping force too much also leads to heavy slipping between belt and pulley, causing damage to the system. By controlling the clamping force in such a way that a limited amount of slip is allowed, the clamping force can be minimized without risking damage to the system. A nonlinear control scheme is used to control slip in the variator. Results show that such a control method is feasible and robust to torque peaks.. INTRODUCTION The quest for vehicle efficiency improvement in the field of automotive power trains has led to many innovations. One of them, the Continuously Variable Transmission (CVT) can be seen as the optimal transmission due to its infinite number of gears. Within certain limits the engine speed can be chosen independent from the vehicle speed, which would lead to faster acceleration and lower fuel consumption. However, due to inefficiencies in the CVT these improvements are not achieved. In a CVT the main losses occur in the hydraulic actuation system, in the pushbelt itself and in the friction contact between the belt and the pulleys. Due to the construction of a CVT the problem of slip is always present. Traditionally this is solved by adjusting a constant minimum clamping pressure, which in normal operation leads to overclamping. This lowers the efficiency because of the energy dissipated by the hydraulics, the bearings and the belt. Other clamping force strategies have been developed to cope with this problem, for example the safety factor principle from VDT and the slip control from LuK (Faust et al., ). As in most cases there is a trade-off between performance and durability, high slip percentages caused by low clamping forces lead to high efficiency but can cause wear. Low slip percentages can be reached by high clamping forces which leads to lower efficiency, less wear, but more fatigue. Between these two regions an optimal can be found where wear and fatigue are low, but efficiency is high. If it is possible to keep the CVT in the optimal slip region efficiency can be improved without significant durability loss (van Drogen and van der Laan, 4). In this case an axial position sensor is used to measure the secondary pulley position, from which the geometrical ratio can be derived, which in turn enables us to compute the amount of slip. With an online clamping force controller it is possible to control the amount of slip, which leads to lower pressures and therefore a higher efficiency. In this paper the control principle will be discussed. The system is tested for critical situations and efficiency.. THEORY In Continuously Variable Transmissions the power transfer from primary pulley to secondary pulley is based on friction. The possibility of transmitting power in a friction system is restricted by the effective traction coefficient µ, which is defined in equation (Bonsen et al., 3).

2 µ [ ] Fig.. Traction coefficient at 3rad/s, ratio overdrive (.6) µ p = T p cos α F clamp R p () In this equation T p represents the primary input torque, R p represents the input radius of the belt on the pulley, F clamp represent the secondary clamping force and α is the pulley angle. The traction coefficient µ represents the capability of the system to transmit torque from driving pulley to driven pulley. A typical traction coefficient curve is shown in figure. This measured curve corresponds to the Stribeck formulas. The traction coefficient increases linearly with an increase in slip but the system becomes unstable because the slip will increase indefinitely. As the torque transmission is increasing the system reaches it s maximum traction coefficient and the belt starts to slip. This macro slip can have a destructive effect on the contact bodies. The slip in the CVT can be defined as shown in equation 4; r s = ω s ω p () r g = R p R s (3) ν = r s r g (4) it is a function of the geometric ratio r g and the speed ratio r s. Here ω p and ω s respectively represent the primary and secondary pulley speed and R p and R s respectively represent the running radii at the primary and secondary pulley. Besides the macro slip some micro slip is always present due to the play between the blocks in the belt. This can be visualized better in measurements with some removed blocks because the gaps between the blocks are larger. The effect of play can be seen clearly in figure. Prediction of micro slip is possible with the formulas from Kobayashi (Kobayashi et al., 998). An increase in slip first leads to an increase in the traction coefficient; next the traction coefficient µ [ ] Fig.. Traction coefficient in low, ω p = 3rad/s, with increased gap (.8mm) η [ ] Medium OD LOW Fig. 3. Efficiency at 3rad/s, ratio low (.4), Medium (.) and overdrive (.6) decreases which causes slip to increase exponentially. This will lead to increased wear. Consequently small slip percentages would be preferable if no side effects were present. Because of the influence of the slip on the traction coefficient it incorporates effects on the torque transmission and thus on the efficiency. In figure 3 the efficiency for three ratios are shown. Obviously the influence of slip on the efficiency of the transmission is significant. The efficiency of medium ratios is larger because the bands do not slip on the blocks, in contrast to the low and high ratios where an internal slip is present due to the difference in running radius between the blocks and the bands. 3. CONTROLLER DESIGN The system we want to control is Multiple Input Multiple Output (MIMO) because we have three inputs and three outputs as shown in figure 4. Primary and secondary clamping force and the engine torque are the inputs, and the outputs consists of the primary speed, secondary speed and the geometric ratio. From these the slip can be estimated.

3 + ω F H A B H C H A B ν HA B ω F H C ν 6 A.. ω F ω I H C Fig. 4. Schematical representation of the system Conventional CVT control strategies make use of a predefined clamping force from experimental results. The ratio is closed loop controlled by a hydraulic valve. Here the clamping force setpoint Fc also has to be closed loop controlled based on constant slip. The ratio control is based on the ratio of clamping forces. The MIMO control layout from figure 4 can be divided into three SISO loops. Since interaction is present between secondary and primary clamping forces simply SISO control strategies might not work. The loops are closed sequentially using PID control. The PID controllers are tuned manually. In the system we adjust the pressure to influence the clamping force. But due to the hydraulic system there is a difference between the desired pressure and the realized. The hydraulic system acts as a first order filter with cut-off frequency of Hz and a delay of.5 s. Of course this delay decreases the bandwidth of the control system. 4. SIMULATION The controller described in forgoing chapter is implemented in a drive train model, which has been tested before with good results. The CVT shift speed model is based on the Ide shift speed model (Ide et al., 996), which uses experimental results. In equation 6 the core of the model is shown. Fp = KP KS(r, τ)f s (5) ( ṙ = κ(r)ω p Fp Fp ) (6) T p = µf pr p cos α (7) Here KP KS(r, τ) represents experimental force ratio results as a function of the speed ratio and the desired safety factor. F p and F s represent the before mentioned primary and secondary pulley force. ω p represents the primary pulley speed and κ(r) is a experimentally defined variable, the influence of the ratio on the shift speed. Besides shift behaviour the model should also include slip, therefore the maximum torque transmission is calculated using equation 7. The used drive train simulation model consists of the following components: Engine flywheel: engine + flywheel mass. Variator: theoretical CVT-model including slip model. Ide model: model to describe CVT shift behaviour with experimental data. End gear: end gear ratio. Vehicle: mass and road load. To test the control system some relevant tests have to be performed. Critical situations for a CVT in a car are kick down situations and emergency braking. To simulate these situations a reference velocity and a driver simulator have to be designed. As a reference speed trajectory the NEDC is chosen, the driver is simulated by a PID cruise control. Besides that a brake torque has to be generated in case of desired deceleration. 5. RESULTS First test for simulation is the kick down from standstill to top speed. Target of this test is to keep the peak value of the slip within the % limit. The slip perfectly tracks the reference when no time delay is present as can be seen in figure 8, in figure 9 the slip is plotted in case of a delay of 7ms. This is the maximum delay at which the results are acceptable; above 7ms the system becomes unstable. Emergency braking is relevant to test if the system shifts quickly enough. Modern cars with ABS have a maximal deceleration of 8m/s. A kerb weight of 3kg results in a braking torque of 3.kN m with a r dyn of.3m. In overdrive situation at 5rpm we have to shift down to low as soon as possible. As can be seen in figure 7 the system lacks shifting speed, the low ratio,.48 is not reached before the vehicle stops (v=). The actuation system might be underpowered; increasing the pressure might be useful. On the other hand the ratio is close to.5 and therefore it should not be a problem to start. For measuring the efficiency of the CVT a reference trajectory has to be chosen to benchmark the alternative actuation system. In this case the efficiency of the oil pump is not included because the actuation system is not exactly known and it would not be realistic due to the lack of parameters. Besides that benchmarking the mechanical efficiency indicates the effect of the alternative clamping force control. By replacing the engine driven oil pump with rigid connection in conventional systems with decoupled electro motors, the efficiency of the actuation will be higher. To simulate the efficiency of the Variator the NEDC (New European Drive Cycle) reference trajectory is chosen. The simulation is performed with % reference slip. 6. VERIFICATION The simulations were verified using an experimental setup. A schematic view of the setup is shown in figure 5. The results are shown in figure 6. In this figure it can be seen that for torquesteps of up to 3Nm the clamping force level stays within acceptable limits, as is shown by van Drogen (van

4 J H 6 H G K A I A I H H = K E? K EJ Fig. 5. Experimental setup Slip [%] Torque [Nm] Clamping Force [N] 4 A H J H x Time [s] Fig. 6. Measured slip during run with slipcontrol Drogen and van der Laan, 4). Even for torque peaks of up to 6Nm this is the case. The reference value for the slip was set at %. The reference value for the torque was set to a series of steps of up to 3Nm. Due to the overshoot in the torque signal even higher peak loads were applied. Overall the experiments showed good performance in accordance with the simulations. These simulations were verified using an experimental setup. The results show that the control scheme has acceptable performance for torquesteps of up to 3Nm and torque peaks of up to 6Nm. The next step will be to optimize the slipcontrol and to implement it in a automotive transmission. For the optimization better models are needed for the ratio control to be able to take full advantage of the slipcontrol in the CVT. For implementation measurement of slip is still a major issue which needs to be resolved, because there is no cheap and accurate way to measure slip at this moment. 8. REFERENCES Bonsen, B., T.W.G.L. Klaassen, K.G.O. van de Meerakker, M. Steinbuch and P.A. Veenhuizen (3). Analysis of slip in a continuously variable transmission. IMECE Congress and RD&D Expo 3. Faust, H., M. Homm and F. Bitzer (). Wirkungsgradoptimiertes cvt-anpresssystem. 7. LuK Kolloquium pp Ide, T., H. Uchiyama and R. Kataoka (996). Experimental investigation on shift-speed characteristics of a metal v-belt cvt. JSAE no Kobayashi, D., Y. Mabuchi and Yoshiaki Katoh (998). A study on the torque capacity of a metal pushing v-belt for cvt s. SAE Technical papers. van Drogen, M. and M. van der Laan (4). Determination of variator robustness under macro slip conditions for a push belt cvt. SAE world congress CONCLUSIONS AND FUTURE RESEARCH In conventional CVT control strategies the clamping forces are higher than necessary due to the cautious approach needed to prevent large amounts of slip in the variator. Because slip is not measured, only preemptively measured data can be used to control the system. Over time however some parameters of the system may change. Therefore a large safety is built in to cope with disturbances and parameter variations, which introduces overclamping. This overclamping has two main disadvantages; the mechanical efficiency of the transmission is decreased and higher forces demand higher pressures, which lead to more hydraulic losses. By using online slip control the amount of slip can be adjusted to the percentage where the mechanical efficiency is highest. This will result in higher efficiencies in part-load conditions. Due to the fact that no safety is built in the controller should have a quick response. Time delay due to the actuation system will decrease the bandwidth. Attention should be paid to this point during implementation. The shifting speed is sufficient in case of emergency braking. The hydraulic losses will be smaller due to lower pressures. The simulations show that it will be possible to prevent very high sliplevels due to underclamping when the actuation system meets certain standards.

5 .5 realised ratio desired ratio ratio [ ].5 v = time [s] Fig. 7. Emergency braking shifting behaviour 6 4 slip [%] Fig. 8. Step response for the slip with no delays in the actuation system slip [%] time [s] Fig. 9. Step response for the slip with a delay of 7ms in the actuation system