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Modeling of Pulley Based CVT Systems: Extension of the CMM Model with Bands-Segment Interaction Dct Nr: 2007.024

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Modeling of Pulley Based CVT Systems: Extension of the CMM Model with Bands-Segment Interaction Dct Nr: 2007.024 Traineeship Polytecnico di Bari, Italy Modeling of pulley based CVT systems: Extension of the CMM model with bands-segment interaction Dct nr: 2007.024 J.F.P.B. Diepstraten Coach: Dr. Ing. G. Carbone Dr. P.A. Veenhuizen January 2007 Contents Contents....................................................................................................................................................2 Introduction ..............................................................................................................................................3 1. Introduction to CVT systems................................................................................................................5 1.1 Pulley Based Transmission.............................................................................................................5 1.1.1 Metal Pushing V-belt...............................................................................................................6 1.1.2 Metal V-chain..........................................................................................................................6 2. Existing Models....................................................................................................................................8 2.1 Assumptions ...................................................................................................................................8 2.2 Mechanical Model ..........................................................................................................................8 2.3 Pulley Deformation.........................................................................................................................9 2.4 Momentum Equation ....................................................................................................................10 2.5 Comparison with other models.....................................................................................................11 2.6 Simplified and Dimensionless equations......................................................................................13 3. Band Segment Interaction ..................................................................................................................15 3.1 Assumptions .................................................................................................................................15 3.2 Geometrical model .......................................................................................................................15 3.3 Continuity Equation......................................................................................................................17 3.4 Forces equilibrium........................................................................................................................17 3.5 Dimensionless equations ..............................................................................................................19 3.6 Influence of clearance between the segments...............................................................................19 3.7 Parameters ....................................................................................................................................21 3.8 Driving Pulley ..............................................................................................................................22 3.9 Driven Pulley................................................................................................................................28 3.10 Verify distribution of the kinematical strain...............................................................................35 4. Future Work .......................................................................................................................................40 Conclusions ............................................................................................................................................41 Literature list ..........................................................................................................................................42 2 Introduction Nowadays the car has become the most used transportation application in the world. From some estimation there are nowadays almost 1000 millions registered vehicles over our entire planet [Ref: 1], and this number is still rising. This enormous number of cars has great influence on our environment. The exhaust gases are filled with toxic gases and particles, like nitrogen oxides and sulphur oxides, and also not directly poisonous gases like carbon dioxide and vapour. The toxic gases contribute to smog problems in big cities, and other air pollutions, this leads to all kinds of health problems. Carbon dioxide has a significant contribution to the greenhouse effect. This extended greenhouse effect leads to global warming and climate change we are dealing with. Different solutions are thought of to solve this problem. In the late seventies vehicles became equipped with catalytic converters, these converters reduce the toxic gases in the vehicle exhaust. Also the internal combustion engines have been further developed to produce less exhaust gases. These applications contributed to a decrease of the harmful exhaust gases. In the last decade also other solutions have been thought of. Some of them exist of replacing the combustion engine by a fuel cell, or a combination of the combustion engine with a battery, called hybridization. Another solution is topology change of the drive train. For a few years a sixth gear has been added to the conventional gear box, this to reduce the rotating speed of the engine at high vehicle speed to reduce the exhaust gases. One more solution is the use of a continuously variable transmission, CVT. This transmission is able to provide infinite gear ratios between two constraint limits, without the use of any clutch to disengage the engine from the drive line. By this property the combustion engine can be driven in its optimal working point, the engine speed does no longer depend on the drive line, because this can be freely chosen due the presence of the CVT. This means the combustion engine always can be used in its working point at which it delivers the most power. A well chosen engine speed also leads to a minimum of exhaust gases. This last solution is an interesting one. A CVT can be easily used in place of classical transmission in a normal car. The drive train must be replaced, but the combustion engine and other energy storage devices can keep the “old” configuration. So the already used lay out of the car does not have to be fully changed, as instead is the case of fuel cells or hybrid engines. Further more it has been estimated that fuel reduction of 10% could be obtained using a CVT in comparison with a manual shitted gear box [Ref: 2]. This may significantly reduce the above mentioned environmental problems concerning fossil fuels. Also the driveability of a vehicle equipped with a CVT is very good. The driver does not have to change gear, and by doing this lose his attention on the road. Moreover the comfort rises, because the sudden (de)acceleration during shifting disappears. Torque disengagement will also disappear, because no clutch is used during normal driving. The CVT seems a good transmission to place in modern vehicles. But there are still some problems. A CVT is a complicated transmission and must be controlled by a hydraulic system managed by an electronic control unit (ECU). This control still must be further optimized and investigated, this is necessary to obtain the lowest fuel consumption and emission, and highest driveability and comfort. At this time the control and control strategy are not to be called optimal. The hydraulic clamping forces determine the transmission’s efficiency and maximum torque that is transmitted. The timing and size of these hydraulic forces must be further investigated to reach the optimal desired working point. Another problem is the question wetter the consumer is prepared to buy this new transmission, or not. Especially in Europe the manual shifted gear box has a big market share, about 80% of all new produced cars are equipped with manual gear boxes. In Japan the CVT has already a marking share of 20% and the American market is very promising for the CVT [Ref: 3]. But then the question still remains, will there be enough demand for CVT vehicles? To be able to determine the behaviour of the CVT transmission different approaches exists, one mathematical models, multi-body models and FEM models. In this paper the mathematical model, especially the CMM model, is investigated. The CMM model is derived by Carbone, Mangialardi and Mantriota from the Polytecnico di Bari, Italy. This mathematical model has been compared with experiments done at the Technical University of Eindhoven, the Netherlands. This comparison showed some inequalities between model and experiments. This can be seen in figure 1. In this figure the geometric speed ratio τ (x-axis) is compared with the clamping force ratio SDR / S DN (y-axis). The fat line represents the CMM model, the thin lines the results of the experiments. 3 Figure 1: Comparison CMM model and experiments In this paper a start is made to derive a solution that can cancel these inequalities. The CMM model will be extended with some equations, in such a way that a better approximations can be made with respect to the experiments. Because of time limits the exact new model is not derived, but sufficient equations
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