Effect of continuously variable unit on powertrain dynamics
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This thesis studies the dynamic model and simulation of a Half-Toroidal (HT) type Continuously Variable Unit (CVU) integrated into a conventional powertrain. A simplified parametric model of a HT-CVU is constructed using Finite Element Method (FEM) in which the continuous variable speed unit is discretized into lumped masses, spring and damper elements. Linearized Finite Elements (FE) have been used to model the contacts between the toroids and rollers. The phenomenon of slip and spin associated with the rolling-slipping contacts of the traction drives are modelled kinematically. All Finite Elements including the CVU model are integrated into the complete powertrain system. Free Vibration Analysis (FVA) of the multi degree of freedom system is carried out for torsional vibration for High Gear (HGR) and Low Gear Ratio (LGR) conditions. Further, FVA is carried out with a lock-up clutch engaged at high speed range. The results of the FVA indicates significant changes in natural frequencies and corresponding mode shapes for both HGR and LGR condition with a change in HT-CVU gear ratios. Change in natural frequencies and mode shapes for both HGR and LGR conditions are also observed for varying contact torsional stiffness. The change is significant till a certain value of contact torsional stiffness. Further increase in contact torsional stiffness within the HT-CVU does not affect the natural frequencies and corresponding mode shapes significantly. The results of the modal analysis carried out for a HT-CVU integrated powertrain with a lock-up clutch engaged at high speed range illustrates the ability of the lock-up clutch to simultaneously suspend engine and roller element excitation. However, for certain natural frequencies the modal analysis of the integrated powertrain system indicates suspension of engine and input toroid but increased excitation for the roller element of the HT-CVU. The transient dynamic analysis is carried out to understand the behaviour of the CVU integrated into the complete powertrain and to identify and possibly correct potential problems associated with the system. The simulation is carried out for constant and variable throttle conditions for the powertrain with and without a lock up clutch engaged at high speed ranges. A piecewise curved gear ratio map is assumed for all conditions. All analyses are carried out for throttle 'tip-in' condition. The results of the transient dynamic analysis indicate that the transient responses of input and output rollers of the HT-CVU exist when clutch change occurs during vehicle acceleration period from stand still condition. The clutch change also leads to disturbances in the HT-CVU output torque to driveline and in vehicle speed. This leads to imperfect drive feel for the driver. The simulated vehicle velocity indicates powerful acceleration characteristics of the HT-CVU integrated powertrain. Engine harmonics is modelled as a rich collection of various forcing frequencies. These frequencies impress on the response of both the roller and output toroid and are observed in the simulation. Stability analysis is carried out on the powertrain to understand the effect of damping in the tyres and damping within the HT-CVU on the stability of the powertrain. Severe or even unstable response of the HT-CVU takes place if the damping in the HT-CVU and/or the tyres is insufficient during the initial acceleration period and later after the clutch change occurs and when the vehicle is at high speeds. The results of the stability analysis lead us to reason with confidence that the tyre and HT-CVU damping have an effect on the dynamic characteristics and the stability of the system. The response of the powertrain becomes stable when a lock-up clutch is applied over the high speed ranges even if the damping in the tyres remains insufficient. The modal damping ratios for stable and unstable conditions are also discussed. Future investigations need to be carried out in order to understand in depth the fluid-metal interaction in the HT-CVU. This can be achieved by modelling in non-linear drag torque which would act on the HT-CVU elements.
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