The gear train architecture utilized in DCT is the same parallel shaft arrangement as the conventional manual transmission with synchronizers for smooth gear transition, and enjoys the efficiency much higher than automatic transmission with torque converter. Conventional geartrain arrangement for a 6, 7, or 8-speed DCT makes the overall transmission length unmanageable for packaging in a vehicle. Dependency, which allows two output gears to share one input gear, can be employed to reduce the overall length of the transmission. The dependencies present challenges to accurately determine the interrelating parameters such as center distances, speed gear and final drive ratios and pitch diameters, etc. Mathematical algorithms and nomograms have been developed to demonstrate interrelationship of the key parameters. Overall top gear and low gear ratios and ratio spread have been computed for a given application using engine torque and power signature that satisfy the acceleration, gradability, and top speed requirements. The intermediate ratios subsequently have been determined by employing mathematical technique to achieve uniformly, progressively smaller ratios steps. The mathematical algorithms developed for single or double dependency have been applied to iteratively calculate pitch diameters of common input gear and the two sharing output gears as well as the center distances of the two output shafts to the input shaft. Finally, number of teeth for the dependency gearsets has been determined by applying continued fraction method.
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