This paper deals with the problem of identifying the mathematical model of a dry-clutch transmission system, from input-output data experimentally collected on a real vehicle. The proposed identification procedure is based on a set-membership identification approach, where a-priori information on the structure of the physical model are taken into account in the selection of the model class. Parameter uncertainty intervals and the Chebyshev center of the feasible parameter set are computed by applying suitable convex relaxation schemes. The quality of the obtained model is tested on several validation data sets.