This work presents a systematic study on the correlations between process parameters and rivet plastic deformation, produced by force-controlled friction riveting. The 5 mm diameter AA2024 rivets were joined to 13 mm, nominal thickness, polyetherimide plates. A wide range of joint formations was obtained, reflecting the variation in total energy input (24-208 J) and process temperature (319-501 °C). The influence of the process parameters on joint formation was determined, using a central composite design and response surface methodology. Friction time displayed the highest contribution on both rivet penetration (61.9%) and anchoring depth (34.7%), and friction force on the maximum width of the deformed rivet tip (46.5%). Quadratic effects and two-way interactions were significant on rivet anchoring depth (29.8 and 20.8%, respectively). Bell-shaped rivet plastic deformation-high mechanical interlocking-results from moderate energy inputs (~100 J). These geometries are characterized by: rivet penetration depth of 7 to 9 mm; maximum width of the deformed rivet tip of 9 to 12 mm; and anchoring depth higher than 6 mm. This knowledge allows the production of optimized friction-riveted connections and a deeper understanding of the joining mechanisms, further discussed in Part II of this work.