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Comparative studies of the classical and new design of a chaff cutter’s cutting drum have been conducted within the frames of the study in order to determine their functional characteristics at the time of cutting rye straw into pieces of specific length (into chaff). A classical design of a cutting drum is of the shape of a roller and is suitable for material layer cross-cutting. However, the new drum design has the shape of a double truncated cone and, with the use of it, diagonal cuts in two directions can be realized. The studies were conducted for four designs of cutting drums with cutting angles α = 0° (classical design) and α = 15°, α = 30°, and α = 45° (new design). Three indicators were applied for the assessment: capacity, unit energy consumption, and the unit cutting resistance. The obtained results show that the use of a new drum design makes it possible, depending on the assumed parameters of the cutting process and the material’s compaction degree, to increase the process’s efficiency by up to 25%, lower the unit energy consumption up to 34%, and lower the unit cutting resistance by up to 8%. The conducted experimental studies have unequivocally shown that the use of a new cutting drum design, as compared to the classical one, results in a considerable increase in the cutting process’s performance. Studies on the new design of a chaff cutter’s cutting drum, of the shape of a double truncated cone, belong to original ones that so far have not been described in the available literature. Full article