**7. Conclusions**

Differential speed rolling, i.e., rolling with different angular speeds of the work rolls when both rolls are independently driven by two motors, is the most suitable way to implement asymmetric rolling in industry. A relatively low speed ratio of the work rolls (*SR* ≤ 1.5) can be used for reducing rolling force, improving sheet flatness, minimizing the ski effect and obtaining thinner sheets. A high speed ratio of the work rolls (*SR* = 2 ... 4) can be used as an SPD method for grain refinement and improvement of the texture and mechanical properties of large-scale sheets of Mg, Al and Ti pure metals and alloys.

The mechanics of the differential speed rolling process as an SPD method are based on simultaneous pure and simple shear, which combine the advantages of simple shear (rotation of the material as with ECAP) and the advantages of pure shear (compression and elongation of the material as with symmetric rolling). The mechanism for creating shear strain during differential speed rolling is the presence of the cross-shear zone in the deformation zone, in which the forces of contact friction are oppositely directed. The equivalent strain *ε* ≥ 3 ... 4 can be obtained by single-pass differential speed rolling without lubrication (at high contact friction), when shear angle *ϕ* is no less than 80◦ due to the high speed ratio of the work rolls (*SR* = 2 ... 4), large work roll diameter (D ≥ 300 mm), high thickness reduction per pass (*ε* ≥ 50%) and thinner initial thickness of the sheet (*h*0 ≤ 2 mm).

Based on the analysis of publications related to asymmetric (hot, warm, cold, cryo) rolling, it was found that a superior balance of strength and ductility of Mg, Al and Ti alloys could be achieved:

a. ultrafine-grained (0.6 μm) AZ31 sheets with YS of 382 MPa, UTS of 401 MPa and TE of 6.8% could be fabricated by differential speed rolling with high speed ratio of work rolls (*SR* = 2) at 150 ◦C followed by immediate water quenching;


It should be noted, and it is very important, that the resulting mechanical properties of Mg, Al and Ti alloys are much better than those of conventionally cold-rolled materials and at least not worse than those of counterparts subjected to conventional SPD methods, such as ECAP, while having an undeniable advantage in terms of the possibility of the production of large-scale sheets. Future prospects for the development of differential speed rolling technologies lie in the optimization of process parameters, as well as in the industrial application of these technologies to a wider range of processed materials.

**Author Contributions:** Conceptualization, D.P.; formal analysis, A.P., P.T.; investigation, D.P.; writing—original draft preparation, D.P.; writing—review and editing, A.P., P.T.; supervision, A.P.; project administration, A.P.; funding acquisition, A.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** The study was carried out within the framework of the implementation of the Resolution of the Government of the Russian Federation of 9 April 2010, No. 220 (Contract No. 075-15-2019-869 from 12 May 2019) and by a gran<sup>t</sup> of the Russian Science Foundation (project No. 20-69-46042 of 20 May 2020).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.
