The technique of obtaining a hyperboloidal gear engagement with linear contact between a cylindrical involute wheel and a hyperboloid producing worm is considered. The resulting cutting tool greatly simplifies the manufacturing technology of hyperboloid worms and hyperboloid gears along with improved accuracy and roughness of the machined teeth and lower manufacturing costs.

The submitted contribution deals with the wear of thin coatings applied to convex–concave gearings for gear made from C45E steel. The influence of the tribological characteristics (friction coefficient, wear, adhesion and hardness) of the TiN, TiCN coatings and the combined coating of TiCN + MoS₂ on convex–concave gearing is described, from the aspects of scuffing formation. Scuffing tests were done on C–C gears. Coatings were applied by arc–ion-plating (AIP) and magnetron sputter-ion-plating (MSIP) methods. The thickness of the deposited coating and its chemical composition were determined by SEM and EDX analysis. Load-bearing capacity was evaluated by a Niemann tester. The TiCN + MoS₂ combined coating with the MoS₂ layer on the top reached the lowest coefficient of friction. However, after a rapid wearing of the MoS₂ layer, this value dropped to a comparable value of TiCN. The nano-hardness of the TiCN layer was higher in comparison with TiN. Thin and soft MoS₂ layers cracked already at lower load levels and separated from the substrate at the 5th load stage. The formation of scuffings for selected coatings documented in this article was solved for convex–concave gearing working also in interaction with Biogear S 150 and Biohyd MS 46 oils.

Wear of TiAlCN coatings deposited on HCR (High Contact Ratio) gears was studied by the Niemann test during which the tested gears were loaded up to the 12th load stage. The resistance against scuffing was evaluated based on the criteria of allowable roughness (max. Rz 7 µm) and weight loss (max. 10 mg). The extent and character of wear were influenced by coating thickness, contact pressure and meshing frequency. The wear of thicker TiAlCN coatings on the tooth face started with the smoothing of surface protrusions. The next stage of wear was characterized by depletion of TiAlCN coating. After depletion to a thickness of about 2 µm, the layer was pressed into the soft substrate, and it subsequently cracked. At higher load stages, the layer was partially detached, but the critical roughness indicating scuffing was not exceeded. Thinner TiAlCN coating on the tooth flank cracked and fully detached at lower load stages compared to thicker layers and wear of uncoated soft substrate caused the increase in roughness above the critical value representing scuffing.

Wear of nonstandard involute gears with two types of coatings, AlCrN and CrAlSiN, was studied. The coatings were applied by cathodic arc deposition. The gears were tested using a Niemann tester at a graduated load up to the 12th load stage and were compared to noncoated gears. Both Biogear S150 gear oil and PP90 universal hydraulic oil were applied during these tests. The thickness of deposited coatings and wear of gear teeth were studied by SEM and their chemical compositions were determined by EDS analysis. Maximal contact pressure of 1350 MPa was calculated in the region of the tooth flank at the 12th load stage. Maximal frictional stress was also calculated on the tooth flank. The resistance against wear of gears was evaluated based on the critical weight loss and mainly based on the critical surface roughness of gears. The critical roughness was exceeded at the 10th load stage for noncoated gears. For the gears with AlCrN and CrAlSiN coatings, the critical roughness was exceeded at the 11th load stage. Wear of AlCrN and CrAlSiN coatings was nonuniform along the height of tooth. Wear on the tooth flank was characterized by fragmentation of thin coatings and subsequent detaching of fragments from the steel substrate. The steel substrate was worn by microcutting, which caused the highest roughness on the tooth surface. On the tooth pitch, surface protrusions of coatings were smoothed, and coatings cracked and locally detached subsequently. On the tooth face, surface protrusions were also smoothed but coatings remained compact without crack initiations. Both experimental oils, Biogear S150 and PP90, proved to be suitable during Niemann tests as their temperatures did not exceed the limit value of 80 °C.

The paper presented determines that the rotation velocities of gears and radii connecting the axes of rotation of the gears with the point of their teeth gearing are not equal with each other. It is explained by the relative slip of involute gear profiles during their rolling. This phenomenon will become a prerequisite for further development of creation of mathematical models in the context of theory of gear hydraulic machines. The models can explain a number of specific phenomena in the operation of gear hydraulic machines, such as pressure and input pulsations, dynamics of hydraulic oil in the cut-off plane, combined torque pulsations in gear hydraulic motors and others.