Abstract: In practical applications, gears often exhibit varying lubrication conditions, resulting in significant fluctuations in the friction coefficients of gear pairs. These variations directly affect the transmission efficiency of gears. The present study focuses on variable hyperbolic circular arc toothed tooth (VH-CATT) cylindrical gears, which typically operate under the mixed lubrication conditions. To calculate the friction coefficient of VH-CATT cylindrical gears, the curvature, speed, load, and other pertinent parameters in the contact area were calculated in this paper. Furthermore, by integrating measured roughness data from gear surfaces, the friction coefficient of VH-CATT cylindrical gears under the mixed lubrication conditions was derived using the load sharing theory. Subsequently, a transmission efficiency calculation model for VH-CATT cylindrical gears was established. Through drawing the Stribeck curve, the influence of surface morphology parameters, lubricant parameters, normal load, etc. on the friction coefficient, friction performance and transmission efficiency of VH-CATT cylindrical gears under mixed lubrication were investigated. To further illustrate the interaction of these parameters, consider an example where a VH-CATT gear operating under mixed lubrication experienced a sudden increase in normal load. Without proper lubrication, this increase could lead to rapid wear and a significant increase in friction coefficient, affecting both friction performance and transmission efficiency. However, with an appropriate lubricant, the protective oil film could absorb the increased pressure, reducing wear and maintaining a low friction coefficient. The results showed that the friction coefficient exhibited a pattern of first decreasing and then increasing as the rotational angle increases. Notably, the friction coefficient attained its lowest value at the node. This phenomenon could be attributed to the concurrent presence of sliding and rolling friction during gear meshing. However, in the vicinity of the node, the gears were primarily in a state of pure rolling, resulting in the predominance of rolling friction. Furthermore, the friction coefficient exhibited a decreasing trend as the rotational speed increases. This observation was explained by the fact that the convolution speed of the gear pair augments with an increase in rotational speed. The alteration in surface topography parameters gave rise to an expansion of the mixed lubrication zone, subsequently elevating the friction coefficient at equivalent velocities. Concurrently, a surge in the lubricating oil's viscosity escalated the coefficient of friction, resulting in the Stribeck curve shifting towards the left and the mixed lubrication zone broadening towards the boundary lubrication zone. The load's impact on the Stribeck curve was primarily observed in the transitional phase between the mixed and boundary lubrication zones. As speed increased, transmission efficiency gradually rose towards a state of stability. Conversely, at lower gear speeds, the viscosity and roughness of the lubricating oil exerted a notable influence on gear transmission efficiency. In conclusion, the influence of surface morphology parameters, lubricant properties, and normal load on the friction coefficient, friction performance, and transmission efficiency of VH-CATT cylindrical geared under mixed lubrication was multifaceted and requires careful consideration. By optimizing these parameters, it was possible to significantly enhance gear performance and durability, leading to improved overall system efficiency and reliability.