The geometric shape of the convex track has a significant impact on the sliding electrical contact characteristics in electromagnetic orbit launch devices. This article uses finite element software to establish a bidirectional coupling simulation model of structural field and electromagnetic field for a 20 mm diameter launch device, and studies the influence of convex track arc surface on pivot rail contact pressure and current distribution under different curvature radii. The simulation results show that as the curvature radius of the track arc increases, the contact pressure between the pivot and the track gradually shifts from the center to the edge, and the high current density area also moves from the center of the contact surface to the edge. In a 20 mm caliber launch device, when the curvature radius of the curved surface is 10 mm, the efficiency of the launch device is the highest and the current density distribution is the most uniform. By studying the variation of current density at the contact interface of the pivot rail with the curvature radius, a theoretical basis is provided for optimizing the geometric shape of the convex rail.