Determination of the Stress State of the Disk Using the Stress Function

Abstract

The solution of the problem of the elasticity theory of a plane-stressed state of a wave generator disk with a through central hole is presented. An active load is applied on the outer cylindrical contour of the disk of radius R₂. The reactive load is applied along the inner contour – the central hole of the disk of radius R₁. The development and creation of high-performance transmission gears with minimal overall weight indicators and increased load capacity is an urgent problem of improving the quality and competitiveness of mechanical drives of road and construction equipment. The layout of the completed machines, technical and economic characteristics are largely determined by the overall dimensions, weight, load capacity and reliability of the built-in gearboxes. The most promising direction for optimizing the quality indicators of wave transmissions is the differentiation of the power flow by a number of parallel power flows that reduce the size, weight and noise effect. The relative weight and cost of wave reducers are 1.5–2 times lower than planetary ones, which contributes to the use of wave reducers in road and construction equipment. The most loaded nodes of a large wave gear train include a wave generator that integrates the reactive load of the gearing through disks mounted on a high-speed shaft with a given eccentricity. Minimizing the vibration of the disks is achieved by reducing their weight, precision manufacturing and assembly. The problem of the stressed state of the disks is relevant, and the results obtained are used to optimize the design and size of the bearing elements of the wave gear.