Technological and contact analysis of Hirth joints including manufacturing tolerances

The present work proposes a novel method for determining the influence of the machining tolerances on the effective contact area of Hirth joints. The proposed method is based on a general Finite Element Model (FEM) capable to simulate any meshing condition of Hirth joints including positioning and machining tolerances using the Monte Carlo method. The FEM was developed based on an accurate measurement campaign of several Hirth joints which allowed to determine the geometric parameters affecting the meshing and the related ranges of variation. The machining reference surfaces and the sequence of technological processes which produce the Hirth joint starting from a raw disc were identified through contactless measurement techniques. The related machining tolerances were measured by employing a high-precision Coordinate Measuring Machine (CMM). A mean value and a standard deviation were associated with each geometrical parameter of the joint. The proposed method can be used for the preliminary design and the quality check of the Hirth joint. In particular, the Prussian blue test, which represents the typical test used to verify the joint's compliance with the technical specification, was simulated. The results highlight the reduction of the effective contact area of the Hirth joint due to the presence of manufacturing tolerances, which can lead to worse mechanical performances and early failure, and could be used to define the machining tolerances limit of Hirth joints.