Loosening of threaded joints, especially those operating under dynamic loading conditions, is a common and traditional problem for machines, mechanisms and structures. This study develops scientific approaches to the frictional lock of bolted joints to prevent unintentional self-unscrewing. An analytical version of the theory of threaded joint, which is equipped with a spring-loaded collet, is developed in the paper. The mixed contact problem of the interaction of the cyclic-symmetric system of the collet nut blades with the inner bolt and the outer spring, which is fitted with tightness, was set up and solved. In order to obtain analytical solutions to the problem, original one-dimensional models of structural elements of the connection were constructed. Based on the solutions of the contact problem, the moment of friction force is calculated from the initial gap between the blades and the thread, from the value of the spring tightness, from the parameters of the rigidity of the blade and the clamping spring. Finally, the value of the maximum friction torque that counteracts the self-unscrewing of the collet nut is evaluated, and some features of the threaded joint with the collet nut design are considered.

This work presents a stress-strain state analytical estimation of restored tooth hard tissues with consideration of their contact interactions with a monolithic filling or a dental onlay. The tooth with a defect is simulated as a continuous isotropic cylindrical body with a non-through hole, and the filling or onlay is simulated as an elastic deformable cylinder. The contact between the tooth and the fillings (onlay) is simulated as the ideal contact. The final strength estimation of the restored tooth is carried out according to the energy criterion. The authors suggest a linear index of tooth damage for practical application of the obtained results. This index can be easily obtained by direct measurement. The differential approach is developed to select a restoring method of the tooth with the defect to provide a reliable restoration of the anatomical crown of the tooth.