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.