Generalized gap function in the dynamic interaction problems of elements of vibrational technological machines with “not holding” ties

Issues of formation of rational modes of dynamic interaction of contacting elements of vibrating machines in problems of increase in quality of technological vibrohardening processes are considered. Mathematical models and criteria of an estimation of forms of movement with “not holding” ties are developed. For analytical research of “not holding” ties the concept of the generalized gap function is entered. The model of dynamic interaction of a solid with a vibrating surface is developed at introduction of additional external forces and elastic interactions. On the basis of a method of gap function criteria of a separation are formulated and forms of movement of a material particle in dynamic interaction with a vibrating surface are proved. The generalized approach for problems of dynamic synthesis of the vibrating technologies realized in modes continuous tossing is offered. Conditions of realization of multiple modes continuous tossing when the period of free flight of a material particle makes an integer of the periods of a basic vibrating surface are formulated. Generalization of considered models on a compound solid, interaction between which elements has “not holding” character is offered. The problem of definition of gapless conditions of movements at vibrating influence on a compound solid by a surface is posed. Conditions of formation of reaction in the oscillatory system formed by several solid elements with “not holding” ties, connected among themselves by means of elastic interaction and power factors are defined. In respect of practical appendices, the problem of development and experimental approbation of the measuring devices fixing modes of continuous tossing is posed