Goal. It lies in the synthesis of inertia-rigid parameters of three-mass interresonant vibrating machines for producing its in-phase motion. Significance. Three-mass interresonant vibrating machines rarely used in manufacturing because they are difficult in calculation, design, production, operation and readjustment. New approach to calculation and design of three-mass interresonant vibrating machines allow us to engrain them as a technological equipment on factories. Method. The refinement of analytical expressions is carried out using the classical approaches for linear vibrational systems with harmonic perturbation. For this the physical model of the three-mass interresonant oscillation system is considered and its mathematical model is developed as a system of linear differential equations. On the basis of this the solution is formed (the values of the amplitudes of oscillations). Unknown parameters remain rigid, provided that the inertia is constructed. Therefore, using the determinants of the matrix of coefficients for unknowns, the necessary mathematical operations are performed that satisfy the imposed conditions for the establishment of rigid parameters. Results. Analytical dependencies in the article allow us to design three-mass interresonant vibrating machines, which has a significance dynamic potential and, consequently, they are more energy efficient than one- and two-mass vibrating machines. Scientific novelty. This article proposes an analytical dependencies for calculation of three-mass interresonant systems with an inertial exciters, which has in-phase motion of intermediary and reactive masses. Practical significance. Established analytical expressions can be widely used in the design of vibration process equipment. Preciseness and the relative simplicity of the proposed analytical expressions allows for their widespread use in practice.
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