A New Principle of Generating Polyharmonic Oscillations in Vibrating Machines

Vibrating machines are widely used in industry in various technological processes and often polyharmonic vibrations are more effective than harmonic ones. By now, various approaches for forming such oscillations are known, but due to the complexity of the proposed technical solutions, this problem remains very relevant. The paper considers the schematic diagram of a single-mass vibrating machine with inertial excitation and non-axial shaft connection in a transmission drive by means of a Hook hinge. In such a design, the unevenness of rotation of the driven shaft is observed even with uniform rotation of the driving shaft. As a result, when rotating the unbalances mounted on the driven shaft, a polyharmonic disturbing force is formed. This leads to the fact that in certain frequency ranges of the disturbing force intense polyharmonic components appear in the law of motion of the working organ, the values of which can be comparable or even exceed the amplitude of the main. In particular, at an angular velocity of rotation of the drive shaft, several times lower than the natural oscillation frequency of the system, superharmonic resonances of orders 3:1 and 5:1 are excited. The paper presents the results of analytical analysis of such system, which is based on the decomposition of the perturbing force into a finite Fourier series and the subsequent use of the principle of superposition, analytical dependences describing the stationary laws of motion of the working body are given. The obtained analytical results are confirmed by numerical simulation.