This paper develops and evaluates a cam-actuated variable-length crank for reciprocating frame-saw drives equipped with springs placed perpendicular to the slider path. An invariant formulation is used to synthesize a periodic slider motion in which the spring force projected along the stroke cancels the slider inertia force. This yields a second-order differential equation with a non-dimensional stiffness parameter for the perpendicular-spring layout; the corresponding cam (variable crank length) is then recovered from the synthesized law of motion. Numerical studies for a representative frame-saw geometry confirm that the proposed synthesis eliminates inertial loading of the slider and produces a pronounced quasi-constant-velocity segment in mid-stroke (about 40 % of the stroke within a 5 % tolerance). The theoretical cam profile is well approximated by an ellipse (semi-axes 0.4996 and 0.4106 in non-dimensional form) with a maximum radial deviation of 0.00235; the associated pressure angles are about 13°, i.e., comfortably within typical limits. These results demonstrate that combining a cam-modulated variable crank length with a perpendicular-spring environment enables kinematic balancing with feasible pressure angles and motion shaping favorable for wood and stone cutting.

Purpose. A design solution was substantiated and a screw dispenser for small doses of finely dispersed food products was put into production. Methodology. During the design process, basic methods for calculating machine parts were used in conjunction with the capabilities of CAD and CAE systems. Experimental studies of dosing accuracy were established on the basis of 30 randomly selected samples and methods of mathematical statistics. Results. Rational designs of single- and double-flow vertical screw dispensers were proposed, and a set of verification calculations was performed for strength and reduction of metal consumption of basic structural elements. The drive design is based on the use of frequency-controlled asynchronous electric motors with gear-belt transmissions. The screws have individual drives, and the movements of the agitator and mixers are synchronized on a single separate drive. Scientific novelty. The design solution for a vertical screw feeder, additionally equipped with mixers and a stirrer, has been substantiated. The influence of the operating conditions of the feeder and its kinematic characteristics on the accuracy of dosing has been experimentally established. Practical value.A vertical screw feeder has been developed for packaging in single or paired soft bags, which can be a functional dosing unit for various types of packaging machines for finely dispersed products with a dose size of up to 20 g.

Goal. It consists in substantiating the inertial-rigid and force parameters of a high-efficient discrete three- mass inter-resonance oscillation system of a vibratory machine with an electromagnetic drive and in forming its mathematical model taking into account the drive. Significance. Despite the widespread use of one- and two-mass vibratory machines in the industry, their three-mass analogs in the inter-resonance oscillation zone have significant dynamic potential. New approaches to the calculation and design of three-mass inter-resonance vibratory machines would facilitate their mass introduction in enterprises of various industries as technological equipment. Method. A mathematical model of a three-mass inter-resonance oscillatory system of a vibrating machine with an electromagnetic drive in the form of a system of linear differential equations is considered. Based on it, dependencies are formed to determine the required inertial-rigid and force parameters of a highly efficient vibratory machine. Based on the already known power parameters of the system is a technique for establishing the necessary parameters for the design of the vibratory machine electromagnetic drive. The above parameters are embedded in the mathematical model of the vibratory machine. The time dependences of the motion of oscillating masses are investigated taking into account the processes occurring in the electromagnetic vibrator. Results. Inertial-rigid, force parameters of the oscillatory system are substantiated. A mathematical model of a three-mass inter-resonance oscillatory system is formed, which takes into account electromagnetic processes in the drive. Scientific novelty. A mathematical model of a three-mass inter-resonance oscillatory system of a vibratory machine is formed, taking into account the processes occurring in the electromagnetic drive, where the force action of the electromagnet is formed through the current in the coil of the vibrating exciter. Practical significance. The proposed method of calculations of three-mass inter- resonance vibratory machines with electromagnetic drive can be used in the design of high-efficiency vibratory process equipment.

Purpose. The study aims to investigate the influence of the motion kinematics of the cylindrical container of a vibrating machine on the magnitude of the impact impulse during contact between the granules of the processing medium and the container wall. Relevance. Vibration processing of parts is a complex system whose efficiency depends on many factors, such as the parameters of the drive and the elastic suspension of the container, the shape and dimensions of its working elements, the properties of the processing media themselves, and the factors of interaction between the processing medium and the container. In known analytical methods, the container motion of vibrating machines is described by the equations of rigid body mechanics, while the working medium receives impact impulses from the container walls. Analyzing the container’s motion kinematics and determining the magnitude of the impact impulse during granule–wall contact allows for a more accurate determination of processing parameters in vibrating machines. Methodology. The container–working medium system is considered under the assumption that the impact during collision between the wall and the working medium is instantaneous and elastic. The motion of the granules of the processing medium in the vibrating container is based on the laws of Newtonian mechanics and probability theory. Results. During the analysis of the contact between the container wall and the particles of the working medium, it is taken into account that the particle concentration in the layer near the container walls is not constant but periodically varies. The dependence of the change in the root mean square (RMS) velocity of the working medium particles during wall motion was determined. Scientific novelty. New mathematical relationships have been obtained for determining the RMS velocity of the working medium at any given moment in time. Practical significance. Based on the conducted research, dependencies of the RMS velocity of the working medium during vibration processing of products have been obtained.