Theoretical investigations into the capabilities of a coaxial inertial drive with various operating modes for vibratory conveyors and screens are conducted in the paper. The coaxial inertial exciter is designed with one asynchronous electric motor and the kinematically synchronized rotation of two unbalanced masses. Three variants of angular speeds ratios, namely ω₂/ω₁ = 1, ω₂/ω₁ = –1, and ω₂/ω₁ = 2, are considered. Based on these relations, the circular, elliptical, and complex motion trajectories of the working members are implemented. In the first two cases, single-frequency harmonic oscillations take place. In the latter case, the double-frequency periodic oscillations are excited. The dynamic behavior of the motor’s shaft during its running-up and running-out is considered. The influence of the inertial parameters of the unbalanced rotors and the relative phase shift angle between them on the elliptical trajectories of the vibratory system’s mass center motion is investigated. The use of forced kinematic synchronization provides the motion stability of the vibratory system for all considered working regimes.

A comprehensive numerical method was developed to ensure energy-efficient operating modes of a linear motion module powered by an induction motor. The proposed approach is based on minimizing inertial torque, accounting for the inertial properties of the drive components and the load carriage, followed by structural-parametric optimization and dynamic modeling. For the optimization of the drive system, comprising an intermediate gear stage and a primary ball screw mechanism, a normalization-based method combined with numerical parameter sweep was employed. The optimization process yielded optimal values of the screw lead and the number of gear teeth, which were further validated in terms of Pareto optimality. The carriage design was optimized with respect to mass, strength constraints, and dynamic stiffness using the finite element method. For the developed linear motion module, dynamic behavior was simulated by means of a system of nonlinear differential equations, taking into account the electromagnetic characteristics of the induction motor and the nonlinearities of the gear mesh. As a result of the comprehensive approach, the kinematic, force, and energy characteristics of the linear motion module, which was optimized at the design stage, were determined.

A scissor lift design was developed with a load capacity of 100 kg and a lifting height of 1 m. The platform lifting mechanism is actuated by a traction electric motor via rollers moving along the guides. A calculation model of the scissor lift was created, resulting in a statically indeterminate system. Support reactions and an actuating force were determined depending on the platform lifting height. The analytical results showed that the actuating force increases nonlinearly during platform lifting, ranging from 1.674 kN to 6.45 kN, while the actuator rod stroke is 441 mm. Similarly, the simulation conducted using SolidWorks Motion yielded the actuating force in the range of 1.62 kN-6.5 kN and the rod stroke of 443.5 mm. The study established the patterns of variation of the main kinematic and force parameters of the scissor lift, which exhibit nonlinear characteristics. A piecewise linear variation of the actuating force was synthesized to ensure a trapezoidal motion profile of the platform. This type of motion profile was selected to provide comfortable and safe movement for people, particularly those with disabilities. The strength of the main structural elements of the scissor lift, namely levers, traction crossbar, guides and rollers, was ensured.

The problem of optimizing the drive design parameters for a high-speed linear system is solved based on minimizing the inertial torque. New analytical expressions are obtained for determining the optimal gear ratio of the intermediate transmission, taking into account the moments of inertia of rotating masses, the carriage mass, and the screw pitch. An optimization problem is proposed to determine the number of gear teeth and the screw pitch by minimizing a function that includes the relative error between the actual and calculated gear ratio, as well as the total number of teeth required to ensure the specified travel speed of a carriage. At the next calculation stage, the number of gear teeth is refined based on the nearest standard screw pitch values. The resulting parameters are evaluated using a transient dynamic analysis according to key kinematic and energy characteristics.

Goal of the article is to determine the support and bending moments, loads on the supports, as well as the normal stresses in the continuous rotary unit housing, which is subjected to complex mechanical and thermal loads. Significance. The rotary kiln housing, as a rotating shell, bends under the load both in the spans between the supports and at the supports themselves, and also deforms in the cross-section. These deformations create longitudinal and transverse bending moments. Their increase or decrease occurs due to the redistribution of pressure on the supports, caused in turn by the deflection of the axis of rotation and the geometric axis of the housing, uneven wear of the rollers, bandages, sub-bandage shims, and bearing liners. Therefore, strength estimation of the rotary unit housings will ensure their reliable operation and extend their operating life. Methodology. The rotary unit housing was considered as a multi-span continuous beam with tubular cross-section, for which the support moments and support reactions were determined. When determining stresses, the housing was regarded as a multi-span cylindrical shell. Results. The proposed mathematical relationships allow the determination of support moments, loads on the supports, and stresses in the rotary unit housing. Scientific novelty. Mathematical dependencies have been developed for calculating the support moments, loads on the supports, and stresses in the rotary unit housing. Practical significance. The results of the estimation will allow predicting the performance of rotary unit housings and extending their operating life.

Goalof the articleis to develop a mathematical model of the behavior of thevariable structure system that are affected by oscillations. The dynamic of variable structure systems is considered on the example of аmotion of theinertial vibrating exciter on elastic supports.Significance. A large number of mathematical models of elastic system dynamic under the action of moving inertial load mostly coversonly the general approach to solving these problems, or describes a specific type of equipment that is narrowly used in certain industries. The proposed mathematical model of the oscillating system offers much greater possibilities. It allows to modify the developed approach to modeling the dynamic of variable structure systems depending on their parameters. Method. Using theLagrange's equations of the second kind, the dynamic of the inertial vibration exciter on elastic supports is modeled and the factors influencing its behavior are analyzed. Results. The presented mathematical model of the massive body behavior on elastic supports with a rigidly mounted shaft allows to substantiate the inertial-rigid and force parameters of the oscillatory system. Scientific novelty.A mathematical model of the body behavior on elastic supports with a rigidly mounted shaft, which transmits rotational motion to two imbalances through an elastic connection, has been developed. Practical significance.The proposed method of calculations allows furtherto investigate ways to stabilize the variable structure system and reduce the inertial load onstructural elements, which allowsto justifythe necessary parameters of technical systems.