Nadiia Maherus

Scissor lifts are versatile lifting mechanisms that must satisfy stringent safety and reliability requirements. Therefore, accurate determination of their force and kinematic parameters is essential. An analytical approach for the design calculation of a bottom-driven scissor lift was developed. The proposed approach incorporates extension and compression springs to reduce the required driving force in the lowest platform position and improve the energy efficiency of the mechanism. A force analysis model of the scissor lift was developed, and the support reactions and the required driving force were determined as functions of the platform lifting height. Based on the kinematic analysis, the extreme linear and angular displacements of the scissor mechanism arms were determined. The functional dependences of the upper and lower spring deformations on the inclination angle of the scissor arms were established, characterizing the operating behavior of the load compensation system. The results demonstrate that the proposed spring compensation system reduced the required driving force by 26.5% and the internal forces in the scissor mechanism by 19.8–39.6% compared with the configuration without spring compensation. The developed analytical approach enables the determination of the force and energy characteristics of a bottom-driven scissor lift and the selection of reasonable spring parameters to reduce drive energy consumption.

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 study the influence of temperature on the stress state of the housing of a continuous rotary unit, to determine the static and geometric parameters in the lining of the housing under the influence of high temperatures. Significance. The housing of a rotary unit, as a rotating shell, under the influence of loads not only bends and deforms in cross-sections, but also is significantly exposed to temperature effects, since the temperature during material firing reaches 1600...2300 ºС. Therefore, the wear factors of rotary kiln components, their operational parameters, the influence of thermal load on the stress state of such a shell of the furnace housing are a relevant task that requires further study. Methodology. When calculating the parameters of the housing of a rotary unit, the thermal deformation of the cross-section of the metal shell in the axial and annular directions, as well as significant thermal expansion of the lining, were taken into account. It was assumed that the temperature changes along the length of the housing, but is constant in each cross-section. The radial expansion of the lining in each arbitrary cross-section was also considered the same. A three-layer shell was considered, the inner layer of which is the inner surface of the lining. Results. The proposed mathematical relationships allow determining the influence of temperature on the change in static and geometric values in the lining of the rotating unit housing. Scientific novelty. Mathematical relationships have been developed for calculating static and geometric values in the lining of the rotating unit housing. Practical significance. The results of the calculations will allow predicting the operation of rotating unit housings and extending their service life.

The objective of the present article is to ascertain the forces emanating from the interface between the girth gear and the pinion, which exert a direct influence on both the loading of the kiln supports and the selection of an optimal open-gear drive configuration for large-scale rotary units. Significance. Ensuring the straightness of the kiln shell axis constitutes a pivotal challenge in the design and operation of large rotary units. Deviations, even those measuring a mere millimeter, in long, heavily loaded kilns have been shown to redistribute support reactions, increase shell bending, raise radial loads in bearing assemblies, and induce noise and vibration. These phenomena, in turn, have been demonstrated to accelerate wear and increase the risk of failure. Mitigation of these adverse factors necessitates a thorough examination of gear-mesh loading to ensure stable, full-face tooth contact, as well as design solutions that are impervious to installation and assembly inaccuracies. This approach is a simple yet effective means of enhancing the reliability and service life of open-gear drives and their associated drive systems. Methodology. The study examined the loads generated in the gear contact zone and investigated how the geometric arrangement of the drive elements affected these loads. Results. The proposed mathematical relationships facilitate the evaluation of forces within the gear mesh, thereby establishing the dependence of mesh parameters on the geometric arrangement of the lever-mounted pinion. Scientific novelty. Mathematical relationships have been developed to quantify the influence of gear-mesh parameters and the geometric positioning of rotary-kiln open-gear drive elements on contact zone loads and their transmission to the support assemblies. The practical significance of the aforementioned topic is as follows: The paper presents an efficient open-gear drive configuration for a large-scale unit, providing calculation results to support the selection of appropriate geometric parameters, thereby ensuring effective operation.

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.

Goal of the work is to apply periodic Ateb-functions to investigate dynamic processes of strongly nonlinear systems with a finite number of degrees of freedom. Significance. Practically all problems in mechanics and engineering related to system oscillations, when strictly formulated, are nonlinear, as they are mathematically described by nonlinear differential equations. This often poses significant challenges in studying their behaviour, as finding a solution in exact form can be difficult. One way to overcome this complexity is utilizing special functions, such as Ateb-functions. Therefore, the application of periodic Ateb-functions for investigating the dynamic processes of highly nonlinear systems with a finite number of degrees of freedom is a relevant task, as it allows for increased accuracy and efficiency of estimations. Method. The methodology is based on finding partial solutions of the "normal" oscillations form, which do not correspond to linearized systems. The normal modes of oscillation of highly nonlinear conservative systems, whose potential energy is a homogeneous function of degree ν+1, are described using periodic Ateb-functions. In cases where linearization of the original system is not possible, such an approach to studying the oscillatory processes of highly nonlinear systems with multiple degrees of freedom is the most feasible. Results. The presented methodology for investigating normal modes of oscillations can be generalized to highly nonlinear systems with small perturbations of autonomous and non-autonomous types. Scientific novelty. Mathematical relations have been established to determine the normal modes of oscillations in highly nonlinear mechanical systems. Practical significance. The application of periodic Ateb-functions for investigating dynamic processes in highly nonlinear systems will enhance the accuracy and efficiency of estimations.

The goal of the work is to develop a mathematical model of a workpiece bending process by copier to determine the necessary parameters of the process and increase its efficiency. Significance. The quality of the process of workpiece bending by copier depends on many factors and is accompanied by both elastic and plastic deformations. Therefore, a mathematical description and analysis of the workpieces is an urgent issue, because it will allow to justify the parameters of the process and increase its efficiency. Method. The dependence between stresses and strains was used for an analysis of the bending process, instead of Hooke's law. Since there is a linear stressed and a volumetric deformed state for the narrow workpiece, then, according to the assumption of the flat cross-sections, a relative deformation of the arbitrary fiber is a linear function of its movement from a neutral layer. It was determined a bending moment in the section of the workpiece having the curvature radius of the neutral layer and considered the equilibrium of the workpiece bent element from the last point of contact with the copier to the point of a force application. As a result, a system of equations was obtained that eliminates the task of elastic-plastic deformation of the workpiece. Results. Using the mathematical model of the workpiece bending process by copier allows to determine the necessary parameters of the process, in particular, the clamping force, the size of which, in addition to other factors, is significantly influenced by the gap, with the increase of which the value of the clamping force will decrease. Scientific novelty. Mathematical dependencies have been established to determine the main parameters of the workpiece bending process by copier. Practical significance. The results of mathematical modelling will allow to increase the efficiency and quality of that process

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.