Eastern-European Journal of Enterprise Technologies

Determining the deformation of an absolutely elastic axis of curved rods under bending

Serhii Pylypaka — 2024-12-27

The object of this study is the deformation of an elastic axis with a large deflection of a cantilever clamped absolutely elastic rod under the action of an applied concentrated force. The rod in the free state can have a rectilinear or curved elastic axis. This fact implies a difference in the analytical description of the bending process. However, there is a factor by which some similarity can be found between the bending of rectilinear and curved rods. This factor is the curvature of the elastic axis of the rod in a free state. According to this feature, they can be divided into rods of constant and variable curvature of the elastic axis. The former include rectilinear rods and those that in the free state have the shape of an arc of a circle, and the latter – rods with a variable curvature of the elastic axis. There is a difference between the bending of these groups of rods: in the first case, the deformation of the elastic axis of the rod during its bending will be the same regardless of which end will be cantilever pinched.

A distinctive feature of the current research is that the bending of rods with variable curvature of the elastic axis was carried out by alternate pinching of their opposite ends. Moreover, the rods of constant and variable curvature were of the same length s=0.314 m, the same cross-section of 0.005×0.02 m. That has made it possible to visually show the difference between the shape of the elastic axis of the bent rod under the action of the same force when the pinch end is changed. When attached to the rods of the working bodies of agricultural machines, pulsating dynamic loads are smoothed out due to their elasticity. It is important for practice to be able to calculate the value of their deviation, which should be within the given limits.

The results are explained by the fact that in the analytical description of the shape of the elastic axis of a curved rod, a technique was proposed in which the length of the axis can start counting both from one end and from the opposite end

Determining the characteristics of contact interaction between structural elements with varied properties of surface layers

Mykola M. Tkachuk — 2024-12-27

The object of this study is the stressed-strained state of contacting elements of close-shaped machine-building structures. The presence and flexibility of surface layers and coatings are modeled. There are cases of the matching shape of the contacting surfaces of bodies, as well as the perturbation of the shape of these surfaces. The task being solved relates to the fact that the analysis methods of such bodies contact interaction are not yet sufficiently developed.

It was established that for the case of the matching shape of contacting surfaces, the contact area does not depend on the level of loads. In this case, the contact pressure distribution is proportional to the operating load. Such features of the solution do not depend on the properties of the materials of surface layers. A different case is when the shape of the contacting surfaces of bodies is disturbed. In particular, it was established that the properties of the materials of surface layers exert a strong influence on the shape and dimensions of bodies contact area, as well as on the distribution of contact pressure (the difference is 1.5–2.5 times or more).

The theory of variational inequalities is used to model the stressed-strained state of contacting bodies. As a result, the problem about contact interaction of bodies with surfaces of close shape is reduced to the problem of minimizing the modified energy functionality. The minimization is carried out on a set of distributions of displacements, which describes conditions of bodies not penetrating each other. The finite element method is used to discretize the problem of determining the stressed-strained state of contacting bodies. The parametric model built makes it possible to determine the stressed-strained state of contacting bodies when the disturbance of the nominal shape of the bodies and the properties of their surface layers is varied

Determining the vertical load on a container with a floor made of sandwich panels transported by a flat wagon

Alyona Lovska — 2024-12-27

loads in the structure of a container with a floor made of sandwich panels under operational modes.

To ensure the strength of the container, as well as the safety of the cargo transported in it, it is proposed to design a floor based on sandwich panels. It is assumed that each of these panels is made of two metal sheets in a layer between which an energy-absorbing material is placed. Given the presence of energy-absorbing material in the structure of the sandwich panel, the vertical dynamic loads acting on the cargo container during its transportation will be reduced.

To substantiate the proposed solution, mathematical modeling of the vertical load on the container during its transportation by a flat wagon was carried out. It is found that the accelerations acting on the container of the improved design are 5.7 % lower than those acting on the container of standard design.

The calculation of the strength of the container was carried out under operational schemes of its loads. It has been established that the strength of the container is ensured.

A special feature of the results is that the reduction of the load on the container is achieved not by strengthening its structure but by introducing flexible connections into it.

The field of practical application of the results is railroad transport. The conditions for the practical use of the findings are the use of energy-absorbing material in the structure of sandwich panels that form the floor of the container.

The results of the research will contribute to improving the strength of containers under operating conditions, the safety of the cargo transported in them, as well as increasing the efficiency of the functioning of container transportation

Developing of neural network computing methods for solving inverse elasticity problems

Anastasiia Kaliuzhniak — 2024-12-20

This paper examines the use of neural network methods to solve inverse problems in the mechanics of elastic materials.

The aim is to design physics-informed neural networks that can predict the parameters of structural components, and the physical properties of materials based on a specified displacement distribution.

A key feature of the specified neural networks is the integration of differential equations and boundary conditions into the loss function calculation. This approach ensures that the error in approximating unknown functions has a direct impact on optimizing the network's weights. As a result, the resulting neural network approximations of unknown functions comply with the differential equations and boundary conditions.

To test the capabilities of the designed neural networks, inverse problems involving the bending of plates and beams have been solved, focusing on determining one or two unknown parameters. Comparison of predicted and exact values demonstrates high accuracy of the constructed neural network models, with a relative prediction error of less than 3 % across all cases.

Unlike analytical methods for solving inverse problems, the primary advantage of physics-informed neural networks is their flexibility when addressing both linear and nonlinear problems. For instance, the same network architecture can be employed to solve various boundary-value problems without modification. Compared to classical numerical methods, the parallelization capability of neural networks is inherently supported by modern software libraries.

Therefore, the application of physics-informed neural networks for solving inverse elasticity problems of plates and beams is effective, as evidenced by the achieved relative errors and the computational robustness of the method. In practice, the proposed solution can be used for relevant calculations during the design of structural elements. The developed software code can also be integrated into automated design systems or computer algebra systems

Estimating the influence of the rigidity of support assemblies on the resonance phenomena and the vibration state of a hydraulic unit

Oleksii Tretiak — 2024-12-27

Many factors affect the vibration of the hydraulic unit, including the natural oscillation frequencies of the structural elements, which in some cases may contribute to an increase in vibration because of the occurrence of resonance phenomena.

In this work, the case of design optimization of the support assemblies of the shaft pipeline of the hydrogenerator-motor was considered, installed at HSPP during its reconstruction in order to improve vibration parameters. The effect of increasing the stiffness of the upper crosspiece and reducing the weight of the rotating parts on the value of the first and second critical rotation frequencies was analyzed. Based on the results of computations, operability of the proposed new reinforced structure of the upper crosspiece of the hydrogenerator-motor with increased rigidity was confirmed. Using this design could increase the first critical rotation frequency from 9 Hz (540 rpm) to 17.6 Hz (1056 rpm). This would lead to the avoidance of resonance phenomena caused by the proximity of the first critical rotation frequency of the rotor to the rated rotation frequency (600 rpm).

The computations were performed in a three-dimensional setting in two stages for each of the considered design cases. At the first stage, the supporting elements rigidity of the shaft line of the hydrogenerator-motor were studied by determining the structural element elastic deformations when it was loaded by a transverse force. At the second stage, these determined stiffnesses of the support elements were used as input data for calculating the critical rotation frequencies of the hydraulic unit rotor

Determining the dynamic indicators of the pneumatic spring for high-speed rolling stock in the zone of a rail joint along a railroad track

Andrii Kuzyshyn — 2024-12-27

The object of this study is the pneumatic spring of the high-speed railroad rolling stock that moves over the rail joint of a railroad track with a vertical ledge.

The task solved was establishing the dynamic behavior of the rubber cord shell of the pneumatic spring of the high-speed railroad rolling stock, taking into account the design features of the railroad track, namely the rail joint.

The methodology for experimental testing of the pneumatic spring of the high-speed railroad rolling stock using the proposed dynamic test installation is given. Experimental tests of the pneumatic spring were carried out within the rail joint of the railroad track, which has a vertical ledge of 7.0 mm. It was established that the maximum value of the accelerations of the rubber cord shell of the pneumatic spring occurs in the vertical plane. The maximum vertical accelerations of the rubber cord shell of the pneumatic spring were 2.4 m/s², horizontal transverse accelerations – 0.85 m/s², and horizontal longitudinal accelerations – 0.9 m/s².

It was determined that the deformations of the pneumatic spring in the vertical plane are higher than the deformations in the horizontal plane. The value of the maximum vertical deformations of the pneumatic spring was 4.1 mm, while the maximum value of horizontal deformations was 1.2 mm.

The natural frequencies and logarithmic decrements of oscillations damping were determined based on the obtained records of the free oscillations of the rubber cord shell of the pneumatic spring. It was established that the value of the first natural frequency of oscillations of the pneumatic spring is 3.21 Hz.

The logarithmic decrement of oscillation damping of the rubber cord shell of the pneumatic spring was determined based on the constructed graph of oscillation damping with an approximating exponent. It is 0.2147.

The obtained values of the dynamic indicators of the new pneumatic spring could be used in the future to control changes in the physical and mechanical properties of the rubber cord shell of the pneumatic spring under the operational conditions of the railroad track. In practice, engineers and scientists will be able to take into account the obtained dynamic parameters of the spring when designing and improving the pneumatic spring for high-speed train movement

Determining the stability of a fire truck tanker against overturning while driving through crossed forest terrain

Kamran Almazov — 2024-12-27

The object of this study is to consider dynamic processes in the tank of a fire truck with different levels of water filling. The task to be solved is to determine the data on the fluctuation of the center of mass of a dynamic system, which consists of the water tank of a fire truck tanker truck, when it moves through rough forest terrain at different speeds. The data make it possible to predict the danger of a fire truck tipping over. In the process of solving the task, an estimation model of a fire truck tanker truck was built together with a water tank, using the LS-Dyna dynamic systems simulation software package. In order to reproduce the dynamic impact on the fire truck tanker with the water capacity exerted by the relief of the rugged forest area, the time dependences of the angles of current position of the fire truck tanker – roll angle, yaw, and pitch – were established. The resulting dependences were used as boundary conditions to reproduce the dynamic influence of the terrain. The turning angles of the water tank of a fire truck were determined depending on the unevenness of the terrain, the geometry of which was calculated by a pseudo-random number generator. Using the explicit method for integrating the dynamics equations, implemented in the code of the LS-Dyna software package, the patterns of fluctuations of the center of mass of the water tank of the fire truck tanker depending on the level of filling and speed of movement were defined.

Using results from the mathematical modeling of dynamic processes in the fire truck tanker, a numerical algorithm was developed for this fire truck tanker to maintain its stability against overturning. Therefore, the results of this study have a direct practical application in the field of fire truck tanker design safety and could be used to improve and devise new technologies in this field