Ukrainian Journal of Mechanical Engineering and Materials Science

10

Authors: Andriy Kozak

Automatic dosing system for loose materials is widely used in construction, food and pharmaceutical industries to prepare various mixtures. The main criterion for optimization of such systems is the accuracy of dosing of each component of the mixture, which depends on the speed component dosing and other process factors. Technological requirements for product quality in production and the high cost of individual components of the mixture strictly regulate the developers of the automated system loose materials size dosing errors. Ensuring compliance with the maximumpossible mix recipe requires dosing of each component with high accuracy, which is a daunting task for engineers. Precision dispensing in automated systems is a function of the large number of systematic and random factors: size, shape and relative position of individual particles of the material; coupling coefficient of each other and of the structural elements of the dispenser; relative humidity of material dosage and indoor air; the height of the fall of the material in the receiving container; the value of the dispenser tilt to a level of horizon; electromechanical vibration and noise, etc. Developed simulation model of frequency-controlled electric screw feeder that is different from the known one facts that modeling of screw feeder is considering mass “falling pillar” which is constantly changing as the accumulation of material in the hopper.

10

Authors: Alexander Оrgiyan, Anna Balanyuk, Vladimir Kobelev, Ivan Tvorischuk

On the basis of precision theory we propose the method of computation of static and dynamic errors of cross-sectional shapes of holes in fine boring of smooth and stepped holes. We consider particular cross-sectional shape errors caused by such factors: – Error of the tooled hole form caused by the axis hope displacement in the workpiece relative to the spindle axis; – Error of the tooled hole form caused by the hole out-of-roundness in the workpiece; – Error of the tooled hole form caused by unevenness of the cutter radial compliance at the angle of spindle rotation. According to time characteristics the errors can be divided into static with frequency substantially less than the lowest natural frequency of the process system, and dynamic, caused by vibrations. Static error rate is usually a multiple of the spindle speed. The computations of deviations from the roundness of the cross section caused by vibrations are determined by computing the amplitudes of forced vibrations. Computations of individual static errors based on the average values of compliance, the material being processed and the processing mode are reduced to construction of nomographs for various materials. Dynamic errors are determined by computation of forced vibrations amplitudes on the basis of systems of ordinary differential equations describing the vibrations of a machine closed dynamic system. These equations allow to compute the amplitude of the forced vibrations of smooth and stepped boring bars. A distinctive feature of the computations for multiple tooling is allowance for mutual influence of excitations arising at each step of a boring bar. It is assumed that at multiple tooling each of the working cutters creates its own errors, the values of which are found by the nomograms for single-cutter tooling. Full tooling error at each step caused by some source of error is determined as the sum of the errors: of both, own and additional, caused by all working cutters. Additional errors can be found through coefficients of influence through dividing by the respective cutter's own compliance and through multiplying by the appropriate factor of influence. We obtained results of computations and experiments of the dependence of the total error on the ratio of the boring bar steps lengths. Analysis of roundness charts of the bored holes shows that vibrations can be a factor largely determining the shape of the cross section of the hole. Experiments have shown that when the rotation speed changed the excitations of the spindle poles changed too. Under unfavorable excitation frequencies the tooling errors increase by 1,5–2 times. The study results allow us to compare the two most common ways to reduce the errors caused by elastic deformations: the use of the dynamic damper and the processing of holes in two runs. The experimental results confirm the non-monotonic dependence of the amplitudes of forced vibrations on the ratio of the boring bar steps lengths.

20

Authors: Yuri Chovnyuk, Yuri Gumeniuk, Mykhailo Dikterjuk

Most authors have ignored the effect of rotatory inertia and shear deformation. This practice is justified for slender flexible arms. According to the Timoshenko beam theory, the deflection due to shear force and rotatory inertia should be taken into account in modelling for high speed and high precision requirement when the ratio of the cross-sectional dimensions to length increases. Based on Hamilton’s principle and Timoshenko’s flexible beam theory, the dynamic model of a single non-slender flexible link is derived, and it is shown that the elastic motion is governed by a pair of coupled partial differential equations with coupled boundary conditions. Then the abstract form of the dynamic equations is studied, and the properties of the spectrum of the elastic operator appearing in the evolution equation are given. Furthermore, the eigenvalue problem of the elastic operator is solved in explicit form. The formulation and well-posedness of the state-space equation, as well as the transfer function of the dynamic control system of the non-slender flexible link, are studied by spectral analysis. Spectral analysis is used to study the well-posedness of the dynamic control system. The tracking control problem is studied and a feedback control scheme that controls the rigid-body motion and elastic behaviors simultaneously is derived based on a n-modal model. Closed-loop configuration of a control system, equivalent circuit of a dc-motor and the overall system block diagram are proposed. The stabilization of the closed-loop system is studied analytically. Finally, the tracking control problem is studied, a stabilizing feedback control law based on a n-modal model to suppress vibrations of the flexible link is derived, and the necessary and sufficient conditions that can guarantee the stability of the closed-loop system, are given. Simulation results are given as well.