Cantilever Bar Research Articles

Nonlinear system optimization of cutting tools with dynamic vibration absorbers in deep hole boring: A stability analysis

Deep hole boring vibrations pose challenges due to low stiffness of long cantilever bars, impacting accuracy and standards. Nonlinear modeling provides deeper insights into chatter. Integrating dynamic vibration absorbers enhances boring bar stability. In this study, a nonlinear model is developed to investigate the vibration stability of the boring process, with the model's dimensionless parameters analyzed and solved using the Runge-Kutta method. The impact of nonlinear parameters associated with the damping and stiffness of the absorbers on the vibration characteristics of boring bars is thoroughly examined. The findings reveal that there exists an optimal range for the damping and stiffness of the absorbers, where vibration amplitude is significantly reduced, especially under conditions of high excitation force. Moreover, it is demonstrated that the introduction of cubic stiffness elements can further diminish vibration amplitude. These results offer valuable guidance for the design and optimization of DVA in deep hole boring, contributing to improved machining performance and accuracy.

Propagation of material uncertainty in modal parameters and its influence in damage quantification of shear buildings

Structural health monitoring (SHM) plays a crucial role in post-disaster mitigation in investigating the serviceability of an existing structure. The physical properties, namely mass density, cross-sectional area, Poisson’s ratio, modulous of elasticity, etc., vary spatially throughout a real system. These uncertainties propagate in the modal parameters involved in SHM techniques. In this study, the elastic modulous has been considered the primary source of uncertainty. A detailed literature survey has been performed to identify the suitable probability distribution recommended for defining material uncertainty. Although the Gaussian distribution cannot replicate realistic material behaviour, its explicit implementation makes it prevalent. However, based on the principle of maximum entropy, the gamma distribution is the most appropriate recommendation among all non-Gaussian continuous distributions ranging [0, ∞). The Karhunen–Loève (KL) expansion has been adopted to discretize the stochastic field to determine the spectral mass and stiffness of a multi-damaged axially vibrating prismatic cantilever bar-type structure. Closed-form orthogonal pairs of eigensolutions of the KL expansion considering (Adhikari and Friswell, 2010) exponential covariance function have been derived. The expressions for spectral mass and stiffness for a multi-damaged cantilever bar considering material uncertainty have been developed. The uncertainty propagation in the modal properties has been estimated. The complete procedure has been followed to identify uncertainty propagation in damage severity of a common class of civil structures like shear buildings. The influence of material uncertainty in determining the damage severity of a structure with numerable degrees of freedom using a non-destructive approach has been explored. Extensive simulations have been performed to evaluate the effectiveness of the present study in a multi-damaged bar as well as shear building. Statistical parameters, namely mean and standard deviation of natural frequencies, modal displacement and damage severity have been determined. The uncertainty propagation has been reflected in the mean value for varying input stochasticity. However, the standard deviation remained consistent for undamaged as well as damaged structure irrespective of material uncertainty type. Considering gamma distribution in material stochasticity, the spread of uncertainty propagation has been more than the Gaussian distribution. However, experimental studies need to be performed further to investigate the stochastic behaviour in modal parameters of a real structure.

Abutment-Bar Structure Connection Geometry: An Important Design Parameter for Implant-Supported Bar-Retained Overdentures With Cantilever Extension.

When extended distally due to higher loading in the posterior region, implant-supported bar-retained overdentures with cantilever bar extension exhibit greater bending moments on the implants closest to the cantilever bar and increased stresses in the overdenture components. In this study, a new abutment-bar structure connection was introduced to minimize undesired bending moments and reduce the resulting stresses by increasing the rotational mobility of the bar structure on the abutments. Copings of the bar structure were modified to have 2 spherical surfaces, sharing the same center, located at the centroid of the top surface of the coping screw head. The new connection design was applied to a 4 implant-supported mandibular overdenture to create a modified overdenture. Both the classical and modified models had bar structures with cantilever extensions in the first and second molar areas and were analyzed for deformation and stress distribution using finite element analysis, which was also conducted for both the overdenture models without cantilever bar extensions. Real-scale prototypes of both models with cantilever extensions were manufactured, assembled on implants embedded in polyurethane blocks, and subjected to fatigue testing. Both models' implants were subjected to pullout testing. The new connection design increased the rotational mobility of the bar structure, minimized the bending moment effects, and reduced the stress levels in the peri-implant bone and overdenture components, whether cantilevered or not. Our results verify the effects of rotational mobility of the bar structure on the abutments and validate the importance of the abutment-bar connection geometry as a design parameter.

Strains in the implant collars supporting a cantilevered cross-arch bar prosthesis. An in vitro study.

To examine the strains in the collar area of implants supporting a cantilevered cross-arch bar prosthesis during vertical load application. A milled cross-arch metal framework supported by four implants in a trapezoidal design was supported in polymethylmethacrylate. T-strain gage rosettes were attached to the crestal areas of the implants with two grids, one recording circumference strain of the crestal area of the implant and the second recording vertical strain, torquing strains of the implant. The framework was subject to vertical loading from an MTS 810 mechanical system. Loading sites were directly on anterior and posterior implants, and on a cantilever at 7.5, 15, 22.5, and 30mm (0.5, 1.0, 1.5, and 2.0 of the anterior-posterior spread) distal from the posterior implant on the right side. The anterior-posterior (A-P) spread from anterior to posterior implants was 15mm. Sites were loaded individually with 50 and 100N. The data from the rosettes were transferred to a desktop computer and processed using StrainSmart 5000 software. Means and standard deviations were calculated for the 10 trials at each of the loading sites. Two-way ANOVAs were done separately for each dependent variable, the vertical grid, and the circumferential grid. The independent variables were the load magnitude and the load site. Tukey's test was used to compare groups post hoc. When directly loading the implants, loading the anterior implant resulted initially in compression followed by increasing tensile strain with 100N loads. Loading the implant adjacent to cantilever (the posterior implant) resulted in greater strain at the collar than that observed with anterior implant with minimal bending strains. When loading the cantilever, anterior implant showed increasing bending strain at greater cantilever length, whereas the circumferential strains were greater for the supporting implant adjacent to the cantilever, particularly at 100N loads, p≤0.001. Limiting cantilever lengths to A-P spread ratios of 0.5 are preferred. Ratios greater than 1.0 should be avoided as flexing of the collar may occur. The dimensions of the implant, particularly wall thickness, adjacent to the cantilever should be carefully considered when planning the cantilevered implant-supported prosthesis.

The Sliding Keys on Inclined Deflecting‐cantilevers (SKID) device: Empirical and analytical sensitivity analysis with application in post‐tensioned frames

AbstractPreviously, the authors presented a new theoretical energy dissipating technology termed a Frictional Sliding on a Sprung Slope (FSSS) device. Its purpose was to provide significant energy dissipation to post‐tensioned (PT) frames structures. The FSSS device has a triangular‐shaped hysteretic curve, which has a zero‐force activation threshold. This enables activation for any earthquake magnitude and provides progressively greater energy dissipation with an increase in structural oscillations. In addition, it is designed to allow full self‐centring of the PT framed structure. In this paper, a physical prototype FSSS is designed, constructed and experimentally tested. The prototype replaces the theoretical springs, bearings and the constraints with pairs of cantilever bars. Consequently, it is renamed a Sliding Keys on Inclined Deflecting‐cantilever (SKID) device. Six scaled SKID configurations having different manufacturing parameters were built and tested. Also, five materials were used to investigate the sensitivity to the friction coefficient of the sliding pads. Both cyclic and fatigue tests were conducted to assess SKID performance empirically. A finite element model of SKID was then implemented in OpenSees and benchmarked against the experimental results. More than 700 one‐story one‐bay PT frames with different SKID devices (PT‐SKID frames) were numerically tested to investigate the dynamic characteristics of the structural system affecting the seismic response. Based on the extensive experimental and numerical analyses, design suggestions are provided, and the PT‐SKID self‐centring features are discussed.

Generalized formula for estimating the oscillation frequency response of a cantilever bar with point masses

This paper presents a study of natural oscillations of a cantilever bar with five point masses with variable geometric and stiffness parameters (distances between locations of the masses, coefficients of variability of the bending stiffness of the bar sections). Using the exact method of forces based on the Mohr formula, there have been obtained expressions in general form for calculating the main unit coefficients of the secular equation, which makes it possible to perform calculations and to determine the oscillation frequency response of natural oscillations with a wide range of changes in the initial parameters of the physical and geometric state of cantilever bars. A numerical example has been given to illustrate the proposed theoretical approaches. The results have been compared with the results based on calculating a similar can tilever bar with one( reduced by masses) degree of freedom. A graphical dependence of the oscillation frequency response value on changing the value of the bending stiffness along the length of the cantilever bar gas been obtained. The theoretical provisions and applied results presented in the work will be widely used both in the practical design of bar systems and in scientific research in the field of mechanics of a deformable solid body.

Nonsmooth modal analysis of a varying cross-sectional area bar in unilateral contact

Nonsmooth modes of vibration allow for identification of resonant behaviours and attendant vibratory frequencies in structures prone to unilateral contact conditions on the boundary. The prominent approach for finding nonsmooth modes of vibration entails finding continua of periodic solutions to the system in question. In this paper, nonsmooth modes of a one-dimensional bar of varying cross-sectional area prone to unilateral contact with a rigid obstacle are determined. While numerical and analytical techniques were previously proposed, they were limited to constant cross section bar and could not be applied on the varying area bar for which the classical d’Alembert solution no longer exists. In this article, nonsmooth modal analysis of the varying area bar is performed via a novel treatment of the Signorini conditions within the finite element framework: the nodal boundary method. The nodal boundary method solves the Signorini problem by switching between two sets of shape functions describing either (1) inactive contact motion (motion away from the rigid obstacle) or (2) active contact motion (bar in contact with the rigid obstacle). In the proposed nodal boundary method, the motion of the contacting node does not participate in the resulting governing Ordinary Differential Equation (ODE). Instead, its motion is prescribed by the boundary conditions and is dictated by the motion of internal nodes. The nodal boundary method results in a discontinuous ODE in the internal nodes which can be solved both analytically and via numerical techniques. Solutions obtained by the nodal boundary method exhibit several advantages over existing numerical techniques: no chattering at contact, no penetration of the rigid obstacle, and existence of periodic solutions. Specifically, these periodic solutions are readily detectable via the shooting method with sequential continuation. The nodal boundary method is used successfully for the nonsmooth modal analysis of different models of the varying area bar. Besides, application of the nodal boundary method for nonsmooth modal analysis of the uniform area cantilever bar in Dirichlet or Robin boundary conditions is also demonstrated for comparison with existing literature.

A novel seismic energy dissipating device, Sliding Keys on Inclined Deflecting-cantilevers (SKID): Theoretical and experimental evidence

An innovative physical realisation of the previously reported conceptual frictional sliding on a sprung slope (FSSS) device is proposed in this paper. The device uses the end stiffness of cantilevers as the “sprung-slope”, which generate amplitude varying normal and frictional forces along the sliding plane. This novel configuration is here termed a Sliding Keys on Inclined Deflecting-cantilevers (SKID) device. The SKID device is proposed for application with post-tensioned (PT) frames to improve lateral stiffness and energy dissipation capability without inhibiting their self-centring features. The configuration and theoretical properties of the device are presented. In particular, the reliability of using cantilever bars as a means of generating an amplitude-dependent normal force at the sliding surfaces is discussed. Then, two 1/4 scale-reduced prototypes, which have (i) negative unloading stiffness (SKID A) and (ii) positive unloading stiffness (SKID B), were designed and manufactured. Both specimens were subjected to the same quasi-static cyclic loading protocol. It was found that they exhibited stable and repeatable triangular-shaped hysteretic curves. The theoretical hysteretic load/deflection envelopes are compared with test specimen results, verifying a satisfactory consistency between the theoretical and physical SKID device.

The Ideal Hybrid Framework Material? - A Literature Review

Hybrid denture prosthesis have been used popularly in prosthodontics as a tooth replacement option. with some controversy. Hybrid dentures consist of one of the most novel options in the restoration of the edentulous arches. The implants are only placed only in the anterior region and the prosthesis is provided in the posterior region with the assistance of a cantilevered bar or framework. Conventionally the framework for such a prosthesis is fabricated using titanium or cobalt-chromium metal. Traditionally the frameworks were fabricated using metal casting. However, with the advent of digital dentistry CAD CAM frameworks have become very popular which have allowed the use of an array of materials such as zirconia,peek amongst other traditionally used metals.With a focus on materials used in the fabrication process of hybrid dentures, the goal of this study was to summarise the pertinent literature in this area.In conclusion, hybrid dentures seem like a viable treatment option which can be fabricated using multiple materials such as PEEK,zirconia,titanium,cast base metals, noble metals etc.

Clinical performance of implant supported mandibular overdentures with cantilever bar and stud attachments: A retrospective study.

Treatment of edentulous patients with implant-supported over-dentures improves denture's retention and stability. Published data concerning implant-supported overdenture with cantilever bars that claimed that can affect the survival and bone loss of implants are scarce. The purpose of this study was to evaluate 5-year clinical performance of mandibular implant-supported over-dentures with different attachment systems. In this retrospective study, 103 patients who had received mandibular over-dentures supported by two implants were evaluated in a 5-year follow up. Studied groups were patients with Spherblock ball attachment (58 patients), Dolder bar with cantilever (36 patients), and Locator attachment (9 patients). Marginal bone-loss around implants, prosthetic complications, soft tissue status of the implants (gingival index, plaque index, pocket depth, and bleeding on probing) were used to compare studied groups. Visual Analogue Scale (VAS) criteria was used to assay patient's satisfaction. One-way ANOVA, Scheffe, Kruskal-Wallis, Mann-Whitney, and Fisher's exact tests, were used for the data analysis (α=0.05). One hundred and three patients (46 male, 57 female, mean age 64.7 ± 8.6) with 206 implants (Strauman) were studied. The implant survival rate was 100% with mean bone loss of 0.22 mm around implants in 5 years. Prosthetic complications including attachment wear and denture fracture occurred more often with ball attachments. The number of attachment replacement, and post insertion appointments were significantly less in patients with bar attachments (p < 0.05). Pocket depth and gingival index were less in the ball attachment (p < 0.05). Mandibular overdenture supported by two implants can be considered a successful treatment in edentulous patients. The frequency of prosthetic complication is higher in unsplinted than splinted superstructures.

Prosthetic complications with mandibular bar-retained implant overdentures having distal attachments and metal frameworks: A 2- to 12-year retrospective analysis

Statement of problemLong-term reports on 2-implant-retained overdentures having metal frameworks and bars containing distal attachments are scarce. PurposeThe purpose of this retrospective study was to evaluate prosthetic complications with 2-implant-retained mandibular overdentures with metal frameworks having either screw- or cement-retained cantilevered bars with distal attachments. Material and methodsSeventy-three edentulous study participants who had been treated with mandibular overdentures with 2 implants were included. The parameters assessed were acrylic resin fractures (base fracture, fracture at midline), debonding of teeth, opposing prosthesis fracture, need for relining or rebasing, abutment and bar screw loosening and fracture, ball or bar attachment or clip wear, fracture or detachment, bar fracture, and implant loss. Statistical analysis was performed by using the Mann-Whitney U test as the data were not normally distributed. The categorical variables between the groups were analyzed by using the Fisher exact test (α=.05). ResultsTwenty-seven prostheses had a cement-retained bar, and 46 bars were screw-retained. Of 73 overdentures, 68 were metal-reinforced. The mean observation time was 5.9 years with a range between 2 and 12 years. The most common complication was wear of the Rhein 83 polymer attachment followed by bar screw loosening. The cumulative survival rate for overdentures was 91.9% at 6.8 years. The service life of cement-retained prostheses was significantly longer (P<.05). Bar, resin base, and mid-line fractures were only seen with cement-retained prostheses. The number of times an attachment change was required did not differ between cement- and screw-retained bars. Of 191 implants, 3 were lost, and the cumulative survival rate was 93.5% at 7.5 years. No significant difference was found between retention types in terms of implant loss (P>.05). ConclusionsBased on the participant population observed, the survival rates of 2-implant-retained mandibular overdentures and their implants in the medium term were high. Wear of the polymer attachment was commonly seen. Overdentures with cement-retained bars had bar or acrylic resin fractures. Mandibular 2-implant-retained overdentures with a screw-retained bar containing bilateral distal attachments had fewer prosthetic complications and high implant survival in the medium term.

ANALYSIS OF STRESS DURING THE PLACEMENT OF REMOVABLE DENTURES OVER IMPLANTS

Implant-supported removable dentures are one of prosthetic dentistry modalities to replace missing teeth and have a long history of the development. Dentures placed over implants offer opportunities to restore dentition defects resulted from various causes. Different defects of the dentition require their own restorative techniques. In recent years, implant-supported prostheses have become more commonly preferred over full dentures. For patients with low distal bone levels and problems with placement and stabilization, 4-implantsupported dentures seem to be a good option. Four bar implants for supporting dentures are considered more reliable in terms of fixing the prosthetic structures over them. The aim of this work is to analyze the effect of implant-supported denture placement on the implants themselves and peripheral tissues, depending on the denture models, level of implant placement, the angle of placement, as well as the length of the console in the structure. Results. In 10 different mathematical models, the angles of implant placement in the bone were taken as equal to 90°, 17° and 30°, and the level of placement was equal to 1 mm and 3 mm (in accordance with the configuration of the jaw bone). The length of the cantilever bar system prepared on implants was 0 mm, 5 mm and 10 mm in different models. The load on the model was actually equal to the chewing pressure, 100 N (approximately 10.2 kg), when chewing a 1 cm solid food mass. The pressure was applied from 3 different points: from the anterior section, when the centre of the bolus was at the place of contact between the central incisors; in the right posterior region, when the centre of the bolus was at the contact between the 2nd premolar and the 1st molar; from the left posterior region, when the centre of the bolus was in the area of contact between the 2nd premolar with the 1st molar. After 3D analysis, the Von Mises stress findings in the implant area and the corresponding color scales were obtained, as well as the maximum and minimum stress values in accordance with the color scale. Conclusion. Based on the analysis and comparison of the obtained values, the study has determined that the stress distribution is optimal for some implant models, for others it can be too small or too large due to uneven stress values. The study of models based on the method of 3D three-dimensional stress analysis by the finite element method and the results of these studies are elucidated in the article.

Cantilevered Versus non-cantilevered resilient bar attachment for 2-implant retained mandibular overdentures. A short term crossover study of chewing efficiency and bite force.

Aim of the study: This study compared chewing efficiency and maximum bite force between cantilevered and non-cantilevered resilient bar attachment used for 2-implant retained mandibular overdentures. Materials and methods: Eight completely edentulous participants (4 men, 4 women) with atrophied mandibular ridges receive 2 implants in the canine region. After 3 months, each patient received Hader bar with 7mm distal cantilevers and mandibular overdenture with 3 clips (CHB group). After another 3 months, distal cantilevers were sectioned and patients received Hader bar without cantilevers and mandibular overdentures with one clip (HB). Chewing efficiency (using unmixed fraction (UF) in a colored gum) and bite force were measured 3 months after using conventional dentures CD, CHB, and HB. Results: The highest unmixed fraction (UF) was noted with 5 cycles and the lowest number was noted with 50 cycles. UF decreased with the increase of number of chewing strokes. For all chewing strokes, the highest the UF was noted with CD, followed by HB, and the lowest UF was noted with CHB. At 30 and 50 strokes, there was a significant difference between each 2 groups, and HB showed significant higher UF than CHB. The highest maximum bite force was noted with CHB, followed by HB, and the lowest was noted with CD. Conclusion: it could be concluded that both cantilevered and non-cantilevered bar attachments for 2 implant overdentures achieved higher chewing efficiency and maximum bite force than conventional dentures in patients with atrophied mandibular ridges.

Study of quasi-static behavior of a system with partially distributed parameters under combined loading

The problem of the existence of a quasi-static process described by the solution of a system of differential equations is considered. The possibility of quasi-static deformation of a cantilever bar, at the end of which there is a concentrated mass exceeding the mass of the bar has been studied. The bar is loaded with tracing and horizontal forces. A condition has been obtained under which the bending of a bar can be studied on the basis of the solution of the static problem used in the theory of small vibrations.

Research on the dynamic identification method of weak parts in cantilever structures.

Determining the weak parts of a structure is one of the key issues in the field of machine tool stiffness improvement. However, studies show that overcoming the static deformation with acquisition difficulty is a complex problem in practical structures. This study considers the machine tool cantilever structure, as a cantilever beam and bar structure, where the objective is to propose a weakness index, to identify the weak part, using system reconstruction to extract the measured static deformation data and the fitting data. Stiffness reduction is used to simulate weak parts, while the effectiveness of the method is evaluated, in the case of various weakness values and of different noise levels, using the finite element simulation approach. The validity of the proposed method is illustrated through comparison of the theoretical results to the experimental ones, using the cantilever structure of a test machine tool. The research content provides some means of improving the machining accuracy of machine tools.

Finite element analysis of beam with different loading condition

Abstract This examination researches the diversion and the stressful appropriation in a length, thin cantilever beam or bar light emission rectangular cross section segment made of straight versatile the material behavior and mechanical properties that are homogeneous mixture. The redirections of a beam are basically a modeling of 3D issue. A flexible extending one way is joined by a pressure in opposite ways. This undertaking, structural and dynamic examination is a cycle to decide the stress, strain and distortion. Shaking qualities of a formation or a machine segment while it is being planned. It was gotten a significant choice to give an accommodating commitment in understanding control of numerous vibration wonders which experienced practically speaking. In present work we thought about the pressure and regular recurrence for various material have identical cross sectional area of the shafts are T, I and C shaft. The beam is planned and dissected in ANSYS 14.0 software. The beam shaft is fixed toward one side is vibrate to acquire the normal recurrence, modal shape in addition to redirection by the various segments and equipment.

Influence of the foundation bed stiffness on the dynamic properties of the building as of a multi-mass cantilever bar

Relevance. The study of the interaction of buildings and structures with the base during an earthquake is one of the most important tasks of the theory of earthquake resistance. The response of the structure to seismic impact depends to a large extent on the ratio of the stiffness characteristics of the soil, foundation, and foundation structure. Moreover, taking into account a rather high degree of statistical variability of the characteristics of the soil foundation, it is possible to ensure the required level of safety of a structure only through the use of probabilistic models and a quantitative assessment of the reliability of the construction-base system as a whole. At present, for the calculation of the construction - base system for seismic loads, deterministic discrete models of the finite element method are mainly used. But these models are poorly adapted for probabilistic calculations and require extensive statistical data, which are currently insufficient. Therefore, in problems of reliability assessment, it is advisable to use simplified analytical models, which make it possible to derive the value of the statistical variability of its reaction with relatively small initial information about the system. The aim of the work - based on the well-known solution for the single-mass model to present an analytical solution in the matrix form of the problem of free horizontal vibrations of a multi-mass cantilever rod on the foundation specified by the elastic half-space model. Methods. A study was made of the effect of the compliance of the soil foundation on the frequencies and forms of horizontal vibrations of the structure. A comparison of the results with the calculation performed by the finite element method is given. Results. The obtained solution is intended to conduct a probabilistic calculation of the construction-base system under seismic loads and evaluate its reliability.

Finite element model updating of boring bar and determination of chatter stability

The use of Finite-Element Models (FEM) has become common practice in structural analysis and design. Commercial Finite element package allows designers to create, simulate, and analyze real-time problems. However, these models often do not represent the actual physical characteristics of the structure. Many factors affect the accuracy of the numerical model; these include simplified assumptions regarding the boundary conditions, unplanned loads on the structure, improper modeling joints, and material imperfections. Interest in the vibration properties arises because nearly all structures are subject to the vibration of one form or another, which is usually undesirable. In machine tools, boring bars are slender and cantilevered, hence they generally vibrate with large amplitudes under the action of cutting forces which result in machining instabilities, i.e. chatter. In this paper, the Iterative inverse Eigen sensitivity updating method is used to update the finite element (FE) model of a boring bar, using experimental modal data. The finite element model of the cantilevered boring bar is modeled using Euler-Bernoulli beam elements. The degree of correlation between the FE model and the experimental model is ascertained by determining the difference in natural frequencies and by using Modal Assurance Criterion (MAC). Suitable updating parameters are chosen and these parameters are iteratively updated using Inverse Eigen sensitivity method to match the dynamic responses of the FE model to that of the experimental model, and the modal parameters of the updated FE model are compared with the experimental model. Better correlation values indicate the enhanced similarities between experimental and analytical models. The updated model is used to obtain tool tip receptance and determine chatter stability. The updated FE model yields improved accuracy in chatter stability estimations.

Analysis of connections and restrictions occurring due to the oscillations of vibrating screen working member and cantilevered screen deck

Research relevance is due to the need of mining companies in a more complete extraction of mineral resources, reduction of crude minerals losses, and extension of deposits’ life. Some enterprises face the problem of complicated high-quality separation of hard-to-screen rock mass. Screen which are common in the industry often become clogged causing decline in the effectiveness of screening. Research aim is to determine the links, build resonant curves and analyze the amplitude oscillations of the working member and cantilevered bars of the screen deck using numerical simulation. Methodology includes the theoretical study of the dual mass oscillatory system with the use of numerical simulation. Results. The motion of the vibrating screen with circular oscillations of the working member, which includes the screen deck of a cascade type with cantilevered bars, is regarded as oscillation of a dual mass system. The amplitudes of oscillations of both masses make in-phase and anti-phase movements relative to the driving force of the drive. The analysis showed that the amplitudes of the working member are practically independent of the screen deck parameters, and bars oscillation amplitudes vary over a wide range. The expressions are given calculating the parameters of cantilevered bars and the values of the initial data of the GIT-51 screen. Resonance curves of amplitude and frequency relations are constructed. The conditions are established under which the oscillation amplitudes of the cantilevered bars take on hyperadmissible values; it is shown that for a particular oscillating system there is a transitional resonance value. Summary. The natural oscillation frequency ratio ranges are established of the entire system with the frequency of forced oscillations in which the oscillation amplitudes of cantilevered bars reach the specified parameters. It is shown that by changing the screen deck parameters at the design stage, it is possible to adjust the inter-frequency range and establish the operating mode of the screen.

Application of the finite difference method for modeling cantilever bar vibrations

The paper is devoted to mathematical modeling of cantilever bars using the finite difference method. This method is widely used in structural mechanics for solving static problems. The novelty lies in the application of the finite difference method to simulate the dynamics of free and forced vibrations of the cantilever. Models have been developed that allow calculating the static and dynamic deflections of the cantilevers during free and forced vibrations, as well as simulating the vibrations of cantilever beams with attached vibration dampers. The resulting models of cantilever structures make it easy to modify system parameters, external influences and damping elements. All calculations were performed using the finite difference approach when moving along geometric and temporal coordinates.