Vibration Of Belt Research Articles

Modelling of transverse vibration of conveyor belt in aspect of the trough angle

The transverse vibration of conveyor belts is a crucial aspect in their proper and safe design, as the correct determination of vibration frequencies is essential to avoid unsafe operating conditions and premature wear of components. This study presents the Moving Compressed Beam (MCB) transverse vibration model, that is based on the interpretation of a conveyor belt as a beam known from the literature. This approach allows you to include in the model the transverse flexural rigidity of a troughed belt-a parameter that is closely related to the belt geometry. While not commonly used in engineering practice, the MSB model was compared with other models during the laboratory tests based on changing of trough geometry. This study emphasizes the significance of considering the transverse flexural rigidity of conveyor belts during the design process, and the MCB model which offers a promising approach in aspect of vibration control.

An experimental procedure for the identification of the dynamic parameters for the rigid-ring tyre model

Several approaches have been developed over the years for the modelling of the tyre behaviour in vehicle-dynamic applications. The so-called ‘rigid-ring’ models are among the classics for the modelling of the belt dynamics. Although there are several works dealing with the vibrating properties of tyres, the problem of the identification of the related rigid-ring model parameters has not been described other than qualitatively or partially. The aim of this work is thus to fill this gap and to devise a procedure for the experimental characterisation of such parameters, namely the frequency and damping of the in-plane and out-of-plane belt vibration modes as well as the associated masses and inertias. An experimental modal analysis (EMA) approach is employed, which involves an instrumented hammer combined with three-axial accelerometers roving on 16 stations equally spaced along the tyre circumference. The method is numerically demonstrated on the finite-element models of a motorcycle tyre and a car tyre. The approach is also experimentally validated on a real tyre. The rigid-ring vibration modes of the motorcycle tyre are in the range 70–220 Hz, while those of the car tyre are in the range 51–85 Hz. The ratios of the mass/inertia of the rigid ring to the mass/inertia of the tyre are in the range 40–87% and 68–74% for the motorcycle and car respectively.

In-Hand Manipulation Inspired by Diabolo Juggling

This letter discusses in-hand manipulation inspired by diabolo juggling. Continuous rotational manipulation using the vibration of a flexible belt attached to the hand is proposed. This method is highly adaptable, enabling the hand to manipulate various types of objects, without requiring complex sensing or control, or a complex mechanism. First, a simplified analytical model composed of a flexible belt and a cylindrical object is introduced. Based on periodic input to the two endpoints of the belt, continuous rotation based on slipping of the object is theoretically discussed. Then, via numerical examples, it is shown that the average angular velocity of the object can be controlled. Finally, the proposed method is experimentally validated using a prototype hand. It is shown that the stable holding and continuous rotation of the object are easily achieved. The versatility of the method is demonstrated through experiments using objects with various shapes, sizes, and masses.

Roller damage detection method based on the measurement of transverse vibrations of the conveyor belt

The article presents the detection of damage to rollers based on the transverse vibration signal measured on the conveyor belt. A solution was proposed for a wireless measuring device that moves with the conveyor belt along of the route, which records the signal of transverse vibrations of the belt. In the first place, the research was conducted in laboratory conditions, where a roller with prepared damage was used. Subsequently, the process of validating the adopted test procedure under real conditions was performed. The approach allowed to verify the correctness of the adopted technical assumptions of the measuring device and to assess the reliability of the acquired test results. In addition, an LSTM neural network algorithm was proposed to automate the process of detecting anomalies of the recorded diagnostic signal based on designated time series. The adopted detection algorithm has proven itself in both laboratory and in-situ tests.

Modeling of serpentine belt accessory drive system coupled vibrations and utilizing nonlinear tensioner to enhance performances

Serpentine belt accessory drive system (SBADS) is a complex hybrid discrete-continuous system and is a typical coupled vibration system with rigid body vibrations and belt vibrations, which consists of rotational vibrations of pulleys and tensioner arm and transverse vibrations of continuum belt spans. Taking an engine front end accessory drive system as an example, the coupling vibration model of belt, pulleys and tensioner arm is established. In the model, hysteretic behavior of tensioner is considered, and a calculation method for estimating the output torque versus the imposed angle of tensioner arm is proposed. In solving the coupled motion equations of the SBADS, transverse displacement of a belt span is discretized as the product of time function and space function by using Galerkin method, the steady-state deflections of belt spans are calculated by singular perturbation method, and the nonlinear dynamic responses of a SBADS are solved by numerical method. The nonlinear dynamic responses of the SBADS are calculated by the established method and validated by the experiment results. Benefits of nonlinear hysteretic behavior of a tensioner on the dynamic responses of a SBADS are studied, and the method for how to utilize nonlinear characteristics of tensioner to enhance the performances of a SBADS is proposed in the end of this paper.

Identification of conveyor belt tension with the use of its transverse vibration frequencies

Belt vibration is related to the tension force along the entire length of the conveyor route. The ability to predict belt vibrations can provide information about the correct operation of the conveyor. Vibration analysis is usually based on theoretical models or stationary tests. In this article the vibration frequency of a working conveyor was measured, in the absence of the material and with the belt loaded. The tests were carried out in motion using a specially made device placed onto the conveyor belt. The distribution of the frequency of transverse vibration of the belt along the entire length of the conveyor route was identified. Using the phenomenon of belt vibration, the increase in belt tension in the top belt strand was determined. The comparison of the measured increases in the tensile force with the values obtained by computer simulation showed the high accuracy of the method.

Experimental and theoretical investigation of CVT rubber belt vibrations

Abstract This article contains the results of experimental tests of vibrations of a continuously variable transmission (CVT) belt transmission driven by a two-stroke internal combustion engine. The measurements were made with the use of a high-speed camera, which allowed to obtain results impossible to obtain with other measurement methods. The nonlinear integro-partial differential equation of vibrations of the moving belt is given. Based on a simplified linear equation, the observed effects on the amplitude–frequency characteristics obtained from the measurements are explained. An approximate formula is given that allows for determining the transmission belt velocities for which resonances occur.

Frequency analysis of transversal vibrations of belt drives with time‐varying belt lengths

AbstractThe dynamic positioning accuracy and the smoothness are key aspects of linear belt drives where vibrations have a negative impact. A FE‐Model, based on a one‐dimensional analytical model of the belt, is derived to study the respective effects for different parameters. The model considers the dominant transverse deflection and a quasi‐static assumption for the longitudinal deformation. The possibility to consider various time‐varying belt lengths, the belt mass, stiffness and tension force is an essential part of the modeling. The non‐linear cable effect is demonstrated by comparison with the linearized solution. Vibrations for the cases of constant and variable belt length are investigated and compared to common in literature used approximation formulas for the resonance frequencies of such systems. The influence on positioning deviations and the use of vibration reduction techniques considering the different belt sections of the linear drive can be derived from the computed results and are topics for future research.

Models of Transverse Vibration in Conveyor Belt—Investigation and Analysis

The transverse vibration frequency of conveyor belts is an important parameter describing the dynamic characteristics of a belt conveyor. This parameter is most often identified from theoretical relationships, which are derived on the basis of an assumption that the belt is a stationary elastic string. Belt vibrations have a number of analogies to other tension member systems, such as, for example, power transmission belts. Some research findings suggest that in the case of a limited length of the belt section, a more accurate description of its vibration can be obtained with a beam model rather than with a string model. Experimental research has so far mostly revolved around measurements of stationary belts. This article presents the results of vibration measurements performed for a moving belt and obtained for various operating parameters of the conveyor, as well as for several configurations of the distance between idler supports. The analysis was conducted on a moving steel-cord belt. Belts of this type are commonly used in the majority of mines and industrial plants. The measurement results were compared with the model of a string and with the model of a beam in tension. Both of the theoretical models allowed for the belt speed, whose influence was demonstrated in both theoretical calculations and experimental tests to be negligible. On the other hand, the tensile force in the belt was observed to have a significant impact on the vibration frequency. Depending on the idler spacing, the measurement results are approximate to those of the beam model or of the string model. For spacing smaller than 1.6 m, the belt shows properties approximate to an elastic beam, while for spacing greater than 1.6 m, the belt behaviour can be better represented through a string model. A beam model is, therefore, more applicable in analyses of vibrations in the upper strand of the belt, while a string model is more useful in analyses of vibrations in the lower strand.

Transversal vibrations of a toothed belt in linear drives during operation

AbstractVibrations of the toothed belt of a linear drive can affect the dynamic positioning accuracy and smoothness which is important for practical applications. An analytical, one‐dimensional model of a belt section is derived, taking into account the preload and flexural rigidity, as well as the non‐linear cable effect and the acceleration forces due to the belt mass. In addition to the case of constant belt length, the temporal change of the length as a result of the axial motion is an essential part of the modeling. The solution of the equation of motion is limited to the dominant transverse deflection of the belt. For the longitudinal extension, the assumption of a quasi‐static solution is taken. A FEM program is implemented to calculate the solution for given operation conditions. The evaluations are made for selected motions according to a path planning with trapezoidal velocity profiles. A modification of individual parameters, based on a practical parameter set, enables the analysis of the respective effects.

Remaining useful life (RUL) prediction of internal combustion engine timing belt based on vibration signals and artificial neural network

Timing belt rupture, which can develop quickly and cause severe harm to various engine components, usually occurs unexpectedly and without prior warning signs. Due to the rapid occurrence of timing belt rupture, fault diagnosis strategies are not indeed efficient. In this paper, a vibration-based intelligent method has been proposed to predict the remaining useful life (RUL) of the timing belt using data mining techniques and multi-layer perceptron neural network (MLP-NN). To achieve this goal, two categories of experimental tests were designed and carried out on the timing belt, namely, fault thresholding (FT) and accelerated life (AL) tests. FT test was performed by comparing the defect-free belt vibration signals with those of a faulty belt to determine the failure threshold. This is while, in the AL test, the engine was continuously run with a defect-free timing belt until initiation of rupture or damage was detected. Four feature functions, regarded as timing belt health indicators, were applied to the collected vibration signals, namely, energy, impulse factor, root mean square, and FM4. The extracted features were then fed to the MLP-NN to predict the timing belt RUL by continuously comparing the feature values and the failure threshold. The results showed that the proposed method is able to predict the timing belt RUL with an accuracy of 90%. In addition, data predicted by the MLP-NN showed high correlation with the actual measured data, which emphasizes the robustness and precision of the proposed method for timing belt RUL prediction.

Hydrodynamic Model of Transport System

A hydrodynamic model of production systems with a flow method of organizing production is considered. The basic macro-parameters of the state of the production flow line and the relationship between them are determined. The choice of a lot of moment approximation for modelling the production line is justified. It is shown that the conveyor-type flow line is a complex dynamic system with distributed parameters. The boundary value problem is formulated for the longitudinal vibrations of the conveyor belt when the material moves along the transportation route. It is assumed that there is no sliding of material along the conveyor belt, and the deformation that occurs in the conveyor belt is proportional to the applied force (Hooke's elastic deformation model). The significant effect of the uneven distribution of the material along the transportation route on the propagation velocity of dynamic stresses in the conveyor belt is shown. When constructing the boundary and initial conditions, the recommendations of DIN 22101: 2002-08 were used. The mechanism of the occurrence of longitudinal vibrations of the conveyor belt when the material moves along the transportation route is investigated. The main parameters of the model that cause dynamic stresses are determined. It is shown that dynamic stresses are formed as a result of a superposition of stresses in the direct and reflected waves. Analytical expressions are written that make it possible to calculate the magnitude of dynamic stresses in a conveyor belt and determine the conditions for the occurrence of destruction of the conveyor belt. The characteristic phases of the initial movement of the material along the technological route are considered. The process of the emergence of dynamic stresses with the constant and variable acceleration of the conveyor belt is investigated. The dynamics of stress distribution along the transportation route is presented. It is shown that the value of dynamic stresses can exceed the maximum permissible value, which leads to the destruction of the conveyor belt or structural elements. The transition period is estimated, which is required to ensure a trouble-free mode of transport operation during acceleration or braking of the conveyor belt. The use of dimensionless parameters allows us to formulate criteria for the similarity of conveyor systems.

Limit angle of the belt conveyor inclination at transporting lumpy loads

One of the ways to reduce capital costs and shorten length of conveyor transport routes is to increase angle of the conveyor inclination. As practice shows, limit inclination angle of general-purpose belt conveyors transporting bulk loads is 18°- 22°, while angle of natural slope of ore and coal is 40° and 35°, respectively. Such a difference between the angles of bulk load slope and limit inclination angle of the belt conveyor transporting the bulk loads is explained by the belt vibration impacting on the state of the transported load during its moving along the belt conveyor idlers. When exposed to vibrations, the solid-yielding state of the granular medium passes into a free-dispersed state at which inertial forces of the particles exceed the forces of internal coulomb friction between the particles. Moreover, as experimental studies have shown, granular medium moves relative to the conveyor belt at anglesof conveyor inclination of 18°–22°, i.e. limit angle of inclination of the conveyor belt transporting bulk load does not exceed 18°–22°. Today, limit angle of inclination of the conveyor belt transporting bulk loads is not studied well. In this research, the authors tried to determine limit angle of inclination of the conveyor belt transporting bulk loads by considering different types of the idlers: with rigid line, damping idlers and suspension idler with rope line. Limit angle of the conveyor belt inclination was determined on the basis of the change in momentum theorem applied to the lump during its moving over the idler and with the assumption that a lump, while passing over the idler, began sliding along the conveyor belt. As a result, analytical dependences of limit angle of the conveyor belt inclination on the conveyor parameters (belt tension and speed), parameters of idlers (distance between them), length of the bulk load and coefficient of friction of the lump against the conveyor belt were obtained. The studies of the obtained dependences showed that belt conveyors with damping idlers featured the widest limit angle of inclination, and inclination angel of the belt conveyors with suspension idlers had the least value. In addition, it was found that with increase of the conveyor belt speed and weight of the transported lumps limit angle of the conveyor inclination decreased and increased with increase of the belt tension. Further, critical speed of the conveyor belt was determined at which piece of load began sliding along the conveyor belt at any angle of the conveyor inclination.

$L_0$ Sparse Regularization-Based Image Blind Deblurring Approach for Solid Waste Image Restoration

The new vision-based object sorting system is a fundamental module in the construction and demolition waste recycling industry, where image deblurring is vital as the system often fails due to the heavily blurred images caused by the vibration of the conveyor belt that carries solid wastes. This paper proposes a novel blind deblurring approach in which a novel penalty function is formulated as the regularization term in the total energy function. This regularization term is based on sparse prior and solved as part of a mathematical optimization problem, which is operated on the dark channel of the input image. The method not only reserves the structure information of the image but also avoids over-smoothing in the final restoration. On synthetic and natural blurred images, the method outperforms other popular methods. Even with less iterations, the convergence rate and quality of the results are superior. We apply this approach for solid waste image restoration and achieve remarkable results with high validity and reliability.

An approach of FEM analysis of the influence of pretension on the transverse vibration of belt drive

Belt drive has been widely used in various types of mechanical transmission. Because the belt is sensitive to the pretension, the tension force directly affects the vibration characteristics of the belt, in order to reduce the impact of the pretension on the belt drive, the finite element software is used to simulate the belt, the effect of the change in pretension on the frequency and amplitude of the transverse vibration in the belt drive is obtained. Reasonable selection of the pretension can reduce the vibration amplitude of the belt, reduce the transmission noise and improve the service life of the belt. This method can provide reference for vibration characteristics analysis and system design optimization of the belt drive structure.

WaistonBelt X: A Belt-Type Wearable Device with Sensing and Intervention Toward Health Behavior Change.

Changing behavior related to improper lifestyle habits has attracted attention as a solution to prevent lifestyle diseases, such as diabetes, heart disease, arteriosclerosis, and stroke. To drive health behavior changes, wearable devices are needed, and they must not only provide accurate sensing and visualization functions but also effective intervention functions. In this paper, we propose a health support system, WaistonBelt X, that consists of a belt-type wearable device with sensing and intervention functions and a smartphone application. WaistonBelt X can automatically measure a waistline with a magnetometer that detects the movements of a blade installed in the buckle, and monitor the basic activities of daily living with inertial sensors. Furthermore, WaistonBelt X intervenes with the user to correct lifestyle habits by using a built-in vibrator. Through evaluation experiments, we confirmed that our proposed device achieves measurement of the circumference on the belt position (mean absolute error of 0.93 cm) and basic activity recognition (F1 score of 0.95) with high accuracy. In addition, we confirmed that the intervention via belt vibration effectively improves the sitting posture of the user.

Design and analysis of five-link-rod rigid constraint support scheme for engine–accessory system vibration control

Vibration generated by engine and its accessories deteriorates product performance. At present, lacking global model, mounting design of engine and accessories are separate, not conductive to solving the vibration of engine, belt, and accessories as a whole. In this article, three problems of the typical structure are analyzed, that is, the belt tension is unstable, static preloading makes engine mount design deviate, and the belt is prone to lateral vibration. Then, a rigid constraint rod is proposed to fix the center distance. The vibrational motion equation is established. By matrix analysis, the accessory mount along the rod is canceled. Then, engine and accessories can be analyzed as independent systems. Among them, the vibration isolation of the engine tends to be good, and for accessories and belts, the influences of the accessory mount stiffness on the force and torque transmission rate and belt vibration response were comprehensively evaluated, and that the infinite stiffness is presented. The innovative design of five-rod structure mainly composed of two connecting rods is obtained which does not transfer vibration perpendicular to rod and the vibration of engine, belt, and accessories are all well controlled. This experiment proves the five-link structure as a useful solution.

Understanding Tire Dynamic Characteristics for Vehicle Dynamics Ride Using Simulation Methods

ABSTRACT The dynamic characteristics of a tire are studied by simulating its rolling over a cleat and observing the effect on in-plane rigid belt vibration modes. Three modeling approaches are used to understand various tire design parameters affecting the tire dynamics relevant for vehicle ride performance. First, a simplified three-degree-of-freedom rigid ring model is used for fundamental understanding of these modes. Next, a detailed finite element model accounting for component compliances is used for studying the sensitivity of the modes to most common design parameter variations employed in tire development. Finally, to study these tire design changes in operation, vehicle simulations using CarSim and FTire models are performed. FTire model parameters corresponding to tire design parameters are adjusted accordingly. Observations are reported of the effects of tire design parameters on cleat responses and on correlation of results between finite element and FTire models.

Development of a flexible belt on an elastic multi-stiffness foundation tire model for a heavy load radial tire with a large section ratio

Abstract The study investigates the planar vibration characteristics of a radial tire with a large section ratio for a heavy load vehicle. A proposed tire model with a flexible belt on an elastic multi-stiffness foundation is investigated via theoretical modeling and an experimental modal analysis. Additionally, the parametric identification of the proposed tire model is discussed. When compared with the conventional sidewall stiffness model for general car tires, the analytical multi-stiffness function of a large section ratio sidewall is derived by combining the membrane feature caused by inflation pressure and the structural deformation caused by sidewall curvature. The Euler beam model specifically assesses the circumferential vibration of the flexible belt. Additionally, we combine the sidewall multi-stiffness function of the membrane pre-tension stiffness, and the structural deformation stiffness is integrated into the flexible belt model. The effect of inflation pressure on the circumferential vibration of the flexible belt is investigated via the experimental modal method and theoretical Euler beam model. The stretching, bending, shearing deformations, and stiffness characteristics of the curved sidewall arc are derived via the virtual work principle. The nonlinear stiffness characteristic of the tire sidewall is calculated relative to the radial deformation of the sidewall segment. The effect of the inhomogeneous section area on the multi-stiffness function is discussed. The experimental and theoretical results indicate the following: (1) The multi-stiffness function of the curved sidewall assesses the pre-tension membrane feature and structural deformation, which is related to the inflation pressure, structural curvature, and material properties; (2) the multi-stiffness function of the curved sidewall is nonlinear relative to the radial deformation of the sidewall arc, and the nonlinear characteristic is highlighted with high inflation pressure; (3) the inhomogeneous feature of the section area affects the multi-stiffness of the curved sidewall. Given the combined sidewall multi-stiffness function of the membrane feature and structural deformation, the elastic foundation model acts as an independent module to enrich the flexible belt beam model. Additionally, a flexible belt on an elastic multi-stiffness foundation tire model is suitable for a radial tire with a large section ratio of a heavy load vehicle or tires under impulsive loads and large deformations.

Study of the Vibration Mechanism and Process Optimization for Abrasive Belt Grinding for a Blisk-Blade

The blisk is a key component of aero engines, and its surface processing quality directly affects the service performance of the aero engine. In using the new open belt grinding process, different degrees of vibration will occur, and they seriously affect the dimensional accuracy and surface quality of the blisk-blade profile. In view of the above-mentioned problems, this paper first built the physical model for the blisk-blade abrasive belt grinding and analyzed the weak stiffness characteristics of the blisk-blade abrasive belt grinding system. Then, based on the kinetic analysis method, the grinding mechanism of the abrasive belt of the blisk-blade was studied, and the process parameters and stability grinding conditions affecting the grinding stability of the blisk-blade belt were analyzed. In addition, the grinding process of the blisk-blade profile belt was simulated by a numerical method. The influence of different process parameters on the grinding vibration of the blisk-blade was quantified, and the optimal combination of process parameters was obtained. Finally, the feasibility of process parameter optimization was verified experimentally. Studies have shown that the weak stiffness of the blisk-blade grinding system always runs through the entire grinding process, but the impact size has a primary and secondary order. The grinding vibration of the blisk-blade belt is related to the process parameters, such as the grinding positive pressure, the belt speed, the feed rate, and the contact wheel hardness. The primary and secondary orders of each influencing factor are grinding positive pressure, belt speed, feed rate, and contact wheel hardness. The optimal combination of various factors was obtained: belt speed $v_{b} = 3$ m/s, grinding positive pressure $F_{n}=4$ N, feed rate $v_{g}=0.6$ m/s, and contact wheel hardness Hs/A55. Through the sand belt grinding verification experiment on the blisk-blade, the grinding belt grinding quality of the blisk-blade surface roughness and blade profile precision is improved after the process optimization.