Belt-pulley System Research Articles

Finite Element Analysis of SMC Core Magnetic Gear for Vehicle Powertrain Systems

The utilization of gears as intermediary components for power transmission in electric drive systems addresses the insufficiency of electric machines in handling torque loads effectively. Gears, commonly employed in the industry, can be either mechanical or magnetic, allowing for the balanced transfer of torque and speed at specified ratios. The mechanical and electrical actuation of in-vehicle accessories persists both in traditional and next-generation vehicles. Particularly concerning safety and the sustainability of spare part production and supply, various electrical accessories continue to operate at the 12 V level in modern vehicles. In this context, the use of the Lundell alternator (claw pole) also continues in next-generation vehicles. While the mechanical accessories are driven by a belt-pulley system connected to an internal combustion engine in conventional vehicles, in next-generation vehicles, both belt-pulley systems and x-drive by wire are present. The low efficiency and operational costs of belt-pulley power transmission systems necessitate the adoption of more efficient transmission systems. This study focuses on the development of a soft magnetic composite (SMC) core magnetic gear power transmission system that can serve as an alternative to belt-pulley systems in both traditional and next-generation vehicles. In the proposed system, mechanical power transfer to the Lundell alternator is realized through the intended magnetic gear. The gear ratio is determined to ensure a speed of 1800 rpm at the input of the Lundell alternator while the drive system operates at 6000 rpm. To achieve low volume and high efficiency for the proposed magnetic gear, the SMC material is considered, and a comprehensive analysis using the Ansys Maxwell finite element software is conducted. As a result of the analyses, in the magnetic gear designed with a transmission ratio of 3:1, when a torque of 11.7547 Nm is applied to the input shaft, a torque transmission of 35.9806 Nm has been achieved with an efficiency of 84.73% through the output shaft.

Digital Twin for Diagnosis of Belt Looseness in HVAC Systems using multi-body dynamics simulation

Most heating, ventilation, and air conditioning (HVAC) systems operate using a belt pulley system that provides high efficiency at a low cost. To monitor the health of the HVAC system, it is essential to detect looseness, which is one of the primary failure modes of belt-pulley systems. The main feature used to identify looseness is belt slip, which can be computed using the ratio of angular velocity and diameter between the drive pulley and driven pulley. However, accurately diagnosing the condition of the HVAC system based on the slip distribution calculated by measuring the rotational speed can be based on empirical criteria. To overcome this problem, this paper proposes constructing a digital twin model for accurate diagnosis of belt loosening in HVAC systems. The proposed approach involves performing multi-body dynamics (MBD) based time-domain analysis considering uncertainty. To validate the proposed model, belt looseness is applied to the HVAC system, and the slip distribution is calculated and compared with the results computed by the digital twin model. Through this comparison, it was demonstrated that the proposed model can be utilized to diagnose belt looseness in the HVAC system.

Design, Fabrication and Testing of Human Powered Water Purifier

Abstract: Human Powered Water Purifier is the system which provides safe drinking water by running a RO systemwith the help of only human power and minimal setup.This can prove to be a major cost effective solution tothe problem of unsafe drinking water in areas where there is no or little access to modern purifiers or they do not have the power source to run them ( either irregular electricity supply or in emergency situations). This paper explains in detail about the design of an indigenous mechanism which makes useof human pedalling on a bicycle & power istransmitted by sprocket and belt pulley system toobtain required RPM for pump to run a water purification system. It includes a brief picture of the need of this type of system, design of various components and the summary of results obtained during the testing of the system. This mechanism has shown positive results in maintaining the pressure andflow Rate from pump by providing about 1200 RPM with mechanism, required by RO Purifier and TDS (Total Dissolved Solids) in water was considerably reduced from 650 ppm to 150 ppm.

Caster Walker GAIT Trainer (CGT): A robotic assistive device

Stroke has become one of the leading causes of lower limb paresis. Costing the patients, a fortune for its diagnosis and prognosis. Clinical experimentations have proven that one can regain ambulation if the rehabilitation is started in the acute or sub-acute stage. Traditional mode of rehabilitation include manual therapies which are labor-intensive and time consuming. Therefore, robotic training are preferred over manual therapies. Nevertheless, there are some limitations such as devices are bulky and complex, some are not portable, others need body weight support system, and costly. To address such issues, this paper proposes development of a new Caster Walker Gait Trainer (CGT) for gait rehabilitation. CGT is an end-effector based passive device in which Stephenson III six-bar linkage has been implemented to mimic the kinematics of a healthy gait. The trainer device uses a belt-pulley system for providing motion to the linkage. The lower limb of the patient gets the drive as he/she pushes the cater walker forward or backward. The paper also proposed the optimal design of defect-free Stephenson III six-bar linkage using loop-by-loop approach. To design the linkage, an optimal problem is formulated, and tear drop ankle trajectory is desired. The optimization problem is solved using a nature-inspired algorithm and it is found that the trajectory generated by the synthesized mechanism is able to mimic the desired trajectory. Then using the notion of inverse kinematics, hip and knee trajectories are obtained from the generated ankle trajectory for validation.

Performance based systematic design methodology for development and flight testing of fuel engine powered quadrotor Unmanned Aerial System for industrial applications

This paper presents a systematic study of the design optimization, development, vibration analysis and flight testing of a single power plant variable pitch quadrotor Unmanned Aerial System (UAS) for industrial applications. The use of variable pitch rotors enables the use of a two-stroke internal combustion engine for powering the four rotors through a mechanical transmission. The proposed methodology is described by carrying out the design of a quadrotor UAS with 2–3 kg payload capacity and have endurance in excess of one hour. The study is conducted in a systematic manner. First, the design of rotors is optimized for minimum power consumption during hover as well as forward flight condition using physics based simulation developed and validated for this purpose. From the rotor optimization, an untwisted rotor blade with taper ratio of 0.6 and aspect ratio of 10 appeared to be an optimal choice for the current design. Next, the powerplant selection is carried out based on the optimized rotor designed earlier. Next, two different approaches for mechanical power transmission design is considered: torque tube-bevel gear and belt–pulley system based designs. The transmission system designed using belt and pulley was nearly 14% lighter and showed greater tolerance to manufacturing imperfections. Next, two prototypes are designed and its static and dynamic analysis is carried out to ensure its airworthiness. A Proportional Integral Derivative (PID) based attitude controller is developed using quarternions for attitude stabilization and trajectory tracking to test the flight in simulation and then subsequently on the actual vehicle by implementing it on PixHawk autopilot board. Finally, system integration is carried out to build two prototypes of engine powered quadrotor UAS. Then, vibration data is recorded using the sensors onboard to conduct the vibration analysis and design an efficient vibration isolator. Performance analysis is also, carried out to estimate the speed for best endurance (11 m/s) and best range (27 m/s) for the variable pitch quadrotor designed. The estimated best endurance achieved is 2.2 h and estimated best range is more than 150 km. This design revisits and solves the challenge of developing an agile helicopter without cyclic pitch control which was first explored nearly a century ago.

Conveyor Belt Drive Physics

We study a simple model of a conveyor belt. We calculate the relation between the torque M and the belt–pulley slip s. We present numerical results for the M(s) relation, and for the frictional energy dissipation as a function of the slip, which is important for the rubber wear. The theory includes both the belt compliance and the pulley tread block stiffness. The theory shows that to minimize the friction and the related rubber wear, the pulley–belt system should be operated not at the slip where the torque is maximal, but at a lower slip. Thus, the belt–pulley system should be slightly “oversized” for the best performance.

Artificial Neural Network Based Fault Diagnosis of a Pulley-Belt Rotating System

Rotating machines are widely used in various industrial fields. Hence, an unexpected stoppage due to, for example, bad operating conditions or manufacturing error, has safety implications along with economic considerations. In this research, a fault detection system for a pulley-belt rotating system is developed and then different faults simulated in a test rig are investigated. Vibration signal monitoring is utilized since it represents a reliable approach for fault recognition in rotating machinery. Time-domain signal analysis technique is applied to extract some indicative features, such as root mean square, kurtosis and skewness. An artificial neural network (ANN) model is developed to detect the simulated faults. However, in addition to the machine healthy condition five fault types, such as unbalance in the driving pulley, wear in the belt and pulleys misalignment, have been simulated in the test rig. Two MEMS accelerometers (ADXL335), interfaced to Arduino MEGA 2560 as a data acquisition device, are used for vibration amplitude measurement. LabVIEW, which is a graphical programming software, is utilized to develop a signal capturing, analysis and feature extraction system. The result showed the effectiveness of the developed system in detection of different fault types in the pulley-belt system.

Dynamic analysis of a pulley-belt system with different pulley radii and support stiffness

Herein we present a new model to describe a pulley-belt system with various ratios of spring constants supporting the two pulleys and various ratios of pulley radii. The main object of this paper is to analyze the effects of differences between the radii of the two pulleys and the two spring constants on the dynamic characteristics of the pulley-belt system. To this end, five equations of motion and eight boundary conditions are derived using Hamilton's principle, and the governing equations are discretized using Galerkin's method. The natural frequencies and the mode shapes corresponding to the various radius ratios of the two pulleys and ratios of the two spring constants are obtained, and the responses are calculated to verify the dynamic characteristics of the pulley-belt system. This study shows the exact cause of the coupling between the rigid-body motions and belt deflection motions, and the difference between natural frequency veering and crossing phenomena is analyzed by confirming the mode shapes near each phenomenon. In addition, we confirm the influences of the radius ratio of the two pulleys and the ratio of the two spring constants on the changes of the natural frequencies according to the moving velocity of the belt.

Stationary and transient analyses of a pulley-belt system based on an Eulerian approach

In some engineering industries such as the transportation domain, the belt drives are widely used to transmit the power and the motion. They have a complex dynamic behavior because of the tension forces, the dimensions and the utilization purposes. In this paper, extant models are summarized to present a better understanding of the belt mechanics and the dynamic behavior of pulley-belt systems. Then, a new approach based on the Eulerian description as well as on the normal and shear stresses is introduced in order to discuss the belt mechanics, to build an analytical model of a pulley-belt system and to investigate its dynamic behavior. It can describe the zones of contact between the belt and the pulleys in the stationary and transient regimes. Analytical solutions and formulations for the tensions and the relative displacements of the belt over the pulleys in the stationary regime are established, while differential equations for the belt tensions and the driven pulley velocity in the transient regime are derived. These differential equations are solved using the explicit Runge–Kutta time-step integration scheme. The study is also conducted to observe slip phenomena due to the contact between elastic and rigid surfaces and multiple zones of slip can be found by means of an iterative Newton–Raphson method.

Electrical Monitoring of Mechanical Defects in Induction Motor-Driven V-Belt–Pulley Speed Reduction Couplings

V-belt–pulley couplings are commonly used for speed reduction in induction-motor-driven industrial applications since they provide flexible transmission of power at low cost. However, they are susceptible to mechanical defects such as belt wear or crack that can cause slippage or damage of the belt and lead to decrease in efficiency and lifetime of the system. There are many limitations to applying existing tests such as visual inspection, thermal or mechanical monitoring as they require visual, or physical access to the system and/or costly sensors. Considering the large quantity of belt–pulley systems employed in industry, the impact of the economic loss incurred by low-efficiency operation, and unplanned process outages is significant. In this paper, electrical monitoring of belt–pulley coupling defects based on the analysis and trending of the stator current frequency spectrum under steady-state and starting conditions is presented. The proposed method is verified on the following: 1) 6.6-kV motor-driven pulpers; and 2) a custom-built motor-driven air compressor with speed reduction belt–pulleys under controlled fault conditions. It is shown that the proposed method can provide automated, remote, and safe detection of belt–pulley defects based on existing current measurements for improving system reliability and efficiency. It is also shown that the proposed method can be applied to vibration measurements for motors where vibration sensors are installed.

Eulerian description of non-stationary motion of an idealized belt-pulley system with dry friction

We develop and validate a mathematical model of a belt drive with dry friction between the belt and the pulleys. Considering an idealized setting, we make use of the Eulerian (spatial) kinematic description for the belt, which moves quasistatically along a given contour. The focus of the paper lies on modelling the friction law in a non-material finite element framework. We also obtained a novel analytical result for the time evolution of the zones of sliding friction and stick. The correspondence of the analytical solution to both the non-material and conventional material finite element simulations has been demonstrated.

EFFECTS OF ROTATIONAL SPEED, CENTER DISTANCE AND DIAMETER RATIOS ON THE DYNAMIC RESPONSE OF PULLEY-BELT SYSTEM DEPENDS ON VIBRATION ANALYSIS

This paper presents the dynamic response related to varying in indispensable parameters of pulley-belt system, a manufactured pulley- belt system has been built and experimental results have been obtained and analyzed accurately which reveal the effects of these parameters on indicated system. Manufactured system assembled from heavy steel structure, variable speed DC motor, speed measurement tool (tachometer), two shafts of 25 mm diameter, four pillow block ball bearings, V-belts and pulleys with different diameters (10, 15, 20, 25) cm. The fabricated system presents mechanical characteristics likes serial changing in rotational speed (500 to 2000) rpm, diameters ratios (1 to 2.5) and center distance (27 to 120) cm. accelerometer ADXL335 (3-axis) mounted on bearing brackets of drive and driven shafts and connected to Arduino type mega 2560 (microcontroller) which sending the data of vibration to the laptop in order to display it in Sigview software as a time and frequency domain band by FFT (fast fourier transform). Results showed the effects of change the values of rotational speed, center distance, and diameters ratios on vibration response of pulley-belt system

Dynamic analysis of a pulley–belt system with spring supports

In this paper, a new dynamic model for a pulley–belt system is proposed, in which the system considers not only the deflection of a belt but also the rigid-body motion of pulleys. This paper focuses on the effects of the rigid-body motion, which determines the dynamic characteristics of the pulley–belt system with spring supports. To this end, by using Hamilton’s principle, four linear governing equations of motion and eight boundary conditions are derived. The Galerkin method is used to discretize the equations of motion. The eigenvalue problems are solved to analyze the natural frequencies and mode shapes that are affected by the rigid-body motion of the system. The natural frequency loci veering and mode exchange are investigated for different moving velocities of the belt and various values of the spring constant. In addition, the beat phenomena in the upper and lower belts are also analyzed. Based on these analyses, we show that the natural frequency veering and beat phenomena are caused by a coupling effect between the rigid-body motion and belt deflection in the pulley–belt system.

Statistic-Based Method to Monitor Belt Transmission Looseness Through Motor Phase Currents

Belt–pulley systems are widely used in the industry due to their high efficiency and their low cost. However, only few works exist about the monitoring of their degradation. This paper details the impact of belt looseness on electrical measurements under steady and transient state in order to identify spectral signatures. This analysis enlightens the advantage of the transient state to detect belt looseness because it exacerbates belt slip. An innovative methodology is then proposed based on the application of a square-wave speed reference in order to monitor belt looseness. A statistical-based indicator is defined from the phase currents in order to automatically detect drifting of the indicator. A normalization process is also applied to increase the detection robustness. The proposed indicator is evaluated on a 30-kW induction machine and a direct-current machine coupled with two trapezoidal belts for three speed and four load conditions. It reaches very good results with almost 90% correct detections for 1% false alarms. These results are way better than those obtained with a classic spectral analysis during the steady state. Moreover, results demonstrate that higher load conditions are more accurate for the monitoring of belt looseness.

A theoretical and experimental disturbance analysis in a product of inertia measurement system

In this research, disturbances in a product of inertia measurement system (POI-MS) are investigated theoretically and experimentally. These disturbances mainly originate from some various mechanical or electrical sources including fluctuations of transmission system (belt-pulley mechanism oscillation), electro-motor non-continuous power generation (electro-motor speed fluctuation) and also misalignment of the rotor system (unbalancing). Knowing sensitivity of the measurement system performance to the mentioned factors will help the designer to eliminate disturbances and increase accuracy of the system. In this study, at first, disturbances in the measured transmitted force of POI-MS is investigated by performing some experiments. In order to reduce time and cost, more disturbance analyses are performed via simulations. In this regard, a dynamic model of POI-MS is developed in MSc. Adams software. This model includes nonlinear stiffness of the air bearings and flexibilities of the belt-pulley system. Then, effect of possible disturbance sources including belt flexibilities, speed fluctuations of electro-motor and unbalances in rotating parts on the performance of the POI-MS is investigated. Finally, some solutions are presented to eliminate disturbances in POI-MS and improve its accuracy.

Triboelectric smart machine elements and self-powered encoder

A new concept for recovering a part of wasted energy caused by friction in typical mechanical components is introduced. Triboelectric charge generation on movable surfaces is the principle used for conducting electrons through external loads. The concept is evaluated by development and study of three versatile elements, including a bearing, gears and belt–pulley systems. Moreover, the first self-sufficient encoder, which is entirely powered by the energy captured by triboelectricity, is presented. Indeed, the capability of using introduced ad hoc modifications on the structure of machine elements is illustrated for measuring and displaying the rotational speed of a belt–pulley system.

Convergence of the Galerkin Method for Nonlinear Dynamics of the Continuous Structure

The Galerkin truncation method is a powerful method for nonlinear dynamics analysis, and has been widely used to discretize the spatial differential operator. Due to more and more new fields of application, the research interest on the Galerkin method is still high today. In this paper, research on the convergence of Galerkin method for nonlinear dynamics of the continuous structure is thoroughly reviewed. At the beginning, the Galerkin method is briefly introduced. Then, the paper reviews the application of the truncation method. This paper also sums up the comparative study on the Galerkin method with other methods, such as the finite difference method (FDM), the finite element method (FEM), and the multiple time scales method. In the investigations concerning the convergence of the Galerkin method, this paper summarizes recent studies on nonlinear dynamics of the axially moving systems, the continua on the nonlinear foundation, and the belt-pulley systems. Finally, the truncation terms of Galerkin method for the continuous structure's nonlinear dynamics analysis is suggested for the future research applications.

Design and Development of Built-in-Clutch Joint for Single-Drive and Multi-Degrees of Freedom Manipulator

This study presents a joint mechanism that enables a manipulator to possess a multiple degrees of freedom with a single drive actuating unit. The joint called a Built-in-Clutch Joint (BCJ) is composed of an electromagnetic clutch, brake, and a belt pulley system. The joint is driven by a motor via the belt and pulleys when the clutch on the BCJ is engaged and the brake is disengaged. In addition, the joint angular velocity can be arbitrarily controlled by changing pulse width of input signal to the clutch. This study confirms the concept of the BCJ, and experimentally evaluates its mechanical design and performance based on the joint reachability and the transmission efficiency.

Steady-State Responses of Pulley-Belt Systems With a One-Way Clutch and Belt Bending Stiffness

A nonlinear hybrid discrete-continuous dynamic model is established to analyze the steady-state response of a pulley-belt system with a one-way clutch and belt bending stiffness. For the first time, the translating belt spans in pulley-belt systems coupled with one-way clutches are modeled as axially moving viscoelastic beams. Moreover, the model considers the rotations of the driving pulley, the driven pulley, and the accessory. The differential quadrature and integral quadrature methods are developed for space discretization of the nonlinear integropartial-differential equations in the dynamic model. Furthermore, the four-stage Runge–Kutta algorithm is employed for time discretization of the nonlinear piecewise ordinary differential equations. The time series are numerically calculated for the driven pulley, the accessory, and the translating belt spans. Based on the time series, the fast Fourier transform is used for obtaining the natural frequencies of the nonlinear vibration. The torque-transmitting directional behavior of the one-way clutch is revealed by the steady-state of the clutch torque in the primary resonances. The frequency-response curves of the translating belt, the driven pulley, and the accessory show that the one-way clutch reduces the resonance of the pulley-belt system. Furthermore, the belt cross section's aspect ratio significantly affects the dynamic response.

Equilibria and Free Vibration of a Two-Pulley Belt-Driven System with Belt Bending Stiffness

Nonlinear equilibrium curvatures and free vibration characteristics of a two-pulley belt-driven system with belt bending stiffness and a one-way clutch are investigated. With nonlinear dynamical tension, the transverse vibrations of the translating belt spans and the rotation motions of the pulleys and the accessory shaft are coupled. Therefore, nonlinear piecewise discrete-continuous governing equations are established. Considering the bending stiffness of the translating belt spans, the belt spans are modeled as axially moving beams. The pattern of equilibria is a nontrivial solution. Furthermore, the nontrivial equilibriums of the dynamical system are numerically determined by using two different approaches. The governing equations of the vibration near the equilibrium solutions are derived by introducing a coordinate transform. The natural frequencies of the dynamical systems are studied by using the Galerkin method with various truncations and the differential and integral quadrature methods. Moreover, the convergence of the Galerkin truncation is investigated. Numerical results reveal that the study needs 16 terms after truncation in order to determine the free vibration characteristics of the pulley-belt system with the belt bending stiffness. Furthermore, the first five natural frequencies are very sensitive to the bending stiffness of the translating belt.