•Introduce an analytical model for lathe spindle-housing-belt system with rubbing.•Proposed model with rubbing can predict the abnormal noise of experimental lathe.•Belt parameters affect the ...vibration shape and amplitude insignificantly.•Nonlinear behavior is prone to be triggered by the larger unbalanced excitation.
Vibration response analysis for lathe spindle-housing-belt system with rubbing is performed by finite element method. The emergence of free-running abnormal noise of economical commercial lathes inspires the fusion of the annular rubbing model and spindle-housing-belt system since there is a small clearance between the front bearing cover and shaft to realize good sealing. The longitudinal and transverse dynamic equations for tight and loose sides of the V-belts are established when geometric and material parameters and initial tension of belt are integrated into the belt’s stiffness coefficient. The Lankarani-Nikravesh contact model depending upon intrusion and rotation speeds is used to describe the shaft-housing interaction. The calculated value of the proposed model agrees well with the modal and harmonic excitation test results, measured free-running rotor orbit signal and housing acceleration data with rubbing. It indicates that the model is promising to predict the abnormal noise of the laboratory lathe. Numerical simulations suggest that the belt’s dynamic parameters have a negligible influence on the vibration shape and amplitude of system. When the rubbing force is applied, nonlinear behavior is prone to be triggered by the larger unbalanced excitation. As the higher rotation speed is used, the interaction load is strengthened due to the speed-dependent of the Lankarani-Nikravesh model.
•Disregarding viscoelastic effects, overestimates the maximal transferrable torque.•The presented model estimates belt tension, speed and strain of any belt drive.•For strain tensioned belt drive, ...the relaxation of the belt shows high sensitivity.•Tension pulley can compensate for negative viscoelastic effects of the belt.•Tension pulley tensioning introduces a way to monitor the belt health in operation.
In this work an analytical model of a steady-state flat belt drive with multiple driving and driven pulleys is presented. The belt is characterised by a novel bilinear elastic constitutive description with a superposition of residual strain due to viscoelastic effects, such as relaxation, and considering inertia effects. Both prevalent tensioning methods for the drive are examined: the pretensioning of the belt to a target pre-strain, and the utilization of a tension pulley to ensure adequate tension in the drive.
The model is discussed based on a case study. The enhanced accuracy in modelling the mechanical response of the belt results in more accurate estimation of the maximal transmissible power as well as the state of tensile strain of the belt. Traditionally, the maximal transmissible power and tensile strain of the belt are overestimated. Consequently, the potential for failures arising from drives operating proximate to their operational thresholds can be effectively mitigated. The more accurate description of the belt state can lead to better utilization of the belt capabilities and a larger design space when dimensioning the belt drive.
Furthermore, the advantages of employing a tension pulley for belt drive tensioning are demonstrated under the assumed conditions.
Predictive maintenance to avoid fatigue and failure enhances the reliability of mechanics, herewith, this paper explores vibrational time-domain data in advancing fault diagnosis of predictive ...maintenance. This study leveraged a belt-drive system with the properties: operating rotational speeds of 500–2000 RPM, belt pretensions at 70 and 150 N, and three operational cases of healthy, faulty and unbalanced, which leads to 12 studied cases. In this analysis, two one-axis piezoelectric accelerometers were utilized to capture vibration signals near the driver and pulley. Five advanced statistics were calculated during signal processing, namely Variance, Mean Absolute Deviation (MAD), Zero Crossing Rate (ZCR), Autocorrelation Coefficient, and the signal's Energy. The Taguchi method was used to test the five selected features on the basis of Signal-to-Noise (S/N) ratio. For classifications, an expert system was used based on artificial intelligence where a Random Forest (RF) model was trained on untraditional parameters for optimizing the accuracy. The resulted 0.990 and 0.999, accuracy and AUC, demonstrate the RF model's high dependability. Evidently, the methodology highlights the features potential when progressed into expert systems, which advances predictive maintenance strategies for belt-drive systems.
•Geomertically nonlinear contact problem of rod mechanics is solved semi-analytically.•Concentrated contact interactions are intrinsic for Kirchhoff rods.•Non-material finite elements allow for ...spatial refinement for moving structures.•Problem-specific compound coordinate system allows separating variables.•Nonlinear finite element approximation is required for compensating jumping metric.
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We propose a non-material finite element scheme for modelling large deformations of a closed flexible rod supported by two rigid pulleys in the field of gravity. The mixed Eulerian–Lagrangian kinematic description of circumferential and transverse displacements is beneficial for simulations of moving belt drives. The necessary C1 inter-element continuity in a compound coordinate system with Cartesian and polar domains requires a nonlinear finite element approximation. The theoretically predicted singular reaction force distribution prevents us from using the technique of Lagrange multipliers for normal contact. A novel semi-analytical solution of the static problem based on the integration of the equations of the nonlinear theory of rods in the free spans as well as in the segments of contact with pulleys is presented for the sake of validation. We demonstrate the mutual convergence of simulation results for a benchmark problem and additionally justify them by comparison against conventional Lagrangian finite element solutions.
•Thermal-integrated ANCF solid-beam element is developed.•The heat generation caused by frictional creep is included in the model.•The transmission ratio loss caused by the temperature rising is ...captured.
Due to the apparent heat generation and the observed multiple thermal effects in the long-term operation of belt drive system, the thermo-mechanical coupled analysis for the flexible multi-body system is necessitated. A previously proposed absolute nodal coordinate formulation solid-beam element is adopted to create its thermal integrated counterpart since its deformation modes are appropriate for capturing the deformation of V-belt geometry. By means of the unified description of the temperature field and displacement field, the analysis for heat transfer and the continuum mechanics could be integrated in the V-belt drive system. The heat generation caused by frictional creep and the hysteresis loss due to the material viscosity, as well as the thermal deformation, are all included in the model. By describing the flange of pulley groove using a parameterized revolving segment centered by the pulley axis, the contact between V-belt and the flange of pulley groove could be implemented efficiently without complex 3D geometric description of the pulley. The contact force is calculated using penalty method, and the frictional force is determined by the Coulomb friction law in integral form. Numerical results demonstrate the feasibility of the proposed analysis method.
•New analytical and numerical techniques for predicting the lateral run-off in steel belt drives.•Novel non-material kinematic description in the 3D contact problem for an elastic shell.•Transient ...FE-simulation of a slack, geometrically imperfect steel belt in operation.•Justified convergence with respect to mesh size and time step size.•Successful validation of simulation results against physical experiments.
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A non-material shell finite element model is developed and applied to the example problem of a slack steel belt moving on two rotating drums. For the first time in the open literature we demonstrate an approach for predicting the time evolution of the lateral run-off velocity of the belt in response to its geometric imperfection and angular drum misalignment. We adopt a novel Eulerian–Lagrangian kinematic description featuring a mixed parametrisation of the configurational space with a Eulerian circumferential coordinate and two Lagrangian coordinates for the transverse and lateral deflections. A nonlinear finite element approximation provides the necessary C1 inter-element continuity in this compound coordinate system. Using the model of elastic tangential contact, we account for the convective term in the local increments of the relative displacement between the contacting surfaces during the time integration. A thorough convergence study with respect to the mesh and time step sizes justifies the approach. Together with the successful validation against the results of a series of physical experiments, this makes the present contribution an important step towards a model-based controller design.
Almost all the problems of a serpentine belt drive system such as maximum tension, belt slip on the pulley, squeal noise and self-exciting string vibration of the belt are caused by a resonant ...phenomenon of the belt drive system. In this report, the following items are described on the resonant phenomenon. (1) Eigenvalue analysis that is the method to get the natural frequency, resonant speed and vibration mode of the belt system. (2) Tension mode that can estimate the span of self-exciting belt vibration occurrence, and slip mode that can estimate the pulley of squeal noise occurrence. (3) Some application examples of eigenvalue analysis and methods to avoid or reduce the resonant phenomena.
•The model of a real multiple pulley serpentine belt drive system is established.•Results show the vibration modes of the system can be divided into different types.•The vibration coupling between ...different mode types is investigated.•Different mode types show different variations when system key parameters change.•The applicability of a simplified model is discussed.
Serpentine belt drive system is widely used as engine front end accessory drive system in automotive industry. It is a complex hybrid discrete-continuous system whose vibrations are mainly composed of rotational vibrations of pulleys and the tensioner arm, and transverse vibrations of continuum belt spans. In this paper, an efficient method to evaluate the natural vibration characteristics of serpentine belt drives is proposed and investigated. The equations of motion of an actual multiple pulley serpentine belt drive are established and reformulated into an extended operator form, in which belt spans are modeled as axial moving beams with bending stiffness so that the belt–pulley coupling is comprehensively quantified. The natural frequencies and modes of the system are comprehensively calculated. The model is verified by a real example. Furthermore, the influences of some parameters such as belt bending stiffness and belt axial speed on natural vibration characteristics and degree of coupling are investigated, and the applicability of the traditional single beam model is discussed. The proposed method can also be used to efficiently solve eigenvalue problems of other hybrid systems composed of continuums and discrete bodies.
Parameter identification used to obtain the analytical mathematical model of the mechanical system is requisite to allow high-performance control. The typical online indirect parameter identification ...method, which simultaneously estimates six parameters using the least square method with an adaptive filter, has achieved a good effect. Nevertheless, the drawbacks, such as the heavy computational burden and the adaptive filter invalidation, restrict its use for real-time identification. To address these issues, the simplified discrete-time output error model is proposed, which can be used to estimate four key parameters online instead of six. Furthermore, this article presents an adaptive filter parameter correction algorithm via the pole assignment to guarantee its stability and effectiveness. Finally, the proposed method can significantly reduce the calculation burden of typical identification method. The experimental results indicate that the proposed identification method maintains a high precision.
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