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A prototypical three-pulley serpentine belt system. The tildes on the physical quantities have been dropped for simplicity.
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A model of dry friction tensioner in a belt-pulley system considering transverse belt vibration is developed, and the influence of the dry friction on the system dynamics is examined. The discretized formulation is divided into a linear subsystem including linear coordinates and a nonlinear subsystem addressing tensioner arm vibration, which re-duc...
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... 1970s, serpentine belts have been widely used in the automotive industry to drive vehicle accessories. A tensioning system, known as a tensioner, plays an important role in serpen- tine drives by automatically adjusting the belt tension during op- eration. It consists of an idler pulley tensioner pulley at the end of a rigid arm tensioner arm Fig. 1. The arm pivots around a fixed point and the pulley is pinned at the free end of the arm 1-6. This assembly leads to geometric nonlinearity in the system model 1-5, and the arm motion causes belt-pulley coupling 3,7,8 by moving the end points of the two adjacent ...
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... and Parker 8,12 establish a hybrid continuum-discrete model incorporating belt bending stiffness. Figure 1 depicts this prototypical serpentine belt drive, consisting of a driving pulley, a driven pulley, a tensioner, and a serpentine belt. The driving pul- ley 1 and the driven pulley 3 are subject to accessory moments M ˜ 1 and M ˜ 3 . ...
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... the sinusoidally driven locked arm linear system, Q m varies sinusoidally, i.e., Q m = Q m cr sint + where Q m cr 0 is the critical torque. Figure 10 shows how the critical Coulomb torque Q m cr varies with frequency for various belt bending stiffness. These are upper bounds that enforce t t = 0. ...
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... than the resonant regions, the curves in Fig. 10 show that the critical Coulomb torque tends to decrease with increasing bending stiffness. Away from resonance, the torque generated by the summation term of the right-hand side of 26 is small com- pared to that from the first term, i.e., the torque f p+3 derived from the driving pulley rotation dominates the pivot torque. With this ...
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... maximum dynamic tension in each span is shown in Fig. 11. On one hand, increasing dry friction torque monotonically diminishes the tensioner arm rotation until the tensioner is effec- tively locked. On the other hand, pulleys 2 and 3 vibrate more near the resonances of the natural modes of the locked arm system that involve large pulley amplitudes, such as the modes at = 5.5, 5.7, 6.3 ...
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... The lubrication condition of these mating surfaces is crucial to the overall performance of the device [1][2][3][4][5]. Research findings indicate that the contact stiffness of machine tool mating surfaces accounts for over 60% of the overall device stiffness [6,7], making them the "weak link" in mechanical equipment systems. It is evident that precise adjustment and optimization of the contact characteristics of rough surfaces can improve the performance of machine tools and enhance their machining accuracy and service life significantly [8]. ...
This study aims to investigate the mechanical characteristics of contact between mating surfaces in the state of mixed lubrication, with a specific focus on the distribution of surface asperity heights in mechanical precision machining parts, which deviates from a Gaussian distribution. To achieve this, a normal contact model is developed for mating surfaces experiencing mixed lubrication, incorporating the non-Gaussian contribution nature of surface asperities and accounting for relative motion between mating surfaces. This model allows us to derivate the stiffness information in both solid and liquid domains to comprehend the contact behavior of mating surfaces under mixed lubrication conditions. The investigation results reveal that several key factors including normal load, viscosity, relative motion velocity, and non-Gaussian roughness parameters influence the normal contact stiffness of non-Gaussian rough surfaces in mixed lubrication mating surfaces significantly. These findings provide valuable insights that enhance our understanding of the performance of mating surfaces under mixed lubrication, and serve as a reference for the optimization design of mechanical equipment.
... The main disadvantage of string models is that they neglect the bending stiffness of the cross-section and the bending moments that occur www.nature.com/scientificreports/ in a loaded conveyor belt. Prior research 41,42 indicates that this parameter exerts a substantial influence on the transverse vibrations of the belts. Hence, these models do not always allow for a correct prediction. ...
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.
... The stick-slip motion of tensioner arm was studied. Farong and Parker [18] studied the influence of coulomb damping of tensioner on dynamic performance of a belt-pulley system and discussed the energy dissipation caused by dry friction of tensioner. Kwon and Ih [19] investigated the transverse vibrational power that flowed in the moving belt passing through a tensioner, and found that the vibration of the belt spans flows into the tensioner. ...
... In the previous studies [4][5][6][7][8][9][10][11][12], the modeling methods for obtaining the hysteretic behavior of tensioner are mature. However, the tensioner is simplified as a linear stiffness and a viscous damping in analyzing a belt drive system [13][14][15][16][17][18][19]. The hysteretic model for describing a tensioner is not added into the dynamic analysis, and the equivalent viscous damping of tensioner is regarded as a linear and constant value [20]. ...
... The x c is determined by the known excitation of crankshaft; however, the amplitude of oscillation angle (h m ) is unknown. In the existing methods, an approximation value of equivalent viscous damping is used for calculating the vibration responses of a belt drive system, which may cause some computational errors [13][14][15][16][17][18][19]. Besides, the oscillation angle of tensioner arm is measured from the real belt system firstly, and the results are added into the input data for obtaining the real viscous damping of tensioner [20]. ...
A friction-type tensioner is widely used in a belt drive system for maintaining belt tension constantly and reducing vibration. Owing to friction dampings, the curve of the reaction torque and the imposed angle of tensioner arm is a hysteretic loop. Here, the hysteretic behavior of tensioner is considered in dynamic analysis of a belt drive system. A hysteretic model for describing the applied torque versus the imposed angle of tensioner arm is established. And an iterative algorithm is proposed for estimating the nonlinear equivalent viscous damping of tensioner under a varying excitation frequency. A timing belt drive system is taken as an example. Based on the existing research, the dynamic models for a belt, an automatic tensioner and rotational pulleys of system are also given. The vibration responses of a belt system, such as the oscillation angle of tensioner arm, the transmission error between pulleys and the hub load applied on pulley, are calculated and compared with the measurements, which are validated the presented method. The influence of damping ratio of tensioner on dynamic responses of system is investigated, and the influence of iteration parameters on the iterative efficiency is discussed. The presented method is beneficial to modifying the existing method for calculating the vibration responses of a belt drive system.
... Shangguan and Zeng 16 and Feng et al. 17 investigated the stick-slip motion of tensioner arm in a belt drive system, and analyzed the influence of tensioner parameters on dynamic performance of system. Farong and Parker 18 investigated the influence of dry friction of tensioner on dynamic performance in a belt-pulley system, and discussed the energy dissipation caused by the hysteretic behavior of tensioner and the stick-slip phenomena of tensioner arm. ...
... In the previous studies, [5][6][7][8][9][10][11][12][13][14][15][16][17][18] the research works are focused on the parameters identification and the physical model of tensioner. The analytical model stated in Zhu et al. 5 is suitable for a specific form, and the method for obtaining the hysteretic behavior of tensioner in a dynamic manner is not given. ...
... On the other side, the tensioner is simplified as a linear torsional spring and an equivalent viscous damping in the dynamic analysis of a belt drive system. [13][14][15][16][17][18] The equivalent viscous damping of tensioner is an approximation value in analysis, which can only be obtained by a known vibration amplitude and frequency of tensioner arm. 15,16 Thus, the contributions of this article are: ...
An automatic tensioner that consists of a torsional spring and friction damping elements is widely used in belt drive system. The relation of the applied torque versus the imposed angle of tensioner during loading and unloading processes is described as a hysteretic loop. An analytical model is established for estimating the hysteretic behavior of a tensioner, and measurements for hysteretic loop in quasi-static and dynamic excitation are carried out to validate the analytical model. Taking one engine timing belt drive system as a studying example, the method and the procedure for estimating vibration responses of the nonlinear tensioner are given. An iterative algorithm for predicting the accurate equivalent viscous damping of tensioner is carried out in analyzing a belt drive system. The vibration responses of tensioner are validated by the measurement of timing belt drive system. The developed method presented in this article is useful for predicting the hysteretic behavior of tensioner, vibration responses, and the parameters optimization of a belt drive system.
... Scurtu et al. found the periodic energy transfer between the longitudinal excitation and the transversal vibration [6]. Zhu and Parker studied the periodic solutions for a belt Àpulley system under the periodic driving pulley excitation [22]. Furthermore, Ding and Li studied the nonlinear response of the pulley Àbelt system excited by the periodic motion of the crankshaft [23]. ...
The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete–continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the firing pulsations and the frequency of the foundation motion. Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differential equations is achieved by using the Galerkin truncation. Under various relations between the excitation frequencies, the time histories of the dynamical system are numerically simulated based on the time discretization method. Furthermore, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numerical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pulley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foundation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firing pulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur. © 2015 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
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.
The friction type tensioner is an energy absorbing component in belt drive system which has hysteretic torque and nonlinear damping. In this paper, a hysteretic model is used for describing the tensioner’s operating torque versus the imposed angle, and considered into the dynamic analysis of a belt drive system. The modeling process for calculating the vibration responses of a belt drive system is presented, and two iterative methods are proposed for estimating the tensioner’s nonlinear damping in a varying excitation frequency. One timing belt drive system is taken as a case study. The system’s vibration responses, such as the oscillation angle of tensioner arm, the transmission error between pulleys and the hub load on pulley are calculated and compared with the measured values, which validate the presented methods. The influence of iterative method on the computational efficiency and iterative accuracy are both discussed. At last a modified method is presented to improve iterative efficiency. The presented technique can improve the computational efficiency with a good computational accuracy.
This paper aims to show through a factorial experimental design significant factors on the polymeric bushing wear PA66, including their amplitude, frequency and spring height, when interacting with a steel axle SAE1018 (from Society of Automotive Engineers - SAE) in a tension belt applied. It was verified that factors as amplitude and frequency are significant and it was possible to propose a mathematical model to predict this wear behaviour for the proposed test. Moreover, an adhesion wear behaviour was verified, whereof a polyamide film was observed on the axle transferred by the bushing. Through the microscopy report analysis, it was possible to see the transfer film topology characterisation for a better comprehension of the adhered polyamide film from the bushing to the axle surface.
This chapter provides thorough analyses of the dynamics of axially moving beams. The equations of motion are derived using diverse beam theories: the Euler–Bernoulli, Rayleigh, and Timoshenko beam theories. Other aspects of axially moving beams such as the cantilever beam, viscoelastic beam, fluid-conveying pipe, nanoscale beam, and composite beam are also discussed. One approximate model based on the Galerkin method is presented.
