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Angular speed of the alternator pulley. Crankshaft speed: 750 rpm; alternator load: minimum load. Experimental values (dotted), simulator results (solid)
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Multiribbed serpentine belt drive systems are widely adopted in accessory drive automotive applications due to the better performances relative to the flat or V-belt drives. Nevertheless, they can generate unwanted noise and vibration which may affect the correct functionality and the fatigue life of the belt and of the other components of the tran...
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Citations
... One of the common and useful ways to model mechanical systems is via the bond graph method, where exchanges of energy are modeled to simulate the behavior of the system. The method is discussed in depth in [1][2][3][4]. Bond graphs can also be used to generate algorithms to monitor operations in industries [5]. ...
Energy flow (bond graph) modelling gives important information about the flow of energy to each component of a dynamic system and is especially useful for complex non-linear mechanical systems. This work presents a systematic development of a bond graph model of fused filament fabrication (FFF) 3D printer gantry. The model incorporates structural and belt stiffness, damping and input torque. The model was checked for correctness and causality using the 20-SIM software. The model was further validated using MATLAB-Simulink using parameters obtained for an example printer characterized in a lab environment. The bond graph model gives a unique view into modelling of the extruder carriage dynamics in FFF and can be applied to specific problems. It will also give interesting information on the controllability and system integration of the printer hardware.
... One of the common and useful ways to model mechanical systems is via the bond graph method, where exchanges of energy are modeled to simulate the behavior of the system. The method is discussed in depth in [58][59][60][61]. Bond graphs can also be used to generate algorithms to monitor operations in industries [62]. ...
Fused Filament Fabrication (FFF) 3D printers are widely used for rapid prototyping and industrial applications. This research attempts to construct a dynamic modelling of an FFF 3-D printer gantry (2-D) to reduce manufacturing defects from extruder carriage error. Physical examples of machine-related errors were analyzed, and a major source of the errors observed were due to machine vibration and compliance. A six-dimensional non-linear dynamic model of the printer gantry was developed to explore the system vibrations; this model was derived using Newton-Euler method and considers the effects of damping, belt pre-load, and ramp up from input motor torque. The Lagrangian dynamic model was derived to get additional insight on energy transfer aspects and conservative Newton-Euler model validation. Using these models, a state-space model of the full system was developed for positioning and control. Examples of predictive control systems are demonstrated with their implementation in state-space control model. With appropriate value of design parameters, the passive control co-designs are expected to reduce machine related and vibrational errors in the prints without affecting the print speed. Detailed experimental case-studies of an example printer were performed by varying its speed, acceleration, jerk, and print height. A high-speed camera was used to record the gantry positions for each variation run. MATLAB vision was used to measure the position and velocity of the gantry. Most physical characteristics of the printer were either measured or analyzed (in Ansys) to present a realistic model to implement the dynamic model developed. The three models developed, i.e. ideal input model, dynamic model and the physical model from the experiments were compared to validate the dynamic model and to measure the errors in each. This work also presents a systematic development of a bond graph model of fused filament fabrication (FFF) 3D printer gantry. The iii model was checked for correctness and causality using the 20-SIM software. This model was further validated using the dynamic model created in MATLAB Simulink. The bond graph model gives important information about the flow of energy to each component of a dynamic system and is especially useful for complex non-linear mechanical systems. iv ACKNOWLEDGEMENTS
... This not only used the classical creep and shear theories to analyze the effects of seating and unseating of a flat belt drive, but it also helped understand the flat belt mechanics taking into account the many other factors mentioned earlier. Studies to investigate the effect of shear deflection and axial deformation in the rubber layer between the pulley and the belt fibers on the rotational dynamic behavior of the transmission were used to make a numerical model for comparison with the experimental results that were obtained (Tonoli et al., 2006). The study of the power transmission from a pulley to a thin, elastic flat belt in the creep region had been successfully carried out by Belofsky (1973). ...
... Modern V or multi-ribbed belts used in automotive applications as well as in conveyor belts are built up of several functional layers [1]. Even flat belts development is in field of specific composition and structure of three basic section of belts: tension and compression sections and cords. ...
The paper presents the results of comparison measuring of absolute vibrations for textile machine driven by flat layered belts with high velocity 50-60 m/s. The dynamic properties of flat belt are important as the flat belt surface is in direct contact with shaft of special textile bearing (115,000-135,000 rpm). Interaction of textile bearing vibration and driven belt may produce significant amplitude and frequency vibration modulation influencing the torsional vibrations and kinematic slip of rolling elements and additional loading of cage. Thus, the bearing life is significantly shortened what is undesirable effect. However, the dynamic properties of driving flat belt are able to influence the vibration of high-speed bearing as it was measured. The two tested flat belts involved one polyester and aramid fabric, respectively, keeping same temperature, belt tension, rotational speed and driven forty bearings. The belt involving the aramid fabric brought the promising results.
... In high performance engines, multi-ribbed belts are commonly used due to their superb capability in terms of flexibility, high power capacity, low noise and vibration levels and excellent reliability in lifetime conditions (Tonoli et al., 2006). V-ribbed belts used in automotive applications are made by several functional layers. ...
... In high performance engines, multi-ribbed belts are commonly used due to their superb capability in terms of flexibility, high power capacity, low noise and vibration levels and excellent reliability in lifetime conditions (Tonoli et al., 2006). V-ribbed belts used in automotive applications are made by several functional layers. ...
... Apart from using the creep theory and shear theory discussed above for theoretical analysis of contact mechanics between belt and pulley, many other simulation methods like multibody dynamics methods [117,118,[204][205][206][207][208][209][210][211][212][213][214][215][216] and, FE methods [217][218][219][220][221][222][223][224][225][226] , etc., have also been widely used to simulate static and dynamics of belt drive systems especially belt-pulley contact behaviors. ...
... Apart from the methods mentioned above, three dimensional (3D) FE models were established by many researchers [217][218][219][220][221][222][223][224][225][226][227] to calculate static and dynamic responses of belt drive systems especially belt-pulley contact behaviors. In these FE simulation models, hyperelastic models like the Moonley-Rivlin model and Ogden model are the mostly used material constitutive models for the rubber compounds in a belt. ...
... Based on a hyperelastic material model, Xu et al. [218] built a 3D FE model to simulate tracking performances of an automotive serpentine belt drive system using the commercial FE software ABAQUS. The effect of the shear deflection in the rubber layer between the pulley and the belt fibers on the rotational dynamic behaviors of the belt transmission was then specifically analyzed by Tonoli et al. [219] . Similarly, Shieh and Chen [220] established a 3D FE model of a V-belt drive system to investigate three frictional contact behaviors between the V-belt and pulley flanges. ...
In this paper, studies on dynamic modeling, simulation and experiment of power transmission belt drives are comprehensively reviewed. In the past few decades, many investigations are conducted on dynamicmodeling, simulation and experiment of different kinds of power transmission belt drive systems. In the dynamic modeling and simulation of the belt drive systems, surveys are focused on vibrations of a single axially moving belt span, rotational vibrations of pulley components, coupled belt-pulley vibrations and contact mechanics between the belt and pulley as well as some experimental investigations. Influences of tensioner dry friction and one-way clutch on dynamics of the belt drive systems including system rotational vibrations and coupled belt-pulley vibrations are separately reported. The investigations are also surveyed on modeling and predicting complicated belt-pulley contact behaviors like belt creeps and slips on pulleys, contact force distributions of the belt and pulley, and variation of wrap angles ofa belt around pulleys, etc., which are categorized by different approaches including the creep theory, shear theory, multi-body dynamics and finite element methods. Fatigue life estimation and failure analysis of power transmission belt drives are discussed in detail as well. In addition, experimental techniques are reviewed on parameters identifications, and measurements of static and dynamic performances including energy/power loss, system vibration, dynamic belt tension, belt deformation, stress and strain distribution in the belt and pulley, and contact friction force, etc. Finally, conclusion of this work is summarized and topics of future potential studies on the power transmission belt drive systems are suggested.
... The first part is the meshed teeth model [11][12][13], where the tooth belt is modeled as spring-mass discrete units. The second part is the rotational vibration model for each pulley [14][15][16][17][18][19], where the belt is modeled as a longitudinal spring with stiffness and damping. The third part is a coupled model for the belt, where the belt is modeled as a moving string or a moving beam [20][21][22][23][24][25][26]. ...
... The oscillation angle and the slippage of the belt are predicted Leamy et al. [16] extended the model in Ref. [15], and analyzed a flat belt driving system using an incremental harmonic balance method considering the viscous dampings of the belt and tensioner. Zenerino et al. [17] investigated the effect of shear deflection in the rubber layer between the pulley and the belt fibers by the Firbank's model. The modeling method in Refs. ...
... The modeling method in Refs. [15][16][17] was only suitable for one specific layout. Shangguan et al. [18] and Feng et al. [19] established unified formulas for modeling a belt drive system including a driving pulley, driven pulleys, a belt and a tensioner. ...
A modeling method for a generic layout of timing belt driving system (TBDS) is presented, and the formulas for modeling a meshed teeth belt, an automatic tensioner, and rotational pulleys are established. A numerical method consisting of an iterative algorithm for calculating the dynamic responses of system is proposed. One engine TBDS with a crankshaft, a camshaft and a tensioner is taken as a studying example. The method and the procedure for obtaining the dynamic responses are described and studied. The dynamic performance of the TBDS, such as oscillation angles of pulleys and tensioner arm, and the transmission error between pulleys, are calculated and compared with the measurement, which validates the presented method. The influence of tensioner performance (stiffness and damping), meshed teeth model and different belt pre-tensions on the dynamic responses of a TBDS system are investigated. The tensioner behavior and belt tension are also analyzed based on the calculated dynamic responses. The developed method presented in this paper can be used for predicting the dynamic responses, optimizing the parameters of an engine TBDS, and reducing the design period and the cost for prototype validation.
... This model has been proposed after that rubber belts reinforced in the axial direction were introduced. The model was then discussed and used by other authors [2,5,9] , also for estimating the transmission efficiency [10] . As already discussed for the creep model, also in the Firbank model the extension of the arc along which shear occurs and of the one along which creep occurs is obtained to satisfy the variation of the belt tension along the whole contact arc. ...
In the present work a novel mathematical model for the analysis of the contact actions between belt and pulleys, particularly suited for flat reinforced rubber belt, is presented. The model considers the tension member, composed of the reinforcement fibers, inextensible, and the rubber matrix, which is subjected to tangential stress, as a continuum bed of elastically deformable bristles, fixed to the tension member on one side and in contact with the pulley on the other side. The deformation of the matrix is inversely proportional to the bending stiffness of the bristles, while friction conditions determine the local adhesion/sliding behavior between belt and pulleys. The proposed model can give a detailed description of the contact conditions along the whole contact arc and is able to describe the stick–slip phenomenon which has been experimentally observed by some authors. The model assesses also the power losses due to the contact stresses and to the elastic deformation of the matrix. The results of the model are discussed in comparison with results from classical models, Grashof and Firbank models, available in the technical literature.
... In this context, Gerbert provided a first analytical formulation for flat belts and then extended it to V and V-ribbed belts. 2 The characteristics of modern V-ribbed belts allow to attribute most of the speed losses due to belt-pulley contact to the circumferential shear acting on the rubber layer between the tension layer and the pulley. 3 By converse, torque losses depend on the hysteresis of the belt during its wrapping motion around the pulleys of the BDS. Three main loss sources were identified, i.e. bending, longitudinal loading and radial compression of the belt. ...
... The investigated BDS layout features 7 pulleys:(1) crankshaft, (2) air conditioning compressor,(3,7) idlers,(4) tensioner arm AT1, (5) BSG,(6) tensioner arm AT2. crankshaft, air conditioning compressor, two idlers, BSG and twin arm tensioner. ...
In the present work, an experimental analysis of the performances of a twin arm tensioner is conducted. The investigated device is used in an automotive belt drive system mounting a belt starter generator. This configuration represents the latest trend of micro-hybrid technologies and is devoted to keep the tension of the belt within a reasonable range, while obtaining the highest possible efficiency in both motor and generator modes. At first, the functionality of a twin arm tensioner is investigated with a static model. Afterward, the performances of a real tensioner are experimentally assessed through a dedicated test rig in quasi-static conditions. The system is benchmarked in terms of angular displacement of the tensioner arms, belt tensions on the corresponding spans, and sliding arc in different operating conditions. Finally, experimental and simulation results are compared. It is shown that the proposed static model is able to capture the behavior of the real device and highlight its functionality.