Mechanics and Sliding Friction in Belt Drives With Pulley Grooves

2005 ◽  
Vol 128 (2) ◽  
pp. 494-502 ◽  
Author(s):  
Lingyuan Kong ◽  
Robert G. Parker

The steady mechanics of a two-pulley belt drive system are examined where the pulley grooves, belt extension and wedging in the grooves, and the associated friction are considered. The belt is modeled as an axially moving string with the tangential and normal accelerations incorporated. The pulley grooves generate two-dimensional radial and tangential friction forces whose undetermined direction depends on the relative speed between belt and pulley along the contact arc. Different from single-pulley analyses, the entry and exit points between the belt spans and pulleys must be determined in the analysis due to the belt radial penetration into the pulley grooves and the coupling of the driver and driven pulley solutions. A new computational technique is developed to find the steady mechanics of a V-belt drive. This allows system analysis, such as speed/torque loss and maximum tension ratio. The governing boundary value problem (BVP) with undetermined boundaries is converted to a fixed boundary form solvable by a general-purpose BVP solver. Compared to flat belt drives or models that neglect radial friction, significant differences in the steady belt-pulley mechanics arise in terms of belt radial penetration, free span contact points, tension, friction, and speed variations.

2004 ◽  
Vol 127 (5) ◽  
pp. 957-966 ◽  
Author(s):  
Lingyuan Kong ◽  
Robert G. Parker

Steady state analysis is conducted on a multipulley serpentine belt drive with a spring-loaded tensioner assembly. Classical creep theory is extended to incorporate belt bending stiffness as well as the belt stretching and centripetal accelerations. The belt is modeled as an axially moving Euler–Bernoulli beam with nonuniform speed due to belt extensibility and variation of belt tension. The geometry of the belt-pulley contact zones and the corresponding belt tension and friction distributions are the main factors affecting belt slip. Bending stiffness introduces nontrivial span deflections, reduces the wrap angles, and makes the belt-pulley contact points unknown a priori. The free span boundary value problems (BVP) with undetermined boundaries are transformed to a fixed boundary form. A two-loop iteration method, necessitated by the tensioner assembly, is developed to find the system steady state. The effects of system parameters on serpentine drive behavior are explored in the context of an actual automotive belt drive.


Author(s):  
Berna Balta ◽  
Bülent Balta ◽  
Abdülkadir Cengiz ◽  
Fazıl Önder Sönmez ◽  
Armağan Arıcı

Efficient belts can provide the same magnitude of energy savings as energy-efficient motors. Therefore, belt drives deserve greater attention, so that their losses should be minimized. The belt drive power losses are a combination of torque losses and speed losses. However, the determination of belt drive behavior in terms of power losses requires extensive experimental investigations. Therefore, in this study, belt slip and torque losses were investigated experimentally with a laboratory constructed test bench. Measurement System Analysis (MSA) was performed in order to investigate the test rig reliability. Special attention was paid for experimental test setup, testing and modeling of torque loss behavior of V-ribbed belt drive systems. Significant design parameters were investigated.


2010 ◽  
Vol 450 ◽  
pp. 357-360 ◽  
Author(s):  
Qing Bao Wei ◽  
Xin Chen ◽  
Da Yu Zheng

V-belt is made of a special anisotropic material, its material and pulley groove structure make the V-belt drive mechanics complicated. The elasticity limit, seating and unseating effects, radial compliance makes us consider the macro features of the drive and not to consider the material heterogeneity. We focus on the steady mechanics of V-belt drive in the state of sliding friction between groove and belt. The pulley groove leads to two-dimensional radial and tangential friction forces whose direction depends on the relative speed between belt and the pulley along the contact arc. The belt model is analyzed with comparing method which is performed through acquiring the equivalent coefficient of friction, and replacing the coefficient of friction in the flat belt mechanical equilibrium equations for v-belt analysis. Through the sample calculation it is proved that this method is simple and valid for V-belt mechanical analysis.


Author(s):  
Mate Antali ◽  
Gabor Stepan

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.


2006 ◽  
Vol 128 (5) ◽  
pp. 555-567 ◽  
Author(s):  
Andrea Tonoli ◽  
Nicola Amati ◽  
Enrico Zenerino

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 transmission. The aim of the paper is to analyze the effect of the shear deflection in the rubber layer between the pulley and the belt fibers on the rotational dynamic behavior of the transmission. To this end the Firbank’s model has been extended to cover the case of small amplitude vibrations about mean rotational speeds. The model evidences that the shear deflection can be accounted for by an elastic term reacting to the torsional oscillations in series with a viscous term that dominates at constant speed. In addition, the axial deformation of the belt spans are taken into account. The numerical model has been validated by the comparison with the experimental results obtained on an accessory drive transmission including two pulleys and an automatic tensioner. The results show that the first rotational modes of the system are dominated by the shear deflection of the belt.


2015 ◽  
Vol 35 (1Sup) ◽  
pp. 42-49 ◽  
Author(s):  
Luis Fernando Rodríguez-García ◽  
Sandra Milena Pérez-Londoño ◽  
Juan José Mora-Flórez

<span>Current electric power systems have an increasing penetration of electric vehicles, and its effect has to be considered in different <span>studies, such as optimal dispatch or voltage stability, among others. Additionally, considering that power system analysis becomes <span>complex when the number of buses increase, this paper presents a methodology for aggregation of load areas that use a measurement-based load modeling approach based on an evolutionary computational technique and a classical reduction method. This aggregate <span>load area model is proposed to reduce areas that consider electric vehicle (EV) load models. The proposed method provides a static <span>equivalent load model and an equivalent network that can be used to reduce the computational effort required by power system<br /><span>studies. In order to validate the application of the proposed methodology, a 30-bus power system considering several disturbances <span>and levels of penetration of the electric vehicles was used. The results show that the equivalent network model allows the reproduction <span>of different events with an acceptable accuracy when it is compared to the original system behavior.</span></span></span></span></span></span></span><br /><br class="Apple-interchange-newline" /></span>


2016 ◽  
Vol 12 (1) ◽  
pp. 25-49
Author(s):  
László Kátai ◽  
Péter Szendrő ◽  
Péter Gárdonyi

The V-belt drive is a rather popular, widely used form of power transmission in agricultural and food industry engineering. At the same time, its stability, the lifetime of V-belt is influenced by several environmental factors, namely in the food industry by the contamination affecting the belt sides, the ambient temperature, humidity and the occasionally aggressive (acidic, alkaline air, air saturated with gases, etc.) medium. In the case of agricultural machinery, the vibration caused by uncertainly oriented pulleys with bearing in different plate structures (often being shaken in the fields) as well as alignment adjustment inaccuracies jeopardize the reliability of the parameters of the drive. Furthermore, the efficiency is determined by several factors together: the slippage occurring during drive transmission, the hysteresis loss resulting from the external and internal friction occurring with the belt entering and exiting the pulley. Experimental equipment and calculation methods were developed to determine the dynamics of temperature increase generated by the belt and pulley relationship. The temperature generated in the V-belt was measured as a function of pretension, pulley diameter and bending frequency. The so-called damping factor characterizing the contact with the pulley (the external friction when entering and exiting the groove) and the hysteresis loss (inner friction) are also determined. On the basis of the damping factor (ζ ≈ 400 Ns/m2) of the V-belt involved in the experiments the other losses (Poth) occurring from the pulley—V-belt contact and internal friction may be estimated. The drive parameters may be optimized with the mathematical model describing the effect of the pulley diameter and belt frequency on the increase in temperature. A standardized calculation method as well as design factors valid for the properly adjusted drive and normal operating conditions determined through empirical and laboratory experiments are used for the sizing of V-belt drives. The lifetime of V-belt drives designed in this way, used in extreme conditions typical of agricultural machinery will not be appropriate and will not provide clear, predictable information for maintenance planning. In such cases the results of our own many lifetime tests conducted in the given circumstances can be safely relied on. The agricultural harvesting machines are large plate-body self-propelled structures on which most of the power supply of the (threshing, cleaning, moving, etc.) machine units handling the crop is realized via belt drives. The distance and angular displacement of the axes involved in the drive can vary within wide limits. The misalignment and angular displacement of the pulleys can be the result of installation instability — due to the plate structure — and the deformation of the plate structure occurring during the operation as well. V-belt drives operate satisfactorily under such conditions as well, however these faults are unfavourable in terms of belt lifetime and result in the reduction of drive efficiency. A further aim of our research is to examine through experiments the lifetime and efficiency of V-belts used in agricultural machines as a function of drive adjustment errors. According to the results of the measurements of the geometrical adjustment errors of V-belt drives performed in the field, the pulleys of agricultural equipment are not always positioned in the medium plane of the drive. In our experiments these data served as independent variables. Figure 1 shows the arrangement of a V-belt drive in a grain harvester with the laser pulley alignment measuring instrument installed as an accessory. In the case of many machine types in 80% of the tested drives three times the permissible error was measured, and because of off-road use, due to dynamic load these errors further increased as a result of the frame deformation. The results of both the belt bending testing and the geometrical adjustment testing of the drive offer great help in the design of belt drives. At the same time they can be the source of lifetime and efficiency forecasts.


Author(s):  
Tamer M. Wasfy

An asperity spring friction model that uses a variable anchor point spring along with a velocity dependent force is presented. The model is incorporated in an explicit timeintegration finite element code. The friction model is used along with a penalty-based normal contact model to simulate the dynamic response of a two-pulley belt-drive system. It is shown that the present friction model accurately captures the stick-slip behavior between the belt and the pulleys using a much larger time-step than a pure velocity-dependent approximate Coulomb friction model.


2019 ◽  
Vol 126 ◽  
pp. 00038
Author(s):  
Vladimir Konovalov ◽  
Sergey Konovalov ◽  
Victoria Igumnova

The article shows importance of use of dump plowing for formation and maintenance of soil structure and pest control and diseases of cultivated plants. A significant drawback of plowing process is indicated, which is its high energy intensity. To reduce energy consumption, it is proposed to use rotating field boards, which allow replacing sliding friction forces with rolling friction forces. The article presents a description of design of plow’s body with rotating field board and notes that without a preliminary analytical study and justification of initial parameters, their use may not be effective. Analytical relations connecting value of radius of rotating field of board, rate of collapse of soil, allowable value of indentation of field board into soil and specific force of cutting resistance of soil that ability to use it for baseline technical parameters. To analyze obtained dependence, the article presents its graphical solution. The authors obtained an expression for determining the value of arm’s force of reference reaction from soil to balance a plow’s body, in addition, this indicator can be used to adjust a body when working on soils with different physical and mechanical parameters and at different depths.


Author(s):  
Jacopo Brunetti ◽  
Walter D’Ambrogio ◽  
Annalisa Fregolent

AbstractIn complex vibrating systems, contact and friction forces can produce a dynamic response of the system (friction-induced vibrations). They can arise when different parts of the system move one with respect to the other generating friction force at the contact interface. Component mode synthesis and more in general substructuring techniques represent a useful and widespread tool to investigate the dynamic behavior of complex systems, but classical techniques require that the component subsystems and the coupling conditions (compatibility of displacements and equilibrium of forces) are time invariant. In this paper, a substructuring method is proposed that, besides accounting for the macroscopic sliding between substructures, is able to consider also the local vibrations of the contact points and the geometric nonlinearity due to the elastic deformation, by updating the coupling conditions accordingly. This allows to obtain a more reliable model of the contact interaction and to analyze friction-induced vibrations. Therefore, the models of the component substructures are time invariant, while the coupling conditions become time dependent and a priori unknown. The method is applied to the study of a finite element model of two bodies in frictional contact, and the analysis is aimed to the validation of the proposed method for the study of dynamic instabilities due to mode coupling.


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