Dynamics of a belt-drive system using a linear complementarity problem for the belt–pulley contact description

The setting of a looped drive belt on two equal pulleys is considered. The belt is modelled as a Cosserat rod, and a geometrically nonlinear model with account for tension and transverse shear is applied. The pulleys are considered as rigid bodies, and the belt-pulley contact is assumed to be frictionless. The problem has two axes of symmetry; therefore, the boundary value problem for the system of ordinary differential equations is formulated and solved for a quarter of the belt. The considered part consists of two segments, which are the free segment without the loading and the contact segment with the full frictionless contact. The introduction of a dimensionless material coordinate at both segments leads to a ninth-order system of ordinary differential equations. The boundary value problem for this system is solved numerically by the shooting method and finite difference method. As a result, the belt shape including the rotation angle, forces, moments, and the contact pressure are determined. The contact pressure increases near the end point of the contact area; however, no concentrated contact force occurs. Mathematics Subject Classification

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“…[12] for the application in the contact between rods). This approach is applied for belt drives in [11,28,33].…”

Section: Figmentioning

confidence: 99%

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

et al. 2017

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“…Strojniški vestnik -Journal of Mechanical Engineering 63(2017) [7][8] numerical result [23] in order to validate the numerical model. The measured values of the external and contact forces that result in a pre-stressed state of the rigid-flexible assembly during the experiment are used to build the dynamical model with the pre-stress effect.…”

Section: Absolute Nodal Coordinate Formulation In a Pre-stressed Largmentioning

confidence: 99%

“…Strojniški vestnik -Journal of Mechanical Engineering 63(2017) [7][8] For example, the virtual work Eq. (7) due to the distributed gravity of the finite element can be obtained using the shape function, Eq.…”

Section: Multibody Dynamicsmentioning

confidence: 99%

“…While in a floating frame of reference formulation a mixed set of absolute reference and local elastic coordinates are used, in the absolute nodal coordinate formulation (ANCF) only absolute coordinates are used, which include global displacement and global vector gradients [4]. The ANCF is a non-incremental method and it has been used for solving many different problems in mechanics, such as vehicle components [5] and [6], the modeling of belt drives [7], railroad applications [8], bio-mechanics [9] and also in the field of digital image correlation (DIC) [10]. The main features of the ANCF are a constant mass matrix, zero centrifugal and Coriolis inertia forces and the possibility for exact modeling of rigid-body movement.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Skrinjar

Slavič

Boltežar

2017

Stroj. vest. - Jour. Mech. Eng.

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The design process for dynamical models has to consider all the properties of a mechanical system that have an effect on its dynamical response. In multi-body dynamics, flexible bodies are frequently modeled as rigid, resulting in non-valid Keywords: ANCF, pre-stress, multibody system, measurement Highlights • A numerical model of a rigid-flexible multibody system is used in the analysis of kinematic properties during switch-off. • A flexible body is modeled with the Absolute Nodal Coordinate Formulation to include the pre-stress effect. • The influence of different parameters on the switch-off time and the contact distance is investigated. • The numerical model was validated and shows good agreement with the experimental values. INTRODUCTIONWhen modeling dynamical systems the proper material and contact properties of the numerical model are crucial for simulating an accurate dynamic response. One of the properties to be considered is the effect of pre-stress on rigid and flexible bodies, as it can have a significant impact on the dynamical response of multibody mechanical systems.The modeling of deformable bodies in a multibody system can be done using a floating frame of reference (FFR) [1], which is based on the classic finite element (FE) method that is widely used in a variety of applications [2] and [3]. While in a floating frame of reference formulation a mixed set of absolute reference and local elastic coordinates are used, in the absolute nodal coordinate formulation (ANCF) only absolute coordinates are used, which include global displacement and global vector gradients [4]. The ANCF is a non-incremental method and it has been used for solving many different problems in mechanics, such as vehicle components [5] and [6], the modeling of belt drives [7], railroad applications [8], bio-mechanics [9] and also in the field of digital image correlation (DIC) [10]. The main features of the ANCF are a constant mass matrix, zero centrifugal and Coriolis inertia forces and the possibility for exact modeling of rigid-body movement.The modeling of the pre-stress effect on bodies in mechanical systems is an interesting research topic in civil-engineering applications [11], where the static [12] and dynamic responses of structural elements are considered [13]. The effect of pre-stress is introduced to the ANCF finite elements to create an accurate model of a leaf spring, where pre-stress is evaluated based on the known geometrical states in the undeformed and deformed configurations that define the vector of absolute nodal coordinates [14]. In [15] the effect of the non-dimensional axial pre-stress of eigenfrequencies on a simply supported beam is researched. The pre-stress effect is included in the model of a flexible multibody belt-drive [16], where the belt-drive is modeled with ANCF two-dimensional shear deformable beam elements that account for the longitudinal and shear deformations.When modeling mechanical systems [17-20] a validation is needed to evaluate the results from the numerical model, this can be ...

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“…[25] for application to contact between rods). This approach is applied for belt drives in [9,26,27]. In the present paper we obtain the contact pressure and the stress-strain state in a different manner by describing the form of the belt lying on the rigid pulleys (the constraint formulation or the Hertz-SignoriniMoreau conditions for frictionless contact according to [24]).…”

Section: Introductionmentioning

confidence: 99%

On static contact of belt and different pulleys

Belyaev

Елисеев

Irschik

et al. 2017

IOP Conf. Ser.: Mater. Sci. Eng.

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Dynamics of a belt-drive system using a linear complementarity problem for the belt–pulley contact description

Cited by 70 publications

References 40 publications

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

Contact of two equal rigid pulleys with a belt modelled as Cosserat nonlinear elastic rod

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

On static contact of belt and different pulleys

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