Numerical and experimental analysis for the skew phenomena on the flexible belt and roller contact systems

The thin, flexible, flat belt system is frequently employed for power transmission, conveyor systems, and various manufacturing process equipments, such as printers, elevators, and automated teller machines. In general, some critical problems can happen during operation, since a thin flexible belt on rollers can easily skew. This is especially serious for high-speed belt operations. In this skewed situation, due to possible relative roller misalignment, roller deflection, and/or belt non-uniformity itself, a thin flexible belt can move along the perpendicular direction to the travelling direction. In this investigation, an efficient analysis method for simulating skewing phenomena of thin flexible belt systems is presented using the complete integration of large deformable finite element methods and multibody dynamics. A 4-node shell element is used to describe a thin flexible belt and two rigid cylindrical bodies describe the roller. Each cylindrical body is fixed with a pin joint and the positions of the rollers are adjusted to impose a tension to thebelt. For the interactions between the belt and the rollers, an efficient contact search algorithm based on a compliant contact force model is presented in this study. The contact search algorithm is composed of a pre-search and a detailed search to identify points of contact between the belt and the rollers. In the pre-search, a simple algorithm is used to identify lines on the belt that are close enough to the rollers that there might potentially be contact between them. The detailed search is performed by making efficient two-dimensional (2D) comparisons of the cross-section of the roller with a 2D projection of the belt lines identified in the pre-search. Afterwards, the contact force is generated by a compliant force model that uses a stick–slip frictional algorithm. The simulation model is validated against experimental measurement systems for thin flexible belt and rollers. It shows a good agreement with the numerical results. Furthermore CPU time with commercial software ANSYS Workbench is compared to check the performance of the algorithm. The proposed method is more than 10 times faster compared with ANSYS Workbench.

[1]  M. A. Crisfield,et al.  A unified co-rotational framework for solids, shells and beams , 1996 .

[2]  Daniel García-Vallejo,et al.  Modeling of Belt-Drives Using a Large Deformation Finite Element Formulation , 2006 .

[3]  C. Rankin,et al.  An element independent corotational procedure for the treatment of large rotations , 1986 .

[4]  P. Nikravesh,et al.  Canonical Impulse-Momentum Equations for Impact Analysis of Multibody Systems , 1992 .

[5]  Jean-Marc Battini,et al.  On the choice of the linear element for corotational triangular shells , 2006 .

[6]  Anders Eriksson,et al.  Element formulation and numerical techniques for stability problems in shells , 2002 .

[7]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[8]  J. Wittenburg,et al.  Dynamics of systems of rigid bodies , 1977 .

[9]  David P. Smith.  Tribology of the belt-driven data tape cartridge , 1998 .

[10]  Chang-Wan Kim,et al.  An efficient and robust contact algorithm for a compliant contact force model between bodies of complex geometry , 2009 .

[11]  K. Johnson.  Contact Mechanics: Frontmatter , 1985 .

[12]  S. M. Yang,et al.  A generalized recursive formulation for constrained flexible multibody dynamics , 2001 .

[13]  E. J. Haug,et al.  Computer aided kinematics and dynamics of mechanical systems. Vol. 1: basic methods , 1989 .

[14]  최주환.  A) study on the analysis of rigid and flexible body dynamics with contact , 2009 .

[15]  J. García de Jalón,et al.  Natural coordinates for the computer analysis of multibody systems , 1986 .

[16]  Hamid M. Lankarani,et al.  A Contact Force Model With Hysteresis Damping for Impact Analysis of Multibody Systems , 1989 .

[17]  大熊 政明,et al.  Dynamics of Multibody Systems(Second Edition), Ahmed A.Shabana著, Cambridge University Press 1998 , 2011 .

[18]  Gerald Wempner,et al.  Finite elements, finite rotations and small strains of flexible shells , 1969 .

[19]  H Cheng,et al.  Finite element analysis of belt skew caused by angular misalignment of rollers , 2004 .

[20]  M. B. Rubin.  An Exact Solution for Steady Motion of an Extensible Belt in Multipulley Belt Drive Systems , 2000 .

[21]  K. H. Hunt,et al.  Coefficient of Restitution Interpreted as Damping in Vibroimpact , 1975 .

[22]  Carlos A. Felippa,et al.  A unified formulation of small-strain corotational finite elements: I. Theory , 2005 .

[23]  I. Sharf,et al.  A contact force solution for non-colliding contact dynamics simulation , 2006 .

[24]  Javier García de Jalón,et al.  Kinematic and Dynamic Simulation of Multibody Systems , 1994 .

[25]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[26]  Hamid M. Lankarani,et al.  Continuous contact force models for impact analysis in multibody systems , 1994, Nonlinear Dynamics.

[27]  B. J. Hsieh,et al.  Non-Linear Transient Finite Element Analysis with Convected Co--ordinates , 1973 .

[28]  Stephen E. Bechtel,et al.  The stretching and slipping of belts and fibers on pulleys , 2000 .

[29]  S. Kim,et al.  Multifrontal Solver Combined with Graph Partitioners , 1999 .

[30]  K. Bathe.  Finite Element Procedures , 1995 .

[31]  J. N. Fawcett.  Chain and Belt Drives - A Review , 1981 .