Steady Motion of a Slack Belt Drive: Dynamics of a Beam in Frictional Contact With Rotating Pulleys

Abstract

We seek the steady state motion of a slack two-pulley belt drive with the belt modelled as an elastic, shear-deformable rod. Dynamic effects and gravity induce significant transverse deflections due to the low pre-tension. In analogy to belt-creep theory, it is assumed that each contact region between the belt and one of the pulleys consists of a single sticking and a single sliding zone. Based on the governing equations of the rod theory, we for the first time derive the corresponding boundary value problem and integrate it numerically. Furthermore, a novel mixed Eulerian-Lagrangian finite element scheme is developed that iteratively seeks the steady state solution. Finite element solutions are validated against semi-analytic results obtained by numerical integration of the boundary value problem. Parameter studies are conducted to examine solution dependence on the stiffness coefficients and the belt pre-tension.

Endless Elastic Beam Travelling on a Moving Rough Surface With Zones of Stick and Sliding

“…From the second and the third equations we easily express c 3 and c 4 , substitute them into the first one and end up with a quadratic equation for the scaling factor k 2 − 3k + 1 = 0 ⇒ k = 1 2 3 + √ 5 ≈ 2.61803. (16) We chose the root of the quadratic equation, which is greater than 1. The experimental observation in Table 2 is thus justified.…”

“…: +43 1 58801 325201 E-mail: yury.vetyukov@tuwien.ac.at we mention review articles [7,14,18], a comprehensive monograph [1], own works [19,20,21] as well as relevant papers [2,4,6,12]. Particularly interesting in the light of the present research are studies featuring the effect of frictional contact between moving deformable bodies, here we refer to [10,11,16,15,5]. Most mentioned contributions address transient dynamic processes.…”

“…Such solutions remain unchanged for an observer in a spatially fixed frame, although the material particles of the structure are moving according to complicated laws, see e.g. [10,6,15,16].…”

Endless elastic beam travelling on a moving rough surface with zones of stick and sliding

“…Practical importance and modelling complexity promote the rapid growth of the body of literature in the field of axially moving structures; here, we mention review articles [1][2][3], a comprehensive monograph [4], own works [5][6][7] as well as relevant papers [8][9][10][11]. Particularly interesting in the light of the present research are studies featuring the effect of frictional contact between moving deformable bodies; here, we refer to [12][13][14][15][16]. Most mentioned contributions address transient dynamic processes.…”

“…Nevertheless, for certain kinds of problems, it may become important and challenging just to find a steady regime of motion. Such solutions remain unchanged for an observer in a spatially fixed frame, although the material particles of the structure are moving according to complicated laws, see, for example, [10,12,14,15].…”