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Research Papers

Effect of Flat Belt Thickness on Steady-State Belt Stresses and Slip

[+] Author and Article Information
Tamer M. Wasfy

Mem. ASME
Purdue School of Engineering &
Technology at IUPUI,
723 W Michigan Street,
SL 260G,
Indianapolis, IN 46202-5160
e-mail: twasfy@iupui.edu

Cagkan Yildiz

Purdue School of Engineering &
Technology at IUPUI,
723 W Michigan Street,
SL 260G,
Indianapolis, IN 46202-5160
e-mail: cyildiz@iupui.edu

Hatem M. Wasfy

Mem. ASME
Advanced Science and Automation Corp.,
28 Research Drive,
Suite F,
Hampton, VA 23666
e-mail: hatem@ascience.com

Jeanne M. Peters

Advanced Science and Automation Corp.,
28 Research Drive,
Suite F,
Hampton, VA 23666
e-mail: jeanne.peters@ascience.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 2, 2015; final manuscript received December 10, 2015; published online February 3, 2016. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 11(5), 051005 (Feb 03, 2016) (13 pages) Paper No: CND-15-1149; doi: 10.1115/1.4032383 History: Received June 02, 2015; Revised December 10, 2015

A necessary condition for high-fidelity dynamic simulation of belt-drives is to accurately predict the belt stresses, pulley angular velocities, belt slip, and belt-drive energy efficiency. In previous papers, those quantities were predicted using thin shell, beam, or truss elements along with a Coulomb friction model. However, flat rubber belts have a finite thickness and the reinforcements are typically located near the top surface of the belt. In this paper, the effect of the belt thickness on the aforementioned response quantities is studied using a two-pulley belt-drive. The belt rubber matrix is modeled using three-dimensional brick elements. Belt reinforcements are modeled using one-dimensional truss elements at the top surface of the belt. Friction between the belt and the pulleys is modeled using an asperity-based Coulomb friction model. The pulleys are modeled as cylindrical rigid bodies. The equations of motion are integrated using a time-accurate explicit solution procedure.

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References

Figures

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Fig. 1

Cross section of a flat belt and pulley

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Fig. 2

Belt model used in Ref. [29] (left). Brick elements are used to model the belt rubber and truss elements on the top belt surface (shown as black lines) are used to model the cords (right).

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Fig. 3

Twenty-four rigid body and deformation modes of a spatial eight-node brick element[32]

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Fig. 4

Subelements of the eight-node lumped-parameters brick element [32]

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Fig. 5

Contact surface and contact node

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Fig. 6

Asperity-based physical interpretation of friction

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Fig. 7

Asperity spring friction model [16]. Ft is the tangential friction force, Fn is the normal force, μk is the kinetic friction coefficient, and vrt is the relative tangential velocity between the two points in contact.

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Fig. 8

Two-pulley belt-drive model showing the slip and stick arcs on the driver and driven pulleys for the zero thickness belt. ω is the input angular velocity of the driver pulley and T is the applied opposing torque on the driven pulley.

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Fig. 9

Prescribed angular velocity of the driver pulley. The nominal driver pulley angular velocity is 120 rad/s.

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Fig. 10

Time-history of the driver and driven pulleys angular velocities as a function of belt thickness

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Fig. 11

Angular velocity ratio (driven/driver) as a function of the belt thickness

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Fig. 12

Time-history of the driver applied torque and driven pulley opposing torque as a function of belt thickness

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Fig. 13

Belt-drive energy efficiency (output power/input power) as a function of the belt thickness

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Fig. 14

Time-history of the midspan low and high tension belt-spans' tension as a function of belt thickness

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Fig. 15

Driver pulley tangential contact stress and rubber shear stress as a function of the belt rubber thickness

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Fig. 16

Driven pulley tangential contact stress and rubber shear stress as a function of the belt rubber thickness

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Fig. 17

Physical explanation of the negative initial belt shear on the driver pulley

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Fig. 18

Belt rubber shear stress over the normalized belt length as a function of belt rubber thickness

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Fig. 19

Driver pulley normal contact stress and rubber normal stress as a function of the belt rubber thickness

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Fig. 20

Driven pulley normal contact stress and rubber normal stress as a function of the belt rubber thickness

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Fig. 21

Driver and driven pulleys reinforcements tension force over the pulleys as a function of the belt rubber thickness

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Fig. 22

Reinforcements tension force over the belt length as a function of the belt rubber thickness

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Fig. 23

Steady-state experimental strain at the top belt surface versus time for a two-pulley belt-drive obtained in Ref. [12] for a belt with a 0.75 mm traction layer thickness

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Fig. 24

Belt rubber axial stress over the belt length as a function of the belt rubber thickness

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Fig. 25

Belt rubber lateral stress over the belt length as a function of the belt rubber thickness

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